System and method for improved computing efficiency with greater diversity and adaptability

Abstract

Systems and methods are provided that include using models configured to generate offspring genotypes and a fitness evaluator configured to evaluate fitness of the offspring genotypes.

Description

SYSTEM AND METHOD FOR IMPROVED COMPUTING EFFICIENCY WITH GREATER DIVERSITY AND ADAPTABILITY CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application is based on and claims the benefit of U.S. Provisional Patent Application Nos. 63 / 693,650, filed on September 11, 2024; 63 / 718,314, filed on November 8, 2024; and 63 / 746,222, filed on January 16, 2025. The entire contents of each of which is hereby incorporated by reference, for any and all purposes. STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

[0002] N / A BACKGROUND

[0003] The present disclosure relates generally to systems and methods for efficient computing convergence toward high-fitness parameters, while maintaining explorative diversity and adaptability. More particularly, the present disclosure relates to systems and methods for using a models configured to generate offspring genotypes and a fitness evaluator configured to evaluate fitness of the offspring genotypes to improve a variety of processes, from healthcare decision making to drug discovery, and many others.

[0004] Two fundamental mechanisms are known to drive novelty in the biosphere. The first is evolution and the second is learning. Conventionally, evolution is understood as a gradual, slow variational process adapting organisms or lineages across generations to changing environmental conditions through natural selection. In comparison, learning is a rapid transformational process enabling individuals to acquire knowledge and generalize based on subjective experiences within their lifetime. These mechanisms have been extensively researched in separate domains of artificial intelligence, and recent studies have begun highlighting similarities between evolution and learning.

[0005] Evolutionary algorithms (EAs) utilize biologically-inspired variational principles to iteratively refine sets of numerical parameters that encode potential solutions to often rugged, custom objective functions. Traditional black box EAs utilize heuristic population data and associated fitness scores (i.e., evaluations of the objective function reminiscent to the fitness of a 1 QB\166118.01562\98271640.1phenotype in its environment) to sample new, potentially better adapted candidate solutions (i.e., offspring comprising the next generation). Depending on the specific implementation of the EA, this sampling process of novel genotypic parameters can be population based through recombination and mutation operations at the genotypic level of thereby iteratively adapted generations, or even leveraged by sampling novel data-points from successively re-parameterized probabilistic models, e.g., with a Gaussian prior.

[0006] Evolutionary algorithms incorporating generative processes operate on partial, heuristically-derived knowledge of the fitness landscape. These algorithms iteratively train probabilistic models using progressively refined data to identify and exploit genotypic correlations across generations. Through continuous refinement of the generative model, these EAs incorporating generative processes aim to increase the probability of sampling high-fitness solutions, potentially accelerating optimization. While this approach offers computational advantages, it presents notable challenges. The use of parameterized models to learn the manifold of correlated genotypic parameters introduces an inductive bias that may constrain the evolutionary search. This learned structure can limit exploration of novel solutions and lead to premature convergence, potentially leaving promising regions of the search space unexplored. Moreover, traditional evolutionary algorithms face particular challenges in sparse reward environments, where meaningful feedback signals are rare and most parameter configurations yield uniformly poor performance. Conventional gradient-based methods and evolutionary methods such as CMA-ES and simple genetic algorithms often fail to find solutions in such environments, with most evolutionary lineages maintaining poor fitness scores even after hundreds of generations. These sparse reward scenarios are common in robotics, game playing, and complex control problems where success requires discovering very specific parameter configurations.

[0007] Moreover, it has become increasingly recognized that the evolution process does not simply build phenotypes adapted to specific environmental conditions. While this certainly is a by-product, evolution seems to primarily bring forth problem-solving machines on all scales in the biosphere. While selection occurs at the phenotypic scale, most organisms are originally compressed into a single fertile cell. Following recent insights from developmental evolutionary biology, the genome does not represent a direct blueprint of all details of the mature organism, it rather instantiates a generative model to construct the latter: genes encode protein sequences which, when expressed in a cell, reconfigure and constrain the cell’s functionality. Through 2 QB\166118.01562\98271640.1hierarchical steps of development, cells proliferate and organize into tissue, vessels, organs, bones, and so on, until the organism is successive constructed and refined during morphogenesis. Thus, there is an entire layer of physiological computation between an organism’s genes and its anatomical (phenotypic) form and function, rendering the relationship between genes and phenotypic traits not only indirect but, in principle, computationally irreducible and emergent. This self-orchestrated developmental process exhibits fundamental plasticity in both structure and function, enabling the substrate comprising an organism to adapt to novel internal and environmental stressors. Such adaptive capability can be understood as a form of collective intelligence aligning with William James’ definition: “Intelligence is the ability to reach the same goal by different means.” The biosphere is organized as a multi-scale competency architecture, which in turn has dramatic implications on the underlying evolutionary process, which is hardly aligned with current evolutionary search strategies.

[0008] Evolutionary dynamics demonstrates characteristics of adaptive associative memory, operating at both individual lineage and ecosystem levels. This memory-like behavior manifests through Hebbian learning mechanisms, that exhibit a similar dynamic to associative memory in neural networks.

[0009] Evolution and adaptation can occur in leaps36, responding rapidly to changing environmental conditions, sometimes within just a few generations37. This open-ended process appears to inherently promote diversity and adaptability 38–40, though the underlying mechanisms remain incompletely understood.

[0010] Recent approaches have begun bridging the conceptual gaps between evolutionary biology, developmental biology, and technological applications. One promising direction employs Variational Auto-Encoders (VAEs) to create low-dimensional genotypic search spaces for evolutionary algorithms, while conducting fitness evaluations in higher- dimensional parameter spaces. A related approach, termed Deep Optimization, leverages multi-level evolutionary transitions, modeled with deep learning, to solve complex combinatorial problems with polynomial scaling. However, these methods tend to exhibit greedy behavior and require careful curation of the training dataset and architecture to enable exploration in a successively refined latent space representation rather than being constrained by the decoder’s canalizing output. While they effectively compress information from the training set to enable generalization, they do so by prioritizing a low bias–variance trade-off that minimizes variance on training error, ultimately 3 QB\166118.01562\98271640.1limiting their capacity to generalize beyond the training data. Significant questions remain about how biological evolution generates novelty. Computational techniques such as novelty search and quality-diversity algorithms have made progress in addressing these questions, though gaps in collective understanding persist. Recent efforts have started drawing connections between evolutionary processes and broader concepts of intelligence and learning theory. However, no full understanding has developed.

[0011] Thus, there is a continuing need for new systems and methods that can be used to create new and more sophisticated computational and learning or discovery systems for computing and / or optimization. SUMMARY

[0012] The present disclosure overcomes the aforementioned drawbacks by providing a computer system that includes a non-transitory, computer-readable memory having stored thereon a diffusion model configured to generate offspring genotypes and a fitness evaluator configured to evaluate fitness of the offspring genotypes and a computer processor. The computer processor is configured to communicate with the memory to access the diffusion model and fitness evaluator, iteratively train the diffusion model using a dataset of genotypes and associated fitness values and conditionally bias the diffusion model to generate offspring genotypes exhibiting target traits.

[0013] In accordance with one aspect of the disclosure, a method is provided for generating a learning network using evolutionary optimization. The method includes generating offspring genotypes using a diffusion model, evaluating fitness of the offspring genotypes, iteratively training the diffusion model using a dataset of genotypes and associated fitness values, and conditionally biasing the diffusion model to generate offspring genotypes exhibiting target traits.

[0014] In accordance with another aspect of the disclosure, a non-transitory computer-readable medium is provided storing instructions that, when executed by a processor, cause the processor to carry out steps. The steps include generating offspring genotypes using a diffusion model, evaluating fitness of the offspring genotypes, iteratively training the diffusion model using a dataset of genotypes and associated fitness values, and conditionally biasing the diffusion model to generate offspring genotypes exhibiting target traits.

[0015] In accordance with yet another aspect of the disclosure, a computer system is provided that includes a non-transitory, computer-readable memory having stored thereon a neural network that 4 QB\166118.01562\98271640.1was trained using a forward diffusion phase and a reverse evolution phase and a computer processor configured to access the memory to use the neural network to process input data to generate a new output.

[0016] The foregoing and other aspects and advantages of the present disclosure will appear from the following description. In the description, reference is made to the accompanying drawings that form a part hereof, and in which there is shown by way of illustration one or more embodiment. These embodiments do not necessarily represent the full scope of the invention, however, and reference is therefore made to the claims and herein for interpreting the scope of the invention. Like reference numerals will be used to refer to like parts from Figure to Figure in the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Various objects, features, and advantages of the disclosed subject matter can be more fully appreciated with reference to the following detailed description of the disclosed subject matter when considered in connection with the following drawings, in which like reference numerals identify like elements.

[0018] Fig.1 is a schematic illustration of a system in accordance with the present disclosure.

[0019] Fig. 2A is a schematic illustration of a workflow of an algorithm in accordance with the present disclosure.

[0020] Fig. 2B is a schematic illustration of a feature extractor, evaluator, and targeter in accordance with the present disclosure.

[0021] Fig.3 is a set of correlated graphs showing the adaptation of an algorithm in accordance with the present disclosure.

[0022] Fig.4 is a set of correlated graphs showing conditional evolutionary optimization evaluated to explore selected target parameter regions and fitness landscapes.

[0023] Fig.5 is a set of correlated graphs showing dynamic conditioning of genetic parameters in accordance with the present disclosure.

[0024] Fig.6A is a set of correlated graphs showing fitness- and novelty-conditional benchmarks for the Rastrigin task.

[0025] Fig.6B is a set of correlated graphs showing fitness- and novelty-conditional benchmarks for the Twisted-Rastrigin task. 5 QB\166118.01562\98271640.1

[0026] Fig.7 is a schematic and a set of correlated graphs providing performance information on the systems and methods provided in the present disclosure.

[0027] Fig. 8 is a set of graphs showing statistically independent lineages of solving the MountainCar environment over 500 generations with different solvers (columns) and different scaling factors s=1,2,3,4,5,10 (rows).

[0028] Fig. 9 is a set of graphs providing a benchmark of different solvers using contrasting evolutionary efficiency for the different solvers for a fixed scaling factors.

[0029] Fig.10 is a schematic illustration of a system in accordance with the present disclosure. DESCRIPTION

[0030] Neural Cellular Automata (NCAs), computational tools from Artificial Life, serve as generative models for studying morphogenesis in silico through collective multi-agent processes. NCAs are particularly valuable for investigating the indirect encoding relationship between genotype and phenotype, as they capture the emergent, multi-scale properties inherent in biological development. As will be described, hierarchical functional genotypic encoding—a characteristic found in biological systems and modeled by NCAs—fundamentally influences evolutionary processes and enables rapid, modular adaptation to environmental changes, as described in Zhang, Y., Hartl, B., Hazan, H., & Levin, M. (2024). Diffusion Models are Evolutionary Algorithms. arXiv preprint arXiv:2410.02543 and Hartl B, Risi S, Levin M. Evolutionary Implications of Self- Assembling Cybernetic Materials with Collective Problem-Solving Intelligence at Multiple Scales. Entropy. 2024; 26(7):532. https: / / doi.org / 10.3390 / e26070532, which are incorporated herein by reference.

[0031] The multi-scale competency architecture of NCAs manifests through local cell-cell interactions generating global patterns and behaviors. This architecture enables collective pattern formation through distributed computation, while maintaining robust development despite perturbations. Furthermore, it facilitates adaptive responses across multiple spatial and temporal scales, culminating in the self-organization of modular, hierarchical structures. These characteristics mirror biological development’s collective (intercellular) intelligence. However, training NCAs through gradient or evolutionary methods remains challenging. Related promising approaches such as neuro-evolution techniques, growing and self-assembling artificial neural networks, neural developmental programming, and self-modeling approaches have further 6 QB\166118.01562\98271640.1expanded the understanding. These methodologies collectively enhance the understanding of how indirect encoding facilitates the emergence of complex, adaptive behaviors from simple, local rules.

[0032] In contrast, recent breakthroughs in generative deep learning, particularly through diffusion models (DMs), have made significant advances in artificial intelligence. These models utilize stepwise iterative denoising to generate novel, realistic data points that conform to complex target data distributions. Prominent implementations such as Stable Diffusion and Sora demonstrate unprecedented capabilities in generating diverse image and video content through conditional text prompts. The impact of DMs extends significantly beyond visual content generation. In the field of computational biology, these models have advanced protein folding prediction. Within optimization domains, DMs enable generative multi-objective optimization through pretraining on closed datasets. Moreover, their application to generative game play through world modeling demonstrates their versatility as a fundamental architecture for complex generative tasks across diverse domains.

[0033] Generative DMs iteratively transform Gaussian distributions into structured data-points that conform to the training data distribution. Drawing inspiration from dissipative systems of non-equilibrium physics, these models implement a two-phase process: first, a forward (diffusion) process progressively corrupts data points with incremental noise; then, a model learns the reverse (generative) process to predict and remove this noise. This noise prediction enables iterative gradually denoising during the generative process, where initially noisy samples are systematically refined until they match the statistical properties of the training data. The iterative denoising steps create a smooth trajectory through the latent space, allowing the model to capture complex, multi- modal data distributions with remarkable fidelity.

[0034] A key strength of diffusion models lies in their conditional training and sampling capabilities, providing precise control over the generative output and thus offering unprecedented flexibility in directing the generation process toward desired outcomes. In general, DMs are tightly related to associative memory systems, which fundamentally enables these generative models to sample diverse yet high-quality results on custom datasets while maintaining reliable training convergence.

