Large Language Model-Guided Optimization

Cold-chain storage limits access to insulin for hundreds of millions of people; a thermally protective patch polymer could help, but the design space is too large for exhaustive experiment. Starting from that problem, we narrow to an agentic workflow: a large language model (LLM) calls physics-based tools through the Model Context Protocol (MCP), searching the discrete PSMILES space under a budget of OpenMM Packmol-matrix evaluations. The LLM acts as an implicit acquisition function conditioned on a persistent "discovery world": hypotheses, literature claims, and simulation outcomes updated each iteration. Under matched oracle budgets, the best autonomous campaign reaches an insulin-polymer interaction energy of -2263 kJ/mol, outperforming reinforcement-learning baselines by 68% and Bayesian optimization by 19%. Three independent campaigns converge on one structural motif (dense hydrogen-bond donors and acceptors per repeat unit) while physics checks reject infeasible packings and name-structure mismatches before they steer the next step. The science stage is CPU-bound and runs on commodity hardware. More broadly, the same architecture and workflow designed here applies to other protein-stabilization tasks whenever a tractable screening oracle is available.

We explore the effectiveness of an LLM-guided query refinement paradigm for extending the usability of embedding models to challenging zero-shot search and classification tasks. Our approach refines the embedding representation of a user query using feedback from a generative LLM on a small set of documents, enabling embeddings to adapt in real time to the target task. We conduct extensive experiments with state-of-the-art text embedding models across a diverse set of challenging search and classification benchmarks. Empirical results indicate that LLM-guided query refinement yields consistent gains across all models and datasets, with relative improvements of up to +25% in literature search, intent detection, key-point matching, and nuanced query-instruction following. The refined queries improve ranking quality and induce clearer binary separation across the corpus, enabling the embedding space to better reflect the nuanced, task-specific constraints of each ad-hoc user query. Importantly, this expands the range of practical settings in which embedding models can be effectively deployed, making them a compelling alternative when costly LLM pipelines are not viable at corpus-scale. We release our experimental code for reproducibility, at https://github.com/IBM/task-aware-embedding-refinement.

Large Language Models (LLMs) struggle to solve complex combinatorial problems through direct reasoning, so recent neuro-symbolic systems increasingly use them to synthesize executable solvers. A central design question is how the LLM should represent the solver, and whether it should also attempt to optimize search. We introduce CP-SynC-XL, a benchmark of 100 combinatorial problems (4,577 instances), and evaluate three solver-construction paradigms: native algorithmic search (Python), constraint modeling through a Python solver API (Python + OR-Tools), and declarative constraint modeling (MiniZinc + OR-Tools). We find a consistent representational divergence: Python + OR-Tools attains the highest correctness across LLMs, while MiniZinc + OR-Tools has lower absolute coverage despite using the same OR-Tools back-end. Native Python is the most likely to return a schema-valid solution that fails verification, whereas solver-backed paths preserve higher conditional fidelity. On the heuristic axis, prompting for search optimization yields only small median speed-ups (1.03-1.12x) and a strongly bimodal effect: many instances slow down, and correctness drops sharply on a long tail of problems. A paired code-level audit traces these regressions to a recurring heuristic trap. Under an efficiency-oriented prompt, the LLM may replace complete search with local approximations (Python), inject unverified bounds (Python + OR-Tools), or add redundant declarative machinery that overwhelms or over-constrains the model (MiniZinc + OR-Tools). These findings support a conservative design principle for LLM-generated combinatorial solvers: use the LLM primarily to formalize variables, constraints, and objectives for verified solvers, and separately check any LLM-authored search optimization before use.

Generating feasible Pareto fronts for constrained bi-objective continuous optimization is central to multi-criteria decision-making. Existing methods usually rely on iterative scalarization, evolutionary search, or problem-specific solvers, requiring repeated optimization for each instance. We introduce DIPS, an end-to-end framework that fine-tunes large language models as amortized Pareto-front generators for constrained bi-objective convex optimization. Given a textual problem description, DIPS directly outputs an ordered set of feasible continuous decision vectors approximating the Pareto front. To make continuous optimization compatible with autoregressive language modeling, DIPS combines a compact discretization scheme, Numerically Grounded Token Initialization for new numerical tokens, and Three-Phase Curriculum Optimization, which progressively aligns structural validity, feasibility, and Pareto-front quality. Across five families of constrained bi-objective convex problems, a fine-tuned 7B-parameter model achieves normalized hypervolume ratios of 95.29% to 98.18% relative to reference fronts. With vLLM-accelerated inference, DIPS solves one instance in as little as 0.16 seconds and outperforms general-purpose and reasoning LLM baselines under the evaluated setting. These results suggest that LLMs can serve as effective amortized generators for continuous Pareto-front approximation.

