Stochastic Backpropagation

SC-NeuroCore includes an experimental reference path for training through stochastic-computing design variables, not only through a floating-point model that is converted to bitstreams afterwards. The current workflow optimises model weights together with bitstream length, encoding choice, and correlation metadata, then writes deterministic benchmark, SC-NIR export, estimator regression, and executable HDL parity artefacts.

The evidence boundary is local_simulation_and_executable_hdl_parity.

What The Evidence Means

The current workflow can report:

• loss reduction for a deterministic stochastic-backprop reference task;
• trained bitstream-length, encoding, and correlation selections;
• SC-NIR stream metadata and correlation constraints used by the handoff;
• estimator-family variance evidence for pathwise_relaxation, straight_through, and score_function;
• executable local HDL parity for the trained design metadata via iverilog/vvp.

The current workflow does not provide:

• no physical hardware measurement;
• no Vivado timing closure claim;
• no PYNQ deployment claim;
• no board-level power, thermal, or timing evidence.

Treat these artefacts as local software and executable-HDL parity evidence. Vivado implementation reports, PYNQ runs, lab measurements, and physical deployment packets are separate evidence classes.

Python API

Use stochastic_backprop_joint_objective when the training step must expose gradients through both model parameters and stochastic-computing design variables:

Python

import torch

from sc_neurocore.training.sc_estimators import DifferentiableSCConfig
from sc_neurocore.training.stochastic_backprop import (
    SCBackpropDesignSpace,
    SCTrainingObjectiveConfig,
    stochastic_backprop_joint_objective,
)

inputs = torch.tensor([[0.2, -0.4], [0.8, 0.1]], dtype=torch.float32)
targets = torch.tensor([[0.3], [0.6]], dtype=torch.float32)
weight = torch.tensor([[0.25, -0.35]], dtype=torch.float32, requires_grad=True)
bias = torch.tensor([0.05], dtype=torch.float32, requires_grad=True)
length_logits = torch.tensor([0.6, -0.2, 0.1], dtype=torch.float32, requires_grad=True)
encoding_logits = torch.tensor([0.8, -0.3], dtype=torch.float32, requires_grad=True)
correlation_logit = torch.tensor(0.2, dtype=torch.float32, requires_grad=True)

report = stochastic_backprop_joint_objective(
    inputs,
    targets,
    weight=weight,
    bias=bias,
    length_logits=length_logits,
    encoding_logits=encoding_logits,
    correlation_logit=correlation_logit,
    base_config=DifferentiableSCConfig(
        bitstream_length=128,
        encoding="bipolar",
        generator="sobol",
        estimator="pathwise_relaxation",
        input_seed=3,
        weight_seed=11,
        correlation=0.0,
    ),
    design_space=SCBackpropDesignSpace(
        bitstream_lengths=(64, 128, 256),
        encodings=("bipolar", "unipolar"),
        min_correlation=-0.25,
        max_correlation=0.25,
    ),
    objective_config=SCTrainingObjectiveConfig(
        length_cost_weight=1.5,
        correlation_cost_weight=0.4,
        encoding_cost_weight=0.3,
    ),
)

report.breakdown.total.backward()

The returned report contains the relaxed prediction, objective breakdown, selected exportable DifferentiableSCConfig, length probabilities, encoding probabilities, expected bitstream length, selected encoding, selected length, and selected correlation.

Reproducible Artifact Generation

Generate the benchmark report, SC-NIR export manifest, estimator-regression manifest, and HDL handoff directory with one command:

Bash

PYTHONPATH=src python tools/stochastic_backprop_benchmark.py \
  --output benchmarks/results/stochastic_backprop_benchmark.json \
  --export-manifest benchmarks/results/stochastic_backprop_export_manifest.json \
  --estimator-regression-manifest benchmarks/results/stochastic_backprop_estimator_regression_manifest.json \
  --handoff-dir benchmarks/results/stochastic_backprop_handoff \
  --bitstream-length 256 \
  --steps 32 \
  --learning-rate 0.4

The generated evidence set is:

• benchmarks/results/stochastic_backprop_benchmark.json;
• benchmarks/results/stochastic_backprop_export_manifest.json;
• benchmarks/results/stochastic_backprop_estimator_regression_manifest.json;
• benchmarks/results/stochastic_backprop_handoff/scnir_document.json;
• benchmarks/results/stochastic_backprop_handoff/scnir_source_manifest.json;
• benchmarks/results/stochastic_backprop_handoff/stochastic_backprop_trained_design.v;
• benchmarks/results/stochastic_backprop_handoff/stochastic_backprop_trained_design_parity.json;
• benchmarks/results/stochastic_backprop_handoff/stochastic_backprop_handoff_audit.json.

Estimator Regression

The standalone estimator-regression manifest compares the seeded variance of three estimator assumptions over multiple bitstream lengths:

• pathwise_relaxation: differentiable relaxed Bernoulli expectation;
• straight_through: sampled forward pass with a relaxed backward proxy;
• score_function: seeded likelihood-ratio estimate without a baseline.

The manifest acceptance fields check that:

• all variances are finite and nonnegative;
• pathwise variance is zero for the deterministic relaxation;
• the longest configured score-function variance is below the shortest configured score-function variance.

This is a regression signal for estimator stability. It is not a statistical certification of convergence for every network or dataset.

HDL Parity

The handoff bundle emits stochastic_backprop_trained_design.v, a small executable Verilog module that exposes the trained stochastic-design metadata as constant outputs:

• selected bitstream length;
• expected bitstream length in Q16;
• trained correlation in Q16;
• selected encoding flag.

The test suite compiles this module with iverilog and executes it with vvp against stochastic_backprop_trained_design_parity.json. This proves that the trained design metadata survives into executable HDL. It does not prove FPGA place-and-route, timing closure, or board deployment.

Review Checklist

Before using stochastic-backprop evidence in a release packet, check that:

• hardware_measurement_claimed is false in every benchmark/export artifact;
• joint_design.enabled is true in the benchmark and export manifest;
• selected_bitstream_length, selected_encoding, and correlation match between the benchmark and export manifest;
• estimator-regression status is pass;
• stochastic_backprop_handoff_audit.json reports status: valid;
• the trained-design HDL parity test has been run on the checked-out artifact;
• no physical hardware claim is made unless separate raw hardware evidence is attached.