[0035] The step-wise error correction process inherent to diffusion models bears striking resemblance to the mechanisms observed in NCAs, particularly in their application to modeling 7 QB\166118.01562\98271640.1multicellular growth and development. This parallel suggests that diffusion models may be particularly well-suited for simulating computationally irreducible self-orchestrated biological processes, including morphogenesis and evolution. The fundamental similarity in iterative refinement between diffusion models and biological development indicates shared underlying principles governing both artificial and natural generative processes, potentially offering new insights into the nature of generative systems across different domains.

[0036] In Y. Zhang, B. Hartl, H. Hazan, and M. Levin, “Diffusion models are evolutionary algorithms,” (2024), the present inventors establish the mathematical equivalence between successive adaptation in evolutionary processes and the generative mechanisms of probabilistic diffusion models. This equivalence emerges from a fundamental similarity in their iterative refinement processes: evolutionary systems combine directed selection with random mutations, while diffusion models balance progressive denoising with stochastic perturbations. In evolutionary processes, natural selection and genetic recombination guide populations toward higher fitness, while random mutations maintain diversity. Similarly, diffusion models employ iterative denoising to transform random samples into meaningful data, incorporating controlled stochastic elements to ensure generative diversity. Building on these parallels, the concept of model-free Diffusion Evolution is introduced — a framework capable of efficiently exploring complex high-dimensional parameter spaces to generate diverse solutions for evolutionary optimization tasks. This approach achieves performance competitive with mainstream methods, notably without deploying deep learning architectures. This unified perspective illuminates a broader theoretical connection: diffusion models can serve as a crucial bridge between evolutionary and developmental biology concepts and contemporary machine learning approaches. Such integration offers novel pathways for incorporating biological principles into artificial intelligence systems and, conversely, provides new computational frameworks for understanding biological processes. The bidirectional nature of this relationship (vice versa) suggests potential breakthroughs in both fields through cross-pollination of ideas and methodologies. The synthesis of these concepts opens new avenues for research at the intersection of artificial intelligence, evolutionary biology, and developmental processes. This convergence not only enhances the understanding of natural evolutionary systems but also provides powerful new tools for developing more robust and adaptable artificial intelligence systems. 8 QB\166118.01562\98271640.1

[0037] As will be described herein, the present disclosure provides an empirically demonstrates that deep learning-based generative diffusion models can integrate genotypic reproduction processes from genetic algorithms to adapt within specific environmental and external conditions, guiding heuristic populations toward target parameter directions. As will be further described, the evolution diffusion systems and methods provided here are compatible with any of a variety of evolution strategies that can be used in addition to the diffusion mechanism to augment search and analysis, including niche search, surrogate fitness estimations, and the like.

[0038] Referring to Fig. 1, the present disclosure recognizes that probabilistic diffusion models, based on Artificial Neural Networks (ANNs), can be used to incorporate generational reproduction in evolutionary optimization. Fig.1 is a schematic flow-chart is provided that illustrates diffusion model-based evolutionary optimization. That is, Fig. 1A shows an evolutionary process 100 utilizing an ANN-based DM 102 as heuristically refined generative model for offspring-genotype sampling. The EA’s generative model learns from heuristic experience by training 104 on an epigenetic joint dataset 106 of genome, fitness, and (potentially) classifier data of a particular genotype in its environment. Then, the DM 102 is successively refined 108 and used to sample high-quality (high fitness) offspring candidate solutions for a particular environment 110. Via classifier-free-guidance techniques, this generative process can be biased towards desired target traits in the environment on the phenotypic level. This approach allows for the exploration of diverse solutions in complex parameter spaces, achieving significantly higher evolutionary efficiency compared to conventional methods. As will be described, the diffusion model 102 is not trained on existing data, but constantly refines the generative process of the diffusion model on successively evidence acquired throughout the underlying evolutionary process.

[0039] The systems and methods provided herein redefine evolutionary algorithms through a reproduction mechanism enhanced by diffusion models. The systems and methods can incorporate epigenetic associative memory into the evolutionary search process by iteratively training the diffusion model on a heuristically acquired dataset buffer after each generation. This associative memory promotes modular adaptations during reproduction, by capitalizing on prior experiences while minimizing inductive biases.

[0040] Additionally, through classifier-free guidance techniques, the systems and methods provided herein can train generative diffusion models to conditionally associate high-quality parameters with specific genotypic, phenotypic, or even population-wide traits, independently of 9 QB\166118.01562\98271640.1fitness scores. This strategy enables the control of the evolutionary process’s search dynamics without altering the objective function but by conditioning the diffusion model to generate offspring with designated target traits or qualities.

[0041] Consequently, the systems and methods provided herein support biologically inspired multi-objective optimization without the need for complex reward-shaping techniques. This establishes connections between conditional generative deep learning and evolutionary biology, demonstrating how memory and genotypic conditioning can influence evolutionary optimization algorithms to evolve lineages with specific genotypic, phenotypic, or population-wide characteristics.

[0042] The systems and methods provided herein and the data based thereon illustrates that the denoising process inherent in diffusion models can serve not only as a powerful tool for evolutionary optimization but also as a bridge between generative AI, diffusion models, and evolutionary programming—fields that may collectively advance toward more biologically plausible AI frameworks.

[0043] The present disclosure recognizes that the principles of evolution have applications beyond biology and can be useful in addressing complex systems across different domains. The main components of this process, imperfect replication with heredity and fitness-based selection, are versatile and can be applied in diverse fields. In computer and data science, imperfect replication is anathema. However, numerous optimization methods can be employed; among the most widely used is stochastic gradient descent (SGD), which, with advancements like the Adam optimizer, excels in tasks where gradient calculations provide clear direction toward solutions. That said, not all tasks are created equally. For example, some tasks are amenable to gradient-based methods, because gradient calculation can be intractable for many complex problems. For these cases, EAs such as CMA-ES22 and PEPG85 can be used. The present disclosure recognizes that these heuristic optimization techniques can maintain and evolve a population of genotypic parameters over successive generations using biologically inspired operations, including selection, reproduction, crossover, and mutation. Thus, as will be described, these tools can be used to gradually adapt the genotypic parameters of the entire population so individual phenotypic samples perform well when evaluated against an objective- or fitness function. The evaluated numerical fitness score of an individual correlates with its probability of survival and reproduction to drive the evolutionary process toward more optimal solutions. Thus, the present disclosure recognizes 10 QB\166118.01562\98271640.1that algorithms can use evolutionary biology dynamics to discover optimal or near-optimal solutions within vast, complex, and otherwise intractable parameter spaces. Such approaches are particularly valuable when heuristic solutions are needed to explore extensive combinatorial and permutation landscapes.

[0044] EAs can work with either discrete or continuous sets of parameters, with the former being a subset of the latter. The present disclosure will discuss continuous parameter spaces that have domain-specific structures, which are typically a priori unknown, but the systems and methods provided herein are not limited to this context. In such situations, the initial population is often sampled from a standard normal distribution. This population is then progressively refined with each generation to excel on a specific objective function. Essentially, the initially random parameters are heuristically adjusted by evolutionary algorithms, gradually transforming into highly structured parameters that perform effectively on the given task, with the goal of optimizing the objective function to solve the problem at hand.

[0045] The reproduction process of EAs to generate novel offspring parameters can either be population based through recombination and mutation operations at the genotypic level, or even leveraged by sampling novel data-points from successively re-parameterized probabilistic models, e.g., with a Gaussian prior. In essence, evolutionary processes can act like generative models that are parameterized, or trained, based on heuristic information gathered from previously explored areas of the parameter space, at least from the prior generation and considering the current state of their underlying generative model. This setup is aimed at generating offspring that may be better adapted for the next generation. Furthermore, the present disclosure recognizes that these evolutionary processes have similarities to diffusion models.

[0046] Diffusion models can be integrated as offspring-generative processes in EAs. The evolutionary process can be viewed as a transformation of genotype or phenotype distributions – or, more generally, parameter distributions. The current population’s distribution undergoes selection and mutation, evolving into a slightly different distribution after each time step. This perspective highlights the potential of using generative models to simulate evolutionary dynamics. In particular, diffusion models, which have achieved state-of-the-art performance across various generative tasks – including image, video, and audio generation – are well-suited for modeling the complex distributional changes inherent in evolution. Given their capability to capture intricate 11 QB\166118.01562\98271640.1data distributions, the present disclosure recognizes that a well-trained diffusion model can outperform traditional methods in evolutionary strategies.

[0047] Therefore, the present disclosure proposes diffusion model-based evolutionary strategies to generate offspring efficiently by sampling more from high-fitness regions in the parameter spaceusing a fitness evaluator. Given a population {g ( τ ) ( τ ) ( τ )i } at time τ, their fitness values qi = f ( g i )are evaluated using a fitness function f :^ n → ^ . Unlike traditional generative systems orlearning models, the systems and herein can train a generative model on thecurrent population and their associated fitness values, then sample the next generation {g (τ +1)i }, which contains more high- fitness individuals. In one non-limiting example, to achieve this, the ()τ ( τ )samples {g }and their fitness values q can be mapped to a density distribution and train ai i+ diffusion model on it. For example, a function g :^ → ^ to map fitness to a fitness-derivedprobability density, such that p(g) ∝ g[f (g)].

[0048] The diffusion models can include two phases: a forward diffusion phase and a reverse denoising phase. In the forward diffusion phase, noise can be gradually blended into the training data – a process known as diffusion. A neural network is then trained to predict the added noise given the noisy data. In the reverse phase, starting from noisy data, the trained neural network is used to denoise step by step, eventually restoring the noise-free data.

[0049] Formally, during the forward diffusion phase, the noise-free data sampled from g is considered at time zero, i.e., x . It can be blended with noise over time according to a construct,0 for example, such as: x= α x + 1 − α ò Eqn. (1);t t 0 t

[0050] where ~ N (0,I ) , and α decreases monotonically from 1 to 0 as t increases, with α = 1t 0and α = 0. As a result, x ~ N (0, I ) and x ~ g . More explicitly, the present disclosure willT T 0henceforth use the symbols g and x to formally distinguish between genotypic parameters in theT evolutionary process and parameters subjected to the diffusion model, respectively. Thus, thenoise-free (or denoised) data points x can be considered as genotypic parameters x ~ g .0 0

[0051] To denoise, a neural network ^ can be trained to predict the added noise by minimizingθthe prediction loss L: 12 QB\166118.01562\98271640.1T θ=arg min L (θ )=arg min^^p( x) | | ò ( α x+1−α ò , t )−ò ||2 nθ ttEqn. (2).θ θ t =1x ∈^

[0052] Given the difficulty (x) for the training data,diffusion models are trained~t∈ [1, T ] . Therefore, theloss function can be reformulated without explicitly using p(x): L(θ)= E || ò ( α x+ 1 − α ò , t ) − ò | |2Eqn. (3).t ~ U (0, T ), x ~ g θ t t

[0053] thatfollow the distribution of the training data. In the Diffusion Denoising Implicit Model (DDIM) framework, the sampling process is an iterative refinement: ^^x x= α t −1−αtòθ ( xt, t )^ ^ +1− α − σ2 t−1 t−1^ ^ t−1 t^ò θ ( x t , t )+σ t ò t , Eqn. (4);

[0054] By default,σ = (1 − α ) / (1 − α ) 1 − α / α is used. Starting with x ~ N (0, I ) , this iterative processt t− 1 t t t − 1 T

[0055] To apply this to evolutionary tasks, higher probabilities may be assigned to high-fitness individuals during sampling. Inspired by equation (2), a weighting function g[f (x)] can be introduced into the loss function to bias the model towards high-fitness samples: 2L (θ)= E g [ f ( x )] || ò ( α x + 1 − α ò , t ) − ò || Eqn. (5).evo t ~ U (0, T ), x ~ g θ t t

[0056] of the original data and the fitness-derived distribution, i.e., , where px ~ g [ f ( x )] p ( x ) g 0 0 g 0represents the sample distribution.

[0057] This process can be encapsulated into a function, G , which takes the current population(τ) (τ) (τ+1)g and their fitness-derived density p(g ) to produce the new population g :(τ ) ( τ ) ( τ + 1)G : g , p ( g ) → g Eqn. (6). ( )

[0058] This mirrors the evolutionary process: at each step, the sampling distribution p can begbiased with the fitness-derived probability density, effectively sampling more from high-fitness regions (selection). The inherent randomness in sampling introduces variation (mutation). 13 QB\166118.01562\98271640.1

[0059] By framing offspring generation as a generative process, more control can be gained over this process, which is not contemplated by prior conceptualizations. The use of conditional generation to steer evolution provides unique advantages, including controlling population features, maintaining diversity, and even directly influencing fitness.

[0060] The present disclosure provides systems and methods that can be referred to as conditional, heuristically-adaptive regularized evolutionary strategy through diffusion (CHARLES-D), as illustrated in Fig.2A. That is, Fig.2A provides an example of a workflow 200 in the CHARLES- D algorithm and Fig. 2B provides an example of feature extractors, condition descriptors for evaluator features used during training, and target features to guide sampling. The features can be used classify parameters and apply classifier-free guidance to sample data points with target features. Referring to Fig. 2A, starting with a randomly initialized population 202, their fitnessand features 204 are evaluated using a fitness evaluator. Next, a generative model, G , 206 istrained on this population, weighted by their fitness, with features used as conditioning for generation. Following training, external conditions are provided to generate a new population that meets specified requirements. The evaluation-training-generation loop is then repeated. A buffer is maintained to store the population along with their fitness and features for training, enabling full data utilization and preserving population diversity.

