The paper introduces a manifold‑aware encoding strategy for general coded computing (GCC) that preserves the intrinsic low‑dimensional structure of high‑dimensional datasets. Unlike traditional coded‑computing designs that ignore data structure, this approach generates coded samples that follow the natural manifold of the data, inspired by graph‑based manifold learning. Experiments on neural network inference and high‑dimensional polynomial evaluation show that the new strategy consistently and significantly reduces mean squared recovery error under straggling compared with standard GCC.
By Parsa Moradi, Mohammad Ali Maddah-Ali
The paper studies operator learning on function spaces using encoder–decoder architectures. It shows that as input and output resolutions grow, the induced kernels converge to a limiting kernel, enabling regularity assumptions independent of resolution. The authors derive upper and lower bounds for regularized stochastic gradient descent, extend the analysis to neural networks via the limiting neural tangent kernel, and provide error bounds and complexity guarantees for various kernel and encoding constructions.
By Lei Shi, Jia-Qi Yang, Ding-Xuan Zhou
arXiv:2607. 01799v1 Announce Type: cross Abstract: Sparse autoencoders (SAEs) decompose internal activations of neural networks into sparse linear combinations of learned features by fitting an overcomplete dictionary $\mathbf{W}\in\mathbb{R}^{m\times n}$ with $m<n$, and inferring a sparse code $\mathbf{x}\in\mathbb{R}^n$ from $\mathbf{h}\approx\mathbf{W}\mathbf{x}$.
By Rodrigo Mendoza-Smith
The paper investigates the limits of the maximal coding rate reduction (MCR²) framework for out‑of‑distribution (OOD) generalisation. It shows that MCR² can lead to complete prediction failure under distribution shift, even when a perfectly stable feature is available, and that adding invariance principles from IRM or REx does not resolve this issue. The authors conclude that additional assumptions or learning principles are needed to guarantee stable OOD predictions with MCR².
By Menghui Zhou, Gaoshan Bi, Vitaveska Lanfranchi, Po Yang
arXiv:2604. 07328v3 Announce Type: replace Abstract: How does the choice of training data influence an AI model?
By Sam Gunn
arXiv:2608. 00859v1 Announce Type: new Abstract: Kolmogorov--Arnold Networks (KANs) replace scalar edge weights with learnable univariate functions parameterized by multiple basis coefficients.
By Kazi Ahmed Asif Fuad, Lizhong Chen
arXiv:2606. 26705v1 Announce Type: cross Abstract: Feedforward neural network (NN) expressivity is typically studied by emulating optimal basis-expansion schemes.
By Anastasis Kratsios, Simone Brugiapaglia, Bum Jun Kim, Gregory Cousins, Haitz S\'aez de Oc\'ariz Borde
arXiv:2607. 04800v1 Announce Type: new Abstract: Neural networks are thought to represent concepts as directions in their activation space, and superposition lets them encode more concepts than they have dimensions.
By Francisco Ferreira da Silva, Stefan Heimersheim
arXiv:2607. 13749v1 Announce Type: new Abstract: Neural networks trained on modular arithmetic exhibit grokking, a delayed transition from memorisation to generalisation known to depend on model capacity: too little and the network memorises slowly or not at all, too much and it generalises almost immediately.
By Chon-Fai Kam, Xavier Cadet, Miloud Bessafi, Frederic Cadet
Neural networks trained on modular arithmetic exhibit grokking, a delayed transition from memorisation to generalisation known to depend on model capacity: too little and the network memorises slowly or not at all, too much and it generalises almost immediately. What happens at the extreme of this spectrum, when the architecture's expressible function class collapses to a finite-dimensional algebraic variety?
arXiv:2608.22636v1 Announce Type: cross
Abstract: Q-learning with linear function approximation can be unstable because an arbitrary approximation architecture need not preserve the Bellman contracti...
By Shengbo Wang
arXiv:2602. 06737v2 Announce Type: replace Abstract: We present a generalized framework for the range verification of neural networks featuring non-linear activation functions.
By Noah Schwartz, Chandra Kanth Nagesh, Sriram Sankaranarayanan, Ramneet Kaur, Tuhin Sahai, Susmit Jha