Microwave neural network for broadband signal processing and feature extraction

Abstract

A signal modification unit configured for processing high-bandwidth signals includes at least one signal input configured to receive a high-bandwidth signal. The signal modification unit includes a tunable control component configured to adjust one or more parameters for modifying the high-bandwidth signal, wherein the one or more parameters are associated with nonlinear modification of the high-bandwidth signal. The signal modification unit includes one or more waveguide components configured to modify the high-bandwidth signal to generate a modified signal based in part upon the one or more parameters. The signal modification unit includes at least one signal output configured to provide the modified signal as an output of the signal modification unit. The signal modification unit allows for feature extraction of spectral bands and may be used to replace parts of digital neural networks.

Description

34009 / 11339-02 / PCMICROWAVE NEURAL NETWORK FOR BROADBAND SIGNAL PROCESSING AND FEATURE EXTRACTION GOVERNMENT SUPPORT CLAUSE

[0001] This invention was made with government support under FA8650-21-C-7007 awarded by the Defense Advanced Research Projects Agency, and 2025233 awarded by the National Science Foundation. The government has certain rights in the invention.CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority to U.S. Application No. 63 / 742,208, titled "Methods, techniques, and systems for broadband computation and communication", filed January 6, 2025, which is hereby incorporated by reference in its entirety.BACKGROUND

[0003] Although the following text discloses a detailed description of implementations of methods, apparatuses and / or articles of manufacture, it should be understood that the legal scope of the property right is defined by the words of the claims set forth at the end of this patent. Accordingly, the following detailed description is to be construed as examples only and does not describe every possible implementation, as describing every possible implementation would be impractical, if not impossible. Numerous alternative implementations could be implemented, using either current technology or technology developed after the filing date of this patent. It is envisioned that such alternative implementations would still fall within the scope of the claims.

[0004] High-bandwidth applications spanning multi-gigabit communication, high-performance computing, and radar signal processing demand ever-increasing processing speeds. However, these applications face limitations in signal sampling and computation due to hardware and power constraints. In the microwave regime, where operating frequencies exceed the fastest34009 / 11339-02 / PCclock rates, direct sampling becomes difficult, prompting interest in neuromorphic analog computing systems.

[0005] Managing communication and computation at hundreds of gigabits per second for high-performance computing is increasingly computationally expensive. It requires sampling and processing at clock speeds constrained by semiconductor physics and power limitations, where higher speeds lead to increased power consumption and heat dissipation. Traditional electronic signal processing chains used by data centers involve complex synchronization circuits to reconstruct transmissions after signals are distorted during transmission through lossy media. A concern in this process is ensuring that signals are accurately timed and sampled after passing through lossy media, which requires power-hungry parallel processing.

[0006] Typical wideband radar receivers, for example, consist of multiple signal chains, each handling a narrow frequency band. Each chain includes a filter, a mixer to down-convert the microwave signal to a low-frequency baseband, and an analog-to-digital converter. The targets' positions and speeds are inferred with a backend digital computer. However, scaling such an architecture to cover tens of gigahertz of bandwidth for imaging complex target environments is hardware-intensive.

[0007] Prior efforts to combine analog computing modalities with deep learning have not demonstrated the ability to perform fast, reconfigurable computations on wide bandwidth signals. These include systems like memristor crossbar arrays, photodiode arrays, and photonic tensor cores. Machine-learning tasks have been of the low-bandwidth variety like image, speech, or gesture recognition. Recent attempts to operate at radio frequencies, using quantum superconducting circuits, surface plasmon resonance structures, and spintronics with magnetic tunnel junctions, process a few megahertz of bandwidth. Some involve bulky printed circuit boards to form multilevel perceptrons. Recent microwave photonics chips, while capable of broadband computation, are limited to a few immutable math functions and are bulky and power-inefficient. Similarly, Ising machines based on networks of coupled oscillators for combinatorial optimization problems have so far been used in the megahertz range.34009 / 11339-02 / PC

[0008] Another example of a limited analog modality is a CMOS oscillator. Traditional CMOS oscillators rely on symmetry for stable, single-tone oscillation. Complex pulse-sharpening circuits are used to generate weak harmonic combs for spectroscopy. Narrowband combs created by passively coupling linear and nonlinear resonators with high quality factors are limited to simple tasks like low-frequency range finding. Designing electromagnetic structures with quality factors exceeding 40 in commercial CMOS processes is impractical. Stable optical frequency sources such as Kerr-combs and electro-optic frequency combs are well isolated from external drive signals, which limits their applicability for processing broadband inputs.

[0009] Similar to the deficiencies of CMOS oscillators, traditional modems rely on complex clock-and-data recovery circuits to decipher which bits were transmitted through a cable between data centers. These recovery circuits help compensate for the clock frequency mismatches between a transmitter and a receiver. To handle frequency-dependent losses in interconnects and inter-symbol interference, gain-restoring circuits like continuous-time linear equalizers are required at both ends of a channel. At speeds greater than 10 gigabits per second, inter-symbol interference becomes more challenging, and techniques like Maximum Likelihood Sequence Detection are used to infer which bit patterns were transmitted. This technique involves several time-interleaved, high-resolution and power-hungry analog-to-digital converters. The ability to efficiently encode small bits of information by forming complex relationships among them, and later decode those relationships, is fundamental to fast communication systems, cryptography, and artificial intelligence. However, this type of processing at ever-higher bit speeds quickly saturates the memory bandwidth of computational accelerators like graphics processing units. Conventional digital systems face a memory wall that limits throughput, and the energy cost of moving data between memory and processing units dominates total power consumption.

[0010] Therefore, improved systems and methods for broadband computation and communication that address at least one or more of these shortcomings in the art are desired.34009 / 11339-02 / PCSUMMARY

[0011] According to an aspect of the present disclosure, a signal modification unit configured for processing high-bandwidth signals is provided. The signal modification unit includes at least one signal input configured to receive a high-bandwidth signal. The signal modification unit includes a tunable control component configured to adjust one or more parameters for modifying the high-bandwidth signal, wherein the one or more parameters are associated with nonlinear modification of the high-bandwidth signal. The signal modification unit includes one or more waveguide components configured to modify the high-bandwidth signal to generate a modified signal based in part upon the one or more parameters. The signal modification unit includes at least one signal output configured to provide the modified signal as an output of the signal modification unit.

[0012] According to other aspects of the present disclosure, the signal modification unit may include one or more of the following features. The at least one signal input may be configured to receive the high-bandwidth signal as a radio frequency signal. The at least one signal input may be configured to receive the high-bandwidth signal as a microwave signal having a frequency within a range of 8 gigahertz to 18 gigahertz. The one or more waveguide components may comprise at least one nonlinear waveguide including a cascade of coupled nonlinear resonators. The cascade of coupled nonlinear resonators may comprise a plurality of inductive segments each including a nonlinear capacitor. The nonlinear capacitors may comprise anti-parallel diodes configured to generate a capacitance with polynomial nonlinearity. The one or more waveguide components may comprise one or more linear waveguides, each of the one or more linear waveguides comprising a cascade of coupled linear resonators including a plurality of stages each having a switch to adjust an effective length of the linear waveguide. The tunable control component may comprise one or more gain components including one or more cross-coupled transistor pairs configured to provide regenerative saturable gain. The tunable control component may be configured to adjust the one or more parameters in response to a control signal having a maximum data rate that is at least an order of magnitude lower than a data rate of the high-bandwidth signal. The tunable control component may comprise one or more control switches connected between one or34009 / 11339-02 / PCmore pairs of waveguides of the one or more waveguide components, the one or more control switches being configured to selectively couple and decouple the one or more pairs of waveguides in response to the control signal. The signal modification unit may be configured to generate the modified signal as a frequency comb based upon the high-bandwidth signal, the frequency comb being programmable using the tunable control component to adjust the one or more parameters.

[0013] According to another aspect of the present disclosure, a microwave neural network system for processing high-bandwidth signals is provided. The microwave neural network system includes a signal modification unit comprising at least one signal input configured to receive a high-bandwidth signal, a tunable control component configured to adjust one or more parameters for modifying the high-bandwidth signal, one or more waveguide components configured to modify the high-bandwidth signal to generate a modified signal based in part upon the one or more parameters, and at least one signal output configured to provide the modified signal. The microwave neural network system includes a signal input coupling configured to provide the high-bandwidth signal to the signal modification unit. The microwave neural network system includes a signal output coupling configured to receive the modified signal from the signal modification unit. The microwave neural network system includes a control unit configured to control the tunable control component of the signal modification unit. The microwave neural network system includes an analysis unit configured to receive an analysis signal from the signal output coupling and generate output data based upon a frequency profile of the analysis signal, wherein the analysis signal comprises the modified signal or a signal derived from the modified signal.

[0014] According to other aspects of the present disclosure, the microwave neural network system may include one or more of the following features. The control unit may be configured to adjust the one or more parameters for modifying the high-bandwidth signal by providing a control signal to the tunable control component, the control signal comprising a stream of control parameter values. The stream of control parameter values may comprise a control parameter bitstream having a bit rate at least an order of magnitude lower than a high-bandwidth signal bit rate of the high-bandwidth signal. The bit rate of the control parameter34009 / 11339-02 / PCbitstream may be between 100 megabits per second and 200 megabits per second, and the high-bandwidth signal bit rate may be at least 10 gigabits per second. The signal output coupling may comprise a receiver configured to generate the analysis signal by filtering the modified signal to obtain a frequency band that is at least an order of magnitude narrower than a bandwidth of the high-bandwidth signal. The receiver may comprise a tunable bandpass filter including a plurality of mixers configured to down-convert portions of the modified signal into the frequency band based upon a conversion signal received from a tunable oscillator. The analysis unit may be configured to analyze the frequency profile by inferring characteristics of the output data based upon one or more patterns in the frequency profile using one or more trained machine learning models. The one or more trained machine learning models may comprise a linear regression model configured to map spectral features of the frequency profile to the output data. The high-bandwidth signal may comprise a transmission bitstream, and the analysis unit may be configured to analyze the frequency profile of the analysis signal by performing one or more logic operations on at least a portion of the transmission bitstream in the frequency domain. The one or more logic operations may comprise at least one of a bitwise NAND operation, a bitwise XOR operation, a bitwise NOR operation, or a counter of values of bits in the portion of the transmission bitstream. The high-bandwidth signal may comprise a radar waveform containing an indication of one or more targets, and the analysis unit may be configured to generate a flight characteristic of each of the one or more targets as the output data, the flight characteristic comprising at least one of a location, a speed, or a trajectory of the respective target. The one or more waveguide components may comprise at least one nonlinear waveguide and at least one linear waveguide coupled to the at least one nonlinear waveguide through a parametric coupling mechanism controlled by the tunable control component. The microwave neural network system may be configured as an integrated circuit fabricated using a complementary metal-oxide-semiconductor process and occupying a planar area of less than 1 square millimeter.

[0015] According to another aspect of the present disclosure, a method for processing high-bandwidth signals by a microwave neural network system is provided. The method includes receiving, at a signal input coupling of the microwave neural network system, a high-bandwidth34009 / 11339-02 / PCsignal. The method includes controlling, by a control unit of the microwave neural network system, one or more parameters for modifying the high-bandwidth signal. The method includes modifying, by a signal modification unit of the microwave neural network system, the high-bandwidth signal to generate a modified signal based upon the one or more parameters, wherein the signal modification unit comprises one or more waveguide components. The method includes generating, by an analysis unit of the microwave neural network system, output data by analyzing a frequency profile of an analysis signal, wherein the analysis signal comprises the modified signal or a signal derived from the modified signal.

[0016] According to other aspects of the present disclosure, the method may include one or more of the following features. Modifying the high-bandwidth signal may comprise introducing nonlinear distortion into the modified signal through interactions between frequency modes within the one or more waveguide components. Modifying the high-bandwidth signal may comprise compressing power distributed across a wide frequency band of the high-bandwidth signal into a limited frequency band of the modified signal, the limited frequency band being at least an order of magnitude narrower than the wide frequency band. The method may further comprise generating, by a bandpass filter, the analysis signal as a portion of the modified signal within the limited frequency band. Controlling the one or more parameters for modifying the high-bandwidth signal may comprise providing a control signal to a tunable control component of the signal modification unit, the control signal having a data rate that is at least an order of magnitude lower than a data rate of the high-bandwidth signal. The control signal may comprise a control parameter bitstream having a bit rate between 100 megabits per second and 200 megabits per second, and the data rate of the high-bandwidth signal may be at least 10 gigabits per second. The control signal may control a level of nonlinearity of modification of the high-bandwidth signal by selectively coupling and decoupling waveguides of the one or more waveguide components. The high-bandwidth signal may comprise a transmission bitstream, and analyzing the frequency profile of the analysis signal may comprise performing one or more logic operations on at least a portion of the transmission bitstream in the frequency domain without determining contents of the transmission bitstream as a time-domain sequence of bits. The high-bandwidth signal may comprise a radar waveform containing an indication of one or34009 / 11339-02 / PCmore targets, and generating the output data may comprise determining at least one of a location, a speed, or a trajectory of each of the one or more targets based upon the frequency profile. Modifying the high-bandwidth signal to generate the modified signal may comprise generating a frequency comb based upon the high-bandwidth signal, the frequency comb being programmable by adjusting the one or more parameters. Analyzing the frequency profile of the analysis signal may comprise applying one or more trained machine learning models to the frequency profile to infer characteristics of the output data based upon one or more patterns in the frequency profile.