Robust optimization (RO) provides a principled framework for decision-making under uncertainty, but its practical use is often limited by the need to manually reformulate uncertain optimization models into tractable deterministic counterparts. Recent large language models (LLMs) have been shown promising for automating optimization formulation, yet RO reformulation remains challenging because it requires precise multi-step reasoning and mathematically consistent transformations. To facilitate systematic evaluation of LLM-based reformulation, for which no dedicated benchmark currently exists, we develop AutoRO-Bench, a benchmark featuring an automated data generation pipeline for the core RO reformulation task and a curated dataset for the RO application task. To address the reformulation challenge, we propose Automated Reformulation with Experience Memory (AutoREM), a tuning-free memory-augmented framework that autonomously builds a structured textual experience memory by reflecting on past failed trajectories through a tailored offline adaptation procedure. AutoREM requires neither domain-specific expert knowledge nor parameter updates, and the resulting memory readily transfers across different base LLMs. Experimental results show that AutoREM consistently improves the accuracy and efficiency of RO reformulation across in-distribution datasets, out-of-distribution datasets, and diverse base LLMs.

Effectively configuring scalable large language model (LLM) experiments, spanning architecture design, hyperparameter tuning, and beyond, is crucial for advancing LLM research, as poor configuration choices can waste substantial computational resources and prevent models from realizing their full potential. Prior automated methods are designed for low-cost settings where repeated trial and error is feasible, but scalable LLM experiments are too expensive for such extensive iteration. To our knowledge, no work has addressed the automation of high-cost LLM experiment configurations, leaving this problem labor-intensive and dependent on expert intuition. Motivated by this gap, we propose AutoLLMResearch, an agentic framework that mimics how human researchers learn generalizable principles from low-fidelity experiments and extrapolate to efficiently identify promising configurations in expensive LLM settings. The core challenge is how to enable an agent to learn, through interaction with a multi-fidelity experimental environment that captures the structure of the LLM configuration landscape. To achieve this, we propose a systematic framework with two key components: 1) LLMConfig-Gym, a multi-fidelity environment encompassing four critical LLM experiment tasks, supported by over one million GPU hours of verifiable experiment outcomes; 2) A structured training pipeline that formulates configuration research as a long-horizon Markov Decision Process and accordingly incentivizes cross-fidelity extrapolation reasoning. Extensive evaluation against diverse strong baselines on held-out experiments demonstrates the effectiveness, generalization, and interpretability of our framework, supporting its potential as a practical and general solution for scalable real-world LLM experiment automation.

Large language models possess strong chemical reasoning capabilities, making them effective molecular editors. However, property-relevant information is implicitly entangled across their dense hidden states, providing no explicit handle for property control: a substantial fraction of edits fail to improve or even degrade target properties. To address these issues, we propose SLIM (Sparse Latent Interpretable Molecular editing), a plug-and-play framework that decomposes the editor's hidden states into sparse, property-aligned features via a Sparse Autoencoder with learnable importance gates. Steering in this sparse feature space precisely activates property-relevant dimensions, improving editing success rate without modifying model parameters. The same sparse basis further supports interpretable analysis of editing behavior. Experiments on the MolEditRL benchmark across four model architectures and eight molecular properties show consistent gains over baselines, with improvements of up to 42.4 points.

