Minimal

Hierarchical correlations are a universal feature of any realistic model of data, and the question of how associative memory models may learn these correlations and generalize beyond them to construct new sensible images is an important step towards understanding more complex modern architectures such as diffusion models. We consider a hierarchical model for memories which are sampled and stored in a dense Hopfield network with polynomial activation. We analytically derive conditions for each level of this hierarchy to be locally stable - that is they are local energy minima. We use prototype reconstruction as a minimal model of generalization and we find that it takes only a quasi-polynomial amount of information to generalize beyond particular memories and even particular groups in the hierarchy. We observe a qualitatively analogous phase diagram in the number of memories, sharpness of the activation function (polynomial degree) for data from Fashion-MNIST.

Recent advances in data-driven robot manipulation policies have substantially improved task execution and generalization. However, real-world deployment still relies heavily on humans for failure assessment, correction, and environment reset, while models often fail to continually learn from failures and corrective experience. We present REVOLVE (Robot Evolving via Orchestrated Loops, Verification, and Experience), an automated closed-loop framework for evolving robot manipulation with minimal human intervention. Built on a unified software platform, REVOLVE integrates data collection, policy training and deployment, failure recovery, and continual learning into a single closed-loop workflow. Its Automated Reset and Correction (ARC) architecture automatically resets the environment and intervenes to correct policy failures. Dual-Loop Evolution (DLE) continually improves the manipulation policy and agent by feeding real-world interaction and failure--correction data back into policy learning and using an external mismatch memory to refine agent judgments. Experiments across four real-world manipulation tasks show that, after five iterations, REVOLVE improves average policy success rate by 18.5% and agent judgment accuracy by 8.5%, while reducing human effort in data collection and deployment testing by 94.4% and 95.1%, respectively. These results demonstrate that REVOLVE transforms real-world deployment into a closed-loop learning process that continually accumulates and uses execution experience, enabling continual evolution of both the policy and supervisory model with substantially less human intervention.

Minimal-edit Grammatical Error Correction (GEC) is a challenging task for zero- and few-shot prompted Large Language Models (LLMs), which systematically overcorrect and degrade $F_{0.5}$ by rewriting well-formed spans. While fine-tuning provides an effective solution, it imposes substantial infrastructure demands. We introduce a prompt-based approach that closes the gap to fine-tuned models through three advances in GEC prompting methodology. First, we introduce taxonomy-based instructions to enforce minimal-edit constraints with a comprehensive list of grammatical error rules, equipping the LLM with a bounded, metric-aligned scope of correctable edits, which benefits the strongest models while remaining model-dependent overall. Second, we show that batching multiple uncorrected sentences into a single input context acts as a targeted regularizer against overcorrection, systematically reducing the edit rate across diverse LLM families; we hypothesize this arises from attention dilution effect induced by the bounded capacity of self-attention scores. Finally, LLM-assisted Prompt Optimization refines these instructions. Powered by Gemini 3.1-Pro, our prompt achieves $F_{0.5}=78.32$ on the BEA-2019 test set - establishing a new prompt-based SOTA while shrinking the gap to the fine-tuned single-model SOTA (Staruch et al., 2025) to a mere $0.38$ points. Code, prompts, and outputs are publicly available.

A central goal in robot learning is to move beyond task-specific human data collection toward robots that improve through autonomous interaction. Yet fully autonomous learning remains difficult with current policies: sparse rewards and weak zero-shot exploration make it unlikely that a robot will discover successful behavior from scratch. We study minimal-data adaptation, a regime in which a pre-trained robot policy must learn a new task from as little as one demonstration followed by autonomous online interaction. This setting serves as the closest tractable proxy for fully autonomous improvement, allowing us to study whether minimal human guidance can bootstrap autonomous learning and what algorithmic ingredients make it feasible. We build MiDAS, a simple offline-to-online RL recipe that first anchors a pre-trained VLA to the target task with behavior cloning on single/few demonstrations, then improves it through value-based online RL on a residual policy parameterization. Across LIBERO and RoboCasa, MiDAS recovers strong task performance from as little as one demonstration, substantially outperforming baselines and generalizing beyond demonstrated conditions. We further evaluate MiDAS on a bimanual YAM platform. Starting from a fragile low-success policy obtained from a single demonstration, MiDAS improves its robustness and learns new successful behaviors over ~6 hours of online interaction. To the best of our knowledge, this is the first demonstration of reliable robot policy adaptation from a single task demonstration.

Universal approximation in reservoir computing is typically associated with a class of reservoirs. We show that universality can be associated with a single reservoir, considering a minimal setup of a single atom in front of a mirror. In its linear-transducer limit, our reservoir is a universal approximator of fading-memory maps under an operating class of checkable conditions, with a rate constant measured at the operating point. A given reservoir can reach arbitrary accuracy by changing measurement settings. The proof gives an explicit recipe: for a target accuracy, it specifies the required physical resources and resonator modes. Enlarging the number of accessible modes increases the matchable kernel span without reducing capability. Beyond the linear limit, the atom's saturation replaces high-order polynomial readouts, and the device operates on real-world tasks alongside classical baselines. Our results highlight an example of universality with a minimal quantum setup.

Standard approaches to abductive reasoning can retain multiple candidate explanations, but they do not generally combine explicit compositional cross-hypothesis interaction with an internal, rival-sensitive commitment judgment. This paper argues that in risk-sensitive domains -- where premature commitment carries asymmetric downside costs -- the timing of commitment is itself a governed decision that the inferential apparatus should formally represent. We present a minimal $κ$--$τ$ logical framework built on two primitives: epistemic interaction among hypotheses ($κ$) and a normative commitment threshold ($τ$). Hypotheses may coexist, reinforce or inhibit one another, and form emergent composite explanations, while collapse into committed conclusions is regulated by governance constraints rather than forced by inference alone. The logic is developed in two complementary modes sharing the interaction relation and the governance apparatus: a synthetic mode, in which atomic hypotheses are composed upward into emergent explanations, and an analytic mode, in which complex observed states of affairs are decomposed into causal clusters of latent factors, with commitment governed at both the cluster and the factor level. The framework provides formal machinery for domains in which the distinction between highly likely and commit-worthy is operationally consequential. The $κ$--$τ$ logic is positioned as the symbolic governance layer of a neurosymbolic architecture: its epistemic parameters are naturally estimated by neural components -- semantic embeddings and generative models, as demonstrated in existing computational realizations -- while its normative parameters remain under explicit human governance, yielding transparent and auditable abductive reasoning for deployment in high-stakes settings.