[0017] According to another aspect of the present disclosure, a frequency-based feature extraction unit for processing tokens is provided. The frequency-based feature extraction unit includes a tunable control component having at least one signal input configured to receive a bit stream representing a plurality of tokens, the tunable control component being configured to adjust one or more parameters associated with nonlinear modification of the bit stream. The frequency-based feature extraction unit includes a microwave waveguide network coupled to the tunable control component and comprising one or more nonlinear waveguides and one or more linear waveguides coupled to the one or more nonlinear waveguides, the microwave waveguide network being configured to perform feature extraction on the bit stream to generate an extraction signal based in part upon the one or more parameters. The frequencybased feature extraction unit includes at least one signal output configured to provide the extraction signal as an output of the frequency-based feature extraction unit.

[0018] According to other aspects of the present disclosure, the frequency-based feature extraction unit may include one or more of the following features. The at least one signal output may be configured to provide the extraction signal as a microwave signal. The one or more nonlinear waveguides may comprise a cascade of coupled nonlinear resonators including a plurality of inductive segments each having a nonlinear capacitor. The one or more linear waveguides may comprise a cascade of coupled linear resonators including a plurality of stages each having a switch to adjust an effective length of the linear waveguide. The one or more nonlinear waveguides and the one or more linear waveguides may be configured to have oscillatory modes that are parametrically coupled for extracting features between tokens in the34009 / 11339-02 / PCbit stream. The tunable control component may comprise one or more cross-coupled transistor pairs configured to provide regenerative saturable gain. The tunable control component may be configured to adjust the one or more parameters based on at least one of an amplitude, a pulse frequency, or a duration of the bit stream. The bit stream may comprise data for two tokens, and the extraction signal may encode relationships between the two tokens as spectral features. The frequency-based feature extraction unit may be configured as a microwave neural network processor operable to analyze the extraction signal and determine an association score between the tokens represented in the bit stream.

[0019] According to another aspect of the present disclosure, a method for processing a bit stream representing a plurality of tokens by a frequency-based feature extraction unit is provided. The method includes generating from a prompt a plurality of tokens for analysis. The method includes generating from the plurality of tokens a plurality of radiofrequency tokens and combining the radiofrequency tokens into a bit stream. The method includes receiving, at a signal input of a tunable control component, the bit stream. The method includes controlling, by the tunable control component, one or more parameters associated with nonlinear modification of the bit stream. The method includes modifying, by a microwave waveguide network comprising one or more nonlinear waveguides and one or more linear waveguides, the bit stream and generating an extraction signal based in part upon the one or more parameters. The method includes providing the extraction signal to an attention scoring process and determining a token mapping between the plurality of tokens.

[0020] According to other aspects of the present disclosure, the method may include one or more of the following features. The token mapping may comprise a plurality of embeddings of the tokens derived from spectral features of the extraction signal. The plurality of embeddings may encode relationships between successive tokens based upon association scores determined from the extraction signal. Generating from the plurality of tokens a plurality of radiofrequency tokens may comprise encoding each token as a pulse-train token characterized by at least one of an amplitude, a pulse frequency, or a pulse-train duration. Combining the radiofrequency tokens into the bit stream may comprise sequentially applying the pulse-train tokens to a parametric switching port of the frequency-based feature extraction unit. Modifying34009 / 11339-02 / PCthe bit stream may comprise parametrically coupling oscillatory modes between the one or more nonlinear waveguides and the one or more linear waveguides to produce a broadband frequency comb response encoding features of the plurality of tokens. Determining the token mapping between the plurality of tokens may comprise training a linear classifier on spectral features extracted from the extraction signal to predict associations between tokens in the plurality of tokens.

[0021] According to another aspect of the present disclosure, a signal modification unit configured for processing radar waveforms is provided. The signal modification unit includes at least one signal input configured to receive a radar waveform containing an indication of one or more targets. The signal modification unit includes a tunable control component configured to adjust one or more parameters for modifying the radar waveform. The signal modification unit includes one or more waveguide components comprising at least one nonlinear waveguide and at least one linear waveguide, the one or more waveguide components configured to modify the radar waveform to generate a modified signal based in part upon the one or more parameters. The signal modification unit includes at least one signal output configured to provide the modified signal as an output of the signal modification unit, wherein the modified signal comprises spectral features indicative of flight characteristics of the one or more targets.

[0022] According to other aspects of the present disclosure, the signal modification unit may include one or more of the following features. The at least one nonlinear waveguide may comprise a cascade of coupled nonlinear resonators including a plurality of inductive segments each having a nonlinear capacitor configured to generate a capacitance with polynomial nonlinearity. The at least one linear waveguide may comprise a cascade of coupled linear resonators including a plurality of stages each having a switch to adjust an effective length of the linear waveguide. The tunable control component may be configured to adjust the one or more parameters in response to a control signal having a data rate that is at least an order of magnitude lower than a data rate of the radar waveform. The flight characteristics may comprise at least one of a location, a speed, a trajectory, ora flight pattern of the one or more targets. The signal modification unit may be configured to generate the modified signal as a34009 / 11339-02 / PCfrequency comb that encodes features of the radar waveform across a compressed bandwidth narrower than a bandwidth of the radar waveform.

[0023] According to another aspect of the present disclosure, a microwave neural network system for emulating digital operations is provided. The microwave neural network system includes a signal modification unit configured to receive a transmission bitstream at a data rate of at least one gigabit per second. The microwave neural network system includes a tunable control component configured to receive a control parameter bitstream at a data rate at least an order of magnitude lower than the data rate of the transmission bitstream. The microwave neural network system includes one or more waveguide components comprising at least one nonlinear waveguide configured to modify the transmission bitstream to generate a modified signal based upon the control parameter bitstream. The microwave neural network system includes an analysis unit configured to analyze a frequency profile of the modified signal and perform one or more logic operations on at least a portion of the transmission bitstream in a frequency domain.

[0024] According to other aspects of the present disclosure, the microwave neural network system may include one or more of the following features. The one or more logic operations may comprise at least one of a bitwise NAND operation, a bitwise XOR operation, a bitwise NOR operation, or a population count operation that counts a number of ones in the portion of the transmission bitstream. The one or more logic operations may be associated with a pattern of values of the control parameter bitstream, and different patterns of the control parameter bitstream may configure the microwave neural network system to perform different logic operations. The at least one nonlinear waveguide may comprise a cascade of coupled nonlinear resonators including a plurality of inductive segments each having a nonlinear capacitor configured to generate a capacitance with polynomial nonlinearity. The one or more waveguide components may further comprise at least one linear waveguide coupled to the at least one nonlinear waveguide through a parametric coupling mechanism controlled by the control parameter bitstream. The analysis unit may be configured to detect a bit sequence within the transmission bitstream in the frequency domain without recovering the transmission bitstream as a time-domain sequence of bits. The data rate of the transmission bitstream may be at least34009 / 11339-02 / PC10 gigabits per second, and the data rate of the control parameter bitstream may be between 100 megabits per second and 200 megabits per second.

[0025] According to another aspect of the present disclosure, a method for classifying wireless signal encoding schemes using a microwave neural network is provided. The method includes receiving, at a signal input of a microwave neural network, a modulated carrier signal. The method includes modifying, by one or more waveguide components of the microwave neural network, the modulated carrier signal to generate a modified signal, wherein the one or more waveguide components comprise at least one nonlinear waveguide. The method includes extracting spectral features from a frequency profile of the modified signal. The method includes classifying, by an analysis unit, an encoding scheme of the modulated carrier signal based upon the extracted spectral features.

[0026] According to other aspects of the present disclosure, the method may include one or more of the following features. The modulated carrier signal may comprise a carrier wave modulated by baseband signals representing one of a plurality of modulation classes including digital modulation schemes and analog modulation schemes. The digital modulation schemes may comprise at least one of 8-phase shift keying, binary phase shift keying, continuous phase frequency shift keying, Gaussian frequency shift keying, pulse amplitude modulation, quadrature amplitude modulation, or quadrature phase shift keying. The analog modulation schemes may comprise at least one of amplitude modulation double sideband, amplitude modulation single sideband, or wideband frequency modulation. Classifying the encoding scheme may comprise applying a trained linear regression model to the extracted spectral features to map the spectral features to one of a plurality of modulation classes. The at least one nonlinear waveguide may comprise a cascade of coupled nonlinear resonators including a plurality of inductive segments each having a nonlinear capacitor configured to generate a capacitance with polynomial nonlinearity, and modifying the modulated carrier signal may comprise transforming transient changes in the modulated carrier signal into spectral features distributed across a frequency range detuned from a nominal operating frequency of the microwave neural network.34009 / 11339-02 / PC

[0027] According to another aspect of the present disclosure, a signal processing system for generating probabilistic bits from high-bandwidth data is provided. The signal processing system includes at least one signal input configured to receive a high-bandwidth signal comprising a sequence of multi-bit symbols. The signal processing system includes a microwave waveguide network comprising one or more nonlinear waveguides configured to generate a broadband frequency-comb response in response to the high-bandwidth signal. The signal processing system includes a downconversion stage configured to select a sub-band of the broadband frequency-comb response. The signal processing system includes a quantizer configured to sample the sub-band at a rate lower than a Nyquist rate of the high-bandwidth signal to generate probabilistic bits, wherein each probabilistic bit has a bias determined by a corresponding multi-bit symbol of the sequence.

[0028] According to other aspects of the present disclosure, the signal processing system may include one or more of the following features. The one or more nonlinear waveguides may comprise a cascade of coupled nonlinear resonators including a plurality of inductive segments each having a nonlinear capacitor configured to generate a capacitance with polynomial nonlinearity. The microwave waveguide network may further comprise one or more linear waveguides coupled to the one or more nonlinear waveguides, the one or more linear waveguides comprising a cascade of coupled linear resonators including a plurality of stages each having a switch to adjust an effective length of the linear waveguide. The downconversion stage may comprise a passive mixer configured to receive the broadband frequency-comb response and a local oscillator signal, the passive mixer being configured to translate a portion of the broadband frequency-comb response to a baseband frequency range. The quantizer may comprise a one-bit quantizer configured to capture two samples during each multi-bit symbol interval, the two samples being thresholded to produce a static state or a dynamic state, wherein the static state corresponds to sample values of 00 or 11 and the dynamic state corresponds to sample values of 01 or 10. The bias of each probabilistic bit may be characterized by a static ratio representing a fraction of outcomes that produce the static state, the static ratio being determined by properties of the corresponding multi-bit symbol including at least one of a sparsity or a transition structure of the multi-bit symbol.34009 / 11339-02 / PC

[0029] According to another aspect of the present disclosure, a method for transmitting image data using probabilistic bit encoding is provided. The method includes receiving pixel data comprising a plurality of multi-bit pixel values. The method includes encoding each multibit pixel value as a radiofrequency signal. The method includes feeding the radiofrequency signal to a microwave neural network comprising one or more nonlinear waveguides to generate a broadband output signal. The method includes downconverting a sub-band of the broadband output signal to baseband. The method includes sampling the baseband signal at a rate lower than a bit rate of the radiofrequency signal to generate a probabilistic bit for each multi-bit pixel value. The method includes transmitting the probabilistic bits, wherein each probabilistic bit has a static ratio determined by a corresponding multi-bit pixel value.

[0030] According to other aspects of the present disclosure, the method may include one or more of the following features. The one or more nonlinear waveguides may comprise a cascade of coupled nonlinear resonators including a plurality of inductive segments each having a nonlinear capacitor configured to generate a capacitance with polynomial nonlinearity.Sampling the baseband signal may comprise capturing two samples during each multi-bit pixel value interval using a one-bit quantizer, the two samples being thresholded to produce a static state corresponding to sample values of 00 or 11 or a dynamic state corresponding to sample values of 01 or 10. Darker pixel values may be mapped to multi-bit patterns that produce a higher static ratio and lighter pixel values may be mapped to multi-bit patterns that produce a lower static ratio, such that the transmitted probabilistic bits form a dithered representation of the pixel data.

[0031] The foregoing general description of the illustrative embodiments and the following detailed description thereof are merely exemplary aspects of the teachings of this disclosure and are not restrictive.BRIEF DESCRIPTION OF FIGURES

[0032] The figures described below depict various aspects of the system and methods disclosed herein. It should be understood that each figure depicts an embodiment of a particular aspect of the disclosed system and methods, and that each of the figures is intended34009 / 11339-02 / PCto accord with a possible embodiment thereof. Further, wherever possible, the following description refers to the reference numerals included in the following figures, in which features depicted in multiple figures are designated with consistent reference numerals.

[0033] FIG. 1 depicts a schematic of a signal modification unit in the form of a microwave neural network (MNN), according to aspects of the present disclosure.

[0034] FIG. 2A depicts a schematic of a type of feature extraction, specifically token-encoded parametric oscillations, performed by an MNN, according to aspects of the present disclosure.

