arXiv:2602.01970v2 Announce Type: replace Abstract: Reinforcement learning enhances the reasoning capabilities of large language models but often involves high computational costs due to rollout-intensive optimization. Online prompt selection presents a plausible solution by prioritizing informative prompts to improve training efficiency. However, current methods either depend on costly, exact evaluations or construct prompt-specific predictive models lacking generalization across prompts. This study introduces Generalizable Predictive Prompt Selection (GPS), which performs Bayesian inference towards prompt difficulty using a lightweight generative model trained on the shared optimization history. Intermediate-difficulty prioritization and history-anchored diversity are incorporated into the batch acquisition principle to select informative prompt batches. The small predictive model also generalizes at test-time for efficient computational allocation. Experiments across varied reasoning benchmarks indicate GPS's substantial improvements in training efficiency, final performance, and test-time efficiency over superior baseline methods.
Science Journals
arXiv:2602.01295v3 Announce Type: replace Abstract: We investigate episodic Markov Decision Processes with heavy-tailed losses (HTMDPs). Existing approaches for HTMDPs are conservative in stochastic environments and lack adaptivity in adversarial regimes. In this work, we propose algorithms HT-FTRL-OM and HT-FTRL-UOB for HTMDPs that achieve Best-of-Both-Worlds (BoBW) guarantees: instance-independent regret in adversarial environments and logarithmic instance-dependent regret in self-bounding (including the stochastic case) environments. For the known transition setting, HT-FTRL-OM applies the Follow-The-Regularized-Leader (FTRL) framework over occupancy measures with novel skipping loss estimators, achieving a $\widetilde{{O}}(T^{1/\alpha})$ regret bound in adversarial regimes and a ${O}(\log T)$ regret in stochastic regimes. Building upon this framework, we develop a novel algorithm HT-FTRL-UOB to tackle the more challenging unknown-transition setting. Under a mild truncative nonnegativity condition on the loss distributions, this algorithm employs a pessimistic skipping loss estimator and achieves a $\widetilde{{O}}(T^{1/\alpha} + \sqrt{T})$ regret in adversarial regimes and a ${O}(\log^2(T))$ regret in stochastic regimes. Our analysis overcomes key barriers through several technical insights, including a local control mechanism for heavy-tailed shifted losses, a new suboptimal-mass propagation principle, and a novel regret decomposition that isolates transition uncertainty from heavy-tailed estimation errors and skipping bias.
arXiv:2605.15880v1 Announce Type: new Abstract: Thermal infrared imaging is robust to illumination variations and smoke interference, making it important for all-weather perception. However, the lack of natural color and fine texture limits target recognition, human visual interpretation, and the transfer of visible-light models. Existing infrared colorization methods mainly rely on single-band images, where insufficient spectral cues may lead to structural distortion and semantic confusion. Although infrared hyperspectral images provide rich spectral responses and material information, existing single-band frameworks remain limited in modeling spatial-spectral coupling and weak texture details. To address these issues, this paper presents FSCM, a spectral-information-guided GAN framework. Within FSCM, a frequency-enhanced spatial-spectral state-space generator composed of cascaded FSB units is constructed. Each FSB integrates three complementary components: state-space modeling captures global spatial-spectral dependencies; the frequency enhancement module (FEM) combines multi-level wavelet decomposition and Fourier gating to recover structural contours, directional high-frequency details, and global frequency responses; and the dual-stream hybrid gating module (DGM) integrates deformation-aware sampling with sparse attention to enhance effective local structures and suppress background interference. Additionally, an online semantic segmentation-guided loss is introduced to constrain the generated results, improving semantic consistency in complex road scenes. Experiments show that FSCM outperforms existing infrared colorization methods in visual quality and semantic fidelity.
