Analog matrix computation circuit based on probabilistic normalized invariants for gradual label propagation

Abstract

The application relates to analog matrix calculation and a store-calculate integrated circuit, and discloses a progressive label propagation analog matrix calculation circuit based on a probability normalization invariant. A relationship conductance network maps a non-negative row normalization sample-anchor point matrix B, a confidence parameter satisfies, and an anchor point degree is. Therefore, the natural total load of each sample node is, the compensation conductance of each sample is zero, the anchor point feedback conductance is kept static in the same task. The circuit completes closed-loop anchor space solving and sample output by using two sets of physically independent networks and beta branches respectively; after receiving an affected sample set, B and the feedback branch are kept unchanged, only the corresponding sample row and the beta branch are synchronously updated, and the analog acceleration for progressive label propagation is used.

Description

Technical Field

[0001] This invention relates to the field of analog matrix computation and in-memory computing circuit technology, specifically to an analog matrix computation circuit that uses row-normalized sample-anchor relationship matrix and complementary confidence parameters to perform task specialization on an asymptotic label propagation closed-loop matrix solver. Background Technology

[0002] Graph label propagation typically requires repeatedly performing matrix multiplication and addition, state convergence, and label back projection around the relation matrix. Progressive label propagation updates the confidence state and label input of a subset of samples in each round based on the propagation results, and then performs propagation again. Therefore, it includes both the principal relations that remain unchanged within the task and the local states that change with each round.

[0003] Programmable conductance cross-networks can map matrix elements to conductances and perform matrix-vector multiplication using Ohm's law and Kirchhoff's current law. Closed-loop circuits composed of programmable conductance networks and operational amplifiers can also solve linear equations in steady state. The aforementioned cross-networks, closed-loop operational amplifiers, and general matrix equation solving methods are all known technologies, and this invention does not rely on their individual existence as the basis for innovation.

[0004] In general nonnegative regression or matrix solving mappings, the coefficients of each sample row are typically different. To enable different rows to share a uniform scale, it is usually necessary to set row-by-row compensation conductance to round up the natural total conductance load of each row to a uniform value γ, and configure the output feedback conductance accordingly. When the matrix row sum or iteration parameters change, the compensation conductance, uniform load, and feedback parameters may need to be recalculated and configured.

[0005] For asymptotic label propagation that satisfies a probability-normalized structure, the sample-anchor relationship matrix B remains unchanged within the same task, and the confidence parameters α and β vary with the sample state and are complementary on a sample-by-sample basis. If processed using a general solver, it is easy to overlook the inherent load relationships formed by this structure, resulting in sample-by-sample compensation branches, redundant configuration of feedback parameters, and large-scale repeated writing between rounds. Therefore, a simulated matrix calculation circuit is needed to directly transform the probabilistic constraints into circuit identities, thereby eliminating redundant branches, staticizing feedback, and organizing local reconfigurations. Summary of the Invention

[0006] The purpose of this invention is to provide a computational circuit for the progressive tag propagation simulation matrix based on probability-normalized invariants, in order to solve the problems of sample-by-sample compensation conductance, redundant configuration of feedback parameters, and large-scale repeated reconfiguration in progressive rounds when a general closed-loop simulation solver is used for progressive tag propagation.

[0007] To achieve the above objectives, this invention employs a relational conductance network, a first confidence-weighted relational conductance network, a first complementary confidence branch group, a closed-loop operational amplifier group, an anchor feedback branch group, a second confidence-weighted relational conductance network, a second complementary confidence branch group, an output conversion circuit, and a control module to form a complete circuit. Each conductance network uses a positive reference conductance. The corresponding non-negative matrix or parameters are used for scale mapping.

[0008] set up Let B be a non-negative sample-anchor relationship matrix, and let the weights of the i-th row of B be denoted as . And B satisfies the row normalization condition; let and Let be two non-negative complementary confidence parameters for sample i. , .