[0035] FIG. 2B depicts a schematic of a type of feature extraction, specifically broadbandinput-driven oscillations, performed by an MNN, according to aspects of the present disclosure.

[0036] FIG. 3A depicts a schematic of a nonlinear resonance waveguide, such as may be used as waveguide A in the MNN of FIG. 1, 2A, or 2B.

[0037] FIG. 3B depicts a schematic of a linear waveguide, such as may be used as waveguide B, C, or D in the MNN of FIG. 1, 2A, or 2B.

[0038] FIG. 3C depicts a schematic of a nonlinear capacitor, such as the nonlinear capacitors included in the nonlinear waveguide of FIG. 3A.

[0039] FIG. 3D depicts a schematic of a control switch such as may be used in the MNN of FIG.1, 2A, or 2B.

[0040] FIG. 3E depicts a schematic of a pair of cross-coupled NMOS transistor pairs, such as may be used in the MNN of FIG. 1, 2A or 2B.

[0041] FIG. 3F depicts a plot of a measured comblike spectra (power) generated by the MNN for both low and high bias voltages applied to the nonlinear capacitors.

[0042] FIG. 3G depicts a plot impact of low-speed switching between the nonlinear and linear resonators on the MNN's output spectrum.

[0043] FIG. 3H depicts the distortion in the MNN's output signal is a result of frequency-modulated parametric oscillations.34009 / 11339-02 / PC

[0044] FIG. 4A depicts a schematic of an experimental setup to inject radiofrequency (RF) pulse tokens into an MNN, such as the MNN of FIG. 1, 2A or 2B, and record its responses to infer token relationships from spectrograms.

[0045] FIG. 4B depicts a schematic of an experimental setup to test redistribution of spectral components across the output of an MNN, such as the MNN of FIG. 1, 2A or 2B.

[0046] FIG. 5A depicts a schematic of an MNN system, according to aspects of the disclosure.

[0047] FIGs. 5B, 5C, and 5D depict a schematic of a simulated airspace and the response of an MNN system, such as the MNN of FIG. 1, 2A or 2B, to variations in the distances of flying targets from a radar tower.

[0048] FIG. 6 depicts a schematic of an on-chip MNN system, according to aspects of the disclosure.

[0049] FIG. 7 depicts a schematic of a CMOS-integrated MNN mimicking an ultra-high-speed digital computer.

[0050] FIG. 8 is a flowchart of an example method for processing high-bandwidth signals, using an MNN system, in accordance with an example.

[0051] FIG. 9 is a flowchart of an example method for processing a bit stream representing a plurality of tokens by a frequency-based feature extraction unit, using an MNN system, in accordance with an example.

[0052] FIG. 10 is flowchart of an example method for classifying wireless signal encoding schemes, using an MNN system, in accordance with an example.

[0053] FIG. 11 is a flowchart of an example method for transmitting image data using probabilistic bit encoding, using an MNN system, in accordance with an example.DETAILED DESCRIPTION

[0054] Although the following text discloses a detailed description of implementations of methods, apparatuses and / or articles of manufacture, it should be understood that the legal scope of the property right is defined by the words of the claims set forth at the end of this34009 / 11339-02 / PCpatent. Accordingly, the following detailed description is to be construed as examples only and does not describe every possible implementation, as describing every possible implementation would be impractical, if not impossible. Numerous alternative implementations could be implemented, using either current technology or technology developed after the filing date of this patent. It is envisioned that such alternative implementations would still fall within the scope of the claims.

[0055] The present disclosure describes microwave neural network systems and methods for processing high-bandwidth signals using signal modification units. In various examples, signal modification units herein are configured for processing high-bandwidth signals. The signal modification units receive signals spanning tens of gigahertz and perform frequency-domain computation on such signals. In various examples, the signal modification units may include coupled microwave waveguide components that modify incoming high-bandwidth signals to generate modified signals having spectral characteristics suitable for analysis and inference.

[0056] The signal modification units and microwave neural network systems herein may be used in various high-bandwidth microwave applications, including multi-gigabit communication, high-performance computing, and radar signal processing. The systems may demand processing speeds that exceed capabilities of conventional digital sampling and computation approaches. In the microwave regime, operating frequencies may exceed clock rates achievable by digital processors, making direct sampling of such signals difficult. A microwave neural network (MNN) system may address these challenges by operating directly in the frequency domain, processing spectral components of incoming signals without requiring time-domain sampling at the full signal bandwidth. The MNN system can replace otherwise large parts of a digital neural network or application specific digital logic for a task. Advantageously, the MNN moves feature extraction to the front end (at the analog interface) of the signal chain, instead of digitally performing feature extraction further down in the signal chain. The MNN achieves dithering by controlled randomness by acting like a biased true random generator. Just as Large Language Models coordinate among Mixture-of-Experts in software, different MNNs may specialize in complementary tasks— trajectory recognition, target counting, speed estimationwhile communicating with each other in real time. Moreover, multiple input / output channels34009 / 11339-02 / PCopen doors to training schemes such as equilibrium propagation to estimate parameters faster than backpropagation.

[0057] In various examples, the present techniques include a microwave neural network system with a signal modification unit that receives a high-bandwidth signal and is configured to generate a modified signal based upon one or more parameters. The signal modification unit may include one or more waveguide components configured to modify the high-bandwidth signal through nonlinear interactions between frequency modes within the waveguide components. A tunable control component may adjust parameters associated with nonlinear modification of the high-bandwidth signal, enabling the signal modification unit to be reprogrammed for various computational tasks.

[0058] In some examples, the signal modification unit may be controlled by a control signal having a data rate that is at least an order of magnitude lower than a data rate of the high-bandwidth signal. For example, the signal modification unit may process signals at data rates of tens of gigabits per second while being controlled by megahertz-speed control signals. This disparity between the high-bandwidth signal data rate and the control signal data rate may enable programmable manipulation of gigahertz-speed signals using slower control mechanisms.

[0059] In some examples, the signal modification unit may generate a modified signal having a comb-like spectrum that encodes features extracted from the high-bandwidth signal. In some examples, features from a wide bandwidth of the incoming signal may be compressed into a narrower bandwidth of the modified signal, enabling analysis of the modified signal using lower-bandwidth readout circuitry. An analysis unit may receive an analysis signal derived from the modified signal and generate output data based upon a frequency profile of the analysis signal.

[0060] In various examples, the present techniques include a method for processing high-bandwidth signals by a microwave neural network system may include receiving a high-bandwidth signal at a signal input coupling, controlling one or more parameters for modifying the high-bandwidth signal, modifying the high-bandwidth signal to generate a modified signal34009 / 11339-02 / PCbased upon the one or more parameters, and generating output data by analyzing a frequency profile of an analysis signal derived from the modified signal. The method may enable frequency-domain computation on signals that would otherwise require power-intensive timedomain sampling and digital processing.

[0061] FIG. 1A illustrates a signal modification unit 100 configured, in accordance with an example, for processing input signals, including high-bandwidth signals and other data-rich signals. The signal modification unit 100 includes a plurality of waveguide components 102, 104, 106, and 108, which may be microwave waveguide components, for example forming a microwave waveguide network. While four waveguide components 102, 104, 106, and 108 are shown, the signal modification units herein may be configured with fewer or more waveguide components. The signal modification unit 100 may further include at least one signal input 110 for receiving an input signal, such as a high-bandwidth signal. In an example, the signal modification unit 100 is configured to receive and modify a high-bandwidth signal at the at least one signal input 110 to generate a modified signal, through at least one signal output 112 that may be configured to provide the modified signal as an output to another processing unit, display monitor, computer readable storage medium, or other processing system. The signal modification unit 100 further includes a tunable control component 114 that adjusts one or more parameters for modifying the input signal. Those one or more parameters may be associated with nonlinear modification of the input signal, for example, the nonlinear modification of a high-bandwidth signal.

[0062] The waveguides of the signal modification unit 100 may be formed of different linear and nonlinear microwave waveguides. For example, the waveguide component 102 may be a nonlinear waveguide (also designated as component A). The nonlinear waveguide component 102 may include a cascade of coupled nonlinear resonators that provide input-sensitive frequency response characteristics. The signal modification unit 100 also includes three linear waveguide components 104, 106, and 108 (designated as components B, C, and D), which may be arranged with the nonlinear waveguide component 102 into an integrated circuit configuration examples of which are shown in further figures such as FIGS. 2A, 2B, 4A, and 4B. The linear waveguide components 104, 106, and 108 may be tunable transmission line34009 / 11339-02 / PCstructures that support various frequency modes. In this way, the signal modification unit 100 is formed of a waveguide structure that include the nonlinear waveguide component 102 and the linear waveguide components 104, 106, and 108, which together may modify an input signal to generate a modified signal based in part upon one or more parameters being adjusted by an input signal provided to the tunable control component 114.

[0063] As further shown in FIG. 1, saturable gain elements 116 (also designated as component E in FIGS. 4A and 4B) may be positioned between the waveguide components 102, 104, 106, and 108 to compensate for losses and / or to control signal mixing between the waveguide components. In some examples, the gain provided by the saturable gain elements 116 between the waveguide components 102, 104, 106, and 108 may also or alternatively be adjusted by the input signal provided to the tunable control component 114. Two hybrid couplers 118 (also designated as components F in FIGS. 4A and 4B) may be positioned to divide and direct power from input signals at the at least one signal input 110 to the various the waveguide components 102, 104, 106, and 108. In some examples, the hybrid couplers 118 may be miniature quadrature hybrid couplers built on overlapping metal layers that split incoming microwave signals and direct portions of the incoming microwave signals to the respective waveguides. The microwave signals may have a frequency within a range of 8 gigahertz to 18 gigahertz.

[0064] In various examples, the signal modification unit 100 may be configured as a microwave neural network system that is configured as an integrated circuit fabricated using a complementary metal-oxide-semiconductor process and occupying a planar area of less than 1 square millimeter. In some cases, the integrated circuit may occupy a compact, sub-wavelength footprint of approximately 260 micrometers in width and approximately 340 micrometers in height, resulting in a planar area of approximately 0.088 square millimeters. The microwave neural network system may be fabricated in GlobalFoundries' 45nm RFSOI Silicon-on-lnsulator semiconductor process.

[0065] As shown in FIGS. 4A and 4B, an integrated circuit configuration of the signal modification unit 100 may have at least one signal input 110 formed by radio frequency input ports positioned along a left side of a layout 150 and provide connections for receiving input signals, such as high-bandwidth input signals, through the at least one signal input 110. The at34009 / 11339-02 / PCleast one signal output 112 is formed of radio frequency output ports positioned along a right side of the layout 150 for extracting the processed (e.g., modified) output signals through the at least one signal output 112. As shown in the integrated circuit example of FIGS. 4A and 4B, digital control pads 152 may be positioned along an edge of the layout 150 to provide interface connections for receiving input signals for controlling various parameters of the signal modification unit 100 through the tunable control component 114. Power pads 154 may be arranged along a lower edge of the layout on both left and right sides to provide power supply connections for the circuit components.

[0066] FIGS. 2A and 2B illustrate other example configurations of a signal modification unit in accordance with the present teachings, in particular, formed as frequency-based feature extraction units for processing tokens. In FIG. 2A, for example, a signal modification unit 200 includes linear waveguide components (labeled B, C, and D) and nonlinear waveguide component A, all similar to those of the signal modification unit 100. Hybrid couplers, F, as shown, may be similar to those of the signal modification unit 100, as well as gain(s), E. That is, in some examples, the same integrated circuit may form the signal modification unit 200 and / or the signal modification unit 100. The signal modification unit 200, however, is operated as a feature extraction unit, for example to process tokens received as an input signal to a signal input, as shown in FIG. 2A. In comparison to the signal modification unit 100 which receives an input signal at a signal input and another signal at a tunable control component to control operations thereof, in FIG. 2A the signal modification unit 200 is provided with an input signal directly to the tunable control component. In that illustrated example, that input signal is a 0 GHz - .3 GHz signal corresponding to tokens. The signal modification unit 200 generates a 3 GHz wide feature expansion as output signal on a signal output. In FIG. 2B a 0 GHz - 20 GHz input signal is provided to the signal input, not to the tunable control component, and the MNN generates an output signal, which may be formed of sub-bands contain features of the full spectrum, thus providing another form of feature extraction. We thus show that the same MNN may be used for different types of feature extraction, depending on input signal and where the input signal is fed to the MNN. That is, FIGs. 2A and 2B illustrate that two types of feature extraction that may be achieved with the signal modification unit 200 as a MNN.34009 / 11339-02 / PCMicrowave waveguide components in CMOS are coupled to form a neural network. Waveguide components B, C and D respond linearly to input signals, while waveguide component A operates nonlinearly. Their interacting oscillatory modes are sustained by a saturable gain medium. These oscillations can be reprogrammed to extract features of incoming signals in two ways. As shown in FIG. 2A, analog data tokens, with a bandwidth of a few hundred meghertz can be used to control switches that modulate the transient coupling between pairs of waveguide components. Parametric upconversion broadens the MNN's output signal comb across several gigahertz. This process embeds distinguishing features of the incoming data tokens into a spectral response, enabling machine-learning inference to identify relationships between tokens. As shown in FIG. 2B, in another operating configuration, broadband data of several gigabits / second can be directly fed into one of the waveguide components. The MNN distributes features from across the input spectrum throughout its instantaneous comb-like output, so each narrow spectral band contains information from many input bands.Consequently, only a low-speed readout bandwidth of a few hundred megahertz is required to capture the essential features of the broadband input.