[0061] DMs provide a model-free approach for learning denoising-based generative strategies tailored to custom datasets across versatile, problem-specific domains. Once trained on statistically relevant data, they can potentially surpass traditional EAs in generating high-quality offspring genotypes.

[0062] Y. Zhang, B. Hartl, H. Hazan, and M. Levin, “Diffusion models are evolutionary algorithms,” (2024), which was previously incorporated herein, formally connects DMs to EAs and demonstrates that the backward process in DMs can be viewed as an iterative evolutionary process across generations. Here, a paradigm is introduced to shift by sustaining and evolving a heuristic populationGτ = { g τ,1 , g τ ,2 ,..., g τ ,N p } ~ p X τ − 1 that is sampled across successive generationsτ = 1, 2, ... , Nτfrom pXvia a heuristically refined diffusion model G τ−1 → G τ , as describedabove. This model can be constantly refined (i.e., trainedacquired dataset buffer containing elite solutions of previous generations Xτ−1= {Gτ′<τ} that have been sampled by prior versions of the DM. In training the DM, high-fitnessbe weighted more 14 QB\166118.01562\98271640.1heavily compared to low-fitness genotypes using a fitness weighting function g[f(g)]. This approach increases the probability of sampling high-quality data while still maintaining diversityin the generative process, as described above and the appendix following hereafter. Then, G τ+1can be used as a generative model for sampling high-quality genotypic parameters Gτ + 1 ~ p X of thenext generation τ + 1, with successively larger fitness than the prior generations. If desired, one can thus realize a “Heuristically Adaptive Diffusion-Model Evolutionary Strategy” (HADES) for learning good and model-free reproductive strategies in EAs (compared to, e.g., the Gaussian prior in CMA-ES) by training DMs on fitness-weighted datasets of genotypic data, as illustrated in Figs. 1 and 2.

[0063] This approach allows for the adaptive generation of novel offspring parameters by refiningeither randomly initialized “proto”-genotypes xT ~ N (0, σDI ) (default), or recombined and mutatedgenetic material from elite solutions i, j of the prior generation τ , schematically expressed asgτ ,i ⊕ g τ , j +ò t , as further detailed hereafter in the appendix. Notably, the latter option of initiatingthe generative process of the DM with recombined genetic information relates to inpainting techniques, which aim to complete missing information in sample data. In traditional inpainting applications, missing information in masked or patched images is integrated seamlessly into the scene. Similarly, in this context, potentially conflicting parameter combinations from the genetic crossover operation (with potential effects on corresponding fitness scores) can be resolved by the DM, functioning in a manner akin to error-correction mechanisms.

[0064] Intriguingly, with DMs, techniques can be applied such as classifier-free guidance to condition the generation process. This allows an evolutionary optimizer to be implemented with search dynamics controlled without relying on additional reward-shaping techniques. By training the DM with additional information ci= c(gi), which numerically quantifies certain qualities or traits of genotypes gi in their respective environments, the DM learns to associate elements in the parameter space with corresponding classifiers gici.

[0065] Technically, this is achieved by the input of the DM’s ANN asòθ (xt , t )→ ò θ ( x t , t , c ( x t )) . The function c(^) is a custom, not necessarily differentiable, vector-valued classifier function or a measurement of a trait of the data point x, or genotype g, evaluated in the parameter space, fitness space, or even phenotype space. 15 QB\166118.01562\98271640.1

[0066] During sampling, the DM’s generative process can be biased towards novel high-quality data points that exhibit a particular target trait c(T), by conditioning the iterative denoising processof the diffusion model as òθ(x , t , c (T)t ) → xˆ 0 such that c( xˆ 0 ) ≈ C ( T ) . This allows the DM to generatehigh-quality samples traits, similar to how Stable Diffusion and Sora generaterealistic image or video on custom text prompts.

[0067] In one non-limiting implementation, a conditional sampling can be used to gain further control over a heuristic search process with an open, successively refining dataset. While the heuristic nature of the evolutionary process facilitates global optimum exploration, the successively refined DM-based generative process allows for diverse sampling of high-quality genotypic data points that may exhibit target traits defined independently from the fitness score, akin to prompting an image-generative DM with text input.

[0068] This approach can be conceptualized as a “Talk to your Optimizer” application and can be referred using the Conditional, Heuristically-Adaptive Regularized Evolutionary Strategy through Diffusion (CHARLES-D) name. Again, a visualization is provided in Fig. 2. Pseudo code is provided as follows where bolded text corresponds to training and italics correspond to sampling:Require: Population size, Np, parameter dimension, D, initial STDσ I , fitness function f, weightingfunction g, diffusion model G , crossover ration Nc, total evolution steps Ng, classifier function c,and target condition c(T). Ensure: Nc < Np1: G 1 ←N (0, σN × DI ) Initialize populationInitialize dataset buffer3: for τ ∈ [1, 2,...,Nτ ] do4: {g 1 , g 2 ,..., gN }← Gτ5: ∀i ∈ [1, Np ] : q i ← g [ f ( g i ; τ )]6: ∀i ∈ [1, ] Np c i ← c [( g i ; τ )7: X ← X ⊕ {( gi , q i , c i )} Cache associated (data-point, fitness weight, and classifier)-tuples8: Gτ ←train ( G , X ) (Re)train diffusion model on updated dataset buffer16 QB\166118.01562\98271640.19: G^ ← crossover ( G | q , q )Nc ⊕ N (0, σ ( Np − N c ) × Dτ +1 τ i j I ) Sample “proto”-genomes via crossover10: : px c conditional to target traits+1 τ τ + 1refined 11: end for Algorithm 1 – Pseudo-code of HADES (CHARLES-D): novel generations are consecutively sampled by a heuristically refined DM. The seeds for this sampling are yet again sampled form crossover and mutation operations of the current population and from Gaussian nose to allow both adaptation of (combinations of) elite solutions and unbiased sampling by the DM. CHARLES-Dcan be conditionally biased during sampling. Notably, replacing the DM, G , with a multivariateGaussian model, and refraining from the option of using conditional sampling, would essentially recover the DMA-ES algorithm.

[0069] Diffusion models can efficiently learn, generate, and adapt genotypic representations within heuristic evolutionary processes. That is, the present disclosure recognizes that probabilistic diffusion models trained “online” on generations of heuristically varied parameter sets can be efficiently utilized as generative models in EAs, all based on successive denoising operations.

[0070] To demonstrate this, the present disclosure provides a non-limiting example of toy problems that involve solving the dynamic and the static cases of the double peak and Rastrigin problem. Then the disclosure considers Reinforcement Learning (RL) tasks. The systems and methods of the present disclosure are contrasted with the performance with other EAs, demonstrating that the systems and methods provided herein provide substantial improvements and functionality not realized in prior efforts. The systems and methods provided herein realize the simultaneous identification of multiple optima, emphasizing diversity and exploration, while still furthering optimal solutions with high efficiency. Furthermore, the present disclosure demonstrates that classifier-free guidance techniques can be effectively utilized to conditionally bias the generative process in EAs. This approach constrains the search dynamics of the underlying heuristic evolutionary processes, even within complex rugged fitness landscapes, without changing the fitness score function. The systems and methods are analogous to the use of Lagrange multipliers in differentiable optimization, serving to impose constraints that effectively 17 QB\166118.01562\98271640.1guide the search even in rugged, non-differentiable fitness landscapes. In these non-limiting examples, simple feed-forward neural network architectures are used for the diffusion models, which typically consist of 2 hidden layers with a number of hidden units ranging from 24-324.

[0071] As will be shown, the systems and methods provided herein demonstrate that diffusion models can be used to provide a model-free approach that adapts readily to new problems and dynamic environments. Biological evolution is renowned for its adaptability capabilities in (slowly) changing environments. While being increasingly recognized in the computational literature, mainstream EAs typically focus on exploring parameter spaces for globally optimal solutions to complex and often rugged, yet generally static objective functions. To examine the adaptive capabilities of evolutionary processes to changing environmental conditions to mimic a more biologically realistic setting, a time-dependent objective function, f (g,τ ), can be introduced to compare the learning capabilities of HADES against other different mainstream EAs. Specifically, f (g,τ ) can be defied as 22− ( g − μ )2 − ( g − μ )f ( g ,τ ) = cos( ωτ ) e 2 σ + cos( ωτ + φ ) e 2 σ 2 Eqn. (7);

[0072] oscillate phase-shifted by ϕ across generations τ with angular velocity ω; a static double-peak problem is recovered by setting ω = 0 and ϕ = 0.

[0073] Thus, an alternating double-peak function can be used, where one peak has a positive and the other one negative amplitude by setting ϕ = π, ω = 2π / 10, and σ = 0.1. Over time, the amplitudes periodically alternate in sign, reverting the target of the maximization objective. The HADES method and CMA-ES22 can both be applied with a population size of Np= 256 and an initial population of standard deviation (STD) σI= 0.5 evaluating each sampled individual giin every generation τ against f(gi,τ). The population-dynamics are depicted in Fig.3. That is, referring to Fig.3, the HADES method can adapt to dynamic (oscillatory) environmental changes. In dataset 300, dynamically alternating double-peak fitness landscape ranging from fmin= -1 (black) through f0 = 0] to fmax = 1 (white) as defined by equation (7). In graph 302, the population data for the HADES method (blue) and CMA-ES22 (red) optimization in the dynamically changing environment illustrated 300 is shown. The 2D data points (xi, yi) are represented as 1D projectionsx i onto the x = y diagonal illustrated as dashed lines in graph 300. The background color indicatesthe fitness score along x = y, and the radius of the data-points x i scales with fitness fi,18 QB\166118.01562\98271640.1respectively. Fitness of the data shown in graph 302 is shown in graph 304, where the solid line illustrates the maximum fitness evaluation of the population averaged over 10 statistically independent simulations. The shaded area illustrates the average spread of the population’s maximum fitness. While the HADES method reliably identifies the current maximum in the alternating double-peak environment, CMA-ES clearly struggles to adapt a population to the changing environment in time as the majority of population resides in the vicinity of one peak.

[0074] Thus, traditional EAs have very different strategies in updating their generative models across generations due to their inherent inductive biases. Yet, even powerful mainstream approaches, such as CMA-ES, fall short in adapting a population to changing environmental conditions after having seemingly converged on a solution, even for simple problems as the alternating double-peak function discussed here. In contrast, HADES consistently identifies the periodically changing maximal fitness peak by adapting its population by sampling new offspring through an ever-refined DM. This is reflected by the respective time-dependent fitness of both approaches depicted by graph 304 in Fig. 3. Thus, the HADES method offers an efficient and model-free approach to generate high-quality genotypic data, particularly excelling in scenarios that require enhanced adaptability capabilities. The intrinsic representative power of DMs enables reliable learning of subtle signals and correlations within arbitrary parameter sets, while their versatile sampling capabilities during the generation phase allow for precise control over the output characteristics. This combination of robust correlation learning and a flexible generative process makes HADES particularly well suited to explore complex genotypic landscapes where traditional approaches might struggle to maintain both diversity and quality.

[0075] The present disclosure recognizes that neutral multi-objective adaptation via conditional diffusion model evolution reflect insights from developmental biology. Typically, EAs aim to find optima in their respective fitness landscapes by maximizing fitness scores through biologically inspired selection and mutation operations. In rugged fitness landscapes, this approach can be exceptionally effective, enabling exploration for global solutions, a distinct advantage over many gradient-based methods that often get stuck at local optima. However, traditional EAs often struggle with problems that have multiple (unrelated or competing) objectives, as these can create conflicts and frustration in fitness scoring. While mitigation strategies such as problem-specific reward shaping and curriculum learning techniques exist, these approaches typically demand 19 QB\166118.01562\98271640.1careful customization and domain expertise. This limitation highlights the need for more robust and adaptable optimization frameworks that can naturally handle multi-objective scenarios.

[0076] Drawing inspiration from developmental biology, the present disclosure provides an alternative approach. Recent research suggests that biological evolution does more than just create organisms adapted to specific environments. Rather, it produces versatile problem-solving systems. These biological systems — ranging from gene networks to cells, tissues, organs, organisms, and even organismal collectives – demonstrate remarkable capacity to adapt to environmental cues or domain-specific challenges in real-time, while maintaining their overall physiological integrity. Especially during an organism’s development, but also during its lifetime, this adaptation to environmental constraints manifests through sophisticated response mechanisms across multiple scales, while preserving core functionalities without compromising the organism’s fundamental fitness. The present disclosure recognizes the ability to harness this as a form of physiological conditioning of the multi-scale generative processes of biological systems allowing them to adjust to environmental constraints neutral to their system-level fitness. The universality of this principle suggests its applicability to mechanisms at the level of RNA and DNA.

[0077] The present disclosure recognizes that diffusion denoising models are presented as being related to the processes of evolution are also applicable to analysis of gene regulatory networks (GRNs, e.g., see international application PCT / US2024 / 046631, which is incorporated by reference herein in its entirety). Analysis of GRNs includes navigating a problem space including various behavioral end states connected by trajectories, where navigating the problem space can be performed in various ways such as a random search or a curiosity-based search. Similar to GRN analysis, evolution and diffusion denoising models combine intrinsic randomness and iterative refinement to produce a diversity of generated outputs. Thus, the systems and methods provided herein can be applied in applications, such as GRNs, as just one non-limiting example.