[0009] When the relational conductance network, the first confidence weighted relational conductance network, and the first complementary confidence branch work together, the dimensionless total natural conductance load of the i-th sample node is:

[0010] Substituting the row normalization condition and the complementary confidence condition, we obtain that the natural total load of all sample nodes is 2. Therefore, the unified natural row load and the sample-by-sample compensated conductance satisfy the condition.

[0011] The above relationship is rigorously derived from the probability normalization structure, rather than through empirical deletion of compensation branches. Therefore, under the condition of nominal row B normalization and complementary α and β, this invention does not set n per-sample compensation conductance branches for completing the sample row load. Device write errors, line resistance, and peripheral errors may cause the physical conductance to deviate from the nominal relationship. This is a precision constraint during implementation and does not change the structural relationship in the nominal mapping of this invention.

[0012] The anchor degree vector and anchor degree matrix are defined as follows:

[0013] Since B remains constant throughout the same asymptotic label propagation task, λ and θ also remain constant. Substituting γ=2 into the closed-loop feedback ratio, the j-th anchor feedback branch is configured as follows:

[0014] The feedback conductance is determined once by the column of B during task initialization and remains static in subsequent asymptotic propagation rounds formed by variations of α, β, and Y.

[0015] First-confidence weighted relational conductance network mapping The first complementary confidence branch group maps β and receives the tag input Y, the relational conductance network maps B and passes the sample-side signal through... Converging at the anchor point, the closed-loop operational amplifier group and the anchor point feedback branch group obtain the anchor space variable Z in steady state. The second confidence weighted relation conductance network and the second complementary confidence branch group are loaded with the same logic parameters but are physically independent of the first set of networks. They are used to back-project Z to the sample space and output F. The label propagation relation and the anchor point side closed-loop constraint are respectively...

[0016] Substituting the label propagation relationship into the anchor-side closed-loop constraint, we can obtain

[0017] Moving the terms containing Z to the left side of the equation, and defining the coefficient matrix C and the right-hand side R of the closed-loop linear equation, we can obtain...

[0018] The above derivation shows that the steady-state propagation of the tag is equivalent to the closed-loop linear equation CZ=R. Under the operating conditions that C is invertible and the closed loop has a unique stable solution, both yield the same anchor space variable Z. This invention does not explicitly construct or store C, nor does it calculate Z by inverting a digital matrix; instead, it utilizes... network, Current convergence and The feedback directly constrains C to Z in the closed-loop steady state; then F is obtained by the second confidence weighted relation conductance network and the second complementary confidence branch group.

[0019] The control module configures B and ... during task initialization. When the external module generates the set of affected samples based on the propagation results... Afterwards, the control module maintains B and No change, only two sets are updated simultaneously. In the network The original non-zero conductance of the corresponding sample row and the two corresponding β branches. If the number of non-zero values ​​in each row of B is not greater than k, then the adjustment amount of the unique logic parameter value corresponding to the change of state of a single sample is... The value is no greater than k+1. Two physically independent networks need to synchronously write the same logical change to two physical components.

[0020] The control module's operation flow includes obtaining B and λ, configuring B, and two sets of... Two groups of β and Under the condition of γ=2 and no per-sample compensation branch, a closed-loop steady state is established to obtain Z and F, and the affected sample set generated externally is received. and keep B and Unchanged but only for corresponding Local synchronization updates are performed with the β parameter. The specific algorithm for selecting the representative state is completed by an external control module and is not an algorithm that needs to be re-proposed in this invention.

[0021] Compared with the general mapping, the present invention has a sample-by-sample compensation conductance theoretical value of zero when the nominal probability normalization condition is met, and can cancel n compensation branches; The configuration is determined once by the column sum of the task-level static B, and will not be reconfigured due to changes in α and β; when state updates are concentrated on a small number of samples, only the corresponding values ​​are modified. And the β parameter; when the number of non-zero values ​​in each row is no greater than k, the adjustment amount of the unique logic parameter value for a single sample event is no greater than k+1. The above effects are at the level of circuit branches and configuration parameters, and are not equivalent to the unmeasured improvement in overall machine area, total power consumption, or end-to-end latency. Attached Figure Description

[0022] Figure 1 This is a flowchart of the progressive tag propagation and local synchronous reconfiguration process of the present invention;

[0023] Figure 2 A schematic diagram of the circuit principle for canceling the sample-by-sample compensation branch using probability normalization invariants;

[0024] Figure 3 The transient simulation output is for the sample.