[0067] Thus, considering the signal modification units in FIGS. 1, 2A, and 2B, we demonstrate a new type of computing platform (also termed an MNN herein) that can be implemented directly in CMOS technology. The platform can bypass the sequential, clocked time-domain processing of digital logic and instead can perform computations in the frequency domain at milliwatt-scale power levels. The platform formed of coupled microwave waveguide components operates through nonlinear interactions among multiple frequency modes spanning several tens of gigahertz, which serve as the computational basis. We show in FIG. 1 that the MNN, by applying slow 1 / 0 control bits to switch the coupling between waveguide components in time, is able manipulate how the MNN responded to incoming gigabit-per-second data and reconfigure its behavior in distinct ways. A resulting comb-like spectral output, for example, was shown to be highly sensitive to both high-speed broadband data streams and wireless analog signals.

[0068] In example applications of the configuration of FIG. 1, and as further discussed below, observations focused on the steady-state spectral response. We further hypothesized that only34009 / 11339-02 / PCa few gigahertz of readout bandwidth were required for forming a machine-learning inference, rather than the full microwave spectrum of the MNN's output. We interpreted the MNN's parameterized spectral signatures using a linear classifier, performing example tasks such as Boolean logic emulation, frequency-chirped radar detection, and radio-frequency modulation identification, as discussed in various examples further herein.

[0069] Yet, the underlying mechanisms of how information dynamically interacted with the MNN's inherent oscillations overtime, and how relationships between bits were encoded in the output remained a focus point for our analysis of the MNN structures herein. In seeking to understand the rich dynamics of nonlinear mode coupling in the MNN, we identified two distinct mechanisms through which a fast signal's features can be extracted. These are shown in FIGS. 2Aand 2B.

[0070] The first mechanism, illustrated in FIG. 2A, makes it possible to move beyond simple 1 / 0-bit control of waveguide coupling and instead apply "analog tokens" to the tunable control components to tune their interaction. These tokens may encode information through parameters such as amplitude, modulation (pulse) frequency, and duration, and may be realized, for example, as pulse trains forming an input signal to the tunable control component. Remarkably, although these parameterized signals have only a few hundred megahertz of bandwidth, in some examples, they instantaneously reshape the MNN's broadband spectral response across several gigahertz as seen in spectrograms, thereby exposing useful features in the input as they evolve over time. It is therefore possible to use these evolving spectral features to encode relationships between different tokens, i.e., embeddings suitable for downstream inference models. Such operation of the MNN's here can thus be used to support rapid edge decision-making. For example, a vehicle could navigate using compressed pulsebased instructions that the MNN can interpret, rather than relying on complex conditional algorithms. For other examples, the evolving spectral features can be mapped to relationships between different instructions in a digital instruction sets, to relationships between sequential events in a turn-based game, or between parts of speech in language.

[0071] We also demonstrate another configuration FIG. 2B, in which the waveguides are driven directly by signals with spectral content spanning tens of gigahertz, without parametric34009 / 11339-02 / PCswitch modulation. Such inputs may, for example, arise from gigabit-per-second digital bitstreams. Here, we can operate the MNN to seek to determine how much of the input's broadband features are captured by the MNN's nonlinear time-domain response, such that even a low-bandwidth slice of the output spectrum can represent features of gigabit-per-second data. Thus, this configuration enables an MNN to readout essential input features using simple low-bandwidth receivers operating well below the Nyquist sampling rate.

[0072] Indeed, testing the configuration of FIG. 2B, we have observed that even when the same bit-string is repeatedly injected into the MNN's waveguides, the resulting transient responses are not identical from trial to trial. Small phase offsets between the MNN's free-running oscillation and the arrival of the incoming pulse train lead to a distribution of analog outcomes. Importantly, this distribution is not arbitrary: measurements show that it is systematically biased by the input bit-string, with different bit patterns producing distinct distributions of output states. This behavior results in a bit-dependent probabilistic response at microwave speeds, rather than a deterministic digital mapping. Thus, the configuration of FIG.2B could serve as a real-time dithering mechanism— an approach commonly used to transmit high-resolution audio or video using low bit-depth representations. With the MNN, however, dithering emerges natively in hardware, without any digital post-processing, thereby suggesting a route by which high-resolution satellite imagery could be conveyed using only a fraction of the RF bandwidth typically required.

[0073] FIGS. 3A - 3D provide schematics of lumped circuit elements modeling operation of linear and nonlinear waveguide components of the signal modification units 100 and 200, in particular, when configured as a MNN.

[0074] FIG. 3A depicts a lumped circuit model of a signal modification unit in the form of a microwave neural network (MNN) having CMOS microwave waveguide resonators, i.e., for both the linear waveguide components (B,C and D as shown in FIG. 3B) and the nonlinear waveguide component (A as shown in FIG. 3A). These waveguide resonators are coupled by multiple mechanisms: (i) slow parametric switching through a switching circuit labeled Spar(FIG. 3D) ,(ii) saturable gain (FIG. 3E), and (iii) distributed nonlinear capacitances (FIG. 3C) in waveguide component D. Ultrabroadband analog signals or digital bitstreams enter through a Ground-34009 / 11339-02 / PCSignal-Ground-Signal-Ground (GSGSG) waveguide, as the signal input, are split by hybrid couplers, and fed to the waveguide resonators. The resonators' modes are strengthened by the gain medium. The nonlinear output, constituting a comb-like spectrum in a small bandwidth, may be read through another GSGSG waveguide at the signal output.

[0075] As shown in FIG. 3A, in this model, the nonlinear waveguide A has coupled resonances formed of fixed inductive segments interspersed with tunable nonlinear capacitors. As shown in FIG 3B, in this model, a linear, tunable transmission line, with a variable-length return path that supports various frequencies is used for resonators B,C and D.

[0076] As shown in FIGS. 3C-3E, in this model, CMOS Silicon-on-lnsulator devices may be. FIG.3C, for example, illustrates antiparallel diodes effecting polynomially nonlinear capacitance. FIG. 3D. illustrates parametric switches between pairs of resonators that shape the response of the MNN, for example, an inherent comb-like response of the MNN. FIG. 3E illustrates crosscoupled transistor pairs that can be used to provide regenerative, saturable gain.

[0077] FIG. 3F is a plot of a measured comblike spectra (power) generated by the MNN for both low and high bias voltages applied to the nonlinear capacitors, in the absence of external drives or parametric switching. FIG. 3G is a plot impact of low-speed switching between the nonlinear and linear resonators on the MNN's output spectrum. FIG. 3G is a plot of the Fourier Transform of the cyclically fed 12 GBit / sec digital bitstream (shown, input bits ultra-broadband spectrum), sweeping across the microwave spectrum, and the MNN's measured output signal spectrum when this bitstream is fed to its ports (MNN's response). Here, the input data here is [1110101011000100], As shown in FIG. 3H, in this example, the distortion in the MNN's output signal is a result of frequency-modulated parametric oscillations which are simultaneously influenced by the incoming high-speed digital data at 12 GBit / sec as the input signal to the signal input, and the slow parametric bitstream, fed at 150 MBit / sec, as the input signal to the tunable control component. Here, that parametric bitstream fed to the tunable control component was [11100010001000100000110010111010],

[0078] FIGS. 4A and 4B illustrate respective applications of the signal modification unit 100 (also termed "MNN 100"), in different configurations for token analysis. In particular, FIGS. 4A34009 / 11339-02 / PCand 4B demonstrate that the signal medication units herein may create parametrically-coupled oscillations that extract relationships between data tokens. FIG. 4A illustrates an architecture 400 in which two encoded RF pulse-train tokens were sequentially injected into the MNN as input signals to the tunable control component 114. FIG. 4B illustrates an architecture 450 in which the MNN was tested for redistribution of input signal spectral components across the MNN output generate probabilistic bits from multiple repetitions of 8-bit input words (256 total patterns),

[0079] In the architecture 450 of FIG. 4A, the signal modification unit 100 (also termed "MNN 100") receives two radio-frequency (RF) pulse trains from a function generator 402 coupled to the tunable control component 114. The two RF pulse trains are sequentially applied to the tunable control component 114 functioning as a parametric switching port. These two RF pulse trains may be considered as analog "data tokens", with amplitudes (0-1 V), duration (20-100 ns), and pulse frequency (20-100 MHz) varied, in the illustrated example. The spectrograms of the raw tokens themselves are largely uninformative, as they exhibit structure primarily below 200 MHz. In contrast, when the same tokens modulate the MNN's parametric couplingaltering interactions between linear and nonlinear modes— their features unfold into a broadband frequency comb at the signal output. In the example architecture 450, we find that the most expressive portion of this comb lies between 10 and 13 GHz, well beyond the bandwidth of conventional analog-to-digital converters (ADCs). To access this information, we down-convert the comb to baseband (0-3 GHz) using a passive mixer 404 and local oscillator 406, enabling time-domain capture on a modest-bandwidth oscilloscope 408. In the illustrated example, the output signal path from the MNN 100 may include a high frequency filter formed of a stabilizing capacitor and 50-ohm ground termination. That output signal path may feed an optional radio frequency gain stage 410, e.g., implemented with an APM-6849 amplifier. As further shown in the architecture 402, an intermediate frequency gain stage 412 may follow the passive mixer 404 in the signal processing chain. As FIG. 4A shows, the response produced by each token is confined to its own time window, with no observable overlap between successive tokens. The output signal is generated immediately in response to the applied input through input-driven parametric nonlinear coupling.34009 / 11339-02 / PC

[0080] In FIG. 4B, the architecture 450 includes a bit pattern generator 452 that provides highspeed digital input signals to the MNN 100. For example, the bit pattern generator 452 may be an Anritsu MP1763C bit pattern generator operating at 2.5 gigabits per second to generate 8-bit binary patterns that are directly fed to waveguide components 102, 104, 106, and 108, through the at least one signal input 110. The bit pattern generator 452 may connect to this radio frequency at least one signal input 110 of the MNN 100 chip through a 50-ohm termination. Each 8-bit binary pattern may be injected into the MNN 100300 times to characterize a probabilistic response distribution of the MNN for each pattern. The repeated injection of each 8-bit binary pattern may enable statistical characterization of the static ratio values produced by the microwave neural network in response to each pattern.

[0081] An output signal path from the MNN 100 may include a high frequency filter formed of a stabilizing capacitor and 50-ohm ground termination. That output signal path may feed an optional radio frequency gain stage 454, e.g., implemented with an APM-6849 amplifier. A passive mixer 456 may receive the amplified output signal from the radio frequency gain stage 454 along with a local oscillator signal, as shown. The passive mixer 456 may be a WJ-M79 passive mixer that performs frequency downconversion to sample sub-bands of the output signal from the MNN 100. The local oscillator signal may be provided by a swept local oscillator 458 operating between 4 gigahertz and 11 gigahertz. For example, an Anritsu 69347B signal generator may provide the local oscillator signal to the passive mixer.

[0082] In the illustrated example, the local oscillator frequency may be swept across a range of frequencies to characterize the MNN 100 response across different spectral regions. The local oscillator frequency may be swept in 400 megahertz steps from 4 gigahertz to 11 gigahertz, enabling selection of different sub-bands of the broadband frequency-comb response generated by the MNN 100 for downconversion and analysis. Each local oscillator frequency step may select a different portion of the MNN output signal spectrum for translation to baseband frequencies. The sweeping of the local oscillator frequency in 400 megahertz steps may enable characterization of how the probabilistic bit behavior varies across different spectral regions of the microwave neural network response.34009 / 11339-02 / PC

[0083] As further shown in the architecture 450 of FIG. 4B, an intermediate frequency gain stage 460 may follow the passive mixer in the signal processing chain. The intermediate frequency gain stage 460 may be implemented using a TRF37C73 amplifier that provides 20 decibels of gain to an intermediate frequency signal produced by the passive mixer. The intermediate frequency gain stage 460 may amplify the downconverted signal to a level suitable for capture by subsequent measurement equipment. The amplified intermediate frequency signal may then be provided to an oscilloscope for sampling and analysis. An oscilloscope 462 may sample the amplified intermediate frequency signal to capture the baseband representation of the selected sub-band of the microwave neural network output spectrum. In the illustrated example, a Tektronix DSA 8300 oscilloscope may sample the signal at 625 megasamples per second. The oscilloscope may operate with a 312 megahertz bandwidth limitation that defines a passband within which the baseband signal is captured. The 312 megahertz bandwidth may correspond to the sub-band of the MNN output signal spectrum that is translated to baseband by the passive mixer and local oscillator combination.