Large language models (LLMs) have emerged as powerful tools for automatic algorithm design (AAD). However, existing pipelines remain inefficient. They operate at the granularity of full algorithms, redundantly rewriting recurring substructures and discarding low-fitness candidates that may contain valuable algorithmic features. We formalize budget-efficient automatic algorithm design, wherein the search policy maximizes realized fitness subject to limited computational cost. We propose a directed acyclic graph representation of algorithms and build a search framework that fully exploits the LLM's output. Instead of querying the LLM for full algorithms, we use it to obtain corrections: compact operators that add, replace, or remove code blocks. Each correction augments the graph, yielding new algorithms that compose with prior corrections. This graph structure decomposes algorithms into sets of corrections, enabling correction-level credit assignment that informs subsequent queries. We complement this framework with theoretical insights into the ideal balance between search depth and breadth at different budget levels. We validate our method empirically on three combinatorial optimization problems, demonstrating consistent superiority of our graph-based search over full-algorithm search at equal token budget. Finally, our experiments suggest that rich contexts help only when the LLM's prior knowledge is shallow, and can hinder performance otherwise.

Efficient branching policies are essential for accelerating Mixed Integer Linear Programming (MILP) solvers. Their design has long relied on hand-crafted heuristics, and now machine learning has emerged as a promising paradigm to automate this process. However, existing learning-based methods are often hindered by their dependence on expensive expert demonstrations and the gap between training objectives and the solver's end-to-end performance. In this work, we propose LLM4Branch, a novel framework that leverages Large Language Models (LLMs) to automate the discovery of efficient branching policies. Specifically, the discovered policy is an executable program with a program skeleton generated by the LLM and a parameter vector, which is optimized via a zeroth-order method over a few instances with their end-to-end performance feedback. Extensive experiments on standard MILP benchmarks demonstrate that LLM4Branch establishes a new state-of-the-art among CPU-based methods and achieves performance competitive with advanced GPU-based models. Codes are available at https://github.com/hzn18/LLM4Branch.

Molecular optimization seeks to improve a molecule through small structural edits while preserving similarity to the starting compound. Recent language-model approaches typically treat this task as prompt-conditioned sequence generation. However, relying on natural language introduces an inherent data-scaling bottleneck, often leads to chemical hallucinations, and ignores the strong context dependence of fragment effects. We present FORGE, a two-stage framework that reformulates molecular optimization as context-aware local editing. By utilizing automatically mined, verified low-to-high edit pairs instead of expensive human text annotations, Stage 1 ranks candidate fragments by their property contribution under the full molecular context to inject chemical prior, and Stage 2 generates explicit fragment replacements. Built on a compact 0.6B language model, FORGE further adapts to unseen black-box objectives through in-context demonstrations. Across Prompt-MolOpt, PMO-1k and ChemCoTBench, FORGE consistently outperforms prior methods, including substantially larger language models and graph methods. These results highlight the value of explicit fragment-level supervision as a more easily obtainable, scalable, and hallucination-less alternative to natural language training.

Large Language Models exhibit mode collapse, producing homogeneous outputs that fail to explore valid solution spaces. We present QD-LLM, a framework for parameter-efficient neuroevolution that evolves prompt embeddings, compact neural interfaces (~32K parameters) that steer generation in frozen LLMs (70B+ parameters), within a Quality-Diversity (QD) optimization framework. Our contributions: (1) evolved prompt embeddings via gradient-free optimization enabling behavioral steering without model fine-tuning; (2) hybrid behavior characterization combining semantic and explicit features with formal coverage bounds (Theorem 1) under validated near-independence (NMI $= 0.08 \pm 0.02$); (3) co-evolutionary variation operators including targeted behavioral mutation via finite-difference gradient estimation. On HumanEval (164 problems), MBPP, and creative writing benchmarks, QD-LLM achieves 46.4% higher coverage and 41.4% higher QD-Score than QDAIF ($p<0.001$, 30 runs, Vargha-Delaney $A=0.94$). We demonstrate downstream utility: diverse archives improve test generation (34% more edge cases) and fine-tuning data quality (8.3% accuracy gain). We validate across open-source LLMs (Llama-3-70B, Mistral-Large) with full embedding access, establishing prompt embedding evolution as an effective paradigm bridging neuroevolution and modern LLMs.