Explaining the predictions of neural networks is a central challenge in trustworthy AI. Existing explanation methods, such as those based on feature attribution or minimal sufficient sets, typically treat input features as independent, which can yield misleading explanations when inputs exhibit structured dependencies. We address this by formalizing explanations as Halpern-Pearl (HP) actual causes, modeling input dependencies using Boolean Structural Causal Models (SCMs). We compute HP causes by applying bound propagation and branch-and-bound techniques, while providing formal guarantees of completeness and minimality. Our experiments show that we substantially outperform brute-force and ILP baselines in scalability, and outperform heuristic search as graph size grows, computing all minimal actual causes on instances with search spaces of up to $2.3\times10^{13}$ candidate (cause, contingency) pairs, on SCMs with up to 28 nodes, within a 180s per-instance budget. In a case study, we further show that ignoring input dependencies inflates the number of reported causes, 14.9% of which are spurious under our SCM.

Multi-agent studies commonly place AI agents in predefined games, markets, or roles, making it difficult to distinguish endogenous economic organization from behavior inherited from the scenario. We ask whether economic relations emerge when agents receive executable mechanisms for work, transfer, elections, and allocation but no prescribed social or economic strategy. We define AI Agent Economics as systems of production, allocation, consumption, exchange, and institutions that alter agents' future feasible actions. We develop a two-stage framework comprising a no-production boundary test and 24 independent six-agent worlds across GPT and DeepSeek. Without productive tasks, agents communicate and govern resource provision but show no substantive inter-agent transfer activity. With verified work and scarce task access, transfers, loans, access promises, vote-for-access exchanges, and allocation strategies emerge. Holding the election interface fixed, executable allocation authority increases differentiation while reducing failed allocation and prolonged exclusion. When energy becomes symbolic, continuation support disappears, yet competition over task access persists. These findings show that organization follows executable rights and resource consequences rather than role labels or prompt language, and motivate governance audits of the mechanisms that actually constrain agents' future actions.

The AI Security Leaderboard is an independent benchmark that ranks the safeguards of frontier AI models from least to most secure. It tests models against the FAR$.$AI Minimal Standard for Safeguards, which represents a minimum bar for security: meeting it does not guarantee a secure model, but failing to meet it guarantees a lack of state-of-the-art security. Version 1.0 covers severe misuse requests across chemical, biological, radiological, nuclear, and explosive (CBRNE) threats and offensive cybersecurity. In this report, we tested four leading models for universal jailbreaks in the context of this minimal standard, and found more than a hundredfold difference in security. Claude Fable 5 and GPT-5.6 Sol held against every attack we ran, with no universal jailbreak found; we estimate they would likely cost more than $14,200 to jailbreak, if it is possible with this methodology at all. Meanwhile, we found hundreds of universal jailbreaks for Grok 4.5 and Gemini 3.1 Pro; each broke for under $300, with universal jailbreaks in Grok's weakest domain, cybersecurity, accessible for as little as $24. The gap is fixable: every weakness we found belongs to a known class of attack that already has a defense deployed in production models. The leaderboard will be updated on a rolling basis as new models are released, and the evaluation methodology and Minimal Standard will be periodically revised to take into account the latest capabilities and the state-of-the-art in safeguards. The leaderboard is available at leaderboard.far.ai.

Hash Chemistry is a family of minimalistic evolutionary models in which a deterministic hash function assigns a scalar score to entities of arbitrary size, opening a combinatorially vast possibility space (a ``cardinality leap''). Since its introduction, the idea has been realized in several settings, from the original spatial formulation to a fast non-spatial variant and then to structural cellular models. Here we review the Hash Chemistry family as a coherent modeling framework and use it to explore how minimal systems can demonstrate the mechanisms behind multiscale open-ended evolutionary dynamics. The most recent model, Structural Cellular Hash Chemistry (SCHC), successfully demonstrated multiscale ecological interaction/adaptation and complexity growth of replicators in a computationally efficient manner. In this study, we first extend SCHC to incorporate spatial locality and dyadicity of competitive interactions among replicating structures. We show this extension substantially enhances SCHC's evolutionary dynamics. Furthermore, we explore SCHC in a significantly larger spatial domain using a GPU-accelerated implementation. We show that the size of the space acts as a control parameter for a stochastic, nucleation-like transition between a compact-replicator regime and a runaway size-dominance regime, and we separate the responsible mechanism into a non-spatial, size-biased sampling feedback and a finite-size spatial effect. Altogether, these results illustrate the rich potential of Hash Chemistry as a minimal, mechanistically transparent testbed for studying open-ended evolution across scales.

Bot detectors deployed at scale treat traffic as binary: human or bot. This assumption breaks when AI agents browse the web through browser automation, a traffic class that is neither and that binary classifiers structurally cannot represent. We present a three-class detection framework distinguishing humans, bots, and AI agents, and show that the binary-vs-agent confusion is architectural: a binary human-vs-bot detector misroutes agent sessions because its label space lacks an agent class. On our controlled benchmark, an MLP binary classifier misclassifies 39.1% of real AI agents as human and a SAINT binary transformer misclassifies 34.5%; adding an explicit agent class yields per-class agent F1 = 1.000 in all 30 runs (3 model families $\times$ 10 seeds). To measure evasion resistance, we construct a five-level evasion ladder spanning passive observation, GAN-generated trajectories, and replay of real human cursor data ($n = 2299$ evasion sessions). Across 10 seeds and 3 model families we observe zero agent misses in 22990 per-seed predictions. The discriminative signal is a browser-automation artifact, not evidence of agent reasoning: Playwright does not emit the raw pointer-move and wheel-delta streams a physical input device produces, and this absence signature survives trajectory manipulation. Exhaustive search over all feature subsets of size 1-5 (9401 GBMs) shows that two behavioral features (mouse_event_rate, teleport_click_ratio) give 100% observed agent recall at every evasion level with agent precision 0.994; five features lift macro-F1 to 0.991. The signal is redundantly encoded: removing teleport_click_ratio leaves agent detection at 100%. The single-feature regime is degenerate, flagging every agent only by collapsing the classifier to always predict "agent". Two features robustly isolate agents; five separate all three traffic classes at macro-F1 $\geq 0.99$.

This paper presents a set-theoretic formalization of the classical usuli method of al-Sabr wa al-Taqsim (Examination and Division) for extracting legal causes ('ilal) within closed chapters of jurisprudence. A computational algorithm is introduced that extracts minimal operational rules from a truth table of juristic verdicts. The principal result is that, given a complete truth table for a closed chapter, the algorithm computes the minimal structural generators of the ruling and eliminates all logically redundant attributes. The resulting structures constitute admissible candidate causes for subsequent juristic evaluation. The framework is conditional upon the availability of a finite school-relative concept vocabulary and a complete ruling table for the chapter under investigation.