[0084] The resulting data is presented as a graph showing signal power in decibels milliwatts versus frequency in gigahertz. The graph may display the 312 megahertz oscilloscope bandwidth characteristic, with signal power ranging from 0 to approximately negative 200 decibels milliwatts across a frequency range of 0 to 8 gigahertz. The response may show a relatively flat passband within the oscilloscope bandwidth before rolling off at higher frequencies. The flat passband within the 312 megahertz bandwidth may enable accurate capture of the baseband signal content without significant frequency-dependent attenuation.

[0085] The oscilloscope sampling rate may be set to 8 gigasamples per second to observe a time window of up to 1 microsecond while maintaining sufficient resolution. At the sampling rate of 8 gigasamples per second, the oscilloscope may capture greater than 125,000 points per trace during the 1 microsecond time window. The high point count per trace may provide sufficient temporal resolution to characterize the transient behavior of the microwave neural network response to each 8-bit binary pattern. The combination of the 1 microsecond time window and the greater than 125,000 points per trace may enable detailed analysis of how the baseband signal evolves over time in response to the injected 8-bit binary patterns.34009 / 11339-02 / PC

[0086] Thus, in this way, we demonstrate that the MNN 100, in the architecture 450, enables characterization of the probabilistic bit behavior across different local oscillator frequencies and different 8-bit binary patterns. The 300 repeated injections of each 8-bit binary pattern may provide statistical data for computing static ratio values that characterize the probabilistic response of the microwave neural network to each pattern. The sweeping of the local oscillator frequency in 400 megahertz steps may enable identification of spectral regions where the microwave neural network produces strong static ratio diversity suitable for probabilistic bit encoding applications.

[0087] As the architecture 400 of FIG. 4A demonstrates, many different applications can be used to exploit an MNN's sensitivity to pulse parameters to encode meaningful information. To test and refine different applications, we can measure how reliably the spectral response generated by one token supports identification of another token. Specifically, for each ordered token pair (a, b), we can define an association score as the fraction of cross-validation folds in which a linear classifier correctly identifies token a from the MNN response to token b. This score may reveal latent relationships between successive tokens and can be used to estimate likely continuations in a sequence.For example, this concept can be implemented through a turn-based navigation game. In the game, two submarines alternately reflect sonar signals that bounce off boundaries, each attempting to intercept the returning beam. A successful pair of returns defines a rally, and the sequence continues until a submarine fails to intercept the signal. Each interception or miss constitutes an event in a temporal sequence, analogous to a token stream. The submarine's position (x, y) and reception angle (0) define an instantaneous state in a three-parameter space (x, y, 0). Some state transitions are more compatible than others due to geometric constraints and finite movement speed. By simulating numerous optimal-play scenarios, we can derive a Compatibility Matrix that encodes the relationships between states as embedding vectors.

[0088] The MNN's state may be similarly defined by three pulse-excitation parameters. To establish relationships between the states of the MNN, we can analyze pairwise MNN responses to pulse tokens, each producing unique spectral signatures across a 2.5 GHz bandwidth. Feeding these spectrogram features into a trained machine learning models (such as a34009 / 11339-02 / PCtrained linear layer) reveals how likely one token is to follow another, yielding an association matrix. The resulting embeddings may be sparse and structured, showing clear affinities between specific MNN states, and weak relationships between others. In contrast, the Association Matrix constructed from raw token spectrograms used as a baseline for comparison, which contains only sub-200 MHz content, may be blurred and reveal weak relationships between tokens. In various examples herein reference is made to trained layers, trained linear layers, trained classifiers, etc. each of which are examples of trained machine learning models. Theses trained machine learning models can be of any suitable form, including, but not limited to, linear regression models, convolutional neural networks, residual network transformers, etc.

[0089] We then test whether a submarine's transient state can be expressed within the MNN's pulse-parameter space. For example, we can perform a greedy search algorithm (or any suitable search algorithm, such as a random search algorithm) to align the submarine Compatibility Matrix with the MNN Association Matrix. The greedy search algorithm may select the pulse tokens that best reproduce allowed submarine transitions, excluding those that do not capture valid state progressions.

[0090] Finally, we can allow the MNN to guide one of the submarines to evaluate whether our inferred state-to-token mappings enable successful navigation. The other submarine may act as a perfect opponent. The MNN-controlled submarine processes tokens representing both submarines' current states, generates spectrogram features, and uses a classifier to choose the next move. The exchange continues until interception fails. Performance of the process may be quantified by the number of rallies that survived. We test six motion speeds normalized to distance traveled along the grid per rally.

[0091] In short, as the above example application demonstrates, the MNNs herein, in particular with architectures 400, can be used can extract complex, predictive features from sequential inputs and generate inferred state-token mappings that are sufficient to support predictive decision-making in a dynamic setting. Indeed, the performance may improve systematically as additional state information is incorporated into the embedding space,34009 / 11339-02 / PCindicating that the MNN's spectral responses encode meaningful relationships between successive states.

[0092] In other applications of the architecture 400, the MNN's herein can be used to infer linguistic structure directly from messages encoded in analog pulse tokens. By mapping a small vocabulary of tokens to Parts of Speech (PoS) like nouns and verbs, the MNN learns to identify the PoS of successive tokens from their combined spectral response and to predict the next valid PoS within common English sentence templates. Together, these capabilities define a scheme where structured information is communicated and interpreted through the broadband expansion of signal features embedded in microwave pulses.

[0093] For example, the MNN 100 in the architecture 400 may receive a set of microwave pulse-trains that are related to one another, and the MNN 100 may establish logical context for decision-making at the edge. For example, we can train a PyTorch Long Short-Term Memory (LSTM) language model on syntactically valid sentence-fragment ranging from 2 to 7 words in length. For demonstration here, the vocabulary only uses five Parts of Speech (PoS): Noun, Verb, Adverb, Preposition, and Adjective, and with only five words for each PoS (25 total). Training may be performed over these fragments, and the resulting embedding layer provides the learned relationships between words as a cosine-similarity embedding matrix in the model's latent space. These fragments follow the set of valid grammatical templates listed below, which define allowable PoS sequences for varying fragment lengths.

[0094] As in the example of the submarine navigation game, we try to draw parallels between words and their context to the relationships embedded in the MNN's token-association matrix extracted from short analog pulses. We can map between them using a few search algorithms (Greedy, Random, etc.) to maximize correspondence between word behavior and their microwave-token counterparts, using a subset of 25 tokens only. These relationships are shown in Supplementary Table 2.

[0095] To test whether the above mapping is even useful, we first check if the MNN can recognize the Part of Speech (PoS) of a word injected into it. For example, a linear layer (or other trainable machine learning model) may be trained on pairs of words in the vocabulary,34009 / 11339-02 / PCinjected into the MNN, using 10-fold cross-validation. Each token in a PoS pair is classified from the MNN's output signal spectrogram response, with ground-truth labels being the two actual PoS types (Noun-Adverb, Adjective-Noun, etc.).

[0096] We then extend this to test how many times we can correctly classify a PoS in sequence, since this would indicate that MNN-encoded messages can be extended to longer lengths. To evaluate sentence-level comprehension, we created a "word-at-a-time" game. Pairs of token-mapped words are fed sequentially into the MNN 100 according to the architecture 400 of FIG. 4A, with the output signal then fed to one or more trained machine learning models (such as a trained linear classifier (not shown)) to predict their Parts of Speech. If classification fails, the game ends; if correct, one or two more words are added. If both PoS predictions are correct, we inject another two words from a valid template. For odd-numbered templates, the final single word is given as a "bye" to complete the phrase. This continues until an error occurs. From 10,000 trials with attempts to make 2-7-word sentence-fragments, we analyze the MNN's ability to keep extracting the right PoS. It is effectively testing a shared password, where one MNN is used to try to decode a message encoded by another MNN. We first evaluated which algorithms for matching microwave tokens to words worked best by comparing a greedy search with a random one-shot assignment between the pulse-train tokenassociation matrix and the word-embedding matrix. We found that greedy search, when used in combination with the backend linear classifier, correctly identifies the PoS in sentences up to seven words long and performs better than the random search. The greedy search mapping was therefore used for subsequent evaluation. We then compared the MNN's comprehension to a baseline linear model trained directly on raw token spectrograms. The MNN correctly understood sentence structure in over 55% attempts to form syntactically valid fragments, versus fewer than 10% for the baseline. Also, the MNN-aided classifier was seen to decipher PoS through full 7-word fragments, whereas the baseline struggled to reach even 4 words.

[0097] This exercise showed that the MNN's feature expansion— achieved by instantaneously modulating the bandwidth of its output comb— can be used to interpret short pulses containing linguistic meaning. In this framework, the MNN 100 acted as a physical embedding layer, transforming microwave pulse-trains into semantic feature vectors for downstream language34009 / 11339-02 / PCtasks. Although the vocabulary demonstrated here is small, the same principle could be expanded to form the embedding stage of a larger language model.

[0098] As the architecture 450 of FIG. 4B demonstrates, many different applications can be used to exploit an MNN's ability to perform feature extraction that helps interpret high-speed communication signals using low-bandwidth readout, including image processing tasks. In an example application, we used the architecture 450 to perform local oscillator dependent reconstruction image quality using. For example, fast 8-bit pixel data at 2.5 Gb / s may be directly injected into the MNN waveguide components 102, 104, 106, and 108, at the at least one signal input 110, generating a broadband frequency-comb response from the MNN 100. A narrow 325 MHz baseband sub-band was selected using a tunable local oscillator (LO) 458. We sought to determine how much information each output sub-band retained from the original broadband input, since the MNN 100 redistributes signal content across its wide instantaneous comb-like output signal spectrum. Representative single-shot reconstruction images were obtained using p-bits for different LO values. Each image was annotated with its peak signal-to-noise ratio (PSNR). Certain LO frequencies exhibited strong Static-Ratio diversity in the p-bit output, producing effective dithering and clearer structural features, while others show weak spectral diversity and yield washed-out images. Image quality across LO settings was quantified using four metrics. PSNR indicated pixel-wise fidelity and was maximized near LO = 10.8 GHz, corresponding to the perceptually best reconstruction in this sweep. Due to the Gaussian noiselike texture present in the reconstructed images, SSIM, being driven primarily by local contrast, underestimates their perceptual similarity to ground truth. In contrast, spectral correlation (similarity in Fourier magnitude) and gradient-magnitude correlation (similarity in edges and contours) more faithfully tracked the perceptual quality of the MNN-enabled dithering-based reconstruction, correctly identifying the LO ~ 10.8 GHz band as optimal.

[0099] We found that image reconstruction improved over repeated MNN passes by averaging probabilistic bits generated. The PSNR rose as more dithered MNN reconstructions were accumulated, and the pixel intensities were averaged across repeated passes. Averaging over 1, 10, and 1000 passes demonstrated the expected VN improvement associated with Monte-Carlo denoising: repeated stochastic estimates are averaged to suppress noise and34009 / 11339-02 / PCrecover the underlying image structure. High-resolution RGB satellite images were reconstructed by independently processing the Red, Green, and Blue channels. A single pass produces analog-TV-like Gaussian noise, but repeated transmissions (e.g., 100 passes at 2.4 Gbps from a geostationary satellite) provide Monte-Carlo averaging that yields an efficient, high-fidelity reconstruction.

[0100] In any event, the architectures in FIGS. 4A and 4B further demonstrate that the MNN's herein may be configured into different architectures and different systems to open up many applications for use of the disclosed techniques. We have shown that high-level information can be transcribed into short pulses and interpreted intrinsically through a MNN's oscillatory dynamics. This suggests a communication paradigm in which one MNN could act as an encoder, embedding snippets of language or navigation instructions into physical pulse tokens, while another MNN serves as the decoder, rapidly extracting meaning from the resulting spectrum. Although not a cryptographic primitive in the formal sense, such an approach offers a hardware-intrinsic mechanism for obfuscation: the symbol-to-spectrum mapping may be public, but the physical MNN remains the unique device-specific key needed to recover the message.

[0101] Also, our experiments reveal the beginnings of a probabilistic generative capability in the MNN. Fast bitstreams can excite the MNN dynamics to produce probabilistic bits directly. This same physical expressiveness suggests that the MNN could be further optimized for specific image-processing tasks such as an event camera, compressive sensor, or as a wideband spectrum-monitoring front end. Power consumption could be reduced as well. The MNN can be implemented in architectures that may be specifically engineering without needing to alter the MNN itself. For example, integrating miniature mixers, low-power sampling circuits, widely tunable local oscillators, and a lightweight linear backend would allow this physics-level intelligence to operate directly at the edge as an intelligent transceiver.

[0102] Further arrays of MNNs operating in parallel on the same CMOS die can be achieved to expand even further the applications. For example, through a reconfigurable switch fabric, these distinct feature channels could collaborate as a mixture-of-experts model, with nonlinear parameters tuned to emphasize specific high-frequency features for multimodal inference. An34009 / 11339-02 / PCinstruction-set architecture could be used to coordinate these operations, likely supported by a microcontroller on the same chip. In addition, a new class of tunable millimeter-wave circuits could be developed in which linear diffractive neural processing is implemented directly within the waveguides themselves.

