#01Aug 21, 2026
cs.AI
From Regulation to Implementation: A Critical Evaluation of LLM-Assisted Regulatory Compliance in Industry
Adriana Watson, Marco Bücheler, Grant Richards
The European Union (EU) has emerged as a leading regulatory body in the development of sustainability and privacy regulations. While new regulation requirements vary, many include a documentation artifact to ensure compliance. Notably, the Ecodesign for Sustainable Products Regulation (ESPR) introduces Digital Product Passports (DPPs) for life cycle transparency, while the General Data Protection Regulation (GDPR) mandates Data Protection Impact Assessments (DPIAs) to mitigate privacy risks. Creating these compliance artifacts, however, is challenging. Industrial data, which often exists in heterogeneous formats and is scattered across company and supplier systems, is required for DPPs and can be difficult to extract into compliant DPP formatting. Furthermore, DPIA documents require interdisciplinary expertise and follow no standardized format, making development difficult for novel systems. To address the particular complexity of compliance artifact creation for both regulations, researchers have proposed the use of LLMs in the generation process; however, the impact of the aforementioned problems on the output of these systems is largely unaddressed. This work investigates the existing research gap by exploring how data extraction instructions and regulatory vagueness impact the quality and consistency of LLM-produced compliance artifacts. The resulting artifacts are evaluated by benchmarking different models against manually created ground-truth schemas. The results reveal that less strict guidelines, such as DPIA formatting, require higher context prompts to maintain consistency and completeness. Stricter guidelines, such as formatting for Digital Battery Passports (DBP), result in consistent results regardless of prompt context, but may lead to more hallucinations in the output
#02Aug 21, 2026
cs.CL
Memory Augmentation Unlocks Efficient Chain-of-Thought Reasoning
Simeng Zhang, Yilong Chen, Wenyuan Zhang and 4 more
Large language models often rely on Chain-of-Thought (CoT) reasoning to solve complex tasks, but verbose reasoning traces introduce substantial inference overhead. CoT compression shortens generation, yet aggressive compression may disrupt logical coherence and degrade performance. We formalize this trade-off as the \textit{Context-Generation Substitution Law}, where explicit reasoning context substitutes for part of decode-time generation. Based on this principle, we propose \textit{Memory-Augmented Compression}, a training-free framework that constructs reusable reasoning memories from historical traces and retrieves them as prefill-side scaffolds. Rather than using raw demonstrations, these memories summarize reusable reasoning patterns, key constraints, and critical operations to compensate for information lost during compression. Experiments show that Memory consistently improves prompt-based Chain-of-Draft (CoD) compression across mathematical reasoning, complex reasoning, and science question answering tasks, yielding accuracy gains of 21.4, 28.0, 29.5, and 6.61 points over CoD on GSM8K, MATH, BBH, and MMLU-Sci, while achieving a 1.14--1.49$\times$ latency speedup over standard CoT. Memory is also compatible with token-level, reasoning-trace-level, and inference-state compression mechanisms. Further analyzes show that the gains come from relevant reasoning memories rather than simply increasing context length.
#03Aug 21, 2026
math.NA
Basin-Preserving Discretizations of Modern Hopfield Retrieval Dynamics: Energy Cells, Dissipation, and the Attention Limit
Francisco R. Villatoro
The retrieval dynamics of a modern Hopfield network is the gradient flow of a log-sum-exp energy, while the attention update is its exact difference-of-convex minimization step. We study which time discretizations preserve not only energy decay and equilibria but also basins of attraction. We introduce energy cells, connected components of sublevel sets containing one attractor and no other critical point. Our main theorem shows that every finite energy cell below the escape energy is contained simultaneously in the basin of the continuous flow, every relaxed attention map $Ψ_θ=(1-θ)\,\mathrm{id}+θ\,\mathrm{attention}$ for $0<θ<2$, and implicit Euler throughout its uniqueness regime. A parameter-uniform unit-curvature majorant yields unconditional dissipation and a monotone interpolation of each discrete step. We also derive explicit local contraction bounds near well-separated patterns, with a certified optimal slight overrelaxation; characterize proximal tunneling and overshoot beyond the preservation regimes; compare first-order error constants; establish an order barrier for scalar reparametrizations of the relaxed family; construct a second-order scalar-auxiliary-variable scheme; and extend cell preservation to damped difference-of-convex iterations in Bregman geometry, including a certified overrelaxed window under bounded asymmetry. Nine numerical campaigns test the bounds and failure mechanisms. In two-dimensional basin experiments, all observed disagreements between continuous and discrete retrieval occur above the attractor-specific numerically inferred escape level.
#04Aug 21, 2026
math.OC
Primal Acceleration of Newton's Method
Nikita Doikov
We develop a new direct accelerated Newton method for minimizing convex functions with Lipschitz continuous Hessian. The algorithm uses only primal variables and performs just one linear solve per iteration. With a simple predetermined choice of parameters, it achieves the global convergence rate of $O(1/k^3)$ in terms of the functional residual. To the best of our knowledge, this is the first second-order method for this problem class attaining this rate while relying solely on one linear system solve per iteration (without solving auxiliary nonlinear regularized subproblems, such as cubic regularization, performing nonlinear parameter searches, or using dual extragradient corrections). Our method can be implemented in a Hessian-free way, using an inexact linear system solver, while preserving the fast global rate. We further extend our construction to arbitrary geometry through Bregman divergence, and to composite optimization problems.
#05Aug 21, 2026
cs.SE
AI with Authority, from Application to Silicon
Jason Hickey
For sixty years, machine verification has been a major cost overhead, affordable only for exceptional artifacts. Here we report that generative AI inverts this relationship: at AI speed, machine verification is not only economical but essential to productivity --- it is the incorruptible referee that lets one person safely direct autonomous machine work at scale. In five weeks, one researcher on consumer AI subscriptions directed a small fleet of AI agents from application code, through a verified compiler and executive, to a RISC-V processor taped out on a community silicon shuttle; no proof passed through human review, and no RTL was written by a human. The working discipline --- the Salt method --- rests on a proof kernel no hallucinated proof can pass: mathematical claims travel between agents as kernel-checked artifacts, and human attention is reserved for statements, designs, and rulings. Verification is stated link by link, from the Lean 4 kernel to SAT-checked equivalence at the silicon boundary. We publish the complete accounting: theorem provenance, a pre-registered token meter, floor-bounded human time, and an error ledger whose catch numbering runs to #256 --- a monotone counter over the mathematics campaign's append-only flags ledger, maintained 2026-07-07 to 2026-07-20 (one number, #79, was never assigned; later catches are recorded un-numbered) --- against zero incorrect proofs reaching the record.