arXiv subjects

Jonathan Wenshøj

Publications and source records attributed to Jonathan Wenshøj.

4 recordsLinked to original sources

arXiv2026

Algorithmic Simplification of Neural Networks with Mosaic-of-Motifs

Large-scale deep learning models are well-suited for compression. Across a variety of tasks, methods like pruning, quantization, and knowledge distillation have been used to achieve massive reductions in model parameters with only marginal performance drops. This raises the central question: *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, 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 simpler to implement than a trivial 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, $\mathit{Mosaic\text{-}of\text{-}Motifs}$ (MoMos), provides a theoretically justified parameterization that biases optimization toward algorithmically simpler solutions. Empirical evidence from multiple experiments shows that MoMos consistently lowers the algorithmic complexity of neural networks during training while preserving the performance of unconstrained models. These results suggest that parameter compressibility is not only observed after training, but can be induced from the optimization domain.

cs.LG↗

arXiv2026

Characterizing Learning in Deep Neural Networks using Tractable Algorithmic Complexity Analysis

Training large-scale deep neural networks (DNNs) is resource-intensive, making model compression a practical necessity. The widely accepted ''learning as compression'' hypothesis posits that training induces structure in network weights, which enables compression. Measuring this structure through Kolmogorov-Chaitin-Solomonoff (KCS) complexity is appealing, but existing estimators based on the Coding Theorem Method (CTM) and the Block Decomposition Method (BDM) are limited to small binary objects and do not scale to modern DNNs. We introduce the Quantized Block Decomposition method (QuBD), which extends algorithmic complexity estimation to any $k$-ary object. QuBD first quantizes the network weights to a finite alphabet, then estimates the KCS complexity by aggregating per bit-plane CTM estimates. We show theoretically that QuBD yields a strictly tighter estimation gap with respect to true KCS complexity than binarization-based methods. Using QuBD, we study how the algorithmic complexity of neural network weights evolves during training, showing that it decreases as models learn, scales with data budget, increases during overfitting, follows the delayed generalization observed during grokking, and correlates with generalization performance. We further show that algorithmic information resides predominantly in the most significant bit-planes, which can serve as a practical diagnostic for determining appropriate post-training quantization levels. This work offers novel insights into learning mechanisms in DNNs by providing the first scalable, tractable estimates of KCS complexity for large, non-binary objects such as DNN weights.

cs.LG↗

arXiv2025

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.

cs.LG↗

arXiv2025

Oscillations Make Neural Networks Robust to Quantization

We challenge the prevailing view that weight oscillations observed during Quantization Aware Training (QAT) are merely undesirable side-effects and argue instead that they are an essential part of QAT. We show in a univariate linear model that QAT results in an additional loss term that causes oscillations by pushing weights away from their nearest quantization level. Based on the mechanism from the analysis, we then derive a regularizer that induces oscillations in the weights of neural networks during training. Our empirical results on ResNet-18 and Tiny Vision Transformer, evaluated on CIFAR-10 and Tiny ImageNet datasets, demonstrate across a range of quantization levels that training with oscillations followed by post-training quantization (PTQ) is sufficient to recover the performance of QAT in most cases. With this work we provide further insight into the dynamics of QAT and contribute a novel insight into explaining the role of oscillations in QAT which until now have been considered to have a primarily negative effect on quantization.

cs.LG↗