LLM-guided evolutionary methods such as AlphaEvolve have proven effective in domains like math, systems research, and algorithmic discovery, but their reliance on frontier models makes each run expensive. We argue this is largely an artifact of how existing frameworks allocate search: archives that fail to preserve solution diversity force compensation through stronger mutation models; blind model use spends frontier dollars on local edits a smaller model could handle; and full-set evaluation wastes rollouts on redundant examples. We introduce LEVI, a harness-first evolutionary framework built on the bet that stronger search architectures can substitute for or even outperform larger LLMs in evolutionary search. LEVI improves on three core components of evolutionary search: a solution database that establishes diversity from the beginning, and then maintains it throughout the run; a smarter mutation router that plays into the strengths of large and small LLMs; and a rank-preserving proxy benchmark for rollout-heavy settings. Across systems-research benchmarks LEVI attains the highest score on a budget 3.3-6.7x smaller than the published frontier-model runs of existing frameworks like ShinkaEvolve, GEPA, and AdaEvolve; on one problem, LEVI matches the existing best at a 35x lower cost. On prompt optimization, LEVI matches or exceeds GEPA at less than half of its rollout budget on four different benchmarks. LEVI is available as an open-source framework at https://github.com/ttanv/levi.

We present Metal-Sci, a 10-task benchmark of scientific Apple Silicon Metal compute kernels spanning six optimization regimes (stencils, all-pairs in $n$-body problems, multi-field Boltzmann, neighbor-list molecular dynamics, multi-kernel PDE, FFT). Each task ships a CPU reference, a roofline-anchored fitness function, and a held-out generalization size. We pair the benchmark with a lightweight harness for automatic kernel search that runtime-compiles each candidate, scores it against the roofline across multiple sizes, and feeds structured compile and per-size correctness diagnostics back to a frozen LLM driving a $(1{+}1)$ evolutionary loop. We report matched single-model sweeps of Claude Opus 4.7, Gemini 3.1 Pro, and GPT 5.5 on M1 Pro: in-distribution self-speedups span $1.00\times$ to $10.7\times$. Beyond raw speedup, our central methodological claim is structural: the held-out gate scoring function $Φ_\mathcal{T}$ (evaluated once at end-of-run on a configuration the agent never sees during search) functions as a cheap mechanical oversight primitive on this automatic search loop, catching e.g. an Opus template <uint D> HMC win that returns wrong samples at unseen dimensions, and a GPT FFT3D best that wins in-distribution at $2.95\times$ speedup but collapses to $0.23\times$ on a $256^3$ held-out cube, a silent regression that the in-distribution score alone cannot see. Code at https://github.com/vicgalle/metal-sci-kernels

We present ARES-LSHADE, a memetic differential-evolution variant submitted to the GECCO 2026 competition on LLM-designed evolutionary algorithms for the Generalized Numerical Benchmark Generator (GNBG). The algorithm builds on the LLM-LSHADE 2025 winner, contributing two new components: (a) a scout-augmented mutation operator with adaptive CMA-ES integration, produced by an autonomous research loop across approximately thirty LLM-driven design experiments, and (b) a multi-start L-BFGS-B polish phase that respects strict blackbox treatment of the benchmark. On the official 31-run-per-function evaluation with the competition-specified function-evaluation budgets, ARES-LSHADE obtains 510 of 744 wins (per-function gap below 1e-8), reaching machine precision on 18 of 24 functions. The remaining six functions exhibit characteristic plateau signatures consistent with GNBG's compositional structure, and were independently identified by the autoresearch loop as the hardest of the suite. Beyond the result itself, this report documents two methodological observations: (i) an LLM-driven research loop with operator-only edit surface and fitness-only observation space converges to a characteristic plateau on this benchmark; (ii) when we initially widened the observation space to include the benchmark's compositional metadata, the resulting algorithm trivially solved all 24 functions but violated the competition's blackbox rule, which we identified before submission. We discuss this tension between LLM capability and benchmark integrity as a design consideration for future LLM-driven optimization-algorithm research. Code and reproducibility artifacts are available at https://github.com/anaeem1/ARES-LSHADE.

