Computer Science & Mathematics

Software engineering (SE) expertise can shape how coding large language models (LLMs) are trained and which engineering capabilities they acquire. We examine this role through an industrial case study of capability-focused training for a 92B-parameter coding LLM serving more than 100,000 developers. We demonstrate how established SE knowledge can guide the selection of engineering capabilities, the construction of verifiable training data, and the evaluation of model improvements. To target repository-level refactoring, we developed RefactorForge, a pipeline that combines refactoring knowledge, established SE tools, and verification techniques to construct training data. Across 306 Python repositories, RefactorForge generated 5,704 executable tasks and retained 4,572 verified teacher trajectories totaling 72.51 million tokens. Incremental supervised fine-tuning on these trajectories, accounting for 0.46% of the preceding coding mixture's tokens, improved RefactorBench performance by 18.00 percentage points and SWE-Bench ProMax performance by 7.06 points. Under OpenCode, these improvements extended to SWE issue resolution, with gains of 4.97 points on SWE-Bench Verified and 1.23 points on SWE-Bench Pro. Improvements also persisted across other coding-agent harnesses, while greenfield repository generation showed mixed results. We report lessons from constructing capability-focused training data and evaluating its effects across engineering workloads. Building on this industrial experience, we propose a research agenda for expanding SE's role in transforming coding LLMs into SE LLMs: incorporating SE knowledge into model training, applying engineering methods to model development and maintenance, and systematically defining the engineering capabilities these models should acquire.

Language is a natural way to command robots, but converting a single instruction into a long-horizon, contact-rich hand-object interaction remains challenging: synthesized references are noisy, human-to-robot retargeting introduces embodiment bias, and fixed-reference tracking lets small errors snowball. We address this with AdaDexTrack, a modulator-in-the-loop framework for language-conditioned manipulation tracking. A distilled generalist tracker serves as the skill carrier, while a tightly aligned modulator performs three feedback corrections: reference modulation (continual adjustment of what to track), object-latent modulation (online adaptation of the object representation to recruit suitable skills), and positional-target modulation (small state-dependent refinements for execution). The tracker is learned via large-scale specialist to generalist distillation on a corpus of language-conditioned hand-object trajectories; the modulator is trained with RL under the same task objective, ensuring tight coupling. Across large-scale evaluations, AdaDexTrack consistently outperforms prior SOTA on unseen-trajectory and unseen-object sets in both average tracking error and success rate, demonstrating robustness and generalization. We further show zero-shot sim-to-real transfer on real hardware, where adding the modulator yields substantial gains over a tracker-only variant. AdaDexTrack reframes language-conditioned dexterous manipulation as modulated tracking, replacing the open-loop, fixed-reference tracking with in-loop modulation that adjusts the reference, object latent, and positional target, yielding drift-resistant execution from noisy text references.

Repository-level automated program repair must reason about more than a localized failing statement. A candidate change can satisfy a narrow test while violating dependency boundaries, modifying an unsafe path, or relying on context that omits relevant repository structure. ArchGuard-APR is an architecture-aware repair prototype that integrates deterministic repository analysis, immutable repository graphs, explicit architecture profiles, graph-guided context retrieval, role-based repair orchestration, patch-policy enforcement, isolated execution feedback, provider cost controls, and canonical source-free evidence. We evaluate the implemented pipeline through an exploratory paired feasibility study, not a confirmatory effectiveness experiment. Six executions were planned; four completed, and two black-4 conditions ended in pre-provider infrastructure attrition. Across two valid paired tasks, baseline and ArchGuard conditions each produced 0/2 successful repairs, and all four completed outputs were classified as invalid patches. The completed executions consumed 35,431 input tokens and 2,737 output tokens, for a total of 38,168 tokens, at a total cost of USD 0.1296325. No effectiveness advantage was observed, and the sample provides no useful inferential basis. The study instead establishes the engineering feasibility of composing architecture constraints with a reproducible repair pipeline and identifies patch validity and infrastructure robustness as the principal targets for future work.