[0025] Figure 4 This is a comparison chart showing the accuracy of the ideal value and the actual output value of the circuit. Detailed Implementation

[0026] The present invention will be further described below with reference to the accompanying drawings and embodiments. The following embodiments are used to explain the technical solutions of the present invention and are not intended to limit the scope of protection. Figure 2 The circuit shown is divided into an upper closed-loop anchor space solution section and a lower sample output section according to signal function. The upper section includes a first complementary confidence branch group, a first confidence weighted relational conductance network, a relational conductance network, m groups of closed-loop operation units, and an anchor feedback branch group; the lower section includes a second complementary confidence branch group, a second confidence weighted relational conductance network, an n-channel transimpedance amplifier (TIA), and an output terminal. The two sets of complementary confidence branches and confidence weighted relational conductance networks are loaded with the same logic parameters, but are physically independent.

[0027] Example 1: A general n×m mathematical and circuit example.

[0028] In this embodiment, and , , , The number of label channels in round t is denoted as... , , and B is obtained from the external relationship construction module. This invention does not limit the anchor graph construction or feature extraction algorithm used by the external module.

[0029] like Figure 2 As shown in the upper part, the input voltage of the i-th tag via the first complementary confidence branch with conductivity Inject the i-th sample row; the same sample row is also injected through the conductance of each intersection point in the first confidence weighted relationship conductance network. Output line with corresponding anchor point Connected. According to Kirchhoff's current law, the combined quantity formed by the i-th sample row is related to... Proportional, meaning the upper closed loop completes the process first. and The sample side is summed.

[0030] The conductance at the intersection of the upper relational conductance network is as follows: Configuration, and formed by each sample row As input, the summation nodes of the j-th anchor column converge. Thus achieving Each anchor column corresponds to a set of closed-loop operation units; Figure 2 The paired operational amplifiers in the middle are used to perform column current summation, polarity recovery, and anchor point voltage drive, and their output forms And simultaneously connect to the upper and lower sets The j-th anchor line of the conductance network. The output is also fed back into the conductance network. Return the summation node in column B to ensure the closed-loop steady state is satisfied. The diagram only shows some of the anchor point closed-loop units; the remaining anchor point columns use the same connection.

[0031] because and First β branch, first The nominal natural total load formed by both the conductance network and the B-conductance network at each sample node is 2. Therefore, the uniform natural row load γ is fixed at 2, and the conductance is compensated sample by sample. Zero, Figure 2 The upper part passes through the β branch. The closed-loop path from network B no longer includes a compensation conductance column to complete the load of each sample row.

[0032] like Figure 2 As shown below, label input Simultaneously, the signal is fed into the second complementary confidence branch, and the anchor point output is... Simultaneously fed into the second confidence-weighted conductance network. The second β branch and the second... The conductivity network is loaded with the same type as the upper part. and Logical parameters, and formed again in the i-th output line. Each output line is connected to an independent transimpedance amplifier (TIA) channel, which converts the summed current into an output voltage. n TIA channels together constitute the sample label propagation output vector F. The complete physical path consists of one B-conductance network and two sets of... Conductivity network, two sets of β branches, m sets of anchor point closed-loop operation units, and one set of It consists of a feedback branch and an n-channel TIA.

[0033] Programmable conductivity elements can be memristor devices, resistive random access memory devices, phase-change memory devices, or electronically adjustable resistor devices that are non-volatile or can maintain conductivity. The PSpice resistor equivalent implementation can be used to verify the nominal conductivity mapping relationship. The write pulse, read voltage, and calibration method for different devices can be determined according to the device characteristics without changing the aforementioned network connections and parameter relationships.

[0034] Example 2: Progressive local reconfiguration example.