[0103] Further still, integrated MNNs could use physics of programmably coupled waveguides to augment intelligence, creating a new RF lexicon in which meaning can be embedded directly into circuits. Such an approach could bring real-time capabilities approaching those of billion-parameter neural networks directly into wideband radio transceivers, cleanly bypassing the speed limitations imposed by digital clocked systems.

[0104] FIGs. 5A-5D illustrate another application for use of an MNN in accordance with the present techniques, in particular, as a narrowband receiver for target detection. An architecture 500 shown in FIG. 5A illustrates one or more radar towers, such as a ground based transmitting radar antenna 502 and a ground based radar receiving antenna 504 for tracking a target aircraft 506 and for generating a radar spectrum signal (e.g., over a 0 GHz - 40 GHz spectrum). A down-converting mixer and voltage controlled oscillator (VCO) 508 may convert the high-bandwidth spectrum into an intermediate frequency (IF) signal that may be amplified by an IF amplifier 510. In some examples, the result is a baseband signal provided to a mixer 512 that is also coupled to receive a high-bandwidth clocking signal from an up-converting mixer and VCO 514. Thus, the mixer 512 is able to generate a frequency modulated clock / carrier signals that is fed to a signal modification unit 516, which may be configured like the signal modification unit 100, and in particular may be a MNN, thus labeled "MNN 516" in FIG.5A. That is, the MNN 516 may include, inter alia, one or more waveguide components containing at least one nonlinear waveguide and at least one linear waveguide and tunable control component configured to adjust one or more parameters for modifying the radar waveform. The frequency modulated clock / carrier signal therefor represents the radar waveform digitized into a series of Is and 0s and fed to the signal input of the MNN 516 in a similar manner to the configuration illustrated in FIG. 1, which a digitized input signal was provided to the at least one signal input 110. To control operation of the MNN 516, a control signal (e.g., that may have a data rate of approximately 150 megabits per second) is provided to34009 / 11339-02 / PCa tunable control component of the MNN 516 to thereby adjust one or more parameters for modifying the radar waveform. The MNN 516 generates an output signal over a spectrum. That output signal may be mixed, at a mixer 518, with narrowband signal from a source 520 to generate a feed signal to a trained classifier 522, such a two-layer neural network or other trained machine learning model, that classifies the received output signal and generates target detection data and a target detection plot 524 of the same. In various examples, the control signal is a control parameter bitstream that may have a bit rate that is between 100 megabits per second and 200 megabits per second, and the input signal is a high-bandwidth signal with a bit rate that is at least 10 gigabits per second. This is provided by way of example. In other examples, both the control signal (i.e., control parameter bitstream) and the input signal to be affected by the MNN may also have comparable bandwidths and bit rates (e.g., as measured in bits-per-second).

[0105] In this way, we demonstrate in FIGS. 5A - 5D that a signal modification unit system may be configured for processing radar waveforms containing an indication of one or more targets, where a high-bandwidth input signal received by the signal modification unit may comprise a radar waveform that encodes information about targets detected by a radar system. The signal modification unit may may be configured to generate a flight characteristic of each of the one or more targets as the output data, the flight characteristic comprising at least one of a location, a speed, or a trajectory of the respective target.

[0106] As shown in FIG. 5B, the MNN 516 may process radar waveforms from a simulated airspace 550 featuring multiple target aircraft following distinct polygonal trajectories. The targets may move through waypoints along polygonal paths at unique velocities, with the polygonal trajectories varying in orientation, radius, and origin. The flight patterns of the targets may cause instantaneous changes in radar signals reflected off of the targets. When the reflected radar signals are downconverted to low baseband frequencies (552), the flight patterns may alter analog voltage waveforms received by the radar tower 504.

[0107] The radar waveforms may be recorded using a fast-time and slow-time capture approach. For example, the analog voltage waveforms (522) may be recorded over a 0.1 millisecond time base, referred to as fast-time, as each fast-time capture samples the radar34009 / 11339-02 / PCreturns during a brief interval. The fast-time captures may be collected once every sixty milliseconds, referred to as slow-time, resulting in a thousand fast-time samples per minute of a simulated scenario. The fast-time and slow-time capture approach may enable the MNN 516 to track frequency changes over long capture periods and manifest inflections in the radar signal within a narrower output spectrum. A center frequency of a square wave may be modulated based upon an instantaneous analog voltage 522 of the radar return to generate a frequency-modulated signal 554 that may range from 100 MHz to 2.1 GHz, with the center frequency varying according to the analog voltage waveform received from the radar tower. The frequency-modulated signal 554 may be fed to the signal modification unit, i.e., the MNN 516 for processing. The MNN 516 may extract features from the frequency-modulated signal and encode the extracted features generating modified signal 556 fed to the trained classifier 522. The output signal spectrum 556 contains several narrower comb-like spectra resulting from the nonlinear interactions between the frequency-modulated drive and the parameterized oscillations. These complex features are read out over a 2 GHz bandwidth and utilized by one or more trained machine learning models (such as a trained backend neural network) to decipher the targets' flight patterns.

[0108] As discussed in other examples herein, the at least one nonlinear waveguide component of the MNN 516 may comprise a cascade of coupled nonlinear resonators including a plurality of inductive segments each having a nonlinear capacitor configured to generate a capacitance with polynomial nonlinearity. The at least one linear waveguide component may comprise a cascade of coupled linear resonators including a plurality of stages each having a switch to adjust an effective length of the linear waveguide. The nonlinear waveguide component and the linear waveguide components may interact through parametric coupling mechanisms to produce the modified signal having spectral features indicative of the flight characteristics of the one or more targets. A tunable control component is configured to adjust the one or more parameters in response to a control signal having a data rate that is at least an order of magnitude lower than a data rate of the radar waveform. The control signal may modulate the parametric coupling between the nonlinear waveguide and the linear waveguide, enabling the signal modification unit to be programmed for radar target detection tasks. The34009 / 11339-02 / PCMNN 516 may generate the modified signal as a frequency comb that encodes features of the radar waveform across a compressed bandwidth narrower than a bandwidth of the radar waveform.

[0109] The trained classifier 522 is an example of backend neural network of an analysis processing system that extracts from the output signal spectra from the MNN 516 aspects of flight trajectories, such as flight characteristics that may comprise a location, a speed, a trajectory, and / or a flight pattern of the one or more targets.

[0110] FIG. 5C illustrates a confusion matrix 560 indicating that the architecture 500, with the MNN 516, was able to infer the number of targets in each flight scenario, in an example. That is, the confusion matrix 560 shows the predicted number of targets on a vertical axis ranging from one to seven and actual number of targets on a horizontal axis ranging from one to seven. The confusion matrix 560 displays numerical values indicating classification accuracy across different target counts, demonstrating that the microwave neural network system may predict the number of dynamic targets in each simulated flight scenario.

[0111] A plot 562 indicates that the architecture 500 was capable of honing in on a single target, specifically the fastest one, in this example. The architecture 500 was able to closely track the speed of this target based solely on minute changes in carrier frequency, for each flight scenario in the validation set. That is, the scatter plot may compare a target's predicted speed in meters per second against a target's actual speed in meters per second. Data points in the scatter plot may be clustered along a diagonal trend line, demonstrating that the microwave neural network system may estimate target velocities. The architecture 500 may focus on specific targets' movement in the airspace, such as estimating speeds of fastest targets in each flight scenario.

[0112] A plot 564 indicates that the architecture 500 can also identify the presence of polygonal trajectories with confidence, using the validation set comprising 450 flight scenarios. Classification was evaluated using the Fl-score, the harmonic mean of precision (true positives divided by the sum of true positives and false positives) and recall (true positives divided by the sum of true positives and false negatives).34009 / 11339-02 / PC

[0113] That is, the bar chart plot 564 shows Fl score of predicting trajectory on a vertical axis ranging from zero to one against shape of targets' trajectories on a horizontal axis. The shapes of targets' trajectories may include categories for triangle, square, pentagon, hexagon, and heptagon flight patterns. The Fl score, which may be a harmonic mean of precision and recall, may indicate that the microwave neural network system can infer whether flight patterns' shapes were triangular, square, pentagonal, hexagonal, or heptagonal, regardless of a number of aircraft involved. Information gleaned from the flight patterns may provide clues as to whether unidentified aircraft are adversaries or allies.

[0114] FIG. 5C illustrates a schematic 570 of a modulation scheme classification using the integrated MNN 516. As shown, modulated in-phase (I) and quadrature (Q) components of a signal are processed through mixers with a 50 MHz carrier, summed together, and fed to the MNN 516. As shown in FIG. 5D, a confusion matrix 572 for modulation classification, with a suboptimal parametric bitstream, is shown, along with a confusion matrix 574 for classification, using an optimized parametric bitstream. Within the RadioML 2016.10A RF signal classification benchmarking dataset, the following are digital modulation schemes plotted: 8PSK (8-Phase Shift Keying), BPSK (Binary Phase Shift Keying), CPFSK (Continuous Phase Frequency Shift Keying), GFSK (Gaussian Frequency Shift Keying), PAM4 (Pulse Amplitude Modulation, 4-level), QAM16 (Quadrature Amplitude Modulation, 16-level), QAM64 (Quadrature Amplitude Modulation, 64-level) and QPSK (Quadrature Phase Shift Keying). The following are analog modulation schemes plotted: AM-DSB (Amplitude Modulation - Double Sideband), AM-SSB (Amplitude Modulation - Single Sideband) and WBFM (Wideband Frequency Modulation).

[0115] FIG. 6 depicts a schematic 600 of an on-chip (integrated circuit) signal modification unit system, in another example. The integration of a signal modification unit 602 into a low-bandwidth receiver on-chip involves using 4-phase passive mixers 604 to down-convert the outputs of coupled oscillators 606, 608, 610, and 612 (e.g., microwave waveguide components) to low-frequency baseband signals (<50 MHz). These signals should contain compressed features from the MNN's computations on high-bandwidth data and can replace the off-chip spectrum analyzer previously used for readout. The remainder of the integrated circuit in schematic 600 may include the coupled oscillators 606, 608, 610, and 612, couplers 614 and34009 / 11339-02 / PC616, and gain stages 618 similar to the signal modification unit 100. The schematic 600 illustrates a fully integrated version of a fabricated signal modification unit fabricated. In this configuration, incoming microwave drive input signals interact with the parametric oscillations of the signal modification unit to produce distinct comb-like spectra. Instead of feeding directly to the output pads processed signals from the couplers' outputs are directed to two mixers that down-convert portions of these spectra based on the frequency of a tunable external differential oscillator. This configuration may employ an 'N-path' topology, functioning as a tunable bandpass filter at RF frequencies, translating signals in that band to differential, sub-50 MHz outputs. The quality factor of these filters determines the bandwidth of the received baseband input signal. This input signal can then be digitized with a low-bandwidth, sub-50 MHz analog-to-digital converter, either on-or off-chip, and the features used to train a linear backend neural network. For even simpler readout, on-chip peak detectors can instead be used to record the power at the desired frequency.

[0116] FIG. 7 depicts a schematic 700 of a CMOS-integrated MNN mimicking an ultra-high-speed digital computer, in an example. In particular, the schematic 700 demonstrates a CMOS integrated MNN mimicking an ultra-high-speed digital computer without the need for a clock. As shown in sequence portion 702, 32-bit sequences are fed into an MNN 704 at 10 GBit / sec and 5 GBit / sec, cycling to produce a periodic signal output 706. The signal output 706 (shown as a Fourier Transform), produced by a spectrum analyzer, focuses on a compressed frequency band between 11 and 14 GHz. In post-processing, this compressed spectrum may be used to train a linear layer 708 for classification and validation of the mimicked digital operation.Sequence portion 710 illustrates that simple circuits like primitive gate operations (NAND gates 712) and complex, time-consuming sequential logic 714, such as population counters for counting l's in 32-bit data, can be emulated instantaneously without clock bottlenecks. Both sequence portions 702 and 710 achieve approximately equal accuracy, when using well-chosen parametric bitstreams. As shown in the plots in sequence portion 716, the MNN 704, through mode-coupling in the frequency domain, can aid in emulating high-level computational tasks, such as detecting bit patterns in high-speed data streams at tens of gigahertz. For both 5 GBit / sec (right side plot) and 10 GBit / sec data streams (left side plot), it provides high search34009 / 11339-02 / PCaccuracy regardless of the length of the queried bit pattern (ranging from 4 to 8 bits) in a 32-bit input data. This schematic 700 offers an alternative to the Maximum Likelihood Sequence Estimation (MLSE) scheme used in wireline modems, for example. Unlike MLSE, the schematic 700 does not require Serializer-Deserializer receivers or backend analog-to-digital converters and digital signal processing, which rely on complex time-domain signal processing circuits. As shown in FIG. 7, the emulated bit-search and population-counting behaviors can be combined to execute larger algorithms. Digital computers, by contrast, need several clock cycles to process these sequential portions, store data, and handle conditional statements at a couple of gigahertz with several watts of power consumption. In contrast, the MNN 704 operates at tens of gigahertz while maintaining sub-200 milliwatt power consumption.