[0078] DMs offer a particularly suitable framework for incorporating external (environmental) cues in their generative process through classifier-free guidance. At their most basic level, DMsare trained to generate, i.e., sample novel data x 0 from a probability distribution p(x) that conformsto a training dataset X = {g1,… , gN}. The true power of DMs, however, lies in their ability to conditionally sample novel data pointsx(c)0that exhibit desired target traits or features c. Thesefeature vectors c numericallyqualities of the data, which are here formally 20 QB\166118.01562\98271640.1encoded via a custom, not necessarily differentiable mapping c = c(g). Thus, through classifier- free guidance, the generative process of DMs can be explicitly steered to sample biased data points (c)x ^ (c)0from a conditional probability distribution x ^ 0 ~ p ( x | c ) , where the generated output exhibitsspecific desired target traits such that cˆ = c (^(c)x 0 ) ≈ c .

[0079] This approach forms the foundation of modern text-guided image and video generation systems. During training, the DM learns to associate data g with corresponding numerical conditions c = c(g). When deployed, it can generate data conforming to these learned conditions, effectively translating abstract constraints into concrete output characteristics.

[0080] Here, classifier-free guidance can be employed to constrain the genotype sampling process in the HADES method, ensuring that resulting phenotypes meet specific target conditions c(T)in their environments. This process operates independently of fitness scores. This approach is referred to, as referenced above, as Conditional, Heuristically-Adaptive ReguLarized Evolutionary Strategy through Diffusion (CHARLES-D ), which, in contrast to HADES , modifies the denoising process by incorporating target conditions into the error estimate: ^θ(xt, t, c(T)). The implementation involves three primary steps. First, each element giin the heuristic training data X is associated with a numerical feature vector ci = c(gi) that quantifies specific traits. These traits can encompass genotypic parameter qualities, fitness-related metrics, population-level characteristics, and / or phenotypic traits. Second, at each generation, the DM can be trained on paired data (gi, ci); the loss function evaluates the model’s ability to denoise data gi at fixated corresponding features ci that are unaffected by noise. Third, during the generative phase of a new population, custom target conditions c(T)can be employed to guide evolutionary trajectories through the parameter space. This leads to conditionally sampled individuals that increasingly exhibit the desired condition-specific traits while improving their fitness across generations.

[0081] In the first example, the CHARLES-D method was applied to find optimal solutions to the static double-peak objective function given by equation (7) with ω = ϕ = 0, while conditioning the generative process of the DM to predominantly sample genotypicin specific quadrants of the two-dimensional plane. The results are illustrated in Fig.4.

[0082] In particular, Fig. 4 provides a series of graphs providing context to understand that conditional evolutionary optimization can be used to explore selected target parameter regions in two dimensional double-peak fitness landscape. In graphs 400, 402, and 404, a fitness landscape 21 QB\166118.01562\98271640.1(grayscale) and distribution of population data (projected onto the x = y line) is provided for 10 statistically independent simulations vs. generations as violin plot, while conditioning the generative DM to sample novel data points from the first quadrant x, y > 0 (graph 400), second and forth quadrants x y < 0 (graph 402), and third quadrant x, y < 0 (graph 404). Datapoints are projected onto the x = y diagonal. Graphs 406, 408, 410 provide fitness landscape in gray-scale from fmin= 0 (gray) to fmax= 1 (white) with overlaid data-points (colored dots) of an exemplary population from aligned graphs 400, 402, 404, respectively, after 9 generations.

[0083] Starting from a normal distributed population σI = 1, individual genotypic parameters gi = (xi, yi) can be associated with their corresponding quadrant in the parameter space. For data points in the first quadrant (xi, yi> 0), the numerical classifier value c(Q1)= 1 can be assigned. For data points in the second and fourth quadrant (xj × yj < 0), c(Q0)= 0 can be assigned. For data points in the third quadrant (xk, yk < 0), c(Q3)= −1 can be assigned. The process then proceeds through three sequential steps. First, the fitness and feature vectors are evaluated for all individuals of a given generation. Second, the DM undergoes joint training on the set of associated data and quadrant-classifiers (gi, c(Qj)). Finally, when sampling the genotypes of the next generation, a particular target quadrant, T , can be selected to condition the generative phase of the DM by c(QT).

[0084] In Fig.4, population data across consecutive generations is illustrated in this double-peak environment for 10 statistically independent evolutionary lineages. The CHARLES-D method is conditioned to sample from one of three distinct regions. The first quadrant, T = 1, the second and fourth quadrants, T = 0, or the third quadrant, T = 3. Snapshots of converged generations for each case are superimposed on the fitness landscape in Fig. 4. The results demonstrate the remarkable effectiveness of conditioning on the first and third quadrants. That is, despite both fitness peaks being the qualitatively equivalence, the CHARLES-D method consistently converges to the peak located in the conditionally targeted quadrant. Conversely, conditioning DM-sampling on c(Q0)results in frustration effects, as the second and fourth quadrants lack fitness peaks.

[0085] Based on this, it is clear that conditioning in HADES serves as a powerful regularizer for genotypic exploration with DM evolution. This mechanism enables selectively biasing the evolutionary process to either explore or avoid specific regions of the parameter space, or more broadly, solutions with particular genotypic qualities, without altering the problem’s fitness score. This neutral adaptation toward desired qualities is achieved elegantly through DM conditioning with classifier-free guidance techniques. Furthermore, these conditions can be formulated flexibly 22 QB\166118.01562\98271640.1and orthogonally to the optimization problem’s fitness-score, without requiring differentiability. Consequently, CHARLES-D provides an elegant approach to multi-objective optimization that eliminates the need for cumbersome reward shaping techniques.

[0086] The present disclosure recognizes that DM-based generative samplers can be used to provide a more powerful and biologically-inspired framework for modular evolutionary processes. Biological evolution exhibits an inherent capacity to utilize existing, heuristically acquired knowledge for species adaptation in changing environments. This capability stems from the recombination of established genetic material across evolutionary time-scales. Thus, the exploitation of previously explored solutions and their adaptation to novel contexts represents a fundamental principle of biological evolution. Within traditional EAs, the integration of past experience remains largely limited to heuristic information stored in the current population, or within the generative model employed by techniques such as CMA-ES for offspring sampling. Consequently, the generative process in current EAs maintains limited memory of previously explored solutions, leading to inefficiencies from either memory loss or the intrinsic inductive bias of generative models. Generative DMs, however, can be equipped with epigenetic memory by preserving information about previously explored solutions. This capability can be implemented through dataset buffering or DM retraining across multiple generations. These approaches offer a model-free methodology to enhance evolutionary sampling capabilities based on past experience, while simultaneously testing new environmental hypotheses through an iteratively updated generative process. Information holds significant value in optimization, particularly in computationally expensive tasks where maintaining reliable memory is crucial. Refining a model- free generative process via heuristically acquired dataset buffers therefore presents an efficient approach to leverage prior knowledge in evolution. This can be leveraged to significantly improve the capacity of an evolutionary process (as modeled by HADES and CHARLES-D ) to navigate complex parameter spaces more effectively. Moreover, this ability to learn from past experience substantially augments the adaptability and transferability of evolutionary algorithms to changing environments.

[0087] To demonstrate this, the following experiment was conducted. As will be described with respect to Fig. 5, dynamically conditioning genetic parameters was experimentally analyzed. In Fig.5, graph 500 shows static double-peak fitness landscape, ranging from fmin= 0 (gray) to fmax= 1 (white) as defined by equation (7) with ω = ϕ = 0. Dynamical conditioning allows exploration 23 QB\166118.01562\98271640.1of the first quadrant (red) or the third quadrant (blue). In graph 502, the fitness landscape (grayscale) and the distribution of population data (projected onto the x = y line) for 10 statistically independent simulations vs. generations (radii of green-colored data-points scale with fitness) is shown. The average population mean is illustrated by the black solid line, while the gray area marks the STD. The oscillating red-blue color-coding of the fitness landscape reflects the applied condition for the first or third quadrant during DM sampling, respectively leading to jumps of the population from one peak to the other; transition generations are marked by white vertical dashed lines. In graph 504, the mean and STD of maximum fitness (solid green line and shaded area) demonstrate consistently high fitness values, even during transitions of the conditional sampling.

[0088] Experiment: (i) utilize the static double-peak environment described above, (ii) equip CHARLES-D with a memory buffer dataset spanning the past 5 generations, where only the lowest fitness solutions are replaced with current population data, and (iii) implement time-dependent conditioning that alternates between the first and third quadrants in the parameter space. Again,this started with an initial normal distribution population with σI = 1. Then, solutions wereconditionally sampled from the first quadrant for eight consecutive generations using c(QT)= c(Q1)for τ ∈ [1,8] during the DM's generative process, followed by conditioning to the third quadrantfor the next eight consecutive generations using c(QT) = c(Q3) during τ ∈ [9,16] , as shown in Fig.5, in graph 500. This process was repeated periodically for each lineage, with DM initialization and training on the memory buffer dataset after each generation. The experiment was repeated 10 times, with population dynamics and elite fitness- scores presented in Fig.5 in graphs 502, 504. The results reveal that CHARLES-D consistently converges to the specified target peak, maintaining performance even under dynamically modified conditions during evolution. Notably, the epigenetic memory enables the evolutionary process to perform discontinuous but targeted transitions between previously visited high-fitness regions when conditions switch between c(Q1)c(Q3). Rather than exhibiting slow continuous adaptation between peaks located at µ, instantaneous repopulation of the new target peak and heuristic fade-out of the previous one can be observed. This rapid, targeted readaptation maintains consistently high fitness scores across conditioning transitions (see Fig.5, graph 504), contrasting with the oscillatory elite fitness scores observed in the dynamically changing environment discussed in Fig.3, graph 304. This behavior bears striking resemblance to the ecological memory described in Ref.14, though achieved here through a heuristically adaptive DM. 24 QB\166118.01562\98271640.1

[0089] In conclusion, the experiments demonstrated the powerful capability of generative DMs to leverage evolutionary history for enhanced optimization processes. The integration of memory components and conditioning schemes in CHARLES-D and HADES significantly improves the adaptive capabilities of evolutionary algorithms in dynamic environments. The findings extend beyond algorithmic improvements. That is, the finding raise fundamental questions about un- conventional memory mechanisms in biological systems. The observed parallels between DM- based evolutionary processes and biological adaptation mechanisms suggest promising new directions for understanding the principles governing both artificial and natural evolutionary systems.

[0090] Improving on past experience, an investigation of conditioning for higher fitness was conducted that revealed the ability to improve learning performance, but increases greediness. In particular, the application of fitness conditioning was investigated during the DM's generative process. The DM can be jointly trained on associated parameters and fitness scores {gi, fi= f(gi)}, conditioning the sampling process to generate offspring that potentially achieve a higher target fitness than any previously observe, f(T)> maxi (fi).

[0091] Given that the maximum fitness or reward cannot be known a priori, sampling the target fitness for conditionally generating the next generation can be based on Fishers fundamental theorem of natural selection, which states that “The rate of increase in fitness of any organism at any time is equal to its genetic variance in fitness at that time.” This principle on the rate of expected fitness improvement has intriguing links to inverse reinforcement learning (IRL), as it cannot be assumed that conditioning the DM on arbitrarily large fitness (i.e., significantly surpassing the training data) will yield reasonable offspring parameters, especially in early stages of the evolutionary search process.

[0092] However, to avoid this algorithm to become too greedy, two flavors of fitness samplingcan be introduced: (i) Fisher-conditioning c (TF ) ~ μ f + | N ( μ = 0, σ = σ f ) | , and (ii) Greedy-conditioning of target fitness c (TG) ~ N (μ =max ) , where µf is the mean, fc the maximum,and σfthe STD of the fitness scores fiof the current population.

[0093] Illustrative examples of sampling parameters conditional to target fitness values by a DM pre-trained on the double-peak task were used. In Fig.6A, graphs 600, 602, 604, 606, optimization results are provided for different configurations of HADES and fitness-conditional CHARLES-D 25 QB\166118.01562\98271640.1applied to the inverted and truncated Rastrigin task, a periodically oscillating function in the two- dimensional plane with four optima located at |x| = |y| = 3.5. For simplicity, henceforth, the inverted and truncated Rastrigin task simply be referred to as Rastrigin task.

[0094] Again, the double-peak problem was used as minimal toy-example. Referring to equation (7) provides the definition. The results of different HADES and CHARLES-D configurations on the minimal double-peak task was considered and, CMA-ES and the SimpleGA converged the fastest (as shown in the averaged fitness dynamics in graph 602 of Fig. 6A). The Novelty- conditional CHARLES-D instances were second in performance, even better than the fitness- conditional and the baseline algorithms. This is rooted in the fact that the fitness signal of the narrow initial population is small, and all HADES and CHARLES-D instances are used in a non- greedy setting with low selection pressure.

[0095] The vast majority of the Novelty-conditional CHARLES-D instances (but also to some extend the baseline HADES solver) reliably identified and even stabilized on both peaks in the fitness landscape (as illustrated in graph 606 of Fig.6A), while the more greedy fitness-conditional algorithms often collapse onto one solution after many generations. In contrast, the state-of-the- art CMA-ES and SimpleGA methods basically zoom in onto one peak very quickly.

[0096] Referring Fig. 6A, fitness- and novelty-conditional benchmarks for the Rastrigin are illustrated and, referring to Fig. 6B, fitness- and novelty-conditional benchmarks for the “Twisted”-Rastrigin task are provided.

