RI

#1From Errors to Proofs: Minimal-Core-Guided Repair for Neuro-Symbolic Constraint Solving

2026-08-14 | Independent Researcher |2608.14771

This paper replaces generic solver error messages with minimal unsatisfiable cores (MUCs) to guide LLM self-repair when translating natural language constraint problems into Answer Set Programming. The results are backed by a 77-instance benchmark, showing that MUC feedback reduces fabricated solutions on infeasible problems from 79% to 7% for weaker models, though strong models perform well even with generic chain-of-thought. The key insight is that raw solver errors (e.g., 'unsatisfiable') often cause LLMs to blindly delete valid constraints until a problem becomes solvable, whereas structural proof artifacts localize the conflict and allow the LLM to correctly identify genuine infeasibility. This is highly relevant for symbolic OR modeling and LLM-in-the-loop optimization; the community could adapt this by using Irreducible Infeasible Subsystems (IIS) from MIP solvers as a high-quality, leakage-free feedback signal for LLM evolutionary search or autoformalization pipelines.

#1Competing at Every Price Point with Agentic Evolution over a Menu of LLMs

2026-08-17 |2608.16207

Borthwick introduces a cost-targeted evolutionary meta-agent that writes Python programs utilizing a menu of differently-priced LLMs to optimize the cost-accuracy Pareto frontier. The results are highly rigorous, Pareto-dominating nearly all baselines (including hand-engineered systems) on two AstaBench tasks using only 66 to 100 training examples. The key insight is that exposing a priced menu of LLMs to the evolutionary search and using a graded cost-penalty objective (pricing cost overages in error-equivalents) naturally forces the discovery of cheap-first cascades and selective strong-model escalation.

#2Improving the matrix multiplication exponent with modern optimization and AlphaEvolve

2026-08-17 | Google DeepMind, MIT, Carnegie Mellon University, Columbia University |2608.16884

This paper applies gradient-based optimization and AlphaEvolve to the combination loss analysis problem, improving the theoretical upper bound on the matrix multiplication exponent to ω< 2.371177. The results are rigorously verified using rational arithmetic, proving a genuine state-of-the-art advance over the previous 2.371339 bound. The key insight for LLM evolutionary search is the preparation pipeline: the authors relaxed discrete max-entropy constraints into a differentiable tensor program using the Sinkhorn-Knopp algorithm and Jax, enabling hardware parallelization up to 7 million parameters. They then applied AlphaEvolve using 'evolving constructions' to iteratively refine the optimizer while passing the best solution state between generations. This is highly relevant for our work, as it demonstrates how to successfully scale LLM-driven algorithm discovery for massive, highly constrained combinatorial problems.

#3GoalEvolve: From Handcrafted Algorithm Priors to Goal-Driven Evolution of Physical Design Algorithms

2026-08-17 | Fudan University |2608.16733

GoalEvolve is an LLM-based evolutionary search framework that optimizes physical design algorithms by targeting final full-flow metrics rather than stage-local objectives. The results are backed by strong empirical evidence, demonstrating a 30.67% improvement in total negative slack over default OpenROAD and outperforming standard Codex goal mode under matched evaluation budgets. The key insight is the use of 'effect-debt analysis' combined with an Evolutionary Program Database (EPD), which tracks whether a local algorithmic change causes downstream degradation and stores this as persistent mechanism memory to guide future LLM prompts.