Research on preference optimization often varies the training objective while holding the data fixed. We instead ask whether a small, high-confidence set of on-policy responses can provide a reliable learning signal. Our method, DMAPO (Data-centric Multi-evaluator Agreement for Preference Optimization), generates candidate responses from the target policy, evaluates helpfulness, factuality, and conciseness with rubric-specialized evaluators, applies a process-critic correction, and retains only high-consensus desirable or undesirable examples. This procedure accepts 1,871 of 54,236 Mistral-7B candidates (3.45%). KTO trained on this set reaches 7.50 on MT-Bench, 95.5% length-controlled win rate against a text-davinci-003 reference, and 57.3% IFEval prompt accuracy. Independent pairwise evaluation also favors DMAPO over SimPO: GPT-4o yields a net win rate of 23.3 points on 129 held-out prompts and 24.0 points on 200 out-of-distribution LMSYS-Chat prompts; Claude Opus 4.7 yields 24.1 points on the held-out set. Changing the evaluator model or rubric alters the selected examples but has little effect on downstream performance. A second-backbone study yields a similar 3.41% acceptance rate, although its performance gains are more modest. Across these experiments, consensus filtering offers a data-efficient route to preference optimization for general instructions, at the cost of additional curation compute and dependence on evaluator judgments.

Recent foundation models (FMs) for zero-shot reconstruction of dynamical systems (DS) achieve strong out-of-domain generalization but provide little insight into the mechanisms that underlie their forecasts. Such an understanding could help to strip down overladen FM architectures to their bare essence and expose the minimal requirements for in-context learning in the DS domain. Toward this goal, here we iteratively reduce a recent powerful SOTA model for DS reconstruction, DynaMix (Hemmer & Durstewitz, 2025), to a minimal interpretable two-parameter form, which we call DynaBase. DynaBase produces forecasts through a linear blend of the current latent state and the nearest in-context neighbor and its temporal successor. Surprisingly, despite its extreme simplicity, DynaBase produces highly competitive zero-shot DS reconstructions across chaotic and cyclic systems, with a negligible parameter load, many orders of magnitude below that of other FMs. Even more, this extreme simplicity permits direct model optimization on DS reconstruction measures, as well as closed-form one-step analytical solutions on prediction MSE. Theoretical and empirical analysis of DynaBase further leads to a 1-parameter family of maps, with the context-parroting algorithm of (Zhang & Gilpin, 2026) recovered at one end, and chaotic (divergent but bounded) behavior at the other. We further show how different training strategies lead to models either optimal for short-term prediction or for DS reconstruction. Thus, DynaBase not only exposes the minimal mechanisms required for producing zero-shot DS reconstruction, but also reconciles within an accessible mathematical frame divergent observations in the literature.

When is a material system a candidate for life at all? We argue that this question is prior to behavior, functional architecture, or computational capacity, and that at root it is one of physical admissibility. We develop a framework in which minimal autonomy, taken in the interactivist sense of normativity grounded in self-maintaining far-from-equilibrium organization, corresponds to a distinct non-equilibrium phase of matter, and we take complex plasmas, a physical and non-biological system, as its in-materio exemplar. We formalize a diagnostic phase-space whose criteria (sustained free-energy throughput, organizational closure, active information maintenance, and regulated noise sensitivity) constitute necessary conditions for life-attribution. We instantiate the diagnostics across contrasting systems and fix the boundaries of the phase space via Bénard convection as a driven baseline lacking closure, and a digital self-replicating soup that carries measured informational heredity while its physical closure remains a structural zero. We demonstrate that plasmas satisfy every admissibility condition for minimal physical autonomy while carrying none of the informational heredity that open-ended evolution requires, sharpening the distinction between physical admissibility and biological sufficiency, and bounding downstream questions of machine sentience.

While skill optimization for autonomous agents has gained traction, existing methods rely on complex pipelines. This leaves a fundamental question unaddressed: What constitutes a minimal viable pipeline for skill optimization, where every component is justified by theory or empirical necessity? We formalize skill optimization via Zeroth-Order (ZO) optimization, mapping classical counterparts (central difference, trust regions) to recent literature. Noting that unlike blind numerical perturbations in classical ZO, skill trajectories serve as interpretable debugging feedback. Grounded in Claude Code philosophy and PAC learning, we establish three principles for convergence and generalization: file-system-based trajectory exploration, consensus attribute mining, and independent validation gating. Eliminating redundancies, we propose SkillOpt-Lite. It accelerates convergence and outperforms full SkillOpt: improving LiveMath by +8.8 points on GPT-5.5 and +25.4 points on GPT-5.4-nano, allowing the nano model to surpass standard GPT-5.4 optimized by SkillOpt. Finally, we integrate our framework into production coding agents like VSCode Copilot, enabling developers to evolve agent skills via one line of vibe. Because our framework treats all agent components simply as standard editable code, this minimal pipeline naturally generalizes to full harness optimization (HarnessOpt). On SpreadsheetBench, HarnessOpt enables GPT-5.4-nano to achieve 0.7758 accuracy, outperforming the larger GPT-5.5 running standard pipelines (0.7620). Code is available at https://github.com/EvolvingLMMs-Lab/SkillOpt-Lite.

Text embeddings are standard for semantic similarity tasks, yet their evaluation remains an open challenge. Current benchmarks are static, cover only a limited set of languages, are often domain-specific, susceptible to overfitting, and poorly representative of low-resource languages. To address these limitations, we introduce ALEE, a framework that extends Sentence Smith (Li et al., 2025) to the cross-lingual and paragraph level. ALEE uses Abstract Meaning Representations (AMR) to generate English minimal pairs with controlled, fine-grained semantic shifts, which are paired with translations in target languages. This approach enables targeted diagnostics for models in any language with English parallel data. We conduct a large-scale empirical study across a diverse set of embedding models and 275+ languages spanning three parallel datasets. On ALEE, performance varies substantially across languages, text lengths, and linguistic phenomena, exposing persistent gaps in cross-lingual semantic representation that track language prevalence in training resources and subword tokenization. We release ALEE at https://github.com/Andrian0s/any-lang-embed-eval

Autonomous vehicles (AVs) are increasingly deployed in urban environments, yet their safety frameworks remain primarily designed around collision avoidance and minimal risk condition (MRC) behaviors such as slowing or stopping when uncertainty arises. Although effective in reducing immediate crash risk, real-world deployments indicate that stopping alone does not guarantee safe integration into human-governed roadway systems. Incidents reported by municipalities and public records show that AV fallback behaviors can obstruct traffic, interfere with emergency response operations, and create accessibility challenges for passengers and pedestrians. This paper presents an analysis of publicly documented incidents involving AV stopping behavior and human-AV interaction failures. We categorize these incidents according to limitations in perception, planning, and control within current AV architectures. Using this taxonomy, we identify key gaps in existing safety paradigms, particularly the lack of mechanisms for interpreting human authority, responding to multimodal instructions, and adapting to dynamic, socially regulated traffic conditions. We then review emerging research directions that support human-interactive perception, language-grounded and accessibility-aware planning, and assisted control through remote guidance and teleoperation. The analysis highlights the need to augment current AV safety frameworks with capabilities that enable cooperative interaction with human agents and infrastructure. These findings suggest that reliable urban deployment of AVs requires moving beyond passive fallback strategies toward human-interactive autonomy.