[0117] Thus, recognizing that gigabit-speed digital signals, composed of square-wave signals, are actually analog signals with spectral content spanning tens of gigahertz, we show that the signal modification units herein can perform computations directly in the frequency domain using microwave-circuit behavior. The signal modification unit manipulates signals and expresses its output more prominently as oscillatory modes within a narrower band of a few gigahertz, centered around its comb-like spectrum. This approach bypasses the need for strict signal integrity in bit-level, time-domain calculations. It resembles compressed spectrum sensing, as features from an incoming signal's ultra-wide bandwidth are captured and strongly manifested in the signal modification unit's narrower nominal frequency range. Consequently, fewer "compressed" features can be used to train a single-layer digital neural network in postprocessing.

[0118] For example, as we show in the example of FIG. 7, signal modification units herein can accurately emulate digital gate behavior at 10 GBit / sec, without error correction. For example, a representative bitstream could be [01000110000111110111110101010000] and we used the MNN 704 to accuracy predict the bitwise NAND of the inner eight bits of the first sixteen bits, A - [00011111], and the inner eight bits of the second sixteen bits, B - [01111101], The correct result was A NAND B = [11100010], We found that by adjusting the content of the 150 MBit / sec 32-bit parametric bitstream control signal to the MNN 704 and extracting features within only 434009 / 11339-02 / PCGHz of the output spectrum, there exists a set that produces the correct NAND operation (and similarly for NOR), irrespective of the incoming fast 32-bit ultra-broadband digital signal.

[0119] In other words, a "golden" parametric bitstream control signal can frequency-modulate the parametric oscillations to perform computations that, in the abstract spectral domain, effectively emulate the behavior of an 8-bit NAND operation. Further to demonstrate the MNN's behavior as a deep, nonlinear neural network, we implemented the digital backend using a simple linear regression model to map the output spectra to the predicted bits. This demonstrated that the accuracy in emulating gate operations is entirely due to the MNN's inherent nonlinear behavior. Through testing, we demonstrated that the accuracy of the MNN 704 emulating low-level gate operations was the same or similar to when emulating more complex gate operations. That is, the techniques herein achieve accuracy independent of the circuit hardware required for a specific operation on a digital computer, regardless of the number of gates emulated by the MNN 704.

[0120] FIGs. 8- 11 illustrate example methods that may be implemented using signal modification units, in particular MNNs described herein.

[0121] FIG. 8 is a flowchart of an example method for processing high-bandwidth signals by a MNN system. At block 810, a signal is received at an MNN system, for example a high-bandwidth input signal. Other types of input signals, including low-bandwidth input signals may also be used. Low bandwidth inputs may be, for example, about 300 kHz. High-bandwidth inputs may be, for example, up to 20-25 GHz. In operation, input signals may generally be in the range of 1 MHz to 410 GHz, observably, with low-bandwidth inputs between 1MHz and 6GHz and high-bandwidth inputs between 24 GHz and 410 GHz. At block 820, the MNN system controls, through a tunable control component of the MNN system, one or more parameters for modifying the high-bandwidth signal. At block 830, a signal modification unit of the MNN modifies the high-bandwidth input signal to generate a modified signal based upon the one or more parameters, wherein the signal modification unit comprises one or more waveguide components. At block 840, an analysis unit of the MNN system, output data by analyzing a frequency profile of an analysis signal, wherein the analysis signal comprises the modified signal or a signal derived from the modified signal.34009 / 11339-02 / PC

[0122] FIG. 9 a flowchart of an example method 900 for processing a bit stream representing a plurality of tokens by a frequency-based feature extraction unit. At block 910, the method 900 generates from a prompt a plurality of tokens for analysis. At block 920, the method 900 generates from the plurality of tokens, a plurality of radiofrequency tokens and combining the radiofrequency tokens into a bit stream. At block 930, this bit stream is received at a signal input of a tunable control component of a MNN system. At block 940, the method 900, through the tunable control component, controls one or more parameters associated with nonlinear modification of the bit stream. At block 950, the MNN system comprising one or more nonlinear waveguides and one or more linear waveguides, modifies the bit stream and generates an extraction signal based in part upon the one or more parameters. At block 960, the resulting extraction signal from the block 950 is provided to an attention scoring process and determining a token mapping between the plurality of tokens.

[0123] FIG. 10 is flowchart of an example method 1000 for classifying wireless signal encoding schemes using a MNN. At block 1010, the MNN receives, at a signal input a modulated carrier signal. At block 1020, that modulated carrier signal is modified, by one or more waveguide components of the MNN, to generate a modified signal, wherein the one or more waveguide components comprise at least one nonlinear waveguide. At block 1030, spectral features are extracted from a frequency profile of the modified signal from block 1020. At block 1040, an analysis unit is used to classified an encoding scheme of the modulated carrier signal based upon the extracted spectral features.

[0124] FIG. 11 is a flowchart of an example method 1100 for transmitting image data using probabilistic bit encoding. At block 1110, pixel data comprising a plurality of multi-bit pixel values is received to the method 1100. At block 1120, the method 1100 encodes each multi-bit pixel value as a radiofrequency signal. At block 1130, that radiofrequency signal is fed to a MNN comprising one or more nonlinear waveguides to generate a broadband output signal. At block 1140, the method 1100 downconverts a sub-band of the broadband output signal to baseband. At block 1150, the method 1100 samples the baseband signal at a rate lower than a bit rate of the radiofrequency signal to generate a probabilistic bit for each multi-bit pixel value. At block 1160, the probabilistic bits, wherein each probabilistic bit has a static ratio determined34009 / 11339-02 / PCby a corresponding multi-bit pixel value, are transmitted for storage or display of a resulting modified image.

[0125] A number of implementations have been described. Nevertheless, it will be understood that various modifications may be made without departing from the spirit and scope of the disclosure. Accordingly, other implementations are within the scope of the following claims.

Claims

34009 / 11339-02 / PCCLAIMS1. A signal modification unit configured for processing high-bandwidth signals, comprising:at least one signal input configured to receive a high-bandwidth signal;a tunable control component configured to adjust one or more parameters for modifying the high-bandwidth signal, wherein the one or more parameters are associated with nonlinear modification of the high-bandwidth signal;one or more waveguide components configured to modify the high-bandwidth signal to generate a modified signal based in part upon the one or more parameters; andat least one signal output configured to provide the modified signal as an output of the signal modification unit.

2. The signal modification unit of claim 1, wherein the at least one signal input is configured to receive the high-bandwidth signal as a radio frequency signal.

3. The signal modification unit of claim 2, wherein the at least one signal input is configured to receive the high-bandwidth signal as a microwave signal having a frequency within a range of 8 gigahertz to 18 gigahertz.

4. The signal modification unit of claim 1, wherein the one or more waveguide components comprise at least one nonlinear waveguide including a cascade of coupled nonlinear resonators.

5. The signal modification unit of claim 4, wherein the cascade of coupled nonlinear resonators comprises a plurality of inductive segments each including a nonlinear capacitor.

6. The signal modification unit of claim 5, wherein the nonlinear capacitors comprise anti-parallel diodes configured to generate a capacitance with polynomialnonlinearity.34009 / 11339-02 / PC7. The signal modification unit of claim 1, wherein the one or more waveguide components comprise one or more linear waveguides, each of the one or more linear waveguides comprising a cascade of coupled linear resonators including a plurality of stages each having a switch to adjust an effective length of the one or more linear waveguides.

8. The signal modification unit of claim 1, wherein the tunable control component comprises one or more gain components including one or more cross-coupled transistor pairs configured to provide regenerative saturable gain.

9. The signal modification unit of claim 1, wherein the tunable control component is configured to adjust the one or more parameters in response to a control signal having a maximum data rate that is at least an order of magnitude lower than a data rate of the high-bandwidth signal.

10. The signal modification unit of claim 9, wherein the tunable control component comprises one or more control switches connected between one or more pairs of waveguides of the one or more waveguide components, the one or more control switches being configured to selectively couple and decouple the one or more pairs of waveguides in response to the control signal.

11. The signal modification unit of claim 1, wherein the signal modification unit is configured to generate the modified signal as a frequency comb based upon the high-bandwidth signal, the frequency comb being programmable using the tunable control component to adjust the one or more parameters.

12. A microwave neural network system for processing high-bandwidth signals, comprising:a signal modification unit comprising:at least one signal input configured to receive a high-bandwidth signal;34009 / 11339-02 / PCa tunable control component configured to adjust one or more parameters for modifying the high-bandwidth signal;one or more waveguide components configured to modify the high-bandwidth signal to generate a modified signal based in part upon the one or more parameters; andat least one signal output configured to provide the modified signal;a signal input coupling configured to provide the high-bandwidth signal to the signal modification unit;a signal output coupling configured to receive the modified signal from the signal modification unit;a control unit configured to control the tunable control component of the signal modification unit; andan analysis unit configured to receive an analysis signal from the signal output coupling and generate output data based upon a frequency profile of the analysis signal, wherein the analysis signal comprises the modified signal or a signal derived from the modified signal.

13. The microwave neural network system of claim 12, wherein the control unit is configured to adjust the one or more parameters for modifying the high-bandwidth signal by providing a control signal to the tunable control component, the control signal comprising a stream of control parameter values.

14. The microwave neural network system of claim 13, wherein the stream of control parameter values comprises a control parameter bitstream having a bit rate at least an order of magnitude lower than a high-bandwidth signal bit rate of the high-bandwidth signal.

15. The microwave neural network system of claim 12, wherein the signal output coupling comprises a receiver configured to generate the analysis signal by filtering the34009 / 11339-02 / PCmodified signal to obtain a frequency band that is at least an order of magnitude narrower than a bandwidth of the high-bandwidth signal.

16. The microwave neural network system of claim 12, wherein the analysis unit is configured to analyze the frequency profile by inferring characteristics of the output data based upon one or more patterns in the frequency profile using one or more trained machine learning models.

17. The microwave neural network system of claim 16, wherein the one or more trained machine learning models comprise a linear regression model configured to map spectral features of the frequency profile to the output data.

18. The microwave neural network system of claim 12, wherein:the high-bandwidth signal comprises a transmission bitstream; andthe analysis unit is configured to analyze the frequency profile of the analysis signal by performing one or more logic operations on at least a portion of the transmission bitstream in the frequency domain.

19. The microwave neural network system of claim 18, wherein the one or more logic operations comprise at least one of a bitwise NAND operation, a bitwise XOR operation, a bitwise NOR operation, or a counter of values of bits in the portion of the transmission bitstream.

20. The microwave neural network system of claim 12, wherein:the high-bandwidth signal comprises a radar waveform containing an indication of one or more targets; andthe analysis unit is configured to generate a flight characteristic of each of the one or more targets as the output data, the flight characteristic comprising at least one of a location, a speed, or a trajectory of a respective target of the one or more targets.34009 / 11339-02 / PC21. The microwave neural network system of claim 12, wherein the one or more waveguide components comprise at least one nonlinear waveguide and at least one linear waveguide coupled to the at least one nonlinear waveguide through a parametric coupling mechanism controlled by the tunable control component.

22. The microwave neural network system of claim 12, wherein the microwave neural network system is configured as an integrated circuit fabricated using a complementary metal-oxide-semiconductor process and occupying a planar area of less than 1 square millimeter.

23. A method for processing high-bandwidth signals by a microwave neural network system, comprising:receiving, at a signal input coupling of the microwave neural network system, a high-bandwidth signal;controlling, by a control unit of the microwave neural network system, one or more parameters for modifying the high-bandwidth signal;modifying, by a signal modification unit of the microwave neural network system, the high-bandwidth signal to generate a modified signal based upon the one or more parameters, wherein the signal modification unit comprises one or more waveguide components; and generating, by an analysis unit of the microwave neural network system, output data by analyzing a frequency profile of an analysis signal, wherein the analysis signal comprises the modified signal or a signal derived from the modified signal.

24. The method of claim 23, wherein modifying the high-bandwidth signal comprises introducing nonlinear distortion into the modified signal through interactions between frequency modes within the one or more waveguide components.

25. The method of claim 23, wherein modifying the high-bandwidth signal comprises compressing power distributed across a wide frequency band of the high-bandwidth signal into34009 / 11339-02 / PCa limited frequency band of the modified signal, the limited frequency band being at least an order of magnitude narrower than the wide frequency band.

26. The method of claim 25, further comprising generating, by a bandpass filter, the analysis signal as a portion of the modified signal within the limited frequency band.

27. The method of claim 23, wherein controlling the one or more parameters for modifying the high-bandwidth signal comprises providing a control signal to a tunable control component of the signal modification unit, the control signal having a data rate that is at least an order of magnitude lower than a data rate of the high-bandwidth signal.

28. The method of claim 27, wherein the control signal comprises a control parameter bitstream having a bit rate between 100 megabits per second and 200 megabits per second, and wherein the data rate of the high-bandwidth signal is at least 10 gigabits per second.

29. The method of claim 27, wherein the control signal controls a level of nonlinearity of modification of the high-bandwidth signal by selectively coupling and decoupling waveguides of the one or more waveguide components.

30. The method of claim 23, wherein the high-bandwidth signal comprises a transmission bitstream, and wherein analyzing the frequency profile of the analysis signal comprises performing one or more logic operations on at least a portion of the transmission bitstream in the frequency domain without determining contents of the transmission bitstream as a time-domain sequence of bits.

