Algorithmic Simplification of Neural Networks with Mosaic-of-Motifs

Large-scale deep learning models are well-suited for compression. Methods like pruning, quantization, and knowledge distillation have been used to achieve massive reductions in the number of model parameters, with marginal performance drops across a variety of architectures and tasks. This raises the central question: \emph{Why are deep neural networks suited for compression?} In this work, we take up the perspective of algorithmic complexity to explain this behavior. We hypothesize that the parameters of trained models have more structure and, hence, exhibit lower algorithmic complexity compared to the weights at (random) initialization. Furthermore, that model compression methods harness this reduced algorithmic complexity to compress models. Although an unconstrained parameterization of model weights, $\mathbf{w} \in \mathbb{R}^n$, can represent arbitrary weight assignments, the solutions found during training exhibit repeatability and structure, making them algorithmically simpler than a generic program. To this end, we formalize the Kolmogorov complexity of $\mathbf{w}$ by $\mathcal{K}(\mathbf{w})$. We introduce a constrained parameterization $\widehat{\mathbf{w}}$, that partitions parameters into blocks of size $s$, and restricts each block to be selected from a set of $k$ reusable motifs, specified by a reuse pattern (or mosaic). The resulting method, $\textit{Mosaic-of-Motifs}$ (MoMos), yields algorithmically simpler model parameterization compared to unconstrained models. Empirical evidence from multiple experiments shows that the algorithmic complexity of neural networks, measured using approximations to Kolmogorov complexity, can be reduced during training. This results in models that perform comparably with unconstrained models while being algorithmically simpler.

CoDeQ: End-to-End Joint Model Compression with Dead-Zone Quantizer for High-Sparsity and Low-Precision Networks

While joint pruning--quantization is theoretically superior to sequential application, current joint methods rely on auxiliary procedures outside the training loop for finding compression parameters. This reliance adds engineering complexity and hyperparameter tuning, while also lacking a direct data-driven gradient signal, which might result in sub-optimal compression. In this paper, we introduce CoDeQ, a simple, fully differentiable method for joint pruning--quantization. Our approach builds on a key observation: the dead-zone of a scalar quantizer is equivalent to magnitude pruning, and can be used to induce sparsity directly within the quantization operator. Concretely, we parameterize the dead-zone width and learn it via backpropagation, alongside the quantization parameters. This design provides explicit control of sparsity, regularized by a single global hyperparameter, while decoupling sparsity selection from bit-width selection. The result is a method for Compression with Dead-zone Quantizer (CoDeQ) that supports both fixed-precision and mixed-precision quantization (controlled by an optional second hyperparameter). It simultaneously determines the sparsity pattern and quantization parameters in a single end-to-end optimization. Consequently, CoDeQ does not require any auxiliary procedures, making the method architecture-agnostic and straightforward to implement. On ImageNet with ResNet-18, CoDeQ reduces bit operations to ~5% while maintaining close to full precision accuracy in both fixed and mixed-precision regimes.