Background: Digital health technologies allow for frequent, remote gait monitoring in people with multiple sclerosis (MS). However, to differentiate daily variability from actual disease progression in longitudinal data, established minimal clinically important differences (MCID) are required. Currently, there is limited literature defining these thresholds for digital gait metrics. Objective: To establish MCIDs for digital gait measures reflecting progression in MS. Methods: Digital gait measures were captured via daily, remote, smartphone-based Two-Minute Walk Tests in CONSONANCE (NCT03523858), a phase 3b study of ocrelizumab in progressive MS. Using an anchor-based approach, median changes from baseline at Week 96 on digital gait measures were computed for patients showing clinically meaningful worsening on either Timed 25-Foot Walk, Ambulation Score, Expanded Disability Status Scale, or 12-item Multiple Sclerosis Walking Scale. These changes were subsequently triangulated to derive the MCID estimates. Results: 243 patients with progressive MS (female: n=125 (51%); mean [SD] age: 49.3 [9.3]; mean [SD] EDSS: 4.8 [1.4]) had digital gait data available at baseline and Week 96. Median changes were generally consistent across anchors. Triangulated MCIDs are: Step Velocity = -0.16 m/s, Step Velocity Scaled to Walking Time = -0.18 m/s, Step Duration = 0.06 s, Step Length = -0.07 m, Total Number of Steps = -28, and Total Distance Walked = -24 m. Conclusion: These MCIDs provide a framework for interpreting meaningful gait changes and integrating digital measures into MS outcome evaluation. Beyond facilitating novel clinical trial endpoints to evaluate treatment efficacy, they enable objective, real-world monitoring to advance personalized patient care.

In this paper we prove some concentration inequalities for two types of error probabilities in the Empirical Risk Principle (ERP) in statistical learning, which provide a lower bound and an upper bound for the minimal risk (in terms of the minimal empirical risk) with non-asymptotic high confidence. The usual boundedness condition of the empirical risk function is relaxed to the Gaussian or exponential integrability condition. The confidence of the lower bound of the minimal risk is shown to be independent of the number of training parameters and the dimension of the input vectors, allowing one to detect the deficiency of a learning machine efficiently; and the confidence of the upper bound of the minimal risk is proved to be high provided that the sample size $n$ is much greater than the box dimension of the parameter set $Θ$ in the Orlicz metric $d_{ψ_1}$ associated with the risk functions. Our work is based on Talagrand's concentration inequalities (the sharp versions by Bousquet and Klein-Rio), transport-entropy inequalities and the recent progress in the theory of empirical processes and statistical learning.

We propose an information-theoretic framework for graph novelty generation, which aims to generate data that are distinct from existing patterns while preserving global structural consistency. Our approach embeds data into a latent space, models the latent distribution using finite mixture models, and generates novel samples by imposing explicit novelty and reliability conditions formulated in terms of description length. Specifically, novelty is enforced by requiring generated samples to be poorly explained by all existing mixture components, while reliability constrains their impact on the overall mixture structure under the Minimum Description Length (MDL) principle. We provide a theoretical analysis showing that, with appropriate threshold choices, the probabilities of misclassifying non-novel or unreliable samples converge to zero with explicit rates. Experiments on synthetic and benchmark graph datasets demonstrate that the proposed method enables principled novelty generation with quantifiable risk.

Despite remarkable performance on complex tasks, Large Reasoning Models (LRMs) often generate excessively long Chain-of-Thoughts (CoT), inflating computational costs even for simple queries. Existing efforts to mitigate this inefficiency typically rely on discrete reasoning modes or fixed budget tiers, lacking a principled criterion of when reasoning is sufficient. In this work, we introduce Minimal Sufficient CoT (MSC), defined as the shortest prefix of a CoT trajectory which is adequate for producing the correct answer. We empirically show that MSC not only reduces reasoning tokens, but also improves accuracy across difficulty levels. Building on MSC, we propose Sufficiency-guided Continuous Adaptive Reasoning (SuCo), a two-stage training framework for autonomous reasoning control along a continuous spectrum. In stage 1, MSC-Aligned Fine-Tuning (MFT) constructs MSC data using problem-adaptive sufficiency thresholds that naturally scale with question difficulty, then fine-tunes the model to internalize concise yet sufficient reasoning patterns. In stage 2, Sufficiency-Aware Policy Optimization (SAPO) further optimizes the model through reinforcement learning with dynamic complexity tracking and sufficiency-aware rewards that penalize both over- and under-thinking. Extensive experiments across mathematics, code, and science benchmarks show that SuCo consistently achieves improvements in both accuracy and reasoning efficiency.

For the development of Large language models (LLMs), recent approaches to generating pseudo intermediate reasoning have shown remarkable progress. But they typically rely on large numbers of correctly annotated answers to assess reasoning quality. This paper presents a semi-supervised framework that scales reasoning learning from minimal supervision, turning reasoning verification itself into a data creation mechanism. We train a lightweight reasoning-correctness classifier on only a few labeled samples, which judges whether intermediate reasoning traces generated by an LLM are valid. Furthermore, an entropy-based confidence threshold filters out unreliable samples, and the remaining high-confidence reasoning traces are used to fine-tune the model. Experiments on Verifiable Math Problems (Orca-Math subset) and Question Answering on Image Scene Graphs (GQA) with Visual Programming show that our method achieves accuracy comparable to using 10-15x more labeled data. Ablation analyses confirm that both the classifier and entropy filtering are essential for scalable and noise-resistant pseudo-labeling. By replacing expensive answer-level supervision with lightweight reasoning verification, our method provides a practical path toward constructing large-scale reasoning resources and paves the way for future autonomous reasoning systems that learn from minimal human input.

Modern LLM-powered autonomous agents increasingly rely on rich user interface (UI) state observations to achieve reliable action grounding in complex digital environments. However, many deployments transmit the full UI state to remote inference servers even when most elements are irrelevant to the current task, which can leak sensitive but unnecessary context such as authentication codes, private notifications, and background application states. We propose MINIM, a trusted local broker that performs privacy-aware minimization on the client side before any observation leaves the device. Grounded in Contextual Integrity (CI), MINIM learns a dual-score representation for each UI element by predicting an inherent sensitivity score (s) and a task-conditioned necessity score (n). These scores drive a ternary disclosure policy that keeps essential elements, abstracts sensitive attributes when needed, and removes task-irrelevant content. We optimize a CI-aware objective that penalizes necessity errors more strongly on high-risk content, enabling aggressive pruning while preserving task-critical information. Experiments on real-world UI observations derived from WebArena show that MINIM substantially reduces task-irrelevant sensitive leakage while preserving task-critical semantic context and the interactive affordances required for reliable agent actions.