31. The method of claim 23, wherein the high-bandwidth signal comprises a radar waveform containing an indication of one or more targets, and wherein generating the output data comprises determining at least one of a location, a speed, or a trajectory of each of the one or more targets based upon the frequency profile.34009 / 11339-02 / PC32. The method of claim 23, wherein modifying the high-bandwidth signal to generate the modified signal comprises generating a frequency comb based upon the high-bandwidth signal, the frequency comb being programmable by adjusting the one or more parameters.

33. The method of claim 23, wherein analyzing the frequency profile of the analysis signal comprises applying one or more trained machine learning models to the frequency profile to infer characteristics of the output data based upon one or more patterns in the frequency profile.

34. A frequency-based feature extraction unit for processing tokens, comprising: a tunable control component having at least one signal input configured to receive a bit stream representing a plurality of tokens, the tunable control component being configured to adjust one or more parameters associated with nonlinear modification of the bit stream;a microwave waveguide network coupled to the tunable control component and comprising one or more nonlinear waveguides and one or more linear waveguides coupled to the one or more nonlinear waveguides, the microwave waveguide network being configured to perform feature extraction on the bit stream to generate an extraction signal based in part upon the one or more parameters; andat least one signal output configured to provide the extraction signal as an output of the frequency-based feature extraction unit.

35. The frequency-based feature extraction unit of claim 34, wherein the at least one signal output is configured to provide the extraction signal as a microwave signal.

36. The frequency-based feature extraction unit of claim 34, wherein the one or more nonlinear waveguides comprise a cascade of coupled nonlinear resonators including a plurality of inductive segments each having a nonlinear capacitor.34009 / 11339-02 / PC37. The frequency-based feature extraction unit of claim 34, wherein the one or more linear waveguides comprise a cascade of coupled linear resonators including a plurality of stages each having a switch to adjust an effective length of the one or more linear waveguides.

38. The frequency-based feature extraction unit of claim 37, wherein the one or more nonlinear waveguides and the one or more linear waveguides are configured to have oscillatory modes that are parametrically coupled for extracting features between tokens in the bit stream.

39. The frequency-based feature extraction unit of claim 34, wherein the tunable control component comprises one or more cross-coupled transistor pairs configured to provide regenerative saturable gain.

40. The frequency-based feature extraction unit of claim 34, wherein the tunable control component is configured to adjust the one or more parameters based on at least one of an amplitude, a pulse frequency, or a duration of the bit stream.

41. The frequency-based feature extraction unit of claim 34, wherein the bit stream comprises data for two tokens, and wherein the extraction signal encodes relationships between the two tokens as spectral features.

42. The frequency-based feature extraction unit of claim 34, wherein the frequencybased feature extraction unit is configured as a microwave neural network processor operable to analyze the extraction signal and determine an association score between the tokens represented in the bit stream.

43. A method for processing a bit stream representing a plurality of tokens by a frequency-based feature extraction unit, the method comprising:generating from a prompt a plurality of tokens for analysis;generating from the plurality of tokens a plurality of radiofrequency tokens and combining the radiofrequency tokens into a bit stream;34009 / 11339-02 / PCreceiving, at a signal input of a tunable control component, the bit stream; controlling, by the tunable control component, one or more parameters associated with nonlinear modification of the bit stream;modifying, by a microwave waveguide network comprising one or more nonlinear waveguides and one or more linear waveguides, the bit stream and generating an extraction signal based in part upon the one or more parameters; andproviding the extraction signal to an attention scoring process and determining a token mapping between the plurality of tokens.

44. The method of claim 43, wherein the token mapping comprises a plurality of embeddings of the tokens derived from spectral features of the extraction signal.

45. The method of claim 44, wherein the plurality of embeddings encode relationships between successive tokens based upon association scores determined from the extraction signal.

46. The method of claim 43, wherein generating from the plurality of tokens a plurality of radiofrequency tokens comprises encoding each token as a pulse-train token characterized by at least one of an amplitude, a pulse frequency, or a pulse-train duration.

47. The method of claim 46, wherein combining the radiofrequency tokens into the bit stream comprises sequentially applying the pulse-train tokens to a parametric switching port of the frequency-based feature extraction unit.

48. The method of claim 43, wherein modifying the bit stream comprises parametrically coupling oscillatory modes between the one or more nonlinear waveguides and the one or more linear waveguides to produce a broadband frequency comb response encoding features of the plurality of tokens.34009 / 11339-02 / PC49. The method of claim 43, wherein determining the token mapping between the plurality of tokens comprises training a linear classifier on spectral features extracted from the extraction signal to predict associations between tokens in the plurality of tokens.

50. A signal modification unit configured for processing radar waveforms, comprising:at least one signal input configured to receive a radar waveform containing an indication of one or more targets;a tunable control component configured to adjust one or more parameters for modifying the radar waveform;one or more waveguide components comprising at least one nonlinear waveguide and at least one linear waveguide, the one or more waveguide components configured to modify the radar waveform to generate a modified signal based in part upon the one or more parameters; andat least one signal output configured to provide the modified signal as an output of the signal modification unit, wherein the modified signal comprises spectral features indicative of flight characteristics of the one or more targets.

51. The signal modification unit of claim 50, wherein the at least one nonlinear waveguide comprises a cascade of coupled nonlinear resonators including a plurality of inductive segments each having a nonlinear capacitor configured to generate a capacitance with polynomial nonlinearity.

52. The signal modification unit of claim 51, wherein the at least one linear waveguide comprises a cascade of coupled linear resonators including a plurality of stages each having a switch to adjust an effective length of the at least one linear waveguide.34009 / 11339-02 / PC53. The signal modification unit of claim 50, wherein the tunable control component is configured to adjust the one or more parameters in response to a control signal having a data rate that is at least an order of magnitude lower than a data rate of the radar waveform.

54. The signal modification unit of claim 50, wherein the flight characteristics comprise at least one of a location, a speed, a trajectory, ora flight pattern of the one or more targets.

55. The signal modification unit of claim 50, wherein the signal modification unit is configured to generate the modified signal as a frequency comb that encodes features of the radar waveform across a compressed bandwidth narrower than a bandwidth of the radar waveform.

56. A microwave neural network system for emulating digital operations, comprising:a signal modification unit configured to receive a transmission bitstream at a data rate of at least one gigabit per second;a tunable control component configured to receive a control parameter bitstream at a data rate at least an order of magnitude lower than the data rate of the transmission bitstream;one or more waveguide components comprising at least one nonlinear waveguide configured to modify the transmission bitstream to generate a modified signal based upon the control parameter bitstream; andan analysis unit configured to analyze a frequency profile of the modified signal and perform one or more logic operations on at least a portion of the transmission bitstream in a frequency domain.

57. The microwave neural network system of claim 56, wherein the one or more logic operations comprise at least one of a bitwise NAND operation, a bitwise XOR operation, a34009 / 11339-02 / PCbitwise NOR operation, or a population count operation that counts a number of ones in the portion of the transmission bitstream.

58. The microwave neural network system of claim 57, wherein the one or more logic operations are associated with a pattern of values of the control parameter bitstream, and wherein different patterns of the control parameter bitstream configure the microwave neural network system to perform different logic operations.

59. The microwave neural network system of claim 56, wherein the at least one nonlinear waveguide comprises a cascade of coupled nonlinear resonators including a plurality of inductive segments each having a nonlinear capacitor configured to generate a capacitance with polynomial nonlinearity.

60. The microwave neural network system of claim 59, wherein the one or more waveguide components further comprise at least one linear waveguide coupled to the at least one nonlinear waveguide through a parametric coupling mechanism controlled by the control parameter bitstream.

61. The microwave neural network system of claim 56, wherein the analysis unit is configured to detect a bit sequence within the transmission bitstream in the frequency domain without recovering the transmission bitstream as a time-domain sequence of bits.

62. The microwave neural network system of claim 56, wherein the data rate of the transmission bitstream is at least 10 gigabits per second, and wherein the data rate of the control parameter bitstream is between 100 megabits per second and 200 megabits per second.

63. A method for classifying wireless signal encoding schemes using a microwave neural network, comprising:receiving, at a signal input of a microwave neural network, a modulated carrier signal;34009 / 11339-02 / PCmodifying, by one or more waveguide components of the microwave neural network, the modulated carrier signal to generate a modified signal, wherein the one or more waveguide components comprise at least one nonlinear waveguide;extracting spectral features from a frequency profile of the modified signal; and classifying, by an analysis unit, an encoding scheme of the modulated carrier signal based upon the extracted spectral features.

64. The method of claim 63, wherein the modulated carrier signal comprises a carrier wave modulated by baseband signals representing one of a plurality of modulation classes including digital modulation schemes and analog modulation schemes.

65. The method of claim 64, wherein the digital modulation schemes comprise at least one of 8-phase shift keying, binary phase shift keying, continuous phase frequency shift keying, Gaussian frequency shift keying, pulse amplitude modulation, quadrature amplitude modulation, or quadrature phase shift keying.

66. The method of claim 65, wherein the analog modulation schemes comprise at least one of amplitude modulation double sideband, amplitude modulation single sideband, or wideband frequency modulation.

67. The method of claim 63, wherein classifying the encoding scheme comprises applying a trained linear regression model to the extracted spectral features to map the spectral features to one of a plurality of modulation classes.

68. The method of claim 67, wherein the at least one nonlinear waveguide comprises a cascade of coupled nonlinear resonators including a plurality of inductive segments each having a nonlinear capacitor configured to generate a capacitance with polynomial nonlinearity, and wherein modifying the modulated carrier signal comprises transforming transient changes in the modulated carrier signal into spectral features distributed across a34009 / 11339-02 / PCfrequency range detuned from a nominal operating frequency of the microwave neural network.

69. A signal processing system for generating probabilistic bits from high-bandwidth data, comprising:at least one signal input configured to receive a high-bandwidth signal comprising a sequence of multi-bit symbols;a microwave waveguide network comprising one or more nonlinear waveguides configured to generate a broadband frequency-comb response in response to the high-bandwidth signal;a downconversion stage configured to select a sub-band of the broadband frequencycomb response; anda quantizer configured to sample the sub-band at a rate lower than a Nyquist rate of the high-bandwidth signal to generate probabilistic bits, wherein each probabilistic bit has a bias determined by a corresponding multi-bit symbol of the sequence.

70. The signal processing system of claim 69, wherein the one or more nonlinear waveguides comprise a cascade of coupled nonlinear resonators including a plurality of inductive segments each having a nonlinear capacitor configured to generate a capacitance with polynomial nonlinearity.

71. The signal processing system of claim 70, wherein the microwave waveguide network further comprises one or more linear waveguides coupled to the one or more nonlinear waveguides, the one or more linear waveguides comprising a cascade of coupled linear resonators including a plurality of stages each having a switch to adjust an effective length of the one or more linear waveguides.

72. The signal processing system of claim 69, wherein the downconversion stage comprises a passive mixer configured to receive the broadband frequency-comb response and a34009 / 11339-02 / PClocal oscillator signal, the passive mixer being configured to translate a portion of the broadband frequency-comb response to a baseband frequency range.

73. The signal processing system of claim 72, wherein the quantizer comprises a one-bit quantizer configured to capture two samples during each multi-bit symbol interval, the two samples being thresholded to produce a static state or a dynamic state, wherein the static state corresponds to sample values of 00 or 11 and the dynamic state corresponds to sample values of 01 or 10.

74. The signal processing system of claim 73, wherein the bias of each probabilistic bit is characterized by a static ratio representing a fraction of outcomes that produce the static state, the static ratio being determined by properties of the corresponding multi-bit symbol including at least one of a sparsity or a transition structure of the multi-bit symbol.

75. A method for transmitting image data using probabilistic bit encoding, comprising:receiving pixel data comprising a plurality of multi-bit pixel values;encoding each multi-bit pixel value as a radiofrequency signal;feeding the radiofrequency signal to a microwave neural network comprising one or more nonlinear waveguides to generate a broadband output signal;downconverting a sub-band of the broadband output signal to baseband;sampling the baseband signal at a rate lower than a bit rate of the radiofrequency signal to generate a plurality of probabilistic bit for each multi-bit pixel value; andtransmitting the plurality of probabilistic bits, wherein each probabilistic bit has a static ratio determined by a corresponding multi-bit pixel value.

76. The method of claim 75, wherein the one or more nonlinear waveguides comprise a cascade of coupled nonlinear resonators including a plurality of inductive segments34009 / 11339-02 / PCeach having a nonlinear capacitor configured to generate a capacitance with polynomial nonlinearity.

77. The method of claim 76, wherein sampling the baseband signal comprises capturing two samples during each multi-bit pixel value interval using a one-bit quantizer, the two samples being thresholded to produce a static state corresponding to sample values of 00 or 11 or a dynamic state corresponding to sample values of 01 or 10.

78. The method of claim 77, wherein darker pixel values are mapped to multi-bit patterns that produce a higher static ratio and lighter pixel values are mapped to multi-bit patterns that produce a lower static ratio, such that the transmitted probabilistic bits form a dithered representation of the pixel data.

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