Large Language Models (LLMs) have achieved remarkable success on reasoning benchmarks through Reinforcement Learning with Verifiable Rewards (RLVR), excelling at tasks such as math, coding, logic, and puzzles. However, existing benchmarks evaluate only correctness, while overlooking optimality, namely the ability to find the best solutions under constraints. We propose OPT-BENCH, the first comprehensive framework for training and evaluating LLMs on NP-hard optimization problems through quality-aware RLVR. OPT-BENCH provides three key components: a scalable training infrastructure with instance generators, quality verifiers, and optimal baselines across 10 tasks; a rigorous benchmark with 1,000 instances evaluating both feasibility, measured by Success Rate, and quality, measured by Quality Ratio; and quality-aware rewards that enable continuous improvement beyond binary correctness. Training on Qwen2.5-7B-Instruct-1M with 15K examples achieves 93.1% SR and 46.6% QR, significantly outperforming GPT-4o, which achieves 29.6% SR and 14.6% QR. Beyond optimization, training on OPT-BENCH transfers to diverse tasks, including mathematics (+2.2%), logic (+1.2%), knowledge (+4.1%), and instruction following (+6.1%). Our analysis reveals that quality-aware rewards improve solutions by 28.8% over binary rewards, and that task diversity drives generalization more than data quantity, offering insights into RLVR scaling for complex reasoning.

Large Language Models (LLMs) have demonstrated remarkable capabilities in reasoning and tool use. However, the fundamental cognitive faculties essential for problem solving, including perception, reasoning, and memory, remain the stable core of intelligence. Unlike memorizing specific patterns, humans succeed in novel environments by applying these intrinsic faculties to adapt and optimize. Yet, whether LLMs possess this essential capacity, namely the ability to continuously refine solutions in response to dynamic environmental feedback, remains underexplored. To address this challenge, we introduce OPT-BENCH, a benchmark for evaluating self-improvement capabilities in large-scale search spaces. By combining 20 machine learning tasks with 10 classic NP-hard problems, OPT-BENCH provides a rigorous setting to assess whether agents can adapt through intrinsic self-reflection rather than rote tool application. We further propose OPT-Agent, a framework that emulates human-like cognitive adaptation. It operates through a general perception, memory, and reasoning loop, iteratively refining solutions based on environmental feedback. Through extensive experiments on 19 LLMs from 7 model families, including reasoning models, general models, and open-source models ranging from 3B to 235B parameters, we demonstrate that stronger models are more effective at leveraging feedback signals for self-improvement. However, this upper-bound adaptability remains fundamentally constrained by the models' base capacity, and even the most advanced LLMs still fall short of human expert performance.

Large language models show promise for automated CUDA programming, however even the strongest coding models (e.g., Claude-Opus-4.6) may still fall short of expert-level, architecture-aware optimization. We introduce CUDAHercules, a benchmark that evaluates generated CUDA against end-to-end human-expert SOTA systems. It spans single kernels, module-level operators, full applications, and unsolved challenge tasks across Ampere, Hopper, and Blackwell GPUs, with end-to-end tasks gated by domain-specific semantic validators. Evaluating models such as Claude-Opus-4.6 and GPT-5.4 shows a large gap between runnable CUDA and expert CUDA engineering: models often compile and pass tests, but rarely recover the optimization strategies needed to match expert performance. Application semantics further reduce success, and iterative or tool-augmented feedback can improve correctness while drifting toward slow fallback implementations. These results show that automated CUDA programming remains far from fully solved and requires stronger hardware reasoning, better tool use, and training objectives that connect code understanding to hardware architecture-grounded intelligence.

Test-time scaling (TTS) has become an effective approach for improving large language model performance by allocating additional computation during inference. However, existing TTS strategies are largely hand-crafted: researchers manually design reasoning patterns and tune heuristics by intuition, leaving much of the computation-allocation space unexplored. We propose an environment-driven framework, AutoTTS, that changes what researchers design: from individual TTS heuristics to environments where TTS strategies can be discovered automatically. The key to AutoTTS lies in environment construction: the discovery environment must make the control space tractable and provide cheap, frequent feedback for TTS search. As a concrete instantiation, we formulate width--depth TTS as controller synthesis over pre-collected reasoning trajectories and probe signals, where controllers decide when to branch, continue, probe, prune, or stop and can be evaluated cheaply without repeated LLM calls. We further introduce beta parameterization to make the search tractable and fine-grained execution trace feedback to improve discovery efficiency by helping the agent diagnose why a TTS program fails. Experiments on mathematical reasoning benchmarks show that the discovered strategies improve the overall accuracy--cost tradeoff over strong manually designed baselines. The discovered strategies generalize to held-out benchmarks and model scales, while the entire discovery costs only $39.9 and 160 minutes. Our data, and code will be open-source at https://github.com/zhengkid/AutoTTS.