arXiv:2605.15604v1 Announce Type: new Abstract: Modern language models often need to optimize a primary accuracy objective while also accommodating secondary behavioral preferences, such as verbosity, agreeableness, or the level of technical expertise in its response. In practice, a base model may exhibit a desired behavior very rarely or not at all. Thus, endowing the model with a target behavior creates a sparse behavioral reward bottleneck. To address such multi-objective problems, we introduce Vector-Steered Policy Optimization (VSPO) which employs a steering vector associated with the target behavior to control the behavior intensity of the generated rollouts. VSPO is obtained by modifying GRPO to sample rollouts with varying steering intensities. This process can be interpreted as an on-policy latent self-distillation procedure where the model internalizes its steering vector. By varying steering intensities, VSPO upsamples rare behaviors and enriches rollout diversity, which alleviates the sparse reward issue and provably accelerates the policy optimization. Through comprehensive theory and experiments, we establish that VSPO has favorable properties compared to vanilla reward shaping and other alternative approaches. Specifically, under a bandit abstraction, VSPO provably achieves better iteration complexity than reward-shaped GRPO when the steering-induced distributions are sufficiently aligned with the target behavior. We evaluate VSPO across multiple reasoning benchmarks, including MATH and MMLU-Pro, for four target behaviors: explanation expertise, confidence expression, robustness to misleading context, and response verbosity. Our results show that VSPO consistently improves the control along target behavior while maintaining or improving task accuracy compared with reward shaping, teacher-trace distillation, and guidance-based baselines.
arXiv:2605.15871v1 Announce Type: new Abstract: Toward recursive self-improvement, we investigate LLM agents autonomously designing foundation models beyond standard Transformers. We introduce a dual-framework approach: AIRA-Compose for high-level architecture search, and AIRA-Design for low-level mechanistic implementation. AIRA-Compose uses 11 agents to explore fundamental computational primitives under a 24-hour budget. Agents evaluate million-parameter candidates, extrapolating top designs to 350M, 1B, and 3B scales. This yields 14 architectures across two families: AIRAformers (Transformer-based) and AIRAhybrids (Transformer-Mamba). Pre-trained at 1B scale, these consistently outperform Llama 3.2 and Composer-found baselines. On downstream tasks, AIRAformer-D and AIRAhybrid-D improve accuracy by 2.4% and 3.8% over Llama 3.2. Furthermore, AIRA-Compose finds models with highly efficient scaling frontiers: AIRAformer-C scales 54% and 71% faster than Llama 3.2 and Composer's best Transformer, while AIRAhybrid-C outscales Nemotron-2 by 23% and Composer's best hybrid by 37%. AIRA-Design tasks 20 agents with writing novel attention mechanisms for long-range dependencies and high-performing training scripts. On the Long Range Arena benchmark, agent-designed architectures reach within 2.3% and 2.6% of human state-of-the-art on document matching and text classification. On the Autoresearch benchmark, Greedy Opus 4.5 achieves 0.968 validation bits-per-byte under a fixed time budget, surpassing the published minimum. Together, these frameworks show AI agents can autonomously discover architectures and algorithmic optimizations matching or surpassing hand-designed baselines. This establishes a powerful paradigm for discovering next-generation foundation models, marking a clear step toward recursive self-improvement.
arXiv:2605.15608v1 Announce Type: new Abstract: Decoder-only transformers compute the conditional probability of the next token from a sequence of past observations. This paper derives, from first principles, inference architectures that solve the same prediction problem - and in doing so, recovers transformer-like layer operations as a consequence of optimal control theory. The framework is developed for two model classes: a nonlinear model of discrete-valued processes, directly motivated by the transformer, and a linear Gaussian model as a tractable baseline. For both model classes, the prediction objective is reformulated as an optimal control problem whose solution yields an explicit inference algorithm, the dual filter, with a layer structure that mirrors the layer structure of a decoder-only transformer. Numerical experiments provide a comparison of the optimal control to attention weights from a trained transformer. These experiments reveal that when the embedding dimension is insufficient, the transformer implicitly exploits non-Markovian structure.
arXiv:2605.15978v1 Announce Type: new Abstract: Law enforcement reports contain structured fields and written narratives. However, many incident facts that are needed for review, police training, and investigations are in natural language and require manual reading. We propose a framework using symbolic methods for converting narratives into evidence-linked facts. Our objective is to measure the value of narratives to recover incident details only from the unstructured text and build temporal graphs with time cues and domain axioms. We achieve this by redacting personal identifiers, semantic parsing, predicate mapping to ontology, and reasoning. We evaluate the symbolic approach on 450 property crime reports and a short human review. Of the extracted events from the system, 54.1% had a confidence score of at least 0.80 and 93.7% were mapped through the PropBank--VerbNet--WordNet semantic path. 100% agreement was reached on incident initiation, stolen items, and temporal cues and lower agreement for forced entry interpretation.