[0097] The Rastrigin function is defined byf ( x )= An +^2 2i=1[ xi − A cos(2π x i )] with x = (x1, x2);A = 10 can be chosen. For the “twisted”-Rastrigina spiral coordinate transformationx → x^ = r × (cos(θ + ω r ), sin( θ + ω r )) , with r = | x | , θ =atan 2(x 2 , x 1 ) and constant ω can be usedf ( x ^ ) can be evaluated. For both the Rastrigin and twisted-Rastrigin function, the useof the negative function value is evaluated using optimization experiments to truncate the function values for |xi| > 4 to 0. In that way, an oscillatory fitness landscape is established with four maxima located at |xi| = 3.5 for the Rastrigin function, with a maximum fitness value of fmax= -64.625. The maximum of the twisted-Rastrigin function are correspondingly transformed.

[0098] The fitness landscape of the Rastrigin is reflected in graph 600 and “twisted”-Rastrigin task is reflected in graph 608 with overlaid exemplary results (elite solutions in thick colored-coded circles, and final population in small green circles) after 100 generations of optimization with 26 QB\166118.01562\98271640.1different HADES and CHARLES-D solvers (see titles and colored-coded borders) contrasted with SimpleGA and CMA-ES algorithms (bottom row, see text). The fitness landscape is indicated gray scale ranging from fmin= 0 (black) to fmax= 64.62 (white). Graphs 602 and 610 show the maximum fitness from different solver configurations (c.f., color-coding and graphs 600 and 608, respectively). Graphs 604 and 612 show the entropy-based diversity of the population, and graphs 606 and 614 illustrate the number of cumulatively identified solutions across successive generations for the Rastrigin (graphs 602-606) and twisted-Rastrigin (graphs 610-614) tasks, averaged over 50 statistically independent simulations, respectively.

[0099] It is possible to quantify the diversity of the solutions. In one non-limiting example, quantification is achieved by (i) dividing the 2-D plane into a grid of 101×101 in the range x, y ∈ [−6, 6], and (ii) counting the frequencies of all solutions of a particular generation falling into different grid cells, i. The entropy H is then evaluated as: N H=^ P i log2P i , Eqn. (8);

[0100] of data points being located in grid i. This simple and coarse method allows entropy to be quantified focusing solely on the diversity of solutions across different basins and explicitly avoiding contribution of local diversities.

[0101] The insets in graphs 606 and 608 show the cumulatively best fitness vs. generations from all statistically independent simulations for the different solvers, and the colored arrows indicate the generation when the problem was solved in the least number of generations by a particular solver for both tasks. Both the vanilla HADES and the novelty-conditional CHARLES- D methods reliably identify multiple optima at the corners of the fitness landscape (606, 608): on average, 75% of the target peaks are identified, while in 10% of all simulations 100% of the solutions are found successfully. The diversity measures shown in graphs 604 and 612 and 606 and 614 indicate that the novelty-conditional CHARLES-D method maintains an increasingly diverse populations of high-quality genetic material compared to the respective unconditional cases.

[0102] The findings indicate that this fitness conditioning can indeed significantly improve the learning capabilities of CHARLES-D, which opens up new avenues for exploring complex parameter spaces. However, aiming for greater fitness increases across generations might also lead 27 QB\166118.01562\98271640.1to more greedy behavior of the algorithm and thus suboptimal convergence, which is discussed hereafter.

[0103] A good regularizer for exploration and maintaining diversity can be achieved using novelty-conditional sampling. Typically, EAs aim at identifying solutions with optimal fitness values in rugged parameter landscapes. However, depending on the fitness landscape, this can be highly non-trivial and requires a dedicated balance between exploration and exploitation. Recent discussions, originating from developmental biology suggest that biological systems operate under a different paradigm, where agents continuously explore novel situations to maintain their integrity and adapt to changing environments. This inherent drive for novelty leads to the creation of novel challenges, requiring further adaptation, and thus creating a diversification scaffold.

[0104] It has recently been argued that the fundamental drive for novelty in biological systems could be rooted in biological agents on a variety of scales seeking novel stimuli if their sensory inputs stagnate too long. This is reflected in their intrinsic drive for exploration and discovery, but not necessarily aligns with traditional optimization objectives or search strategies. In fact, incorporating novelty or a bias toward quality-diversity into optimization processes such as EAs significantly improve their performance. These techniques reinforce search directions in novel parameter regions while penalizing (over)exploitation of already experienced solutions. Thus the systems and methods provided herein have applications to, as non-limiting examples, processing healthcare or other data and generating new outputs including data useful in or related to drug discovery.

[0105] Instead of directly optimizing for novel and diverse solutions via modified fitness scores, the present disclosure provides the option to use novelty-conditional sampling via HADES. A metric can be used for diversity in the heuristic data buffer of the CHARLES-D method, and condition the DMs generative process to sample diverse genotypes. Specifically, diversity δ cani be defined for a single data point g similar to the non-parametric k-nearest-1Nestimator asδ^ d ^i ^ ^ as the logarithm of its mean distance in parameterspace to all= |g - g| larger than the k-th nearesti jdistance d in the dataset buffer. In practice, this diversity metric can be used as a noveltyknn(N ) condition c δ when conditionally training CHARLES-D during the evolutionary process, andi i(NT)sample points with target conditions c that maximize diversity by favoring large δ.i28 QB\166118.01562\98271640.1

[0106] During sampling of the diffusion model, target conditions c(NT)need to be identified that bias the generative process to bring forth novel data points gν with large diversity measure. These conditions are related to entropy measures of the current population and do not have a well- defined objective target value (the diversity measure is a dynamic property of an individual in a given population rather than an objective trait at the individual level). Thus, the target conditions (NT)c ∼ p is sampled at every generation from a heuristic Boltzmann distributionN (N ) , with E ( f , (N ) f^pN ∝exp( −β E ( f , c )) c )=ii c ( N )where the rescaled fitness +δ0 to positive values by adding δ =0−max min|min ∆| . In that way, target conditions with large δ are sampled with higher probability,i iwhich effectively biases the generative process of the diffusion model towards sampling novel offspring genotypes with larger diversity δ ≥max (δ) than present in the current population, δ.ν i i i

[0107] This approach can be demonstrated on the Rastrigin task discussed above and shown in Figs.6A and 6B. Comparisons can be made of fitness and diversity measures of different parametrizations of HADES and CHARLES-D instances, along with mainstream methods such as a simple genetic algorithm (SimpleGA) and CMA-ES. Specifically, the HADES method can be used as baseline (fitness optimization without diversity condition), and different combinations of Novelty-based conditioning and Fisher- and greedy fitness-conditioning can be used in different CHARLES-D instances, where single or multiple conditions can be used during evolutionary optimization (snapshots of converged populations are presented in Fig.6A, graph 600).

[0108] In simulations, a narrowly distributed initial condition can be used as a start with σI= 0.2, challenging the respective EAs to explore from a central valley of the fitness landscape and find the different peaks located at |x|, |y| = 3.5 through exploration. As shown in graph 602 of Fig. 6A, HADES and the novelty-conditional CHARLES-D method excel at this task: both methods quickly and reliably identify optimal solutions in 50 statistically independent optimization runs. These approaches demonstrate faster convergence than CMA-ES, while the SimpleGA fails to identify the global optima and resides at the nearest locally-optimal peaks to the center. Moreover, these methods intrinsically maintain a high level of diversity evidenced in the constantly high entropy of the parameters in the population, as shown in Fig. 6A, graph 604. This diversity manifests through the fact that these methods can identify multiple optima in complex fitness 29 QB\166118.01562\98271640.1landscapes reliably. This was quantified in Fig.6A, graph 606, which presents the average number of solutions found cumulatively during a single lineage for all investigated algorithms. The results show that the vanilla HADES and the Novelty-conditional CHARLES-D can identify 75% of all target peaks reliably, and in 10% of all simulations, identify all four peaks of the Rastrigin task successfully.

[0109] The greedy fitness-conditioning solved the problem more quickly but demonstrates slower convergence on average compared to the previous two solver configurations. The greedy exploration maintains high entropy and, unexpectedly, exhibits explorative behavior over time: as illustrated in Fig. 6A graph 606, the greedy CHARLES- D configuration, on average, initially identified a single peak, yet despite the convergence of average fitness, the number of discovered solutions steadily increases with successive generations. In contrast, Fisher fitness-conditioning and especially CMA-ES showed limited diversity and typically converge onto one optima.

[0110] Fisher fitness-conditioning and CMA-ES demonstrated limited diversity and typically converge to a single optimum. Nevertheless, CMA-ES consistently identified the global optimum in the Rastrigin problem, where the parameter space aligns well with the method's Gaussian generative model: The algorithm explored the environment by adapting the covariance matrix of a multivariate Gaussian distribution (matching the search space dimension) to best fit the likelihood of the data. The EAs reproduction step is realized by sampling novel data points from this refined generative model, exploring the parameter space through successive Gaussian model adjustments.

[0111] In the Rastrigin example, the directions of the nearest local optima near the centered initial generation align with the global optima. Through expansion of the covariance matrix in a particular principal direction, i.e. (x = y), CMA-ES efficiently identifies a global optima very efficiently in few generations. However, this search strategy exhibits a strong inductive bias and can be inefficient when the search space requires complex reorientations of search directions. The deep-learning-based diffusion models provide a more flexible approach to understanding the parameter space due to the universal approximation theorem, reflected in the adaptable search strategy.

[0112] To illustrate this, a “twisted” variant of the Rastrigin problem was introduced. Bytransforming the coordinate space x→ x ^ non-linearly, the peaks of the Rastrigin function can bewrapped along an outward spiraling pattern, where global maxima are twisted relative to the initial 30 QB\166118.01562\98271640.1local optima near the center (see Fig.6B, graph 608). This geometric modification of the fitness landscape significantly impacts CMA-ES reliability, while the HADES and CHARLES-D methods maintain their performance despite increased complexity (see Fig.6B, graphs 608-614).

[0113] In all situations presented in Figs. 6A and 6B, using the Novelty-condition introduces a repulsive bias between parameter clusters during the DM's generative process. As illustrated in Figs. 6A (graphs 604, 612) and (graphs 606, 614), this leads to two key outcomes: accelerated exploration of high-fitness regions in the parameter space and, simultaneously, to increased population diversity. While CMA-ES, SimpleGA, and Fisher-based CHARLES-D converge to a single solution with limited diversity, both HADES and particularly the Novelty- conditional (greedy) CHARLES-D solvers maintain significantly higher diversity even after fitness convergence. That shows that a single population is capable of exploring multiple solutions at once, and that the population intrinsically explores new parameter space regions if environmental conditions are changing. On average, the Novelty-conditional CHARLES-D method shows increased diversity compared to corresponding non-novelty-conditional configurations.

[0114] Conditioning on novelty effectively applies neutral selection pressure, promoting population diversity while independently optimizing fitness scores. This approach can serve as an effective regularization mechanism for DM-evolution, generating diverse and novel solutions while maintaining the ability to exploit clusters of elite solutions.

[0115] Genetically conditioning behavior: how information traverses scales. The above discussion has demonstrated how the CHARLES-D method can be applied to constrain (i) the search dynamics in the parameter-space, (ii) the fitness quality of the samples across generations, and even (iii) improve population-wide diversity in a diffusion evolution optimization process. Building upon these results, the method can be used in selectively sampling genotypic parameters to achieve desired phenotypic traits. More precisely, the method can conditionally train the DM in CHARLES-D using both (i) genotypic representations and (ii) associated phenotypic qualities of agents in Reinforcement Learning (RL) environments. The goal is to selectively sample RL agents during an evolutionary process that exhibit specific target behaviors, notably without pretraining the DM.

[0116] Traditional RL applications aim to identify policies that enable autonomous agents to effectively navigate their environments: RL agents perceive different aspects of their 31 QB\166118.01562\98271640.1environment, such as state information and a reward signal, and need to propose actions that maximize reward acquisition. The policy of an agent, i.e., its internal decision-making machinery, is often modeled by Artificial Neural Networks (ANNs) receiving environmental states as input, and outputting high-quality actions that enable the agent to navigate its environment efficiently. The challenge thus is to identify ANN parameters that enable agents to maximize reward acquisition corresponding to high fitness scores. This is often achieved by gradient-based RL algorithms which require careful curation of differentiable reward signals. Especially in multi- objective scenarios either cumbersome reward-shaping or curriculum learning techniques are valuable to balance different reward signals, or the environment needs to be extremely general leading to substantial computational overhead and potentially unpredictable behavior. In contrast, EAs have proven highly successful to evolve slim and problem-specific ANN-based RL agent policies simply based on cumulative reward measures and often result in much more robust, transferable, and interpretable agent policies. As illustrated in Fig. 7, HADES proves highly effective for this purpose.

[0117] In particular, Fig. 7 provides a schematic 700 of an ANN-based RL-agent controlling the cart in a cart-pole environment. Fig. 7 also provides a series of graphs 702 of training performance of HADES, Fisher-conditional CHARLES-D, CMA-ES, and SimpleGA on the cart-pole task with different ANN architectures.

[0118] In practice, the DM during CHARLES-D optimization can be conditionally trained, (r ) (r ) jointly on the ANN parameters gi and the associated resting position xi , the resting velocity x^i, and the associated fitness score fi averaged over Ne = 16 episodes. Thus, theclassifier for given ANN parameters gi includes c (r ) ( r ) ^ ( r )i ={ x i , x i , f i } .