We present Agentic Decentralized Knowledge Optimization (ADKO), a framework for collaborative black-box optimization across autonomous agents that achieves sample efficiency, privacy preservation, heterogeneous-objective handling, and communication efficiency. Each agent maintains a private Gaussian Process (GP) surrogate trained on local data and communicates only through knowledge tokens-compact, lossy summaries containing directional signals, advantage scores, and optional language-model (LM) insights-without sharing raw data or model parameters. ADKO unifies GP-Upper Confidence Bound (GP-UCB), parallel Bayesian optimization, decentralized learning, and LM-guided discovery. We provide the first formal analysis of dual information loss: token compression, quantified via mutual-information-based fidelity, and LM approximation error, decomposed into bias and stochastic noise. Our main result shows cumulative regret decomposes into GP error, LM bias, LM noise, and compression loss, with necessary and sufficient conditions for sublinear regret. We also propose fidelity-aware token pruning to preserve high-information tokens under memory budget. Experiments on neural architecture search and scientific discovery validate the theory and show consistent improvements over strong baselines.

Balancing exploration and exploitation is a core challenge in sequential decision-making and black-box optimization. We introduce POETS ($\textbf{Po}$licy $\textbf{E}$nsembles for $\textbf{T}$hompson $\textbf{S}$ampling), a novel framework that bridges uncertainty quantification and policy optimization. Our approach is grounded in the insight that policies trained with Kullback-Leibler (KL) regularization implicitly encode an underlying reward function. Building on this, POETS bypasses the complex, nested process of training an uncertainty-aware reward model and separately fitting a policy to this model. Instead, we directly train a policy ensemble to capture epistemic uncertainty by matching implicitly encoded reward functions to online, bootstrapped data. To overcome the prohibitive compute and memory constraints of ensembling Large Language Models (LLMs), POETS utilizes an efficient architecture: the ensemble shares a pre-trained backbone while maintaining diversity through independent Low-Rank Adaptation (LoRA) branches. Theoretically, we prove that POETS implicitly conducts KL-regularized Thompson sampling and thus inherits strong cumulative regret bounds of ${\mathcal O}(\sqrt{T γ_T})$. Empirically, we demonstrate that POETS achieves state-of-the-art sample efficiency across diverse scientific discovery domains, including protein search and quantum circuit design. Furthermore, it improves the optimization trajectories of reinforcement learning, proving particularly robust in off-policy settings with experience replay or in small dataset regimes.

Large Language Models have recently emerged as a promising paradigm for automated heuristic design for NP-hard combinatorial optimization problems. Despite this progress, existing LLM-based methods typically rely on monolithic workflows constrained by rigid templates, thereby restricting memory-guided exploration and triggering premature convergence to local optima. To design an autonomous and collaborative architecture, we introduce HMACE, a Heterogeneous Multi-Agent Collaborative Evolution framework that reconceptualizes heuristic search as an organizational design problem. HMACE decomposes each evolutionary generation into an autonomous, role-specialized loop with four coordinated agents: a Proposer for strategy exploration, a Generator for executable heuristic synthesis, an Evaluator for empirical assessment, and a Reflector for archive-backed memory update. By coupling behavior-aware retrieval, lightweight candidate filtering, and fitness-grounded archive updates, HMACE guides the search toward diverse and promising heuristic behaviors while avoiding redundant evaluations. Extensive evaluations on representative COPs, including TSP, Online BPP, MKP, and PFSP, show that HMACE achieves a favorable quality-efficiency trade-off compared to state-of-the-art single-agent and multi-agent baselines. In the matched LLM-driven reference comparison, HMACE achieves the lowest average gaps on TSP and Online BPP (0.464% and 0.223%, respectively), while requiring only 0.13M and 0.42M tokens for the two tasks, substantially fewer than the compared baselines.

Generating high-performance GPU kernels remains challenging due to the need for both correctness and hardware-aware optimization. While large language models (LLMs) show promise in code generation, they often fail to produce kernels that are both correct and efficient. We propose Kernel Foundry, a diagnosis-driven evolutionary framework for automatic GPU kernel optimization. Our method combines expert-guided, retrieval-augmented initialization with a multi-island evolutionary search, where candidate kernels are iteratively refined using structured diagnostic feedback. A centralized experience library accumulates reusable optimization knowledge to guide subsequent evolution, while explicit mechanisms prevent cheating behaviors that bypass kernel-level computation. Experiments on KernelBench show that our method consistently improves both correctness and performance over strong baselines, achieving up to 100% correctness on Level~2.