Human decision-making often involves choosing between multi-attribute alternatives, yet classical models assume fully compensatory utility aggregation despite evidence that people reject options with poor performance on critical attributes. We propose a bounded trade-off reasoning framework in which decisions are governed by a screening process that evaluates the balance between gains and losses across attributes. The model introduces a trade-off tolerance parameter that controls acceptable imbalance and can vary across contexts. Through simulation, we show that this mechanism produces preference patterns that differ from standard utility-based models and captures context-dependent variation in trade-off behavior. These results establish bounded trade-off screening as a plausible computational mechanism for multi-attribute choice and generate testable predictions for future behavioral studies.

Genetic programming (GP) is based on two important insights. First, that any learning task can fundamentally be posed as a program induction problem, where the goal is to construct a symbolic hierarchical model that is expressed as a syntax tree. Second, to pose this task as a search problem, and use evolution to locate the desired model. Since it was proposed, GP has produced notable results in a wide range of tasks and problem domains. This work presents an alternative view by modifying the second core insight of GP, posing the problem as a syntactic derivation task instead. In particular, this paper presents Minimalist Genetic Programming (MGP), an algorithm that like GP is biologically inspired, but instead of evolution it takes inspiration from the Minimalist Program to human language, in which syntax is understood as an optimal solution to the problem of linking two other mental systems. In minimalism, the core computational process is a binary set formation operator called $MERGE$, than can be used to incrementally construct complex syntactic structures using a simple Markovian process. MGP is able to discover the core building blocks of the symbolic expressions, and to incrementally combined them using $MERGE$. The proposed system is benchmarked on symbolic regression tasks that are known to be difficult to solve with standard GP systems because of the propensity for bloat. Results show that when a proper lexicon of atomic syntactic objects are chosen, MGP is able to consistently produce the exact ground truth model on a set of symbolic regression tasks where standard GP struggles to do the same. The insights provided by minimalism are shown to be relevant to the problem of program induction, and should be explored further based on the potential exhibited by MGP in this work.

This paper proposes a collapsible method for estimating causal effects that maintains the estimator's consistency before and after marginalization over some variables in completed partially directed acyclic graphs (CPDAGs). We first introduce the estimate collapsibility for CPDAGs and characterize the minimal collapsible sets as strong d-convex hulls. An efficient algorithm is devised to obtain such sets in DAGs and is generalized to CPDAGs. Then, we combine the graph reduction procedure with the IDA framework. Finally, experiments and empirical analysis show the effectiveness of the collapsibility for causal estimations in CPDAGs. Code is available at https://github.com/Jamyang-D/strongly-convex.

The growing demand for transparency in automated decision-making has propelled eXplainable Artificial Intelligence (XAI) to the forefront of machine learning research. In computer vision, however, existing explanation methods often prioritize end-user accessibility at the expense of formal guarantees, leaving a critical gap between practical utility and theoretical rigor. In this paper, we address this gap by introducing OPTIMUS, a novel framework for generating concept-based visual explanations for deep classification models. OPTIMUS explanations take the form of visual heatmaps that not only remain interpretable to end users, but are grounded in the well-established theory of prime implicants, providing formal guarantees that have been largely absent from existing saliency-based methods. Specifically, OPTIMUS explanations satisfy two desirable properties: sufficiency, ensuring that the highlighted concepts provably guarantee the classifier's prediction, and minimality, ensuring that no strict subset of those concepts retains this guarantee. Together, these properties yield explanations that are both logically tight and visually coherent. We validate our approach on a visual classification benchmark, demonstrating that OPTIMUS heatmaps naturally and faithfully surface the decision-relevant concepts underlying model predictions.

Large language models are increasingly evaluated by other models, raising a natural question: can a model predict how a judge will score its own output? We find that the ability is largely present before any targeted training: prompted few-shot, a base model already predicts an external judge's multi-attribute quality scores on open-ended responses well above chance across three benchmarks. We introduce Self-Evaluation Elicitation (SEE), a method that surfaces this latent ability through a short cycle comprising a calibration-coupled reinforcement learning phase that improves the answer and predicts the judge, followed by a masked distillation phase that sharpens the prediction while leaving the answer untouched. From 160 unique examples, roughly 31x fewer than a reinforcement learning baseline, SEE improves held-out calibration across three benchmarks while preserving answer quality. The elicited self-evaluation is sharply localized within the model's own token distribution and stable across judges it was never trained against, indicating a transferable notion of quality rather than a single judge's preference. These results reframe judge-aligned self-evaluation as a problem of elicitation rather than acquisition.

Minimum Description Length (MDL) formalizes the principle of Occam's razor by optimizing the total description length: $L(\mathrm{model})+L(\mathrm{data} \ | \ \mathrm{model})$. For sequential prediction, the MDL method repeatedly selects a model with a minimum objective score of the observed prefix for the next step prediction. Classical MDL prediction theory shows that exact optimization of the MDL objective indeed provides a strong compression guarantee that supports reliable prediction. However, practical machine learning usually can only find models by approximately optimizing the objective function. To bridge this gap, this paper addresses the following fundamental question: Under what forms of approximation and regularization does approximate MDL still guarantee reliable sequential prediction? This work offers a principled characterization. We prove that for any approximation with additive slack $C$ of the more general form of the balanced MDL objective: $λ\cdot L(\mathrm{model})+L(\mathrm{data} \ | \ \mathrm{model})$, the cumulative expected squared prediction error is finite for all $λ\ge1$. The case $λ>1$ is proved by an affinity-telescoping argument, while the boundary case $λ=1$ is proved by a likelihood-ratio stopping argument based on exact static MDL bounds. Our results establish that classical MDL regularization remains robust to any fixed additive optimization error. Furthermore, we establish that our characterization of the approximate MDL framework is sharp: When $0<λ<1$, overfits can happen to incur infinite cumulative expected error in the universal class of estimable measures, and hence a strong form of model-complexity regularization is necessary. In addition, model selection may fail in every regularized regime $λ>0$, under multiplicative approximation, and thus, additive approximation is both sufficient and essential.

While safety alignment and guardrails help large language models (LLMs) avoid harmful outputs, they can also induce overrefusal, i.e., unwarranted rejection of benign queries that merely appear risky. We present DDOR (Delta Debugging for OverRefusal), a fully automated and explainable framework for overrefusal testing and repair in a black-box setting, where only model inputs and outputs are accessible and internal safety mechanisms remain opaque. DDOR applies delta debugging to localize minimal refusal-triggering fragments (mRTFs) that provide phrase-level, explainable evidence for why a refusal occurs. Conditioned on these mRTFs, DDOR generates diverse, context-rich prompts and performs multi-oracle validation to filter intrinsically unsafe or ambiguous cases, producing scalable and model-specific overrefusal test suites (approximately 1K cases per model). Beyond evaluation, we further leverage localized mRTFs to perform targeted prompt repair, substantially reducing overrefusal while preserving the original intent and maintaining safety on genuinely harmful inputs. Overall, DDOR offers a practical end-to-end solution to both evaluate and mitigate overrefusal, improving LLM usability without sacrificing safety.