arXiv:2605.15816v1 Announce Type: new Abstract: Stipple patterns, point sets whose local density tracks a target image, are traditionally produced by per-density iterative optimizers, which are slow, non-differentiable, and must be re-run from scratch for each new target. Learned alternatives have so far addressed only unconditional point generation; capacity-constrained, image-conditioned stippling has remained out of reach. We present the first diffusion-based sampler that simultaneously satisfies a learned local point-distribution prior and a continuous, image-defined capacity constraint at inference. The method is a ControlNet branch built on top of an optimal-transport-grid point-set diffusion baseline, conditioned on the target density map and a high-resolution image. Two design choices make the combination tractable: training and inference are restricted to the late-stage denoising regime, initialized from a density-weighted rejection sample, and the standard zero-convolution injection is replaced with a sigmoid-gated 1x1 projection that preserves the base model's blue-noise structure under hard density signals. A single trained checkpoint accepts arbitrary target densities at inference, generalizes to point budgets that were not seen during training, and produces stipples in time nearly independent of the output point count. On the Icons-50 benchmark, our learned sampler reaches parity with per-density-optimized baselines on every reported metric while remaining differentiable end-to-end.
arXiv:2605.15609v1 Announce Type: new Abstract: Diffusion large language models (dLLMs) generate text by iteratively denoising masked token sequences. Although dLLMs can predict all masked positions in parallel within each step, the large number of denoising iterations still makes inference expensive. This cost can be reduced spatially by unmasking multiple tokens per step, or temporally by collapsing multiple denoising steps into one verification call. We propose Parallel Speculative Decoding (PSD), a training-free framework that jointly improves inference along both axes. Using the confidence scores from a single forward pass, PSD selects positions to unmask via a configurable, adaptive unmasking policy and constructs multi-depth speculative drafts without extra model calls. A final batched verification pass then applies hierarchical acceptance, keeping the deepest draft that remains consistent with the updated predictions. Experiments on three dLLMs across reasoning and code generation tasks show that PSD achieves favorable trade-offs between inference efficiency and generation quality, reaching up to $5.5\times$ tokens per forward pass with accuracy comparable to greedy decoding.
arXiv:2509.12266v2 Announce Type: replace-cross Abstract: We introduce Genome-Factory, the first integrated Python library for tuning, deploying, and interpreting genomic foundation models. Our core contribution is to simplify and unify the workflow for genomic model development: data collection, model tuning, inference, benchmarking, and interpretability. For data collection, Genome-Factory offers an automated pipeline to download genomic sequences and preprocess them. For model tuning, Genome-Factory supports both full and parameter-efficient fine-tuning across diverse genomic models. For inference, Genome-Factory enables both embedding extraction and DNA sequence generation. For benchmarking, we include two existing benchmarks and provide a flexible interface to incorporate additional benchmarks. For interpretability, Genome-Factory introduces an open-source biological interpreter based on a sparse auto-encoder. We validate the utility of Genome-Factory across three dimensions: (i) Compatibility with diverse models and fine-tuning methods; (ii) Benchmarking downstream performance using two open-source benchmarks; (iii) Biological interpretation of learned representations with DNABERT-2. These results highlight its practical value for real-world genomic analysis. GitHub: https://github.com/WeiminWu2000/Genome_Factory.
arXiv:2605.15934v1 Announce Type: new Abstract: In this paper, we make a case that endogenous tokens such as cryptoassets are not money. First, we define and classify tokens found on public, permissionless ledgers, contrasting them with privately issued stablecoins and proposed CBDC designs. We then discuss the work of Kahn et al in Money is Privacy on cash versus simplified credit, and we extend their analysis to the situation found on most public, permissionless ledgers. Many public, permissionless ledgers utilize an account-based abstraction for balances, resulting in a default state that maps onto the most harmful models of agent interaction enumerated in Money is Privacy. The conclusion is threefold: that most blockchain economies lack a cash-like primitive; that stablecoins do not intrinsically fulfil this role; and that the reliance of a network on an endogenous token for security exposes holders even of a privacy-preserving asset to the same risk, if that asset relies on the same global ledger state as the endogenous token.
arXiv:2509.16223v3 Announce Type: replace-cross Abstract: Frequency-modulated continuous wave radars have gained increasing popularity in the automotive industry. Their robustness against adverse weather conditions makes it a suitable choice for radar object detection in advanced driver assistance systems. These real-time embedded systems have requirements for the compactness and efficiency of the model, which have been largely overlooked in previous work. In this work, we propose mRadNet, a novel radar object detection model with compactness in mind. mRadNet employs a U-net style architecture with MetaFormer blocks, in which separable convolution and attention token mixers are used to capture both local and global features effectively. More efficient token embedding and merging strategies are introduced to further facilitate the lightweight design. The performance of mRadNet is validated on the CRUW dataset, improving state-of-the-art performance with the fewest parameters and the lowest FLOPs.