We introduce TrackTok, an efficient video tokenization framework that produces object-centric tokens, i.e., tokens that consistently encode the same semantic objects across time, even as it moves, deforms, or undergoes partial occlusion. Conventional patch-based or existing holistic tokenizers produce token identities often tied to fixed image locations. In contrast, our approach learns temporally persistent object-centric representations that bind visual features across frames into stable semantic units. This enables substantially more compact, continuous latent video representations, reducing the number of tokens required for downstream generative modeling with state-of-the-art flow models, while preserving the semantic structure needed for high-quality synthesis. Our tokenizer offers a favorable quality-efficiency trade-off. TrackTok achieves comparable class-conditional generative FVD on UCF-101 dataset at 8 times fewer latent tokens and better latency, and outperforms existing 1D tokenization baselines on frame prediction task on Kinetics-600 across low token budgets. These results suggest that object-aligned and temporally persistent tokenization is a promising direction for scalable video generation, where reducing latent token counts is critical for efficient modeling. Our code for this work is available at https://github.com/phamleyennhi/tracktok.

Numina Fuse is an agent-native application for formalizing mathematics in Lean 4. Since Lean can compile while not representing its intended informal meaning, and agents now write Lean faster than people can read it, we built Fuse around human supervision of agent work. A user works with an AI orchestrator on a Lean project and supervises it through views of the blueprint, the dependency graph, and the Lean code, while the backend keeps the project's derived state and runs agents for hours without the user present. We describe the development of Fuse throughout 2026, as it moved from a prescribed pipeline of agents paced by human review to an orchestrator that dispatches specialists, provers, and parallel children on its own. We designed for this shift, keeping project state, tooling, and interface design separate from orchestration so that agents could take over more of the work as models improved. We report Fuse's use in a formalization of the three-dimensional Kakeya conjecture and a study of prover models. We close with lessons for the next generation of autoformalization systems. Fuse Desktop, an open-source local version, is available at https://github.com/project-numina/fuse-desktop.

Repeated attempts at interactive tasks uncover facts, useful operations, and failures that can inform subsequent execution. We introduce ReGE, a framework for turning this recorded experience into guidance for a fresh attempt. Its main implementation, ReGE-Syn, uses a single coach call to jointly synthesize bounded execution records and available artifacts into self-contained guidance, connecting task-specific findings with proposed actions and relevant pitfalls. A student starts from the task's initial environment state and adapts this guidance to current observations. Source generation, synthesis, and student execution use the same base model, without parameter updates or a stronger teacher. Across four benchmarks, ReGE improves accuracy by an average of 9.9 percentage points for GPT and 8.8 percentage points for Claude compared with unguided execution. On matched BrowseComp-Plus subsets, ReGE-Syn reduces guidance-construction tokens by 98.2\% on GPT and 95.5\% on Claude relative to adapted AggAgent, with observed success. Combined construction and execution tokens decrease by 15.7\% and 35.4\%, respectively, counting input plus output and excluding source generation. BrowseComp-Plus ablations further associate access to process information with fewer student steps and show that joint synthesis produces substantially shorter guidance than Direct history or Independent summaries, with observed success. These results demonstrate how agents can use their own recorded experience to improve subsequent task completion, and suggest a low-cost way to consolidate the execution records of parallel agent systems such as agent swarms.

Distributed Cyber-Physical Systems (CPS) and Edge AI networks increasingly depend on public-key authentication and key-establishment mechanisms that are vulnerable to cryptographically relevant Quantum Computers (QC). Shor's algorithm threatens widely deployed asymmetric primitives, while Grover's algorithm reduces the effective security margins of symmetric and hash-based mechanisms. Although Post-Quantum Cryptography (PQC) provides a migration path, its larger public keys, ciphertexts, and signatures introduce additional computation, memory, communication, storage, and packet-fragmentation costs that can constrain dynamic multi-agent systems. In this article, we introduce rotational secrecy, an architectural objective that limits temporal key exposure through authenticated transitions between cryptographic epochs. We present Private Authentication for Rotational Secrecy (PARS), a reference mechanism that coordinates policy-triggered key establishment, rotation, and reconciliation among authorized Physical AI agents. For deployments that need distributed agreement on security state, we further develop the PARS-Enabled Edge Security Ledger (PARS-ESL), an optional permissioned architecture maintained by authorized validators or capable edge gateways. PARS-ESL does not store high-volume operational transactions. Instead, it records authenticated state for key epochs, group membership, revocation, algorithm-suite policies, challenge validation, and recovery checkpoints. As a result, resource-constrained agents can take part as lightweight clients, and low-latency operational traffic stays outside the ledger consensus path, protected by the currently active symmetric epoch keys. Our results show that ledger-assisted post-quantum key-epoch management is feasible for selected Edge AI and CPS security-control workloads under the stated trust, compromise, connectivity, and resource assumptions.