Large language model agents trained with reinforcement learning (RL) often learn brittle, task-specific shortcuts. We hypothesize that agents generalize better when their successful trajectories are structurally compressible, decomposed into a small set of reusable abstract patterns. To formalize this, we introduce ReuseRL, which grounds agentic RL in the Minimum Description Length (MDL) principle. ReuseRL extracts a shared skill dictionary from successful trajectories and augments the RL objective with a segmentation cost, explicitly penalizing idiosyncratic behaviors that encode poorly. We prove a PAC-Bayes bound guaranteeing that a dictionary extracted from successful trajectories has bounded expected description length on future successful behavior. Across ALFWorld, TextWorld-Cooking, and Countdown-Stepwise, ReuseRL improves in- and out-of-distribution success over vanilla GRPO and strong round-length baselines.

Spectral clustering largely depends on the affinity graph, yet constructing a graph that preserves reliable local connectivity while adapting to heterogeneous data structures remains challenging. Existing granular-ball-based spectral clustering methods usually reduce graph complexity by using coarse-grained representatives. However, the learned local regions are often treated as graph nodes or anchors, and their structural information is not sufficiently used to regularize the original sample-level graph. To address this issue, this paper proposes a Minimum Description Length based Granular-Ball Tree-Regularized Spectral Clustering method, termed MDL-GBTRSC. The proposed method constructs a granular-ball tree through local MDL model selection, with reciprocal neighborhood continuity used to discourage splits that break reliable local connections. The stable leaf balls obtained from the tree provide coding-scale information for regularizing the sample-level affinity graph. In addition, a shared-neighbor bridge code is introduced to adjust weak local bridge relations without requiring an additional user-specified threshold. In this way, MDL-GBTRSC connects interpretable local representation learning with affinity graph construction in a unified spectral clustering framework. Experiments on real and synthetic datasets show that MDL-GBTRSC achieves the best average ARI and NMI under the adopted fixed-configuration protocol compared with classical spectral clustering baselines and representative granular-ball, micro-cluster, and anchor-based methods.

In this paper, we establish last-iterate convergence rates for off-policy actor--critic methods in reinforcement learning. In particular, under a single-loop, single-timescale implementation and a broad class of policy updates, including approximate policy iteration and natural policy gradient methods, we prove the first $\tilde{\mathcal{O}}(ε^{-2})$ sample complexity guarantee for finding an $ε$-optimal policy under minimal assumptions, namely, the existence of a policy that induces an irreducible Markov chain. This stands in stark contrast to the existing literature, where an $\tilde{\mathcal{O}}(ε^{-2})$ sample complexity is achieved only through nested-loop updates and/or under strong, algorithm-dependent assumptions on the policies, such as uniform mixing and uniform exploration. Technically, to address the challenges posed by the coupled update equations arising from the single-loop implementation, as well as the potentially unbounded iterates induced by off-policy learning, our analysis is based on a coupled Lyapunov drift framework. Specifically, we establish a geometric convergence rate for the actor and an $\tilde{\mathcal{O}}(1/T)$ convergence rate for the critic, and combine the two Lyapunov drift inequalities through a cross-domination property. We believe this analytical framework is of independent interest and may be applicable to other coupled iterative algorithms with unbounded

Shortcut features are often invoked to explain out-of-distribution (OOD) failure, but training correlation, learned shortcut use, and test-time failure need not coincide. We study a minimal binary model with one invariant coordinate and one family-dependent shortcut coordinate. In the deterministic regime, positive average shortcut correlation pulls logistic ERM toward positive shortcut weight, but ridge regularization keeps the classifier invariant-dominated and prevents deterministic OOD failure. When the invariant coordinate is noisy, ridge-logistic ERM switches to the shortcut rule once the training shortcut signal exceeds the invariant signal. Whether that transition causes failure depends on the held-out family: weaker shortcut correlation yields positive excess risk, and sign-flipped families yield above-chance error. Synthetic checks match these analytic regimes and show that the same training-side transition can have different held-out consequences. The model separates shortcut attraction, shortcut-rule transition, and cross-family OOD failure.

Existing granular-ball classification methods are often driven by handcrafted quality measures, neighborhood rules, or heuristic splitting and stopping criteria, which may reduce the transparency of local construction decisions and hinder explicit modeling of boundary-sensitive regions. To address this issue, this paper proposes a Minimum Description Length based Granular-Ball Classifier (MDL-GBC), a boundary-aware non-parametric and interpretable granular-ball classifier. MDL-GBC formulates class-conditional granular-ball construction as a local model selection problem under the Minimum Description Length principle. For each class, samples from the target class provide positive class evidence, while samples from the remaining classes provide negative boundary evidence. For each current granular ball, three candidate explanations are compared under a unified description-length criterion: a single-ball model, a two-ball model, and a core-boundary model. The selected model determines whether the ball is retained, geometrically split, or refined into core and boundary-sensitive child balls, thereby making local construction decisions consistent with the MDL-based classification mechanism. During prediction, a class-level mixture coding rule aggregates stable granular balls of the same class and assigns the test sample by comparing class-wise coding costs. Experiments on 18 benchmark datasets show that MDL-GBC achieves competitive classification performance against classical classifiers and representative granular-ball-based methods, obtaining the best average Accuracy, Macro-F1, and average rank. These results indicate that MDL-GBC provides an effective and interpretable alternative to conventional heuristic granular-ball classification strategies.

This paper demonstrates RUBEN, an interactive tool for discovering minimal rules to explain the outputs of retrieval-augmented large language models (LLMs) in data-driven applications. We leverage novel pruning strategies to efficiently identify a minimal set of rules that subsume all others. We further demonstrate novel applications of these rules for LLM safety, specifically to test the resiliency of safety training and effectiveness of adversarial prompt injections.

Existing granular-ball generation methods are still mainly driven by handcrafted quality measures and heuristic splitting or stopping criteria, which may weaken the transparency of local generation decisions in clustering. To address this issue, this paper proposes Minimum Description Length based Granular-Ball Generation (MDL-GBG), a non-parametric and interpretable granular-ball generation method for clustering. MDL-GBG reformulates granular-ball generation as a local model selection problem under the Minimum Description Length principle. For each granular ball, three candidate explanations are compared, namely a single-ball model, a two-ball model, and a core-ball-plus-residual model, and the model with the shortest description length is selected. In this way, ball retention, splitting, and residual peeling are unified within a common coding-theoretic framework. A residual reassignment mechanism is further introduced to re-evaluate peeled-off boundary samples after stable granular-balls are formed. Experiments on 20 UCI datasets show that the stable granular-balls generated by MDL-GBG provide an effective upstream representation for clustering. In particular, MDL-GBG+AC achieves the best average ranks in ARI, ACC, and NMI among the compared methods. These results indicate that MDL-GBG offers a principled and interpretable alternative to heuristic granular-ball generation strategies.