[0035] During task initialization, the control module receives B and calculates... ;according to Configuration Figure 2 The upper B-conductance network, and according to Configure the feedback branches at each anchor point; then, based on the initial α and β, simultaneously configure the upper and lower sets of... The conductance network and two sets of β branches are then used. The tag vector Y is then applied as the input voltage for each sample row, and the closed-loop arithmetic unit and TIA are operated within the specified reference potential and readout range. B, λ, Θ, and Remain static within the same task.

[0036] After applying Y, the upper first β branch and the first The conductivity network is first formed in the sample row. The B-conductance network then processes the sample side results according to... The data converges to each anchor point column. Each closed-loop operation unit continuously adjusts its corresponding... Until the feedback current balances with the convergence current of column B and a balance is established. The steady state. The steady state Z is transmitted to the lower second part via a shared anchor line. The conduction network, with the second β branch at the bottom simultaneously receiving Y, outputs F from the n-channel TIA. The external control module generates an asymptotic state update set based on F. And the updated α, β, and Y; the present invention receives this set and the updated value, and does not generate The representative point selection rule is used as the new algorithm.

[0037] Control module Perform partial synchronous reconfiguration line by line. For Only the two sets will be updated. The original non-zero position in the i-th row of the conductance network Conductivity, and update the upper and lower β branches Conductivity; if the label input of the sample changes, the corresponding Yᵢ driver is updated simultaneously. For Each conductance state and input remains unchanged; B conductance network and Feedback branches are not rewritten. After the synchronization update is completed, the system waits for the upper closed loop to re-establish a steady state before the lower TIA reads the next round of output F.

[0038] If the state of a single sample i changes, the adjustment amount of the unique logical parameter value is: Since the upper and lower networks are physically independent, the physical write location is twice the logical number. If a round involves multiple samples, the logical adjustment amount is... This count only applies to The parameters corresponding to β do not include changes in the input Y, nor do they represent the total power consumption or total latency of the entire machine.

[0039] Example 3: 16×8 circuit example.

[0040] In this embodiment, n=16, m=8, k=3, and B is a 16×8 non-negative row normalized matrix. Single set The network contains 46 non-zero logical relation values, and a single β branch contains 16 logical values. Therefore, one round requires maintaining 46 + 16 = 62 values. Configurable parameters with β logic. Two sets. The network and the two sets of beta branches are physically independent, corresponding to 124 physically writable locations.

[0041] The four-round progressive propagation involves three rounds of switching. The logical parameter adjustments for the three switching rounds are 3, 4, and 52, respectively, totaling 59. If all 62 logical parameters are reconfigured each time, the total reference value for the three rounds is 186, thus the local adjustment reduces the value by (186-59) / 186 = 68.28%. The physical synchronous write amounts are 6, 8, and 104, respectively, totaling 118; the corresponding total physical reference value is 372, also at a rate of 68.28%. This rate only describes this embodiment. The number of times the parameter corresponding to β is configured does not represent a 68.28% reduction in total power consumption, total latency, total area, or overall write overhead.

[0042] When using a resistive equivalent conductance network for transient simulation, the output data of the second pseudo-class in the fourth round covers 0 to 10 microseconds, and a total of 114 time points are recorded. Figure 3 The output channels of samples S01, S04, S09 and S13 were selected, and the positive tag propagation voltage was plotted after the polarity of the inverted output was reversed; all 114 time points were used for each channel, and transient data were not sampled.

[0043] The four-round anchor space variable Z and the sample propagation result F together form 312 sets of software ideal values ​​and circuit output values, of which the first to fourth rounds have 48 sets, 72 sets, 96 sets and 96 sets respectively. Figure 4 To avoid overlapping scatter points, a fixed random seed 20260901 was used, and 20 groups were sampled without replacement in each round, for a total of 80 data groups displayed; this sampling is only used for the attached chart. Based on all 312 data groups, the root mean square error is 7.4733 × 10⁻⁶. -4 Coefficient of determination The value is 0.999995, and the maximum absolute error is 0.002991. The above results are used to illustrate the numerical feasibility of the 16×8 nominal circuit and do not constitute a necessary limitation in the claims.

