[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-328038-105":59,"doc-detail-328038-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","empirical-minimal-realisation-compression-of-deep-neural-networks-via-controllability-observability-tests","Empirical Minimal-Realisation Compression of Deep Neural Networks via Controllability-Observability Tests","","Deep neural networks often contain hidden-state redundancy, yet many compression techniques act on weights or representations without explicitly characterizing the dynamical role of internal states. This paper introduces a controllability–observability framework for empirical state-order reduction. A depth-indexed nonlinear dynamical system view enables data-driven reachability, observability, and balanced Gramians from hidden snapshots and output Jacobians. The resulting A/B/C tests yield layer-wise reachable, observable, and jointly reachable–observable ranks, used both diagnostically and to set widths of realized reduced networks. Experiments on MNIST and CIFAR-10 compare balanced realisation against pruning, low-rank SVD, quantisation, and linear baselines.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/empirical-minimal-realisation-compression-of-deep-neural-networks-via-controllability-observability-tests/328038/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/empirical-minimal-realisation-compression-of-deep-neural-networks-via-controllability-observability-tests/328038.png","ImageObject",300,407,{"name":92,"@type":93},"Eden","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-29","2026-09-21",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",13,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What problem does the paper address in deep neural network compression?","Question",{"text":113,"@type":114},"Most compression methods reduce weights or representations but do not explicitly determine which hidden-state directions are excited by data and which affect outputs. The paper targets this state-space interpretation gap.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How are reachability and observability estimated for each hidden layer?",{"text":118,"@type":114},"Test A estimates reachability using hidden-state snapshot covariances, while Test B estimates observability using output-logit Jacobians with respect to hidden states.",{"name":120,"@type":111,"acceptedAnswer":121},"What is the role of the balanced reachable–observable ranks in the proposed method?",{"text":122,"@type":114},"Test C combines reachability and observability into a balanced matrix, producing layer-wise ranks that both diagnose hidden-state redundancy and define compressed layer widths for a realized reduced DNN.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},328038,1790667196,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":105,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":145,"preview_page_count":4},1374391974468,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","Empirical Minimal-Realisation Compression of Deep Neural Networks via Controllability–Observability Tests  \nAnis Hamadouche  \nThe School of Engineering & Physical Sciences Heriot-Watt University Edinburgh EH14 4AS, UK[anis.hamadouche@hw.ac.uk](anis.hamadouche@hw.ac.uk)  \nAmir Hussain  \nSDAIA-KFUPM Joint Research Centre for Artificial Intelligence  \nKing Fahd University of Petroleum and Minerals Dhahran, Saudi Arabia [amir.hussain@kfupm.edu.sa](amir.hussain@kfupm.edu.sa)  \narXiv :2607 .05457v 1 [ cs .LG] 5 Jul 2026  \nAbstract—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 MNISTand 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 3 ×. 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.  \nIndex Terms—Deep neural network compression, controllability, observability, balanced truncation, empirical Gramians, minimal realisation, state-order reduction, pruning, low-rank compression, knowledge distillation.  \nI. INTRODUCTION  \nDeep neural networks (DNNs) have achieved strong performance across classification, perception, and representationlearning tasks, but their high parameter counts and wide hidden layers often make them expensive to deploy on resourceconstrained hardware. As a result, neural network compression has become an important research direction. Existing methods include pruning, quantisation, low-rank factorisation, and knowledge distillation [1]–[5] . These approaches can significantly reduce storage or arithmetic cost, but they usually operate directly on weights, neurons, channels, or numerical  \nprecision. They do not explicitly answer a state-space question: which hidden-state directions are actually excited by the data distribution and which of those directions are relevant to the output?  \nThis paper proposes a control-theoretic view of neural compression. We interpret a trained feedforward DNN as a depth-indexed nonlinear state-space system,  \nhℓ+1 = fℓ (hℓ), z = g (hL ) , (1)  \nwhere hℓ denotes the hidden state at layer ℓ and z denotes the output logits. This dynamical-systems interpretation is closely related to prior views of residual networks, neural ordinary differential equations, stable deep architectures, and optimal-control formulations of deep learning [6]–[10] . However, instead of using this viewpoint primarily for stability or continuous-depth modelling, we use it to estimate the useful hidden-state order of a trained network.  \nThe key idea is that not every hidden direction in a wide","cbCaii4KAx5vVcuN","https://ap.wps.com/l/cbCaii4KAx5vVcuN","pdf",328063,"English","# Abstract\n# Introduction\n## Dynamical-systems perspective for compression\n## Empirical controllability/observability tests\n## Projected reduction vs realized compression","[{\"question\":\"What problem does the paper address in deep neural network compression?\",\"answer\":\"Most compression methods reduce weights or representations but do not explicitly determine which hidden-state directions are excited by data and which affect outputs. The paper targets this state-space interpretation gap.\"},{\"question\":\"How are reachability and observability estimated for each hidden layer?\",\"answer\":\"Test A estimates reachability using hidden-state snapshot covariances, while Test B estimates observability using output-logit Jacobians with respect to hidden states.\"},{\"question\":\"What is the role of the balanced reachable–observable ranks in the proposed method?\",\"answer\":\"Test C combines reachability and observability into a balanced matrix, producing layer-wise ranks that both diagnose hidden-state redundancy and define compressed layer widths for a realized reduced DNN.\"}]","Empirical Minimal-Realisation Compression of Deep Neural Networks via Controllability-Observability Tests | PDF",1789978564,33]