[0119] In Fig 7, the solid lines fitness of the differentsolvers (color-coding) which were averaged over statistically independent evolutionary optimization runs. The shaded areas indicate the best performing individual across independent simulations until a certain generation for larger values than the mean, and the STD of all simulations for lower values than the mean. Fig.7 also includes a graph 704 showing the accuracy of predicting a cart-pole agent’s resting position from its ANN parameters (by training a 4 layer ANN with of 48 hidden units and Leaky-ReLU activation on a dataset of 10 unbiased evolutionary runs using the HADES method); this works well for high-fitness individuals (color-coded). In graph 706, the estimated resting position is illustrated for cart-pole agents sampled conditionally 32 QB\166118.01562\98271640.1for target resting positions xC = {-2, -1, 0, 1, 2} (color-coding) by a pretrained DM (2 layers with 324 hidden units and ELU activation for 2000 episodes on the same data as in graph 704). Resting positions of conditionally evolved lineages with the CHARLES-D method that give rise to RL- agent policies with desired behavior of target resting positions xC = {-0.5, 0.5, 1.0} (color coded); the DMs in graph 708 are not pretrained as in graph 706, but trained on heuristic data of the respective evolutionary lineage.

[0120] The goal of the research extends beyond evolving RL agents with high fitness. That is, the goal is to develop agents that exhibit specific target behaviors not encoded in the environment's reward signal, thus remaining neutral to the agent’s fitness. Specifically, classifier- free-guidance can be applied at the genotypic level of CHARLES-D to evolve RL-agents with targeted phenotypic-behavioral traits in their respective environment.

[0121] To validate this approach on a minimal yet descriptive example, the cart-pole system can be employed. In this system, a cart with a hinged pole moves sideways with the objective of maintaining the pole in a vertical position for as long as possible within a defined range, as illustrated in Fig.7, graph 700. The fitness score corresponds to the total number of timesteps NS ≤ 500 before the game termination, which occurs when either the pole-angle exceedingφ lim = ± 12^or the cart moving beyond the boundaries xlim = 2.4. The cart is controlled by an ANN.The network processes four input parameters, i.e. the current position, x ( s ) , velocity x^ ( s ) , poleangle φ (s ) , and pole angular velocity φ^ (s ) , and its outputs determines the cart's movementdirection (left or right). The task issolved if the RL agent consistently achieves a fitness score of 500 across multiple episodes.

[0122] First, RL-agents were evolved with maximum fitness using HADES, comparing its performance against mainstream methods such as CMA-ES and a SimpleGA. As ANN architecture, Recurrent Neural Networks (RNN) were chosen with a different number of layers and hidden units. The results depicted in Fig.7, graph 702, demonstrate, that the HADES method is capable of solving the problem in as little as 3-4 generations, although RNNs can be tedious to train in RL applications, while both CMA-ES and the SimpleGA take longer by an order of magnitude; a population-size of Np= 256 was used and fitness scores were averaged over Ne= 16 episodes. Notably, every implementation utilizes elitism. The absence of this feature would further widen the performance gap between the CMA-ES method and the SimpleGA method. The 33 QB\166118.01562\98271640.1work expanded the comparison to include an analysis of the CHARLES-D method, specifically when conditioning on producing offspring with high fitness. The results demonstrate that even when operating under Fisher-conditional optimization, the performance noticeably exceeds that of the HADES. Notably, every implementation features elitism. The absence of this feature would further widen the performance gap between the methods of CMA-ES and SimpleGA would be even more significant. 1Ns

[0123] Next, the focus can be on controlling the resting position x (r ) = x ( s ) ,N ^ s = N s − N rs which expresses the average position optimization trials, duringand their corresponding behavioral outcomes {gi , x (r )i } can be recorded. To predict the restingposition based on the RL-agent parameters, a deep ANN can be trained, denoted as f(r), such thatxˆ (r ) ( r ) (r ) ( r ) 2i = f ( g i ) . The weighted mean-square error g[ fi ] | xˆ i − x i | canto beminimized, where g [ f ] serves as the weighting factor. in Fig. 7, graph 704,prediction accuracy is particularly strong for agents with high fitness of ≈ f ≈ 500. Notably, theseihigh-fitness agents demonstrate resting positions that span the complete range of x ∈ [ − 2, 2] .(r )

[0124] Using the joint database of parameters and associated behavioral data {g , x }i ifrom earlier HADES evaluations, a generative DM can be trained “offline” on this genetic database, i.e., without utilizing the DM in any further optimization. Then, the DM can be used to ˆconditionally sample novel genotypes g that parameterize the behavior of RL-agents to balancevthe pole at specific target locations x = {-2, -1, 0, 1, 2}. The results in Fig. 7, graph 706cdemonstrate, that the conditional sampling achieves good accuracy in biasing the corresponding RL-agents towards exhibiting the desired target behavior.

[0125] Finally, the CHARLES-D method was used to evolve an initially randomized population of ANN parameters for cart- pole RL-agent controllers toward solutions that exhibit specific target behaviors, namely balancing the pole at resting positions x = {-0.5, 0.5, 1.0}. ThisC was achieved without modifying the reward signal, but instead using conditional training of the (r ) generative DM on the ANN parameters g and their associated mean resting positionsxi imeasured during the evolutionary process. Offspring genotypes are then selectively by (r)conditioning the DM on c = x .c34 QB\166118.01562\98271640.1

[0126] Notably, this experiment was performed independently of the database and pretrained DM discussed in Fig. 7, graphs 704 and 706. Rather, we began with a randomized initial population and a randomly initialized DM, that is solely trained on parameters explored during the respectively evolving populations of cart-pole agents, i.e., in an "online" mode. Fig.7,graph 706 shows the measured resting positions x (r )i for the three independent lineages with xC =-0.5, 0.5, or 1.0. These positions x (r )i correspond to generated agents gi that achieved an averagefitness score of 500 over Ne = episodes.

[0127] The generative process demonstrated clear bias in generating genotypic parameters that encode specific functional behaviors at the phenotypic level that is neutral to the agents’ fitness scores. Beyond intriguing potential biological implications (discussed below), the CHARLES-D method enables efficient multi-objective optimization across various problem domains without requiring complex reward shaping techniques. Through classifier-free-guidance conditioning of the generative process at genotypic parameter level, evolutionary search can be directed toward parameter space regions that yield desired phenotypical behaviors. CHARLES-D effectively channels conditional information (specifically, desired behavior) across multiple layers of abstraction, from the generative phase at the genotypic level to actual behavior of ANN-based autonomous RL-agents at the phenotypic level in physically realistic environments. This bridging occurs through joint training of a generative model on governing genotypic parameters and their associated phenotypic traits. DMs capture the developmental layer between genotypes and phenotypes by learning how to gradually generate parameters, notably through step-wise denoising operations, that conform to conditionally encoded phenotypic traits. In essence, DMs encapsulate the computationally irreducible nature of the developmental process by learning how to actually compute high-quality samples through step-wise error correction mechanisms conditional to specified target features, thereby forming an associative memory of domain-specific generative processes.

[0128] The above-described systems and methods, whether alone or along with the complementary work described in Y. Zhang, B. Hartl, H. Hazan, and M. Levin, “Diffusion models are evolutionary algorithms,” (2024), establishes a connection between diffusion models (DMs) and evolutionary algorithms (EAs) through shared underlying conceptual and mathematical foundations: DMs can be viewed as evolutionary processes in disguise. The above described systems and methods demonstrate that deep-learning based DMs can effectively serve as efficient 35 QB\166118.01562\98271640.1generative models in EAs, enhancing genotypic recombination operations. Rather than relying on pretraining DMs with large general datasets, the systems and methods can be continuously refined relatively shallow DMs using heuristically acquired, high-quality parameters from task-specific evolutionary process. This iterative refinement of the DM's generative process, based on the most recent evolutionary evidence, enables the DM to be adaptive to evolutionary changes.

[0129] DMs leverage Artificial Neural Network (ANN) to sample novel data points conforming to a target parameter distributions. Given their status as universal function approximators, ANNs excel at learning complex correlations within arbitrary datasets, making them ideal for identifying subtle correlations in parameters of evolutionary processes. Through iterative refinement of the DM's generative process using heuristically acquired high-quality data from evolutionary processes, the present disclosure provides the Heuristically Adaptive Diffusion- Model Evolutionary Strategy (HADES ) method. This stands in contrast to other method’s performance with mainstream EA techniques across various numerical optimization scenarios, and report significant improvements in adaptability to changing environments while maintaining reliable convergence to target solutions.

[0130] DMs augment evolutionary processes with unconventional (epigenetic) memory: Using elite buffer datasets collected across generations or persistent traits in constantly retrained DMs allows the generative process to utilize previously experienced information, thus enabling faster adaptation in changing environments. This memory capability proves especially crucial when objective functions are computationally expensive. The findings confirm that maintaining a memory buffer enhances both search result quality and diversity.

[0131] Moreover, via classifier-free-guidance techniques, conditional sampling can be used in DMs to directly bias the evolutionary search dynamics, steering it towards regions in the parameter space that exhibit desired target traits. This leverages multi-objective optimization without the need for complex reward shaping or curricula learning techniques. By conditioning the DM's generative phase across successive generations, control can be demonstrated over: (i) the search dynamics in the parameter-space, (ii) sampling offspring generations with specific fitness distributions similar to inverse reinforcement learning and in addition controlling the diversity or greediness of the population, (iii) biasing the search towards desired phenotypic traits that are neutral to the problem's fitness score, and (iv) even to explicitly maintain population diversity through novelty- or diversity-conditioning. This conditional sampling mirrors image- or video- 36 QB\166118.01562\98271640.1generation techniques that are controlled by custom text-inputs. The Conditional, Heuristically- Adaptive ReguLarized Evolutionary Strategy through Diffusion (CHARLES-D) method introduces conditional sampling during optimization, effectively constraining search result qualities via custom control parameters defined independently to the task’s objective function. Thus, the approaches provided herein represent, as best known, the first “Talk to your Optimizer” application.

[0132] In that way, DMs demonstratively outperform the generative models of mainstream genetic algorithms in flexibility, versatility, and control over the search dynamics: With HADES and CHARLES-D it is possible to successfully solve high-dimensional complex optimization problems, and even bias the search-dynamics toward desired behavior, out- competing mainstream approaches. Through an epigenetic dataset memory buffer, it is possible to dynamically condition the search behavior to revisit promising, previously experienced parameter space regions, similar to an associative memory. Moreover, such unconventional memory properties enable specific conditioning of the generative process across evolutionary generations to actively promote novelty and diversity, as effective novelty search requires memory capability. Eventually, both HADES and CHARLES-D solutions show remarkable diversity, particularly in reinforcement learning tasks.

[0133] Intriguingly, the systems and methods provided herein demonstrate agential aspects: The DM's generative process applies successive denoising steps, transforming initially random input into successively refined highly-correlated, high-quality parameter output conforming to a training dataset. This iterative denoising process represents a perception-action cycle of genotypic parameters similar to Neural Cellular Automata, driving (i.e., poorly adapted) genotypes towards statistically more probable (i.e., better adapted) parameter space regions. Furthermore, this process can demonstratively learn from experience and, through conditioning, responds to external stimuli that are orthogonal, or neutral to a fitness score. This perspective reframes the evolutionary process as an active learning system. Thus, an evolutionary process's classification as being a variational or transformational process depends on the observer's perspective: individuals experience learning as transformational, refining an internal world model while maintaining their “identity.” From an evolutionary or ecosystem perspective, individuals represent temporary “experiments,” while interacting species from a transformational learning system conditional to particular environmental constraints. 37 QB\166118.01562\98271640.1

[0134] A paradigm-shift: Generative Diffusion Models sample Gene-Expressions rather than Genomic Parameters akin to Gene-Regulatory-Networks

[0135] Diffusion models have recently been identified as associative memories, and, in a complementary work (Y. Zhang, B. Hartl, H. Hazan, and M. Levin, “Diffusion models are evolutionary algorithms,” (2024)), as evolutionary algorithms. Correspondingly, evolution can be understood as a form of Hebbian-learning. Evolutionary learning operating at the bio-molecular level, maintaining DNA-based associative memory with self- regulatory capabilities in expressing protein sequences that constrain functionality of their host cell. This perspective presents DNA as a generative model that initializes the developmental process of an organism rather than a direct blueprint of the latter. In this process, genes are expressed in modular response to host-cells configuration, internal state, and environment.

[0136] The work herein demonstrated that DMs, when trained on generating functional parameters conditionally to associated behavioral features, can be used to selectively evolve agent policies exhibiting targeted behavior that is neutral to the fitness score. This can be explicitly shown in experiments with a cart-pole environment where agents balance a pole vertically, but conditional at specific target locations: The same DM model can generate distinct control parameters for a cart-pole agent, enabling pole stabilization at different desired locations, e.g., xA, or xB = xA, simply by conditioning the DM's generative denoising process on policy A or B. Moreover, it is possible to smoothly transform between these policies by exchanging the respective conditions: When shifting from policy A to B, the DM adapts the agent’s controller parameters, accordingly, representing an unconventional form of behavioral control through parameter reconfiguration. This mechanism closely parallels how gene-regulatory networks dynamically reconfigure cell functionality in response to internal or external stimuli.

[0137] Viewing this through the lens of recent interpretations of the genome as a generative model, the DM used here literally represents a lineage’s evolving genome, including its ability to self-regularize and utilize gene expressions that reconfigure phenotype functionality based on environmental constraints (as demonstrated by conditions A or B in the above cart-pole example). This indicates that the parameters in this work do not represent genotypic representations but gene expressions encoding phenotype functionality and behavior, similar to how gene expressions encode protein sequences that control cellular behavior. The complete genome (i.e., represent by the DM) contains much richer information, including an associative memory that is accessible 38 QB\166118.01562\98271640.1when needed. Thus, generative diffusion models are good models for self-regulatory, generative DNA, sampling gene-expressions rather than genotypic representations.

