[Submitted on 5 Jul 2026]
Title:Empirical Minimal-Realisation Compression of Deep Neural Networks via Controllability-Observability Tests
View a PDF of the paper titled Empirical Minimal-Realisation Compression of Deep Neural Networks via Controllability-Observability Tests, by Anis Hamadouche and Amir Hussain
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Abstract:Deep neural networks often contain substantial hidden-state redundancy, but most compression methods operate directly on weights, neurons, or quantised representations without explicitly characterising the dynamical role of internal states. This paper proposes a controllability-observability framework for empirical state-order reduction of deep neural networks. By viewing a trained network as a depth-indexed nonlinear dynamical system, we construct data-driven reachability, observability, and balanced Gramians from hidden-state snapshots and output Jacobians. The resulting A/B/C tests estimate layer-wise reachable, observable, and jointly reachable--observable ranks. These ranks are then used not only as diagnostic measures of hidden-state redundancy, but also as actual compressed layer widths for realised reduced networks. Experiments on MNIST and CIFAR-10 compare the proposed balanced realisation against projection-based reduction, unstructured pruning, structured pruning, low-rank SVD, dynamic INT8 quantisation, and linear baselines. On MNIST, a four-layer SiLU DNN is reduced from state order 1024 to 277, giving 72.95% state compression and 73.48% parameter compression, while maintaining 95.45% accuracy compared with 96.60% for the full model. On CIFAR-10, a larger SiLU DNN is reduced from state order 4608 to 1339, giving 70.94% state compression and 83.09% parameter compression, while preserving accuracy from 54.45% to 54.44% and reducing CUDA inference latency by approximately 3X. The results show that balanced reachable-observable ranks provide a principled empirical minimal-realisation criterion for designing compact neural architectures with little or no loss in accuracy.
Subjects:
Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Dynamical Systems (math.DS)
Cite as: arXiv:2607.05457 [cs.LG]
(or arXiv:2607.05457v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2607.05457
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Anis Hamadouche [view email] [v1] Sun, 5 Jul 2026 22:07:22 UTC (92 KB)
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