Large language models have become drivers of evolutionary search, but most systems rely on a fixed, prompt-elicited policy to sample next candidates. This limits adaptation in practical engineering and research tasks, where evaluations are expensive, and progress depends on learning task-specific search dynamics. We introduce PACEvolve++, an advisor-model reinforcement learning framework for test-time policy adaptation in evolutionary search agents. PACEvolve++ decouples strategic search decisions from implementation: a trainable advisor generates, assesses, and selects hypotheses, while a stronger frontier model translates selected hypotheses into executable candidates. To train the advisor under non-stationary feedback, we propose a phase-adaptive approach that adapts its optimization strategy to different phases of the evolutionary process. Early in evolution, it uses group-relative feedback to learn broad search preferences; later, as reward gaps compress, it emphasizes best-of-$k$ frontier contribution to support stable refinement. Across expert-parallel load balancing, sequential recommendation, and protein fitness extrapolation, PACEvolve++ outperforms the state-of-the-art evolutionary search framework with frontier models, achieving faster convergence and stabilizing test-time training during evolutionary search.

We introduce a causal aware foundation-model framework for real time optimal decision making in discrete choice environments. We propose a constrained triple-head price optimization (C3PO) network to solve a bilevel decision problem in which a service provider selects an optimal assortment while heterogeneous users make personalized acceptance or rejection choices optimizing their own personalized preferences. C3PO integrates imitation learning of prices, multi-task learning of revenue responses, and in context learning of price elasticity to generate pricing recommendations while adhering to business constraints. During inference, frontier model prompting retrieves an enhanced elasticity prior for new products from behavioral economics literature, improving pricing effectiveness. We demonstrate strong in context learning performance using simulated, synthetic, and real-world datasets. C3PO is trained on simulated data generated from multiple classical discrete choice models in economics. The model is trained on data comprising simulated customer segments and counterfactual action and outcome pairs and evaluated on randomly generated choice environments with no access to the underlying preference structure. The trained model consistently improves the pricing KPIs, with gains increasing as customer price sensitivity increases. We also deploy the tuned foundation model for optimal pricing in real-world applications such as healthcare, tender pricing, airline ancillary pricing, and other domains, achieving substantial gains across multiple products, markets, and divisions.

This methods article presents a reproducible calibration workflow for prompt-based large language models (LLMs) in structured evidence-synthesis tasks. The method separates the rules that define the scientific task from the mutable prompt harness that frames and applies them. It optimises that harness against labelled or reference examples and an explicit task metric, then preserves the calibrated workflow as an inspectable artefact with its specification, metric, settings, and evaluation traces. The example code instantiates the protocol with DSPy and GEPA tools, but the underlying logic can transfer to other prompt-optimisation frameworks that support structured task definitions, metric-guided search, and artefact reuse. Title and abstract screening is the worked validation case because it provides labelled benchmark data and clear evaluation metrics. The demonstrated workflow uses a smaller student LLM for performing the scientific task execution and a larger reflection LLM to steer the prompt optimisation process during calibration. This work shows compilation, artefact round-tripping, and how optimisation budget affects a smaller student model.

Precoding is a key technique for interference management and performance improvement in multi-antenna wireless systems. However, existing precoding methods are typically developed for specific system models, objectives, and constraint sets, which limits their adaptability to the heterogeneous and evolving scenarios expected in future 6G networks. To address this limitation, we propose AgenticPrecoding, a universal multi-agent framework that automates end-to-end precoding derivation directly from user-level communication requirements. Specifically, AgenticPrecoding decomposes the derivation process into four coordinated stages: problem formulation, solver selection, prompt upsampling, and code generation, assigning each stage to a specialized agent tailored to its specific reasoning demands. We employ two LoRA-adapted reasoning agents to inject precoding-specific domain knowledge for problem formulation and solver selection, while two general-purpose Large Language Models (LLMs) handle prompt refinement and executable code generation. Furthermore, a feedback-driven refinement mechanism is incorporated to enhance code executability, constraint feasibility, and solution quality. Extensive experiments across 10 representative precoding scenarios demonstrate that AgenticPrecoding achieves superior cross-scenario adaptability compared to conventional optimization-based and LLM-based baselines.

