SpectralNet

SpectralNet: A Resolvent-Inspired Neural Architecture Based on Chernoff Approximations and Photonic Motivation

Sergey V. Shpital

Overview

This repository contains the official PyTorch implementation of SpectralNet, a digital neural architecture motivated by the Chernoff-Remizov constructive line for operator evolution.

The core idea is to interpret a learnable spectral layer as a discrete approximation of a small-step family whose repeated composition approximates a semigroup, while dense aggregation of intermediate states with decaying weights approximates the resolvent as a Laplace transform of the evolution.

Installation

git clone https://github.com/shpital/spectralnet.git
cd spectralnet
pip install -r requirements.txt

Usage

The repository uses Hydra for configuration management. All configurations are located in the configs/ directory. The main execution scripts are located in src/spectralnet/cli/.

1. Training Models

Train SpectralNet (e.g., EXP-004 on CIFAR-10):

python src/spectralnet/cli/train.py \
    --config-name experiment/exp004_vision_cifar10_multiseed \
    training.seed=42

Train Baselines (ResNet-18, MobileNetV2, ShuffleNetV2):

python src/spectralnet/cli/train_baseline.py \
    --config-name experiment/exp_baseline_cifar10 \
    model.baseline_type=resnet18 \
    training.seed=42

Logs, checkpoints, and a lineage.json (containing the exact configuration and metrics) will be saved in results/runs/<timestamp>_....

2. Evaluation Scripts

The repository includes several scripts to evaluate pre-trained models across different dimensions. These scripts automatically scan the results/ directory, find the best checkpoints using lineage.json, and compute metrics.

Robustness Evaluation: Evaluates model robustness against AWGN, Gaussian Blur, and Contrast reduction.

python src/spectralnet/cli/eval_robustness_rmsb.py \
    --mode full \
    --runs_main ./results/runs \
    --runs_rmsb ./results/rmsb \
    --output ./results/robustness_summary.json

Efficiency Metrics: Computes parameters, MACs (requires ptflops or thop), latency, throughput, and peak GPU memory.

python src/spectralnet/cli/eval_efficiency_rmsb.py \
    --runs_main ./results/runs \
    --runs_rmsb ./results/rmsb \
    --output ./results/efficiency_summary.json

Conditioning Analysis: Analyzes the spectral operator $W = D + UV^*$, resolvent weights, and block norm proxy (feature amplification).

python src/spectralnet/cli/eval_conditioning_rmsb.py \
    --runs_main ./results/runs \
    --runs_rmsb ./results/rmsb \
    --output ./results/conditioning_summary.json

3. Utilities

Aggregate Multi-seed Results: Computes mean and standard deviation across multiple seeds for a given experiment.

python src/spectralnet/cli/collect_results.py \
    --runs_dir ./results/runs \
    --exp_name exp004_vision_cifar10_multiseed \
    --output ./results/exp004_summary.json

Numerical Audit (Gradcheck): Runs an isolated PyTorch gradcheck in float64 to verify the differentiability of the complex FFT math and spectral masking.

python src/spectralnet/cli/run_gradcheck.py

License

This project is licensed under the MIT License.

Citation

If you find this work useful in your research, please consider citing:

@misc{shpital2026spectralnet,
      title={SpectralNet: A Resolvent-Inspired Neural Architecture Based on Chernoff Approximations and Photonic Motivation}, 
      author={Sergey V. Shpital},
      year={2026},
      doi={10.5281/zenodo.19452600},
      url={https://doi.org/10.5281/zenodo.19452600},
      publisher={Zenodo}
}