The paper investigates whether compression explains why over‑parameterized neural networks generalize, using the minimum description length (MDL) principle. It introduces prequential regret, a computable metric from the training trajectory, and shows that in the nearly interpolating regime it upper‑bounds the description length of the trained parameters, leading to a high‑probability generalization bound in the PAC‑MDL setting. The study also connects MDL with the algorithm‑level information bottleneck by bounding encoder‑complexity correction with MDL parameter description length, and demonstrates that prequential regret correlates strongly (Pearson > 0.9) with generalization error on CIFAR‑10 and CIFAR‑100.
A central question in modern learning theory is what notion of compression, if any, explains why over-parameterized neural networks generalize. Existing answers measure complexity at different levels,...
Compression is fundamental to intelligence. A model that can represent its training data as a short code has discovered regularities that enable generalization.
arXiv:2610. 39027v1 Announce Type: cross Abstract: What computational role does overparameterisation play during learning?
arXiv:2607. 11883v1 Announce Type: new Abstract: Compression is fundamental to intelligence.
arXiv:2606. 04834v1 Announce Type: new Abstract: Minimum Description Length (MDL) formalizes the principle of Occam's razor by optimizing the total description length: $L(\mathrm{model})+L(\mathrm{data} \ | \ \mathrm{model})$.
arXiv:2606. 11171v2 Announce Type: replace Abstract: We develop indexed Bellman information complexity, a representation-level theory of interactive decision making centered on information indices and reference histories.
arXiv:2505. 23869v4 Announce Type: replace-cross Abstract: A proposition that connects randomness and compression is put forward via Gibbs entropy over set of measurement vectors associated with a compression process.
arXiv:2602. 01903v2 Announce Type: replace Abstract: This work studies online episodic tabular Markov decision processes (MDPs) with known transitions and develops best-of-both-worlds algorithms that achieve refined data-dependent regret bounds in the adversarial regime and variance-dependent regret bounds in the stochastic regime.
arXiv:2606. 30512v1 Announce Type: cross Abstract: Why overparameterised deep networks generalise so remarkably well remains one of the most stubborn open questions in machine learning theory.
arXiv:2407. 12288v5 Announce Type: replace-cross Abstract: The progress of machine learning over the past decade is undeniable.
Compression schemes provide a general framework for deriving data-dependent risk bounds for learning algorithms. For learning rules based on preferent compression, existing results upper-bound the risk in terms of a sample-dependent complexity $\boldsymbol{k}$, defined as the cardinality of the compression augmented by the training examples on which the reconstructed hypothesis is inappropriate.
The paper presents quantitative generalization bounds for fixed‑precision transformer models, addressing both in‑distribution statistical generalization and length generalization. It derives guarantees based on model parameters, quantization space, and alphabet size, and shows how training length and sample size trade off, with longer training being exponentially more efficient. Experiments confirm the theoretical predictions.