Empirical Minimal-Realisation Compression of Deep Neural Networks via Controllability-Observability Tests
Proposes a controllability-observability framework to treat deep neural networks as depth-indexed nonlinear dynamical systems for state-order reduction. Constructs data-driven reachability, observability, and balanced Gramians from hidden-state snapshots and output Jacobians to estimate layer-wise ranks. Achieves significant compression on MNIST (72.95% state, 73.48% parameters) and CIFAR-10 (70.94% state, 83.09% parameters) with negligible accuracy loss. Demonstrates up to 3X reduction in CUDA
Analysis
TL;DR
- Proposes a controllability-observability framework to treat deep neural networks as depth-indexed nonlinear dynamical systems for state-order reduction.
- Constructs data-driven reachability, observability, and balanced Gramians from hidden-state snapshots and output Jacobians to estimate layer-wise ranks.
- Achieves significant compression on MNIST (72.95% state, 73.48% parameters) and CIFAR-10 (70.94% state, 83.09% parameters) with negligible accuracy loss.
- Demonstrates up to 3X reduction in CUDA inference latency on CIFAR-10 while maintaining performance comparable to baseline models.
- Validates the approach against projection-based reduction, pruning, SVD, and quantization, showing balanced realization as a principled criterion for compact architectures.
Why It Matters
This research introduces a novel theoretical lens by applying control theory concepts like controllability and observability to neural network compression, moving beyond traditional weight-centric methods. It offers practitioners a rigorous, data-driven method to identify and eliminate redundant hidden states, potentially leading to more efficient model deployment with minimal retraining overhead. The demonstrated latency improvements highlight its practical value for edge computing and real-time inference applications where computational resources are constrained.
Technical Details
- Framework: Views trained networks as nonlinear dynamical systems, utilizing hidden-state snapshots and output Jacobians to compute reachability and observability Gramians.
- Methodology: Employs "A/B/C tests" to estimate layer-wise reachable, observable, and jointly reachable-observable ranks, which serve as both diagnostic metrics and target widths for compressed layers.
- Experiments: Benchmarked on MNIST and CIFAR-10 using SiLU activation functions, comparing against unstructured/structured pruning, low-rank SVD, dynamic INT8 quantization, and linear baselines.
- Results: On MNIST, reduced a 4-layer DNN from state order 1024 to 277 (95.45% vs 96.60% accuracy). On CIFAR-10, reduced state order from 4608 to 1339 (54.44% vs 54.45% accuracy) with ~3X latency improvement.
Industry Insight
- Architectural Design: Engineers should consider dynamical system properties when designing compact models, as state redundancy may be more significant than weight redundancy alone.
- Efficiency Gains: The 3X latency reduction suggests that state-order reduction can complement existing compression techniques like quantization and pruning for maximum efficiency.
- Theoretical Integration: Bridging control theory and machine learning offers new avenues for model interpretability and optimization, encouraging cross-disciplinary approaches in AI research.
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