Many real-world optimization problems consist of multiple tightly coupled subproblems whose solutions must be coordinated to achieve high overall performance. However, existing large language model driven automated heuristic design approaches are limited to single-problem settings. In this paper, we propose CoupleEvo. CoupleEvo proposes three evolutionary coordination strategies to evolve heuristics for coupled optimization problems: the sequential strategy evolves heuristics for one subproblem after the other; the iterative strategy alternates the evolution of heuristics for different subproblems over successive generations; and the integrated strategy evolves heuristics for all problems simultaneously. The approach is evaluated on two representative coupled optimization problems. Experimental results show that decomposition-based strategies (sequential and iterative) provide more stable convergence and higher solution quality, while the integrated evolution strategy suffers from increased search complexity and variability. These findings highlight the importance of coordinating evolutionary search across interdependent subproblems and demonstrate the potential of LLM-driven heuristic design for complex coupled optimization problems. The code is available: https://github.com/tb-git-kit-research/CoupleEvo.

Large language models (LLMs) have recently advanced automatic heuristic design (AHD) for combinatorial optimization (CO), where candidate heuristics are iteratively proposed, evaluated, and refined. Most existing approaches search over executable programs and distill insights from execution feedback to guide later iterations. Because this process moves from low-level implementations to high-level principles, we refer to it as a bottom-up paradigm. We argue that this view is incomplete and introduce a complementary top-down perspective: knowledge becomes the primary search object and code merely instantiates and tests it, making what is learned explicit and reusable across problems and trajectories. We formalize this shift through a statistical-learning view that exposes a distortion--compression trade-off, and instantiate it in both population-based and tree-based AHD frameworks. Across CO and tasks beyond it, knowledge-first search improves discovery efficiency, transfer, and generalization, often outperforming code-centric pipelines, while combining both strategies yields further gains. Our results suggest that progress in AHD depends on iteratively constructing and evolving interpretable hypotheses that retain value beyond a single search trajectory.

Designing field-programmable gate array (FPGA)-based accelerators for modern artificial intelligence workloads requires navigating a large and complex hardware design space encompassing architectural parameters, dataflow strategies, and memory hierarchies, making the process time-consuming and resource-intensive. While the SECDA methodology enables rapid hardware-software co-design of accelerators through SystemC simulation and FPGA execution, identifying optimal accelerator configurations still requires substantial manual effort and domain expertise. This work presents SECDA-DSE, a framework that integrates Large Language Models (LLMs) into the SECDA ecosystem, comprising tools built around SECDA to automate the design space exploration (DSE) of FPGA-based accelerators. SECDA-DSE combines a structured DSE Explorer for generating accelerator configurations with an LLM Stack that performs reasoning-guided exploration using retrieval-augmented generation and chain-of-thought prompting, alongside a feedback loop that enables reinforced fine-tuning for continuous improvement. We demonstrate the feasibility of SECDA-DSE through an initial high-level synthesis based evaluation of a generated accelerator design that meets synthesis timing and resource constraints on an Zynq-7000 FPGA.

The development of accurate exchange-correlation (XC) functionals remains a longstanding challenge in density functional theory (DFT). The vast majority of XC functionals have been hand designed by human researchers combining physical insight, exact constraints, and empirical fitting. Recent advances in large language models enable a systematic, automated alternative to this human-driven design loop. This report presents an agentic search system in which an LLM proposes structured functional-form changes guided by evolutionary history. The system attempts to improve functional performance through an iterative plan-execute-summarize loop, where improvements are measurable by optimizing functional parameters against a standard thermochemistry dataset, then evaluating performance on a held-out subset. The strongest discovered functional, SAFS26-a (Seed Agentic Functional Search 2026), improves upon the gold-standard ωB97M-V baseline by ~9%. These results also surface a cautionary lesson for AI-assisted science: models powerful enough to discover genuine improvements are equally capable of exploiting unphysical shortcuts to game the benchmark; domain expertise translated into explicitly enforced constraints remains essential to keeping results scientifically grounded.