[0138] The models provided herein are much closer to biology than previous evolutionary methods, by representing DNA as a generative model with associative memory, surpassing previous evolutionary methods in detail and functionality. This representation enables specific response to external conditions and generates problem-specific parameter expressions through conditional denoising processes that are fundamentally rooted in non-equilibrium physics. Such capabilities allow dynamic reconfiguration of phenotype behavior, closely mirroring biological systems’ adaptability, in turn promoting intriguing technological innovations.

[0139] The systems and methods provided herein demonstrate particular effectiveness in sparse reward environments, where traditional optimization methods typically fail. In such environments, meaningful fitness signals are rare, and most parameter configurations yield uniformly poor performance.

[0140] The MountainCar environment exemplifies such challenges: a cart must accumulate sufficient momentum to climb a hill, receiving only a penalty of -1 at each timestep until success. Traditional methods like CMA-ES and SimpleGA fail to find solutions reliably, with most lineages maintaining the default fitness score of -200 even after 500 generations.

[0141] The CHARLES-D method addresses this through specialized conditioning strategies: 1. Horizontal Spread Conditioning (CHARLES-X): Conditions the diffusion model to generate offspring with large spread in the horizontal (x) direction, effectively increasing cart mobility and exploration capabilities. 2. Combined Conditioning (CHARLES-XD): Integrates fitness conditioning with spatial spread conditioning to balance exploitation and exploration. 3. Parameter Scaling Robustness: The method works reliably across different parameter scaling factors (s=1,2,3,4,5,10), showing particular strength at higher scaling factors where traditional methods become even less effective, as illustrated in Figs.8 and 9.

[0142] In particular, Fig.9 shows mean and median fitness (and corresponding quantiles) of 20 statistically independent lineages of solving the MountainCar environment over 500 generations with different solvers (columns) and different scaling factors s=1,2,3,4,5,10 (rows). Fig. 10 shows mean, median, and STD fitness (rows from top to bottom) of 20 statistically 39 QB\166118.01562\98271640.1independent lineages of solving the MountainCar environment over 500 generations with different solvers (labeled) and different scaling factors s=1,2,3,4,5,10 (columns), contrasting evolutionary efficiency for the different solvers (colors) for a fixed scaling factor. For a scaling factor of s=1, solutions are found only occasionally and SimpleGA performs best, closely followed by CHARLES-XD. Starting from a scaling factor of s=2, CHARLES-X and CHARLES-XD identify the correct gradient towards the solution space most efficiently, and result not only in better solutions, but consistently better solutions compared to SimpleGA and CMAES (as shown by the decreased STD). Notably, the condition maximizing the spread in x and maximizing fitness (by minimizing episode time steps) can interfere, which can be dealt with by removing the condition after a fitness gradient signal is observed in the search.

[0143] The present disclosure provides systems and methods that can be implemented using computer systems. Referring to Fig. 8, one non-limiting example of a system 800 in accordance with the present disclosure is provided. The system 800 may include a computing system 810, which can take any of a variety of forms, including a computer, including a laptop, or may be a phone, tablet, watch, or other device, including a wearable. The computing system 810 can include a processor or controller 812, a display 814, one or more inputs 816, one or more communication systems 818, and / or memory 820. In some configurations, the controller 812 can be any suitable hardware processor or combination of processors, such as a central processing unit (“CPU”), a graphics processing unit (“GPU”), and so on. In some configurations, the display 814 can include any suitable display devices, such as a liquid crystal display (“LCD”) screen, a light- emitting diode (“LED”) display, an organic LED (“OLED”) display, an electrophoretic display (e.g., an “e-ink” display), a computer monitor, a touchscreen, a television, a screen of a mobile device, such as a phone or tablet, and so on. In some configurations, the inputs 816 can include any suitable input devices and / or sensors that can be used to receive user input, such as a keyboard, a mouse, a touchscreen, a microphone, and so on.

[0144] In some configurations, the communications systems 818 can include any suitable hardware, firmware, and / or software for communicating information. The computing system 810 can communicate over a communication network 822 and / or any other suitable communication networks. For example, the communications systems 818 can include one or more transceivers, one or more communication chips and / or chip sets, and so on. In a more particular example, the communications systems 818 can include hardware, firmware, and / or software that can be used to 40 QB\166118.01562\98271640.1establish a Wi-Fi connection, a Bluetooth connection, a cellular connection, an Ethernet connection, and so on.

[0145] In some configurations, the memory 820 can include any suitable storage device or devices that can be used to store instructions, values, data, or the like, that can be used, for example, by the controller 812 to present content using the display 814, to communicate with a server 824 via the communications systems 818, and so on. The memory 820 can include any suitable volatile memory, non-volatile memory, storage, or any suitable combination thereof. For example, the memory 820 can include random-access memory (“RAM”), read-only memory (“ROM”), electrically programmable ROM (“EPROM”), electrically erasable ROM (“EEPROM”), other forms of volatile memory, other forms of non-volatile memory, one or more forms of semi-volatile memory, one or more flash drives, one or more hard disks, one or more solid state drives, one or more optical drives, and so on. In some configurations, the memory 820 can have encoded thereon, or otherwise stored therein, a computer program for controlling operation of computing device 810. In such configurations, the processor / controller 812 can execute at least a portion of the computer program. In doing so, information can be presented (e.g., images, user interfaces, graphics, tables), content can be received from the server 824, and so on. For example, the controller 812 and the memory 820, and / or local processors.

[0146] The server 824 can include a communications system 826 for communicating, for example, via the communication network 822. The server 824 can also include a processor / controller 828, a display 830, one or more inputs 832, and / or memory 834. As described with respect to the computing system, the controller 828 can be any suitable hardware processor or combination of processors, such as a CPU, a GPU, and so on. The display 830 can include any suitable display devices, such as an LCD screen, LED display, OLED display, electrophoretic display, a computer monitor, a touchscreen, a television, and so on. The input 832 can include any suitable input devices and / or sensors that can be used to receive user input, such as a keyboard, a mouse, a touchscreen, a microphone, and so on. The communications systems 826 can include hardware, firmware, and / or software that can be used to establish a Wi-Fi connection, a Bluetooth connection, a cellular connection, an Ethernet connection, and so on. Finally, the memory 834 can include any suitable volatile memory, non-volatile memory, storage, or any suitable combination thereof. 41 QB\166118.01562\98271640.1

[0147] Further additions and adaptations are possible, particularly, as the systems and methods provided herein are deployed into particular applications. A variety of non-limiting examples of applications are provided hereinafter.

[0148] Temporal Memory & Predictive Adaptation

[0149] When deployed to this application, the systems and methods provided herein can equip the diffusion evolution system with a form of memory to enhance its adaptability in dynamic environments. The technical approach can integrate temporal markers into the training data, allowing the system to learn from historical environmental patterns, similar to epigenetic mechanisms in biology.

[0150] This implementation reflects a shift from purely reactive adaptation to a proactive or predictive strategy. By recognizing and learning from environmental cycles, the systems and methods provided herein can anticipate future changes and preemptively adjust its population distribution, leading to more efficient and robust performance in environments that change over time.

[0151] Autonomous System Optimization

[0152] When deployed to this application, the systems and methods provided herein can yield self-regulating evolutionary systems that minimize or eliminate the need for manual parameter tuning and reward engineering. The systems and methods can be enhance with mechanisms for agents to evolve their own internal reward models and curiosity-driven objectives, allowing them to autonomously explore and solve problems without externally specified rewards.

[0153] The systems and methods provided herein can create more autonomous and “maintenance-free” optimization systems. By learning how to evolve more effectively over time, these systems and methods can tackle complex problems where optimal parameters are unknown or where defining an effective reward function is itself a significant challenge.

[0154] Generative Genetic Engineering (“Anatomical Compiler”)

[0155] When deployed to this application, the systems and methods provided herein can be used to realize a multi-scale biological modeling system, which can be termed an “anatomical compiler,” capable of translating high-level phenotypic descriptions into the specific biological modifications required to achieve them. Using a natural language interface, a user can specify a desired trait, and the systems and methods provided herein can generate the necessary interventions at the genomic, transcriptomic, or proteomic level. 42 QB\166118.01562\98271640.1

[0156] Thus, a system can be realized that bridges the gap between a conceptual biological goal and its molecular implementation. The systems and methods provided herein enable non- experts to engage in genetic design and realize applications in synthetic biology, agriculture, and regenerative medicine by specifying outcomes while the system determines the most viable biological pathway to achieve them.

[0157] DNA as a Computational Language

[0158] When deployed to this application, the systems and methods provided herein can formally investigate DNA as a computational language system with its own grammar, syntax, and semantics. The approach can include using machine learning models to analyze vast genomic datasets to discover underlying structural rules and create systems that can align genetic sequences with natural language descriptions of their functions.

[0159] The systems and methods provided herein can provide a paradigm shift from viewing DNA as a mere data store to understanding it as an active computational system. This can yield fundamental insights into how biological information is encoded and evolves, while also creating practical tools for translating human intent into functional genetic code for engineering purposes.

[0160] Computational Irreducibility Modeling

[0161] When deployed to this application, the systems and methods provided herein can address the challenge that the relationship between a genotype (genetic code) and its resulting phenotype (organismal traits) is often computationally irreducible, meaning the outcome cannot be predicted without simulating the entire developmental process. The systems and methods provided herein can train generative diffusion models to learn and capture these complex, non- linear developmental mappings.

[0162] The systems and methods provided herein can provide a computational framework that can model and understand biological development without oversimplification. This provides a tool for investigating fundamental biological complexity and the emergence of traits, moving beyond simple optimization to model the generation of adaptive, problem-solving agents.

[0163] Therapeutic Intervention Modeling

[0164] When deployed to this application, the systems and methods provided herein can realize a framework for drug discovery that conceptualizes a diseased biological state as a “noisy” or corrupted version of a healthy state. Pharmaceutical interventions can then be modeled as a 43 QB\166118.01562\98271640.1guided denoising process that transitions the system from the diseased state back to a healthy equilibrium.

[0165] Thus, the systems and methods provided herein can provide an interactive and holistic approach to designing therapies. Instead of screening compounds for a single target, the systems and methods can be used to model the effect of interventions on the entire biological state, allowing for the optimization of treatments that maximize efficacy while minimizing predicted side effects in a personalized context.

[0166] Multi-Scale Biological State Regulation

[0167] When deployed to this application, the systems and methods provided herein can model biological organisms as hierarchical networks of interlocked, problem-solving agents operating at multiple scales (e.g., molecular, cellular, tissue). The systems and methods can realize distributed diffusion processes to simulate how individual cells regulate their states and communicate with each other to achieve coordinated, tissue-level developmental programs.

[0168] Thus, the systems and methods provided herein can realize a unified framework for understanding how system-level organization and behavior emerge from local interactions, bridging molecular mechanisms with organismal phenotypes. This approach can provide significant insights into developmental biology, regenerative medicine, and how biological systems robustly maintain their complex organization.

[0169] Real-Time Agent Metamorphosis

[0170] When deployed to this application, the systems and methods provided herein can realize an AI agent that can undergo fundamental behavioral transformations during operation, without needing to be stopped or retrained. This is achieved by dynamically reparameterizing the agent's neural controller through a diffusion process, allowing it to seamlessly switch between different objectives or adapt its core logic to entirely new environments.

[0171] Thus, the systems and methods provided herein provide a leap from static AI systems to dynamic, metamorphic intelligence with unprecedented flexibility. This includes the “soul-body transfer” concept, where a learned behavioral policy could be transferred between different physical forms, with applications in metamorphic robotics and highly adaptive autonomous systems.

[0172] Predictive Evolution with Real Biological Data 44 QB\166118.01562\98271640.1

[0173] When deployed to this application, the systems and methods provided herein can apply the diffusion evolution framework to real-world biological data, particularly from long-term evolution experiments, to predict adaptive outcomes. By modeling earlier genetic states as “corrupted” versions of later, more adapted states, the systems and methods can be trained to predict future genetic mutations in response to specific environmental pressures, such as increasing antibiotic concentrations.

[0174] Thus, the systems and methods provided herein can be used to create a systematic framework for forecasting evolutionary trajectories. This provides a practical tool for fields like medicine and agriculture to anticipate the evolution of resistance in pathogens or pests, enabling the proactive development of countermeasures rather than purely reactive responses.

[0175] Theoretical Unification of AI Architectures (NCA, GNN, CNN)

[0176] When deployed to this application, the systems and methods provided herein can establish and formalize the mathematical equivalence between Neural Cellular Automata (NCAs), Graph Neural Networks (GNNs), and CNN-based diffusion models. By proving that these architectures can be viewed as specific instances of a more general computational framework, techniques and insights can be transferred between them.

[0177] Thus, the systems and methods provided herein can realize the creation of a unified theoretical foundation that enhances all included architectures. For instance, the robust training methods of diffusion models can be applied to NCAs , and the powerful analytical tools of GNNs can be used to model and control multi-cellular systems, with potential applications in analyzing and disrupting tumor communication networks.

[0178] Criticality-Based Optimization

[0179] When deployed to this application, the systems and methods provided herein can enhance evolutionary efficiency by leveraging insights from physics, specifically the phase transitions and spontaneous symmetry-breaking events that occur in diffusion models. The systems and methods provided herein can be designed to detect these “critical points” during the generative process, where a small change can produce a large-scale effect.