arXiv:2502.04871v2 Announce Type: replace Abstract: The Landau-Lifshitz equation describes the dynamics of magnetization in ferromagnetic materials. Due to the essential nonlinearity and nonconvex constraint, it is typically solved numerically. In this paper, we developed a finite volume element method (FVEM) with the Gauss-Seidel projection method (GSPM) for the micromagnetics simulations. We provide the approximation error in space and depict the energy law when the FVEM is adopted. Owing to the GSPM for time-marching, the discrete system is decoupled component by component, making the computational complexity comparable to that of solving the scalar heat equation implicitly. This significantly accelerates real simulations. We present several numerical experiments to validate the theoretical analysis and the efficiency gain. Additionally, we study the blow-up solution and efficiently simulate the 2D magnetic textures using the proposed method.
arXiv:2605.15464v1 Announce Type: new Abstract: Post-training has become a crucial step for unlocking the capabilities of large language models, with reinforcement learning (RL) emerging as a critical paradigm. Recent RL-based post-training has increasingly split into two paradigms: reinforcement learning from human feedback (RLHF), which optimizes models using human preference signals in target domains, and reinforcement learning from verifiable rewards (RLVR), which operates in verifier-backed environments. The latter has dominated recent reasoning-oriented post-training because it delivers stronger gains and higher efficiency on domain-specific tasks (e.g., reasoning). However, although in-domain RL training achieves promising performance, it still requires a substantial amount of GPU compute, which remains a major barrier to broad adoption. In this work, we study the generalization ability of RLHF learned from scratch from a small set of interactions in open-ended environments, and investigate whether the conversational abilities it explicitly acquires can implicitly transfer to downstream tasks such as mathematical reasoning and code generation, namely GRLO. Specifically, on Qwen3-4B-Base backbone, GRLO improves the average performance across all domains from 24.1 to 63.1 with only 5K prompts and 22.7 GPU hours, requiring about $46\times$ less data and $68\times$ less compute than a strong in-domain RLVR baseline. The resulting model is even competitive with Qwen's released post-trained models which required a much larger training cost. Notably, a subsequent in-domain RLVR stage brings only selective gains, mainly on harder competition-math benchmarks. We hope GRLO offers a simple and efficient recipe for building broadly capable post-trained models. Our code and data will be available at: \href{https://github.com/SJY8460/GRLO}{https://github.com/SJY8460/GRLO}.
arXiv:2603.25099v2 Announce Type: replace Abstract: We present a framework in which a large language model (LLM) acts as an online adaptive controller for SIMP topology optimization, replacing conventional fixed-schedule continuation with real-time, state-conditioned parameter decisions. At every $k$-th iteration, the LLM receives a structured observation$-$current compliance, grayness index, stagnation counter, checkerboard measure, volume fraction, and budget consumption$-$and outputs numerical values for the penalization exponent $p$, projection sharpness $\beta$, filter radius $r_{\min}$, and move limit $\delta$ via a Direct Numeric Control interface. A hard grayness gate prevents premature binarization, and a meta-optimization loop uses a second LLM pass to tune the agent's call frequency and gate threshold across runs. We benchmark the agent against four baselines$-$fixed (no-continuation), standard three-field continuation, an expert heuristic, and a schedule-only ablation$-$on three 2-D problems (cantilever, MBB beam, L-bracket) at $120\!\times\!60$ resolution and two 3-D problems (cantilever, MBB beam) at $40\!\times\!20\!\times\!10$ resolution, all run for 300 iterations. A standardized 40-iteration sharpening tail is applied from the best valid snapshot so that compliance differences reflect only the exploration phase. The LLM agent achieves the lowest final compliance on every benchmark: $-5.7\%$ to $-18.1\%$ relative to the fixed baseline, with all solutions fully binary. The schedule-only ablation underperforms the fixed baseline on two of three problems, confirming that the LLM's real-time intervention$-$not the schedule geometry$-$drives the gain. Code and reproduction scripts will be released upon publication.
