Product Expansion of Random Codes via Analytic Techniques
arXiv:2610.02512v2 Announce Type: replace Abstract: Beginning with the work of Dinur, Lin, and Vidick (FOCS, 2024), tensor codes with constant product expansion…
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arXiv:2610.02512v2 Announce Type: replace Abstract: Beginning with the work of Dinur, Lin, and Vidick (FOCS, 2024), tensor codes with constant product expansion…
arXiv:2608.25716v3 Announce Type: replace Abstract: Quadratic ball discrepancy measures how uniformly a code meets Hamming balls over all centers and radii. Per…
arXiv:2610.39092v2 Announce Type: replace-cross Abstract: Many problems in nonlinear analysis, game theory, economics, and geometry have existence proofs based …
arXiv:2601.21623v3 Announce Type: replace-cross Abstract: Mixed-precision computations are a hallmark of the current stage of AI, driving the progress in large …
arXiv:2508.21189v2 Announce Type: replace-cross Abstract: To achieve the greatest possible speed, practitioners regularly implement randomized algorithms for lo…
arXiv:2610.15393v2 Announce Type: replace Abstract: A model of propagation and accumulation of errors caused by round-off errors during conjugate gradient (CG) …
arXiv:2610.15220v2 Announce Type: replace Abstract: We analyse how errors in independently approximated adjoint waves propagate into the Hilbert Uniqueness Meth…
arXiv:2608.19250v2 Announce Type: replace Abstract: We propose a fully discrete method for linear fourth-order parabolic equations with Dirichlet boundary condi…
arXiv:2607.10652v2 Announce Type: replace Abstract: This paper presents a symplectic Hamiltonian direct discontinuous Galerkin (DDG) method for approximating wa…
arXiv:2609.08219v2 Announce Type: replace-cross Abstract: Neural networks acquire internal representations through learning. In this work, we formulate stochast…
arXiv:2609.06598v2 Announce Type: replace-cross Abstract: The optimal transport (OT) map provides a geometric transformation for aligning probability distributi…
arXiv:2608.25807v2 Announce Type: replace-cross Abstract: Kolmogorov-Arnold Networks (KANs) learn univariate functions on edges, making the choice of edge respo…
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arXiv:2606.08493v4 Announce Type: replace-cross Abstract: Tissue graph counterfactuals ask what a cell would express if its spatial neighborhood were altered, a…
arXiv:2605.08069v2 Announce Type: replace-cross Abstract: We study methods for simultaneous analysis of many noisy and biased estimates, each paired with an eve…
arXiv:2605.07104v3 Announce Type: replace-cross Abstract: Establishing almost sure convergence rates for stochastic approximation and reinforcement learning und…
arXiv:2604.24737v2 Announce Type: replace-cross Abstract: Chain-of-thought (CoT) supervision makes computationally hard learning problems tractable by exposing …
arXiv:2603.24626v3 Announce Type: replace-cross Abstract: Single-cell RNA sequencing (scRNA-seq) enables gene expression profiling at cellular resolution but is…
arXiv:2602.24207v3 Announce Type: replace-cross Abstract: The use of algorithmic predictions in decision-making leads to a feedback loop where the models we dep…
arXiv:2602.20457v2 Announce Type: replace-cross Abstract: We study online alignment of large language models under misspecified preference feedback, where the o…