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Pierfrancesco Beneventano

Pierfrancesco Beneventano contributes to research discovery and scholarly infrastructure.

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Artificial Intelligence Machine Learning math.OC

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preprint2026arXiv

Agentic Systems as Boosting Weak Reasoning Models

Can a committee of weak reasoning-model calls reach the performance of much stronger models? We study verifier-backed committee search as inference-time boosting for reasoning language models. The mechanism is not simply that ``more agents help'': samples expose latent correct solutions, while critics and comparators must recover them without access to the hidden verifier. We formalize this view by separating proposal coverage, local identifiability, progress, and diversity. We prove that coverage can be amplified by repeated sampling, but cannot by itself create useful critics or comparators; reliable amplification requires an additional local soundness signal, such as execution, proof checking, type checking, tests, or constraint solving. We give rank-based bounds showing when local selection errors compose into reliable trajectories, and characterize the proposer-side ceiling: oracle best-of-$k$ converges only to the mass of task slices on which the proposal system assigns nonzero useful probability. Empirically, on SWE-bench Verified, a single \texttt{GPT-5.4 nano} proposal solves $67.0\%$ of tasks. Using the same nano model, our critic--comparator orchestration reaches $76.4\%$ with $k=8$ proposals, matching the standalone performance of \texttt{Gemini 3 Pro} and \texttt{Claude Opus 4.5} Thinking and approaching the $79.0\%$ oracle best-of-$8$ upper bound. Thus, many correct patches are already present in weak-model proposal pools; the main challenge is selecting them. The remaining failures are mostly proposal-coverage failures, indicating shared blind spots that stronger selection alone cannot close.

preprint2026arXiv

Distribution-Aware Algorithm Design with LLM Agents

We study learning when the learned object is executable solver code rather than a predictor. In this setting, correctness is not enough: two solvers may both return valid solutions on the deployment distribution while differing substantially in runtime. Given samples from an unknown task distribution, the learner returns code evaluated on fresh instances by both solution quality and execution time. Our central abstraction is a \emph{solver hint}: reusable structure inferred from samples and compiled into specialized solver code. We prove that the empirically fastest sample-consistent solver from a fixed library generalizes in both correctness and runtime, and that statistically identifiable hints can be recovered and compiled from polynomially many samples. Empirically, we instantiate the framework with LLM code agents on $21$ structured combinatorial-optimization target distributions across seven problem classes. The synthesized solvers reach mean normalized quality $0.971$, improve by $+0.224$ over the average heuristic pool and by $+0.098$ over the highest-quality heuristic, and are $336.9\times$, $342.8\times$, and $16.1\times$ faster than the quality-best heuristic, Gurobi, and the selected time-limited exact backend, respectively. On released PACE 2025 Dominating Set private instances, the synthesized solver is valid on all $100$ graphs and runs about two orders of magnitude faster than top competition solvers, with a moderate quality gap. Inspection shows that many gains come from changing the computational scale: replacing ambient exponential search or general-purpose optimization with compiled distribution-specific computation.

preprint2026arXiv

Does Weight Decay Enhance Training Stability?

In modern deep learning, weight decay is often credited with "stabilizing" training dynamics, diverging from its classical role as a static regularization penalty. We investigate a fundamental question: *does weight decay stabilize training dynamics, and if so, through which mechanism?* Indeed, training stability is understood through different but related notions in the literature. We consider how weight decay affects the parameter-space dynamics and loss sharpness by analyzing its effects at the \emph{Edge of Stability} (EoS). We show that weight decay robustly slows *progressive sharpening}. Furthermore, we uncover a striking architecture-dependent phase transition. In CNNs, weight decay dampens the oscillations at the EoS, while in MLPs, increasing weight decay causes a phase transition in which the sharpness stabilizes at a threshold significantly below the theoretical $\frac{2}η$ boundary. We develop a mathematical framework that accurately models these phenomena and identify the global alignment of the parameter vector and the sharpness gradient as the mechanistic driver of the phase transition. Importantly, we show that these phenomena translate into stability in terms of search in function-space (NTK). Last, this shows that curvature thresholds obtained from convex/quadratic heuristics may not be reliable stability diagnostics under regularization.

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