arXiv:2609.08873v1 Announce Type: cross Abstract: Sparsity is a powerful structural resource in optimization and statistics. We develop frameworks for leveraging sparsity in sampling problems over th...
arXiv:2607. 16568v1 Announce Type: new Abstract: Function-preserving network growth techniques such as Net2Net and progressive stacking expand a model's capacity without destroying its learned function, but existing formulations either tolerate numerical perturbations or require a full rebuild of the training program.
arXiv:2607. 18323v1 Announce Type: cross Abstract: Exhaustive site-by-site interventions on a neural network's computational graph -- activation-patching sweeps, circuit-discovery searches, systematic ablation studies -- mutate the graph at every candidate site, and their cost is dominated by recomputation after each mutation.
Deep equilibrium models promise input-adaptive implicit computation: harder problems should demand more solver iterations, and the solved equilibrium should encode the result of genuine iterative inference. We report a cautionary study of a port-Hamiltonian DEQ with a learned initialization on two reasoning tasks -- ProofWriter entailment over frozen DeBERTa embeddings and a BFS-verified graph-reachability benchmark -- in which the implicit computation is a silent no-op.
arXiv:2606. 26399v1 Announce Type: new Abstract: We study certain extremal problems in combinatorial geometry that ask about configurations of points in an $n \times n$ grid that satisfy strict, global geometric constraints.
arXiv:2607. 11116v1 Announce Type: cross Abstract: Deep equilibrium models promise input-adaptive implicit computation: harder problems should demand more solver iterations, and the solved equilibrium should encode the result of genuine iterative inference.
The paper investigates the use of PDE‑SINDy to discover governing equations for phase‑ordering dynamics, benchmarking against the Allen–Cahn equation and applying it to the Ising model with Glauber spin‑flip dynamics. It systematically studies how data availability, library size, and noise affect term identification and coefficient recovery, finding that stability‑selection with library bagging improves robustness. The recovered coarse‑grained equations successfully reproduce the characteristic phase‑separation and coarsening behavior of the microscopic Ising system.
arXiv:2609.36692v1 Announce Type: cross Abstract: Matrix optimizers have emerged as a promising direction, with Muon standing out as a prominent design. Revisiting Muon through its full-Gram represen...
arXiv:2609.38095v1 Announce Type: new Abstract: Backpropagation (BP) dominates deep learning but imposes a massive memory tax. For example, training OPT-30B with Adam requires $\approx$ 600GB of GPU...
We study certain extremal problems in combinatorial geometry that ask about configurations of points in an $n \times n$ grid that satisfy strict, global geometric constraints. Classical exact solvers suffer from combinatorial explosion for these types of problems, and standard reinforcement learning and transformer-based models struggle with the sparse reward "validity cliff" and quadratic token-consumption limits.
arXiv:2602. 00161v2 Announce Type: replace-cross Abstract: In this paper, we formulate the compression of large language models (LLMs) by optimally deleting transformer blocks (``block removal'') as a constrained binary optimization (CBO) problem that can be mapped to a physical system (Ising glass), whose energies are a strong proxy for downstream model performance.
arXiv:2608. 06762v1 Announce Type: new Abstract: Bisimulation metrics quantify behavioral similarity in Markov decision processes, but their Wasserstein fixed-point operator updates every state pair and incurs quadratic pairwise work.