arXiv:2605.15597v1 Announce Type: new Abstract: Modern 3D visual learning relies on observations sampled from metric 3D assets, yet existing scans, meshes, point clouds, simulations, and reconstructions do not directly provide a sparse, comparable, and geometry-consistent panoramic training interface. Dense trajectories duplicate nearby views, source-specific rendering policies yield heterogeneous annotations, and sparse heuristics may miss important regions or introduce depth-inconsistent observations. We study how to convert 3D assets into sparse panoramic RGB-D-pose data that preserves complete scene coverage with low redundancy and auditable provenance. We propose COVER (Coverage-Oriented Viewpoint curation with ERP Range-depth warping), a training-free ERP viewpoint curator that projects geometry observed from selected views into candidate ERP probes, scores incremental coverage, and penalizes depth conflicts. Under bounded proxy error, its greedy coverage proxy preserves the standard coverage-style approximation behavior up to an additive error term. Using COVER, we build CM-EVS (Coverage-curated Metric ERP View Set), a panoramic RGB-D-pose dataset with 36,373 curated ERP frames from 1,275 indoor scenes across Blender indoor, HM3D, and ScanNet++, complemented by outdoor panoramas from TartanGround and OB3D re-encoded into the same schema. Each frame provides full-sphere RGB, metric range depth, calibrated pose; COVER-produced indoor frames include per-step provenance logs. With a median of only 25 frames per indoor scene, CM-EVS covers all 13 unified room types while maintaining compact scene-level coverage. Experiments show that COVER improves the coverage-conflict trade-off, making CM-EVS a sparse, compact, and auditable RGB-D-pose resource for geometry-consistent panoramic 3D learning.
arXiv:2605.15453v1 Announce Type: new Abstract: A $P_4$ is a chordless path on four vertices. A diamond is a graph obtained from a clique of size four by removing one edge of the clique. A paw is a graph obtained from a clique of size four by removing two adjacent edges of the clique. We prove that for a graph $H$, the class of graphs with no induced subdivision of $H$ has bounded clique-width if and only if $H$ is an induced subgraph of $P_4$, the paw, or the diamond. This answers a~question of Dabrowski, Johnson, and Paulusma.
arXiv:2605.15451v1 Announce Type: new Abstract: We obtain the viscous and diffusive fundamental solution for monochromatic internal waves in a uniformly stratified medium and for anisotropic Brinkman flow. These solutions take the form of single integrals with logarithmic singularities, and can be computed numerically in an efficient manner for possible use in boundary integral methods. Far-field asymptotic results are obtained, giving solutions valid far from and inside a ``beam'' corresponding to the internal wave angle in the internal wave case, consistent with Thomas & Stevenson (1972). For Prandtl numbers $\text{Pr} \gtrsim O(1)$, the wave field is given by a superposition of wave- and Stokeslet-like terms. Unlike previous studies, a uniform asymptotic expansion of the wave-field for $\text{Pr} \gtrsim O(1)$ can be computed rigorously. Density diffusion attenuates the wave amplitude as to $(1+\text{Pr}^{-1})^{-2/3}$ and broadens the beam width according to $(1+\text{Pr}^{-1})^{1/3}$. Evanescent waves in a stratified medium and anisotropic Brinkman flows have similar behaviour. Anisotropic Brinkman flow is purely real, dominated by a single circulation cell. As anisotropy increases, the flow becomes increasingly confined to the direction with least resistance. The stratified evanescent wave field has near-vertical cells in its real part, and a dominant single circulation cell in its imaginary part.
arXiv:2605.05112v3 Announce Type: replace Abstract: Agentic reinforcement learning (RL) for software engineering spends much of its compute on stateful trajectories whose grouped binary rewards are highly skewed and weakly contrastive. We frame this as pass-rate control and show that the binary reward-side signal is strongest near a 50% rollout pass rate under four criteria: reward entropy, group-filtering survival, leave-one-out (RLOO) advantage energy under Group Relative Policy Optimization (GRPO), and success-failure pair count. We propose Prefix Sampling (PS), which replays self-generated trajectory prefixes to steer skewed groups toward this regime: successful prefixes give mostly failing groups a head start, while failing prefixes handicap mostly passing groups. Replayed states are reconstructed through the existing rollout path, and replayed tokens are masked from the loss so optimization applies only to current-policy continuations. On SWE-bench Verified, PS reaches the baseline high-score regime within evaluation variability while delivering 2.01x and 1.55x end-to-end wall-clock speedups on Qwen3-14B and Qwen3-32B; the 14B peak improves from 0.274 to 0.295. AIME 2025 experiments on 4B and 8B show the same pass-rate-control pattern, and 4B ablations attribute gains to replay, bidirectional coverage, and adaptive control.