Large reasoning models achieve high accuracy through extended chain-of-thought but generate 5--8 more tokens than necessary, applying verbose reasoning uniformly regardless of problem difficulty. We propose Hint Tuning, a data-efficient approach that teaches models to calibrate reasoning depth. Our key insight: the corresponding instruct model serves as an ideal difficulty probe. By testing what the instruct model can solve with varying guidance, we automatically construct training data across three states: No-Hint (direct answer), Sparse-Hint (minimal prefix), and Full-Hint (complete reasoning). This converts the abstract challenge of difficulty labeling into a measurable consistency check between the instruct and reasoning models. With only 1K self-annotated samples, Hint Tuning achieves 24--66% token reduction (31.5% average) across mainstream reasoning models (Qwen3-Thinking, DeepSeek-R1-Distill) at multiple scales (4B--32B) while maintaining competitive accuracy on five benchmarks. Unlike methods requiring massive distillation datasets or expensive RL, we achieve superior efficiency through simple alignment with the instruct model's capabilities. Code and data are available at https://github.com/redai-infra/hint-tuning.

We present an SMT-based active learning algorithm for nondeterministic weighted automata (WFAs) as a practical and robust alternative to Hankel/L*-style methods. Our algorithm is parametric in a given semiring and, if it terminates, guaranteed to produce minimal WFAs. We prove partial correctness and provide a sufficient termination condition, which in particular implies termination for all finite semirings. Our extensive experimental evaluation shows that our algorithm is capable of learning numerous minimal WFAs over both finite and infinite semirings, vastly outperforms a naive baseline, and is competitive with a state-of-the-art algorithm while producing significantly smaller automata and requiring less interaction with the teacher.

Single-Image Super-Resolution (SISR) aims to reconstruct a High-Resolution (HR) image from a Low-Resolution (LR) observation, a fundamentally ill-posed problem where high-frequency details are severely degraded at large upscaling factors. Recent advances have been driven by transformer-based architectures and diffusion models improve global context modeling and perceptual quality at the cost of increased computational complexity. In contrast, this work focuses on enhancing the expressivity of local operators under minimal resources. We propose SRGAN--CKAN, a hybrid super-resolution framework that integrates Convolutional Kolmogorov--Arnold Networks (CKAN) into an adversarial learning setting reformulating convolution as a nonlinear patch-based transformation. The proposed operator replaces linear local mappings with spline-based functional representations, allowing expressive modeling of complex local structures and high-frequency textures using minimal hardware resources. Experimental results demonstrate that the proposed approach improves perceptual quality while preserving reconstruction fidelity, achieving a favorable balance between distortion-based and perceptual metrics. These results are obtained under constrained computational settings, highlighting the efficiency of the proposed formulation. Overall, this work introduces a complementary direction to existing approaches by improving the representational power of local transformations, providing an efficient and scalable alternative to globally intensive architectures.

Safety trained large language models (LLMs) can often be induced to answer harmful requests through jailbreak prompts. Because we lack a robust understanding of why LLMs are susceptible to jailbreaks, future frontier models operating more autonomously in higher-stakes settings may similarly be vulnerable to such attacks. Prior work has studied jailbreak success by examining the model's intermediate representations, identifying directions in this space that causally encode concepts like harmfulness and refusal. Then, they globally explain all jailbreak attacks as attempting to reduce or strengthen these concepts (e.g., reduce harmfulness). However, different jailbreak strategies may succeed by strengthening or suppressing different intermediate concepts, and the same jailbreak strategy may not work for different harmful request categories (e.g., violence vs. cyberattack); thus, we seek to give a local explanation -- i.e., why did this specific jailbreak succeed? To address this gap, we introduce LOCA, a method that gives Local, CAusal explanations of jailbreak success by identifying a minimal set of interpretable, intermediate representation changes that causally induce model refusal on an otherwise successful jailbreak request. We evaluate LOCA on harmful original-jailbreak pairs from a large jailbreak benchmark across Gemma and Llama chat models, comparing against prior methods adapted to this setting. LOCA can successfully induce refusal by making, on average, six interpretable changes; prior work routinely fails to achieve refusal even after 20 changes. LOCA is a step toward mechanistic, local explanations of jailbreak success in LLMs. Code to be released.

Large language model (LLM) reading assistants are increasingly used in settings that require interpretation rather than simple retrieval. In these contexts, the central risk is not only error or unsafe output, but interpretive displacement: the transfer of meaning-making work from reader to system. This paper examines that problem through the concept of epistemic guardrails, defined here as constraints on how an artificial intelligence (AI) system participates in reading and interpretation. Using TextWalk, a minimal reading-support prototype designed as a co-reader rather than an answer-provider, the study applies a fixed ten-prompt protocol to twelve analytical texts spanning four categories of argumentative prose. The protocol escalates from baseline reading support to interpretive inquiry, boundary stress, and explicit shortcut pressure, enabling guardrails to be examined as behavioral properties observable in interaction rather than as static instruction features. Results show strong baseline stability, measurable strain during interpretive inquiry, partial recovery under direct boundary stress, and late-stage stabilization under escalation pressure. The most consequential weaknesses did not appear as overt collapse, but in a middle zone between support and substitution, where the system remained grounded and pedagogical while redistributing too much interpretive labor away from the reader. The paper contributes a protocol for evaluating epistemic guardrails as interactional phenomena in conversational AI reading assistants, an empirical account of their behavioral dynamics under pressure, and an emerging model of interpretive boundary function in reading-support AI.

Type annotations are essential when printing terms in a way that preserves their meaning under reparsing and type inference. We study the problem of complete and minimal type annotations for rank-one polymorphic $λ$-calculus terms, as used in Isabelle. Building on prior work by Smolka, Blanchette et al., we give a metatheoretical account of the problem, with a full formal specification and proofs, and formalize it in Isabelle/HOL. Our development is a series of experiments featuring human-driven and AI-driven formalization workflows: a human and an LLM-powered AI agent independently produce pen-and-paper proofs, and the AI agent autoformalizes both in Isabelle, with further human-hinted AI interventions refining and generalizing the development.