[0180] Thus, the systems and methods provided herein can provide a more intelligent and targeted mutation strategy. Instead of relying on random mutations with fixed rates, the system would identify and exploit these critical points to make changes that have a higher probability of 45 QB\166118.01562\98271640.1producing significant, beneficial adaptations, thereby eliminating the need for manual mutation rate tuning and potentially accelerating the optimization process.

[0181] Asynchronous Distributed Architecture (Parallel HADES)

[0182] When deployed to this application, the systems and methods provided herein can realize a fundamental redesign of the system's architecture to enable massive scalability and computational efficiency. The new architecture can be distributed and asynchronous, allowing multiple agents to evolve independently on different computational nodes and share information periodically without requiring all processes to synchronize.

[0183] Thus, the systems and methods provided herein can realize the elimination of computational bottlenecks that limit the scale of current evolutionary systems. This biologically- inspired design, mimicking cellular communication, enables the processing of massive datasets and allows for the emergence of symbiotic coevolution, where different sub-populations can specialize on different aspects of a complex problem.

[0184] Bidirectional AI-Evolution Enhancement

[0185] When deployed to this application, the systems and methods provided herein can providea synergistic, two-way relationship between evolutionary algorithms and diffusion models. In one direction, evolutionary principles are used to create novel, gradient-free guidance methods for diffusion models, allowing them to be controlled by any function, including non-differentiable objectives or human feedback. In the other direction, pre-trained diffusion models are used as powerful priors to initialize and guide evolutionary algorithms, dramatically accelerating their search process.

[0186] Thus, the systems and methods provided herein provide a hybrid framework that leverages the strengths of both domains to overcome their respective limitations. It expands the controllability of generative AI while simultaneously making evolutionary search more efficient and informed by prior knowledge.

[0187] Alternative Gradient-Free Neural Network Training

[0188] When deployed to this application, the systems and methods provided herein can be used to realize a new paradigm for training neural networks that replaces the standard backpropagation algorithm with a diffusion-based weight optimization process. This approach does not require the calculation and storage of gradients, which is one of the most memory- intensive parts of training large models. 46 QB\166118.01562\98271640.1

[0189] Thus, the systems and methods provided herein can realize a training method that significantly reduce the memory footprint required for training neural networks. This enables the development and training of models that are currently too large to fit on existing hardware, potentially pushing the boundaries of what is possible in artificial intelligence.

[0190] Causal Entropic Diffusion Intelligence

[0191] When deployed to this application, the systems and methods provided herein can create intelligent behavior based on the principle of maximizing future options, known as causal entropic force. Instead of being programmed with an explicit goal, an agent would act in a way that keeps the most potential pathways open for its future self. This leads to emergent problem- solving behavior, as actions that lead to dead-ends (low future options) are naturally avoided.

[0192] Thus, the systems and methods provided herein provide a pathway to more general and less brittle AI. By optimizing for freedom of action rather than a specific, pre-defined objective, such a system could exhibit flexible and robust intelligence without requiring extensive goal engineering from a human programmer.

[0193] Advanced Artificial Life Architectures

[0194] When deployed to this application, the systems and methods provided herein can be used to design artificial life that exhibits a high degree of biological realism, particularly in its resilience and adaptability. This includes the “Theseus” agent concept—an entity that can maintain its core identity while continuously changing and adapting across vast changes in scale (from a single unit to trillions).

[0195] Thus, the systems and methods provided herein can be used to realize a framework for creating more robust and life-like AI systems that embody principles of biological degeneracy and regeneration. The systems and methods can be applied to the search and generation of novel artificial life forms, combining generative models with evolutionary search to explore the space of possible life.

[0196] It is to be understood that the present disclosure is not limited in its application to the details of construction and the arrangement of components set forth in the following description or illustrated in the following drawings. The present disclosure is readily extended to other aspects and implementations and may be practiced or carried out in various ways. Also, it is to be understood that the phraseology and terminology used herein is for the purpose of description and should not be regarded as limiting. The use of “including,” “comprising,” or “having” and 47 QB\166118.01562\98271640.1variations thereof herein is meant to encompass the items listed thereafter and equivalents thereof as well as additional items. Unless specified or limited otherwise, the terms “mounted,” “connected,” “supported,” and “coupled” and variations thereof are used broadly and encompass both direct and indirect mountings, connections, supports, and couplings. Further, “connected” and “coupled” are not restricted to physical or mechanical connections or couplings.

[0197] As used herein in the context of computer implementation, unless otherwise specified or limited, the terms “component,” “system,” “module,” “controller,” “framework,” and the like are intended to encompass part or all of computer-related systems that include hardware, software, a combination of hardware and software, or software in execution. For example, a component may be, but is not limited to being, a processor device, a process being executed (or executable) by a processor device, an object, an executable, a thread of execution, a computer program, or a computer. By way of illustration, both an application running on a computer and the computer can be a component. One or more components (or system, module, and so on) may reside within a process or thread of execution, may be localized on one computer, may be distributed between two or more computers or other processor devices, or may be included within another component (or system, module, and so on).

[0198] In the methods described herein, the steps can be carried out in any order without departing from the principles of the disclosure, except when a temporal or operational sequence is explicitly recited. Recitation in a claim to the effect that first a step is performed, and then several other steps are subsequently performed, shall be taken to mean that the first step is performed before any of the other steps, but the other steps can be performed in any suitable sequence, unless a sequence is further recited within the other steps. For example, claim elements that recite “Step A, Step B, Step C, Step D, and Step E” shall be construed to mean step A is carried out first, step E is carried out last, and steps B, C, and D can be carried out in any sequence between steps A and E, and that the sequence still falls within the literal scope of the claimed process. A given step or sub-set of steps can also be repeated.

[0199] Furthermore, specified steps can be carried out concurrently unless explicit claim language recites that they be carried out separately. For example, a claimed step of doing X and a claimed step of doing Y can be conducted simultaneously within a single operation, and the resulting process will fall within the literal scope of the claimed process. 48 QB\166118.01562\98271640.1

[0200] The term “substantially” or “about” as used herein refers to a majority of, or mostly, as in at least about 50%, at least about 60%, at least about 70%, at least about 80%, at least about 90%, at least about 95%, at least about 96%, at least about 97%, at least about 98%, at least about 99%, at least about 99.5%, at least about 99.9%, at least about 99.99%, or at least about 99.999% or more.

[0201] As used in the claims, the phrase “at least one of A, B, and C” means at least one of A, at least one of B, and / or at least one of C, or any one of A, B, or C or combination of A, B, or C. A, B, and C are elements of a list, and A, B, and C may be anything contained in the Specification.

[0202] The following discussion is presented to enable a person skilled in the art to make and use aspects of the disclosure. Various modifications to the illustrated configurations or processes will be readily apparent to those skilled in the art, and the generic principles herein can be applied to other aspects and applications within the scope of the present disclosure and the understanding of one of skill based thereon. Thus, the present disclosure is not intended to be limited to particular embodiments or aspects shown, but is to be accorded the widest scope consistent with the principles and features disclosed herein. The following detailed description is to be read with reference to the figures, in which like components or elements in different figures have like reference numerals. The figures, which are not necessarily to scale, depict selected aspects and configurations or processes and are not intended to limit the scope of the disclosure. Skilled artisans will recognize the examples provided herein have many useful alternatives and fall within the scope of the disclosure. 49 QB\166118.01562\98271640.1

Claims

CLAIMS 1. A computer system comprising: a non-transitory, computer-readable memory having stored thereon a diffusion model configured to generate offspring genotypes and a fitness evaluator configured to evaluate fitness of the offspring genotypes; and a computer processor configured to: communicate with the memory to access the diffusion model and fitness evaluator; iteratively train the diffusion model using a dataset of genotypes and associated fitness values; and conditionally bias the diffusion model to generate offspring genotypes exhibiting target traits.

2. The system of claim 1, wherein the processor is further configured to maintain a buffer dataset of genotypes and associated fitness values from multiple generations.

3. The system of claim 2, wherein the processor is further configured to train the diffusion model using the buffer dataset.

4. The system of claim 1, wherein the target traits comprise at least one of genotypic traits, phenotypic traits, or population-wide traits.

5. The system of claim 1, wherein the processor is further configured to conditionally bias the diffusion model using classifier-free guidance techniques.

6. The system of claim 5, wherein the classifier-free guidance techniques comprise conditioning the diffusion model on a target fitness value.

7. The system of claim 6, wherein the target fitness value is determined based on a statistical property of fitness values in a current population. 50 QB\166118.01562\98271640.

18. The system of claim 1, wherein the diffusion model operates in a compressed latent space using random projections to handle high-dimensional parameter spaces.

9. The system of claim 1, wherein the processor is configured to adapt to time- dependent fitness landscapes through epigenetic memory buffering.

10. The system of claim 1, wherein the diffusion model samples gene expressions rather than direct genotypic parameters, modeling biological gene regulatory networks.

11. The system of claim 1, wherein the processor is configured to use mathematical equivalence between diffusion processes and evolutionary algorithms to make bidirectional algorithmic improvements.

12. The system of claim 1, wherein the processor is configured to: retrain the diffusion model only at specified generation intervals; match computational performance of traditional evolutionary algorithms; maintain solution quality while reducing training frequency.

13. A method for generating a learning network using evolutionary optimization, comprising: generating offspring genotypes using a diffusion model; evaluating fitness of the offspring genotypes; iteratively training the diffusion model using a dataset of genotypes and associated fitness values; and conditionally biasing the diffusion model to generate offspring genotypes exhibiting target traits.

14. The method of claim 13, further comprising maintaining a buffer dataset of genotypes and associated fitness values from multiple generations. 51 QB\166118.01562\98271640.

115. The method of claim 14, wherein iteratively training the diffusion model comprises training the diffusion model using the buffer dataset.

16. The method of claim 13, wherein the target traits comprise at least one of: genotypic traits, phenotypic traits, or population-wide traits.

17. The method of claim 13, wherein conditionally biasing the diffusion model comprises using classifier-free guidance techniques.

18. The method of claim 17, wherein the classifier-free guidance techniques comprise conditioning the diffusion model on a target fitness value.

19. The method of claim 18, wherein the target fitness value is determined based on a statistical property of fitness values in a current population.

20. The method of claim 13, further comprising: adapting conditional parameters of the diffusion model based on parameter scaling factors; maintaining optimization effectiveness across multiple scaling ranges; automatically adjusting exploration strategies based on parameter space dimensionality.

21. The method of claim 13, further comprising: applying multiple simultaneous conditions including fitness-based and spatial distribution conditions; dynamically balancing competing conditional objectives; removing conditions when fitness gradient signals are detected.

22. A non-transitory computer-readable medium storing instructions that, when executed by a processor, cause the processor to carry out steps comprising: generating offspring genotypes using a diffusion model; evaluating fitness of the offspring genotypes; 52 QB\166118.01562\98271640.1iteratively training the diffusion model using a dataset of genotypes and associated fitness values; and conditionally biasing the diffusion model to generate offspring genotypes exhibiting target traits.

23. The non-transitory computer-readable medium of claim 22, wherein the operations further comprise maintaining a buffer dataset of genotypes and associated fitness values from multiple generations.

24. The non-transitory computer-readable medium of claim 23, wherein iteratively training the diffusion model comprises training the diffusion model using the buffer dataset.

25. The non-transitory computer-readable medium of claim 22, wherein the target traits comprise at least one of: genotypic traits, phenotypic traits, or population-wide traits.

26. The non-transitory computer-readable medium of claim 22, wherein conditionally biasing the diffusion model comprises using classifier-free guidance techniques.

27. The non-transitory computer-readable medium of claim 26, wherein the classifier- free guidance techniques comprise conditioning the diffusion model on a target fitness value determined based on a statistical property of fitness values in a current population.

28. A computer system comprising: a non-transitory, computer-readable memory having stored thereon a neural network that was trained using a forward diffusion phase and a reverse evolution phase; and a computer processor configured to: access the memory to use the neural network to process input data to generate a new output.

29. The computer system of claim 28, wherein the input data includes healthcare data and the new output includes drug discovery data. 53 QB\166118.01562\98271640.

130. The computer system of claim 28, wherein the input data includes genetic data and the new output includes gene regulation information.

31. The computer system of claim 28, wherein the output the new output forms parameters of a generative or optimization process.

32. A method for optimization in sparse reward environments comprising: applying conditional constraints to guide evolutionary search toward promising parameter space regions; introducing conditions that increase population diversity without reward shaping; using horizontal spread conditioning to enhance agent mobility in parameter space; achieving reliable solution identification across multiple parameter scaling factors.

33. A computer system comprising: a conditional diffusion model configured to inject expert domain knowledge via conditioning parameters; a processor configured to bias exploration toward high-fitness regions using domain- specific constraints; a memory storing condition parameters that encode expert knowledge independent of fitness functions.

34. A method for contrastive evolutionary learning comprising: using conditional diffusion models to exclude particular traits or solution classes; applying negative conditioning to avoid undesired parameter regions; implementing contrastive search dynamics that promote desired while avoiding undesired characteristics.

35. A method comprising using entropy-based novelty conditioning to automatically maintain population diversity during evolutionary optimization. 54 QB\166118.01562\98271640.

136. A method for sparse reward environment optimization using conditional constraints to guide evolutionary search without reward shaping. 55 QB\166118.01562\98271640.1

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