The paper introduces a dimension‑free PAC‑Bayes generalization bound for deep neural networks by placing the prior over the non‑parametric space of data distributions using a Dirichlet Process. This shift eliminates the dependence on the number of network parameters, yielding a bound that remains non‑vacuous even for over‑parameterized models. Experiments on MNIST with up to 4.2 million parameters show the new bound staying stable at 8.8 %–9.4 %, whereas classical weight‑space bounds become vacuous.
arXiv:2606. 08218v1 Announce Type: cross Abstract: Compositional priors describe the generic properties of layered functions in deep Bayesian models, where deep neural networks with random weights are a canonical example.
arXiv:2609. 20883v1 Announce Type: new Abstract: Despite the widespread use and success of generative AI techniques today, theoretical guarantees on learning a distribution supported in $d$ dimensions from $n$ samples degrade as $O(n^{-1/\Theta(d)})$, though shown to be minimax optimal.
arXiv:2609. 25710v1 Announce Type: cross Abstract: The statistical accuracy of neural networks depends on both their approximation power and the complexity of the class fitted from data.
arXiv:2610. 02663v1 Announce Type: cross Abstract: Despite the remarkable empirical success of flow-matching models, their statistical generalization guarantees remain underdeveloped.
The paper introduces a new closed‑form scaling law that extends Chinchilla’s original formula to handle data‑constrained regimes. It decomposes loss into undercapacity, undertraining, and overfitting components, saturating between an irreducible loss and an uninformed baseline. The authors validate the model on diverse architectures and domains, achieving state‑of‑the‑art RMSE across multiple LLM scaling‑law grids and enabling cost‑aware training allocations.
arXiv:2607.10912v2 Announce Type: replace Abstract: 3D Gaussian Splatting represents scenes as finite mixtures of anisotropic Gaussians whose number of components $K$ is set by heuristic density cont...
arXiv:2608. 10869v1 Announce Type: new Abstract: Worst-case multiclass bounds do not become smaller when the best classifier is already nearly correct: what is missing is an optimistic rate, a guarantee whose fluctuation scales with the oracle risk itself.
The paper investigates how well practical machine‑learning algorithms approximate Solomonoff’s universal predictor when trained by minimizing log‑loss over diverse datasets. It establishes tight bounds on the worst‑case increase in prediction error caused by approximating the Bayesian mixture predictor, showing that while the excess error can be large in low‑prior environments, it remains bounded on average and under distribution shifts. The authors also extend their analysis to finite‑sample settings relevant to neural networks and Transformers.
arXiv:2610.07655v1 Announce Type: cross Abstract: Discrete diffusion models have emerged as a practically successful framework for generative modeling on discrete product spaces, yet their statistica...
arXiv:2609.27988v1 Announce Type: cross Abstract: Methods operating on Vision Transformer (ViT) feature spaces typically rely on Euclidean distance or cosine similarity. This assumes that every direc...
arXiv:2602. 13298v4 Announce Type: replace-cross Abstract: This paper presents a controlled comparative study of convolutional neural network (CNN) topology and image classification performance across the architectural families VGG, ResNet, and GoogLeNet, evaluated on CIFAR-10 under a unified training protocol.
arXiv:2606. 07931v1 Announce Type: cross Abstract: We prove a variance-aware pointwise majorizing-measure theorem for centered Gaussian processes.