[0044] In one implementation, progressive label propagation can employ the label propagation process of PSSCNCD. As a known label propagation algorithm, this invention focuses on hardware task specialization for the algorithm structure that satisfies the row-normalized sample-anchor relationship matrix and complementary confidence parameter conditions, and does not advocate proposing the PSSCNCD algorithm itself.

[0045] When the number of samples exceeds the capacity of a single conductive network, the samples can be approximated in batches and reused in the same circuit by an external control system. Each batch can have an independent anchor space state. This approximation is not guaranteed to be strictly equivalent to full closed-loop propagation and does not constitute an essential technical feature of the independent claims of this invention.

Claims

1. A circuit for calculating an asymptotic label propagation simulation matrix based on probability-normalized invariants, characterized in that, It includes a relational conductance network, a first confidence-weighted relational conductance network, a first complementary confidence branch group, a closed-loop operational amplifier group, an anchor feedback branch group, a second confidence-weighted relational conductance network, a second complementary confidence branch group, an output conversion circuit, and a control module; the relational conductance network is used to reference conductance. The proportional mapping of the non-negative sample-anchor relationship matrix B, and the sample-side current through Converging to the anchor point side, B satisfies The first confidence-weighted relational conductance network is used for mapping. ,in The first confidence parameter for each sample A diagonal matrix with diagonal elements, the first complementary confidence branch group is used to measure conductance. Access label input Y, each sample and satisfy The anchor point output of the closed-loop operational amplifier group forms the anchor space variable Z. The anchor point feedback branch group is connected between the corresponding anchor point output and the summing node. The feedback conductance of the j-th anchor point feedback branch is... ,in The second confidence-weighted relation conductance network and the second complementary confidence branch group are loaded with the same logic parameters as the first confidence-weighted relation conductance network and the first complementary confidence branch group, respectively, and are physically independent of each other. They are used to generate the sample label propagation result F based on Z and Y through the output conversion circuit; due to the natural total conductance load of each sample node... The circuit's uniform natural row load γ is fixed at 2, and no sample-by-sample compensation conductance branch is provided to fill the sample row load to γ; the control module is used to keep B and the anchor feedback branch group unchanged in the same progressive tag propagation task, and to adjust the affected sample set generated externally. Only the original non-zero conductance of the corresponding sample row in the two sets of confidence-weighted conductance networks and the two sets of complementary confidence branches are updated synchronously.

2. The analog matrix calculation circuit according to claim 1, characterized in that, and , and Let B be an m-dimensional and an n-dimensional vector of all ones, and let B be the i-th row. satisfy Anchor point degree vector Depend on Determine the anchor point degree matrix. The steady-state relationship of the closed-loop operational amplifier group satisfies The anchor point feedback branch group includes m feedback branches that remain static within the same asymptotic label propagation task where B remains unchanged, and the feedback conductance of the j-th feedback branch is... .

3. The analog matrix calculation circuit according to claim 1, characterized in that, The first confidence parameter vector α and the second confidence parameter vector β are element-wise non-negative and satisfy the following conditions: Unified natural load Sample-by-sample compensation conductivity .

4. The analog matrix calculation circuit according to claim 2, characterized in that, The first confidence-weighted relation conductance network and the second confidence-weighted relation conductance network are two physically independent n×m conductance networks. The first complementary confidence branch group and the second complementary confidence branch group are two physically independent groups of n conductance branches. The two conductance networks and the two groups of conductance branches are loaded with the same logic parameters. B, λ, θ and the anchor feedback branch group are task-level static parameters. , Y represents the asymptotic round-related parameters, and Z and F represent the runtime states under closed-loop steady state. When the asymptotic state of a single sample i changes, the only logical parameter that needs to be changed is... The confidence-weighted relation values ​​and corresponding values ​​of the original non-zero positions in the sample row. Values, their quantity is And it is no greater than k+1.

5. The analog matrix calculation circuit according to any one of claims 1 to 4, characterized in that, The programmable conductivity network and conductivity branches employ memristor devices, resistive random access memory devices, or adjustable resistor devices capable of maintaining programmable conductivity states.

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