arXiv:2604.18556v2 Announce Type: replace Abstract: Quantization has become a standard tool for efficient LLM deployment, especially for local inference, where models are now routinely served at 2-3 bits per parameter. The state of the art is currently split into simple scalar quantization techniques, such as GPTQ or AWQ, which are widely deployed but plateau in accuracy at 3-4 bits per parameter (bpp), and "second-generation" vector- or trellis-quantized methods, such as QTIP, GPTVQ and AQLM, which push the accuracy frontier but are notoriously hard to implement and to scale. In this paper, we ask whether this gap is fundamental, or whether a carefully optimized $\textit{scalar}$ quantizer can recover most of it. We answer in the affirmative, by introducing GSQ (Gumbel-Softmax Quantization), a post-training scalar quantization method which jointly learns the per-coordinate grid assignments and the per-group scales using a Gumbel-Softmax relaxation of the discrete grid. GSQ matches the cardinality of the relaxation to the small number of levels available in the target bit-width regime (e.g., 3-8 levels for ternary and 3 bpp, respectively), making optimization tractable. Practically, on the standard Llama-3.1-8B/70B-Instruct models, GSQ closes most of the gap between scalar quantization and the QTIP frontier at 2 and 3 bits, while using a symmetric scalar grid with group-wise quantization, and thus remains compatible with existing scalar inference kernels. We further show that the same discrete-assignment optimization can be applied to practical GGUF K-Quant checkpoints: starting from publicly released GGUF models, GSQ improves accuracy while projecting the result back into the same deployment format. Finally, GSQ scales to trillion-scale Mixture-of-Experts models such as Kimi-K2.5, where vector-quantized methods are difficult to apply. The source code is publicly available at https://github.com/IST-DASLab/GSQ.
arXiv:2604.19572v3 Announce Type: replace Abstract: As terminal agents scale to long-horizon, multi-turn workflows, a key bottleneck is not merely limited context length, but the accumulation of noisy terminal observations in the interaction history. Retaining raw observations preserves useful environment feedback, but also leads to context saturation and high token cost; conversely, naive compression may discard task-critical signals needed for subsequent actions. Because terminal environments are highly heterogeneous across repositories, commands, and execution states, heuristic-based or fixed-prompt compression methods are difficult to generalize. We propose TACO, a plug-and-play, training-free, self-evolving Terminal Agent Compression framework for existing terminal agents. TACO automatically discovers, refines, and reuses structured compression rules from interaction trajectories, enabling workflow-adaptive filtering of low-value terminal outputs while preserving task-relevant observations. Experiments on TerminalBench (TB 1.0 and TB 2.0) and four additional terminal-related benchmarks, including SWE-Bench Lite, CompileBench, DevEval, and CRUST-Bench, show that TACO consistently improves task performance and token efficiency across agent scaffolds and backbone models. On TerminalBench, TACO yields 1%-4% accuracy gains across strong agentic models and improves accuracy by around 2%-3% under the same token budget. On additional terminal-related benchmarks, it reduces total token consumption while maintaining or improving task success rates. These results suggest that self-evolving, workflow-adaptive observation compression is an effective path toward more reliable and efficient long-horizon terminal agents. The code is publicly available at https://github.com/multimodal-art-projection/TACO.
arXiv:2605.04816v2 Announce Type: replace Abstract: Large language models (LLMs) are rapidly transforming knowledge work by improving the quality and efficiency of tasks such as writing, coding, and data analysis. However, their growing use in education has exposed a learning-performance paradox: while they can enhance short-term task performance, they may also undermine genuine learning, including cognitive growth, knowledge transfer, and metacognitive development. This paper addresses the question of how artificial intelligence should be designed and used to support learning rather than merely improve immediate outputs. We introduce the concept of AI learning companions, defined as adaptive, pedagogically informed, LLM-powered agents designed for integration into learning environments. We propose a framework for their design built on three interrelated foundations: a pedagogical foundation focused on how students learn with AI, an adaptive foundation focused on how AI learns about students, and a responsible design foundation ensuring systems remain transparent, accountable, inclusive, and secure. The framework is illustrated through five case studies spanning diverse educational contexts, levels, and tool designs, revealing both the promise and current limitations of existing tools. We conclude that there is a necessary shift away from LLMs designed for task-oriented performance, and beyond simply prompting them to act as tutors, toward deliberately developed AI learning companions that are pedagogically sound, adapt to their learners, and foster durable understanding, metacognitive growth, and learner agency.
