Hilbert Operator for Progressive Encoding (HOPE): A Mathematical Framework for Deconstructing Learned Representations in Deep Networks
Deep neural networks encode complex representations, but deconstructing this internal knowledge remains a challenge. Given the link between learning and compression, network compression offers a promising lens to analyze this knowledge. However, standard compression heuristics often suffer from scale symmetries and architectural biases. To resolve these, we introduce Hilbert Operator for Progressive Encoding (HOPE), a mathematical framework to gradually deconstruct the representations in trained network weights. HOPE shifts network compression from the discrete domain into a Hilbert space of continuous functions. By modeling individual neurons as rank-1 Hilbert-Schmidt operators, HOPE unifies pruning and neuron merging as low-rank subspace projection. Extending this formulation, HOPE introduces macro block eviction to encompass multi-layer structures like entire residual pathways under the same unified metric. This unified approach enables unbiased architectural decisions across layers with different types and sizes. HOPE is a data-free and hyperparameter-free framework. We present proof-of-concept experiments in model compression and fine-tuning to highlight the practical potential of our theory.
Code (0)
등록된 구현이 없습니다.
Tasks
Model CompressionSimilar Papers 제목 키워드 기반
Log-Hilbert-Schmidt metric between positive definite operators on Hilbert spaces
This paper introduces a novel mathematical and computational framework, namely {\it Log-Hilbert-Schmidt metric} between positive definite operators on a Hilbert space. This is a generalization of the Log-Euclidean metric…
image-classificationImage ClassificationOperator-Based Machine Intelligence: A Hilbert Space Framework for Spectral Learning and Symbolic Reasoning
Traditional machine learning models, particularly neural networks, are rooted in finite-dimensional parameter spaces and nonlinear function approximations. This report explores an alternative formulation where learning t…
Interpretable Machine LearningKullback-Leibler and Renyi divergences in reproducing kernel Hilbert space and Gaussian process settings
In this work, we present formulations for regularized Kullback-Leibler and R\'enyi divergences via the Alpha Log-Determinant (Log-Det) divergences between positive Hilbert-Schmidt operators on Hilbert spaces in two diffe…
Gaussian ProcessesSobolev Norm Learning Rates for Conditional Mean Embeddings
We develop novel learning rates for conditional mean embeddings by applying the theory of interpolation for reproducing kernel Hilbert spaces (RKHS). We derive explicit, adaptive convergence rates for the sample estimato…
Learning functions, operators and dynamical systems with kernels
This expository article presents the approach to statistical machine learning based on reproducing kernel Hilbert spaces. The basic framework is introduced for scalar-valued learning and then extended to operator learnin…