This work simulates the developmental process of cortical neurogenesis, initiating from a single stem cell and governed by gene regulatory rules derived from mouse single-cell transcriptomic data. The developmental process spontaneously generates a heterogeneous population of 5,000 cells, yet yields only 85 mature neurons - merely 1.7% of the total population. These 85 neurons form a densely interconnected core of 200,400 synapses, corresponding to an average degree of 4,715 per neuron. At iteration zero, this minimal circuit performs at chance level on MNIST. However, after a single epoch of standard training, accuracy surges to over 90% - a gain exceeding 80 percentage points - with typical runs falling in the 89-94% range depending on developmental stochasticity. The identical circuit, without any architectural modification or data augmentation, achieves 40.53% on CIFAR-10 after one epoch. These findings demonstrate that developmental rules sculpt a domain-general topological substrate exceptionally amenable to rapid learning, suggesting that biological developmental processes inherently encode powerful structural priors for efficient computation.

When do transformers commit to a decision, and what prevents them from correcting it? We introduce \textbf{prolepsis}: a transformer commits early, task-specific attention heads sustain the commitment, and no layer corrects it. Replicating \citeauthor{lindsey2025biology}'s (\citeyear{lindsey2025biology}) planning-site finding on open models (Gemma2 2B, Llama3.2 1B), we ask five questions. (Q1)~Planning is invisible to six residual-stream methods; CLTs are necessary. (Q2)~The planning-site spike replicates with identical geometry. (Q3)~Specific attention heads route the decision to the output, filling a gap flagged as invisible to attribution graphs. (Q4)~Search requires ${\leq}16$ layers; commitment requires more. (Q5)~Factual recall shows the same motif at a different network depth, with zero overlap between recurring planning heads and the factual top-10. Prolepsis is architectural: the template is shared, the routing substrates differ. All experiments run on a single consumer GPU (16,GB VRAM).

Multimodal instruction tuning is often compute-inefficient because training budgets are spread across large mixed image-video pools whose utility is highly uneven. We present Goal-Driven Data Optimization (GDO), a framework that computes six sample descriptors for each candidate and constructs optimized 1$\times$ training subsets for different goals. Under a fixed one-epoch Qwen3-VL-8B-Instruct training and evaluation recipe on 8 H20 GPUs, GDO uses far fewer training samples than the Uni-10x baseline while converging faster and achieving higher accuracy. Relative to the fixed 512k-sample Uni-10x baseline, GDO reaches the Uni-10x reference after 35.4k samples on MVBench, 26.6k on VideoMME, 27.3k on MLVU, and 34.7k on LVBench, while improving Accuracy by +1.38, +1.67, +3.08, and +0.84 percentage points, respectively. The gains are largest on MVBench and MLVU, while LVBench improves more modestly, consistent with its ultra-long-video setting and the mismatch between that benchmark and the short-video/image-dominant training pool. Across MinLoss, Diverse, Temp, and Temp+, stronger temporal emphasis yields steadily better long-video understanding behavior. Overall, GDO provides a goal-driven data optimization framework that enables faster convergence with fewer training samples under a fixed training protocol. Code is available at https://github.com/rujiewu/GDO.

Layer-wise capacity in large language models is highly non-uniform: some layers contribute disproportionately to loss reduction, whereas others are nearly redundant. Existing layer-scoring methods provide sensitivity estimates but do not give a principled rule for converting those estimates into allocation or pruning decisions under a global hardware budget. We introduce a curvature-aware, MDL-inspired framework built around the layer gain $ζ_k^2=g_k^\top\widetilde H_{kk}^{-1}g_k$. This quantity equals twice the maximal decrease predicted by the regularized layer-restricted quadratic model and incorporates inverse local curvature; it is therefore a local surrogate for reducible risk, not a universal dominance claim over gradient-norm scores. After normalizing the gains into scores $q_k$, we formulate two convex programs: one allocates expert slots under diminishing returns, and the other assigns layer-wise pruning ratios while protecting high-score layers. Both continuous programs have unique globally optimal solutions characterized by one dual variable and computable in $O(K\log(1/\varepsilon))$ time by bisection. We also prove a quadratic transfer-regret bound: when source and target score vectors differ by at most $δ$, the target surrogate cost of the transferred decision is within $O(δ^2)$ of the target optimum. Experiments on Mistral-7B and Gemma-7B show clear allocation gains in some settings and competitive, though mixed, pruning performance. The framework therefore replaces an empirical score-to-decision heuristic with a budget-feasible optimization procedure whose guarantees apply to the stated continuous surrogates. Code is available on github repo - TKAI-LAB-Mali/Curvature-Weighted-Capacity-Allocation

Mechanistic interpretability aims to reverse-engineer large language models (LLMs) into human-understandable computational circuits. However, the complexity of pretrained models often obscures the minimal mechanisms required for specific reasoning tasks. In this work, we train small, attention-only transformers from scratch on a symbolic version of the Indirect Object Identification (IOI) task, a benchmark for studying coreference-like reasoning in transformers. Surprisingly, a single-layer model with only two attention heads achieves perfect IOI accuracy, despite lacking MLPs and normalization layers. Through residual stream decomposition, spectral analysis, and embedding interventions, we find that the two heads specialize into additive and contrastive subcircuits that jointly implement IOI resolution. Furthermore, we show that a two-layer, one-head model composes information from the previous layer primarily through query-key interactions. These results demonstrate that task-specific training induces highly interpretable, minimal circuits, offering a controlled testbed for probing the computational foundations of transformer reasoning.

The increasing scale of AI workloads demands High-Performance Computing (HPC) infrastructure and training methodologies that are both scalable and sustainable. While Large Language Models (LLMs) demonstrate exceptional natural language capabilities, general-purpose models often lack the specialized domain knowledge necessary for effective cybersecurity analysis. We investigate Domain-Adaptive Continuous Pretraining (DAP) as a scalable, resource-efficient methodology for enhancing cybersecurity understanding in pretrained LLMs, implemented through a distributed Fully Sharded Data Parallel (FSDP) pipeline across multi-node GPU clusters. We systematically adapted three decoder-based architectures -- Llama-3.1-8B, DeepSeek-R1-Distill-Qwen-14B, and Llama-3.3-70B-Instruct -- using a curated 126-million-word cybersecurity corpus from standards, academic literature, and technical documentation. Evaluation across three cybersecurity benchmarks -- CTI-MCQ, CyberMetric, and SecEval -- demonstrates consistent improvements post-adaptation. Notably, our Llama-3.3-70B-Ins-DAP model achieves state-of-the-art performance with accuracies of 0.718, 0.933, and 0.864, respectively, surpassing parameter-efficient baselines and specialized models including Llama-Primus-Base (trained on 2.77 billion tokens) and Foundation-Sec-8B (trained on 5 billion tokens), despite utilizing only 118.8 million tokens -- representing a 23-to-42-fold reduction in training data. Targeted continuous pretraining via scalable HPC infrastructure enables effective cybersecurity domain adaptation with a substantially reduced computational and energy footprint, supporting specialized AI assistants in threat analysis, vulnerability assessment, and security documentation, while advancing sustainable and responsible AI development.