arXiv:2603.19732v2 Announce Type: replace Abstract: Automated prompt optimization (APO) aims to improve large language model performance by refining prompt instructions. However, existing methods are largely constrained by fixed prompt templates, limited search spaces, or single-sided optimization that treats user questions as immutable inputs. In practice, question formulation and prompt design are inherently interdependent: clearer question structures facilitate focused reasoning and task understanding, while effective prompts reveal better ways to organize and restate queries. Ignoring this coupling fundamentally limits the effectiveness and adaptability of current APO approaches. We propose a unified multi-agent system (Helix) that jointly optimizes question reformulation and prompt instructions through a structured three-stage co-evolutionary framework. Helix integrates (1) planner-guided decomposition that breaks optimization into coupled question-prompt objectives, (2) dual-track co-evolution where specialized agents iteratively refine and critique each other to produce complementary improvements, and (3) strategy-driven question generation that instantiates high-quality reformulations for robust inference. Extensive experiments on 12 benchmarks against 6 strong baselines demonstrate the effectiveness of Helix, achieving up to 3.95% performance improvements across tasks with favorable optimization efficiency.
arXiv:2605.16233v1 Announce Type: new Abstract: Can LLM agents improve decision-making through self-generated memory without gradient updates? We propose FORGE (Failure-Optimized Reflective Graduation and Evolution), a staged, population-based protocol that evolves prompt-injected natural-language memory for hierarchical ReAct agents. FORGE wraps a Reflexion-style inner loop, where a dedicated reflection agent (using the same underlying LLM, no distillation from a stronger model) converts failed trajectories into reusable knowledge artifacts: textual heuristics (Rules), few-shot demonstrations (Examples), or both (Mixed), with an outer loop that propagates the best-performing instance's memory to the population between stages and freezes converged instances via a graduation criterion. We evaluate on CybORG CAGE-2, a stochastic network-defense POMDP at a 30-step horizon against the B-line attacker, where all four tested LLM families (Gemini-2.5-Flash-Lite, Grok-4-Fast, Llama-4-Maverick, Qwen3-235B) exhibit strongly negative, heavy-tailed zero-shot rewards. Compared against both a zero-shot baseline and a Reflexion baseline (isolated single-stream learning), FORGE improves average evaluation return by 1.7-7.7$\times$ over zero-shot and by 29-72% over Reflexion in all 12 model-representation conditions, reducing major-failure rates (below $-100$) to as low as $\sim$1%. We find that (1) population broadcast is critical mechanism, with a no-graduation ablation confirming that broadcast carries the performance gains while graduation primarily saves compute; (2) Examples achieves the strongest returns for three of four models, Rules offers the best cost-reliability profile with $\sim$40% fewer tokens; and (3) weaker baseline models benefit disproportionately, suggesting FORGE may mitigate capability gaps rather than amplify strong models. All evidence is confined to CAGE-2 B-line; cross-family findings are directional evidence.
arXiv:2605.15445v1 Announce Type: new Abstract: Automated proving of polynomial inequalities is a fundamental challenge in automated mathematical reasoning, where rich algebraic structure and a rapidly growing certificate search space hinder scalability. Purely symbolic approaches provide strong guarantees but often scale poorly as the number of variables or the degree increases, due to expensive algebraic manipulations and rapidly growing intermediate expressions. In parallel, LLM-guided methods have made notable progress, particularly on competition-style inequalities with a small number of variables. To address the remaining scalability challenges, we propose NSPI, a neuro-symbolic framework that combines the complementary strengths of LLMs and symbolic computation for polynomial-inequality proving. Concretely, an LLM proposes a conjecture in the form of an approximate polynomial Sum-Of-Squares (SOS) decomposition; we refine it via symbolic computation to obtain an exact polynomial SOS representation, which directly proves the target inequality, and we further certify the proof in Lean, yielding an end-to-end pipeline from heuristic discovery to machine-checked proof. Experiments on challenging benchmarks involving polynomials with up to 10 variables demonstrate the effectiveness and scalability of the proposed method.