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Related Articles from SNS
Beyond $\ell_2$-norm and $\ell_\infty$-norm: A Curvature-Inspired $\ell_p$-Norm Scheme for Deep Neural Networks
Announce Type: new Abstract: The existing optimizers for deep neural networks (DNNs) typically rely on either the $\ell_2$ norm or the $\ell_\infty$ norm, resulting in optimizers that do not adapt well to substantial changes in curvature across parameter dimensions. Generally, the training process of DNNs often exhibits strong curvature anisotropy in the early period, whereas in the later period, the training process of DNNs tends to move toward flatter regions with weaker anisotropy....
Removing bottlenecks in the recognition of small $(k,\ell)$-graph classes
arXiv:2510.17665v2 Announce Type: replace Abstract: A graph is a $(k,\ell)$-graph if its vertex set can be partitioned into $k$ independent sets and $\ell$ cliques. This family simultaneously generalizes split, bipartite, and co-bipartite graphs. While the recognition problem is NP-complete whenever $k\geq 3$ or $\ell\geq 3$, the remaining small cases are polynomial-time solvable.
Generalized TV--$\ell_p$ Structured Priors for Bayesian $T_1$ Mapping
arXiv:2606.05381v1 Announce Type: new Abstract: We propose an extended family of structured spatial priors that incorporates the total variation (TV) function with $\ell_p$ norms. The prior is proven to be proper and incorporated into a Bayesian regression framework to enable uncertainty quantification in $T_1$ mapping, with posterior inference performed using the No-U-Turn Sampler (NUTS). This TV--$\ell_p$ construction is proven to constitute a well-defined family of prior distributions,...
Iterative Thresholding Pursuit with Continuation for $\ell_{1-2}$-Regularized Sparse Recovery
Announce Type: new Abstract: Sparse recovery aims to reconstruct sparse signals from underdetermined and possibly noisy linear measurements. Existing $\ell_{1-2}$ iterative thresholding schemes are first-order methods. We propose an iterative thresholding pursuit method with continuation (ITP-C) for $\ell_{1-2}$-regularized sparse recovery.
Improved Distribution Estimation in $\ell_\infty$
arXiv:2605.30509v1 Announce Type: cross Abstract: We present improved bounds for estimating discrete probability distributions under the $\ell_\infty$ norm. These include minimax bounds in expectation and high-probability tail bounds. We resolve some of the open questions posed in Kontorovich and Painsky (JMLR, 2025) -- including a fully empirical version of the tightest risk bound they presented and identifying the form of the worst-case extremal distribution.
The Tell-Tale Norm: $\ell_2$ Magnitude as a Signal for Reasoning Dynamics in Large Language Models
arXiv:2606.06188v1 Announce Type: new Abstract: Recent work has sought to understand Large Language Models (LLMs) reasoning, yet a principled, model-intrinsic signal that captures its layer-wise reasoning dynamics remains underexplored. We bridge this gap by demonstrating that the l2 norm of hidden states serves as an endogenous signal of the model's reasoning intensity. Using Sparse Autoencoders (SAEs) as a diagnostic probe, we observe that LLMs' internal reasoning is marked by a sharp...
Residual-Weighted Randomized Jacobi: Sharpened Bounds via Residual Concentration and Asynchronous Extension
arXiv:2606.01232v1 Announce Type: new Abstract: We study randomized stationary methods for symmetric positive definite linear systems in which component $j$ is selected with probability proportional to $|r_j|^\ell$. This power-weighted family interpolates continuously between uniform randomized Jacobi as $\ell \to 0$ and Gauss--Southwell greedy relaxation as $\ell \to \infty$. For the central case $\ell = 2$, we sharpen the standard one-step convergence analysis using the inverse...
Kikuchi Graphs of Random Hypergraphs are Approximately Johnson
arXiv:2606.08597v1 Announce Type: new Abstract: We prove that level-$\ell$ Kikuchi graphs of random $2r$-uniform hypergraphs spectrally approximate the Kikuchi graph of the complete $2r$-uniform hypergraph at a sampling rate that is sharp up to a logarithmic factor, in the regime $r\leq \ell \leq n/2$. Our proof is based on the matrix Bernstein inequality, but, unlike prior works, we apply it to an appropriate collection of blocks of Johnson eigenspaces. Our analysis relies on a new, simple...
Sensitivity as a Double-Edged Sword: A Trade-off Between Discriminability and Adversarial Robustness
Announce Type: new Abstract: Modern neural networks are highly susceptible to adversarial perturbations. In this work, we identify that part of this vulnerability stems from the sensitivity of the widely used fully connected (FC) classifiers to such perturbations. In contrast, simple $\ell_2$ distance-based classifiers exhibit significantly greater robustness.
Theoretical Analysis of Sparse Optimization with Reparameterization, Weight Decay, and Adaptive Learning Rate
arXiv:2605.25134v3 Announce Type: replace Abstract: Sparse optimization is a fundamental challenge in various practical applications. A popular approach to sparse optimization is $\ell_p$ regularization. However, it may encounter optimization instability due to the unbounded gradients when $0<1$.