Long-horizon manipulation requires actions whose validity depends on earlier interactions, yet visual progress can conceal missing task prerequisites. We propose RoboLongR, an offline-to-online framework that learns history-dependent rewards to guide policy adaptation to new tasks. Its central objective is causal consistency: aligning rewarded progress with prerequisites supported by execution history. Stage-shuffle supervision encourages execution-order sensitivity, recurrent memory preserves evidence of earlier interactions, and two-round training refines trajectory segments using predicted progress. The resulting rewards guide stage-conditioned policy refinement from behavior cloning to online reinforcement learning. Sparse terminal feedback connects policy experience to reward learning by triggering correction for repeated high-scoring failures. Pretrained on demonstrations from 88 RLBench tasks and Open-X data, RoboLongR achieves 31.8% average success on 18 long-horizon tasks excluded from reward pretraining, exceeding the strongest evaluated baseline by 9.2 percentage points. Across four real-robot tasks, it achieves 57.5% success, a 32.5-percentage-point improvement over the comparison method. Reward-level controls probe sensitivity to synthetic order perturbations, while ablations examine the contributions of individual components to policy improvement.

We study the efficiency--complexity tradeoff for resource-limited agents through directed first-passage percolation. Nonnegative i.i.d. edge weights represent physical energy expenditure, while the logarithmic size of a constrained path family measures representational complexity. For translation-invariant families, a path-joining property yields deterministic large-distance costs in rational directions and joint convexity in constraint parameter and direction, under suitable moment and feasibility assumptions. Our main result concerns the limiting cost parameterized by path-family entropy. Using techniques from analytic combinatorics in several variables (ACSV), we establish its almost-sure existence and joint continuity in entropy and direction for nested families satisfying additional generating-function conditions, on the corresponding entropy range. Path-count asymptotics supply the change of parameter linking this cost to the constraint-parameterized cost. Two planar examples constrain the number of turns or the number of East-runs of length at least two.

Vision-language-action (VLA) models enable robots to follow instructions in typed text, limiting broader deployment in natural speech. The traditional solution by prepending a speech recognition before VLA to convert speech into texts would incur additional latency and propagate errors. To address this, we present Speech-$π_{0.5}$, which maps raw speech directly to motor commands without explicit textual transcriptions. Specifically, built on $π_{0.5}$, we use a cross-modal projection to convert voice frames directly into audio tokens with significant response latency reduction. To further improve the accuracy, we adopt split LoRA adaptation with dedicated audio and task adapters, under a two-stage training. Speech-$π_{0.5}$ achieves $3\times$ lower response latency than ASR pipeline while maintaining competitive task success on LIBERO, and generalizes robustly to unseen accents where a single adapter degrades significantly.

Language-aware 3D Gaussian Splatting (3DGS) has advanced language-driven 3D scene understanding by incorporating semantic and relational cues into reconstructed scenes. However, relation-aware grounding depends not only on representing such information, but also on whether the underlying scene-side evidence is reliable and sufficient. Multi-view semantic aggregation can incorporate weak observations, while object relations can remain under-observed along the available camera trajectory, leading to ambiguous evidence for target disambiguation. We present RelateGS, a structured language-aware Gaussian representation that selectively refines semantic and relational evidence for 3D visual grounding. RelateGS suppresses unreliable observations during semantic feature uplifting and consolidates multi-view object observations into a persistent 3D graph. The graph further identifies under-observed object relations and guides targeted re-querying of informative existing frames to complement their evidence. Experiments on Sr3D+ and Nr3D demonstrate competitive 3D grounding performance, improving the previous best by 7.9 and 1.7 percentage points at [email protected], respectively.

In this work, we used temperature-dependent electron paramagnetic resonance (EPR) spectroscopy to reveal the effect of high-temperature annealing in N2 and air on paramagnetic and electronic properties of ZnO microparticles. EPR spectral simulations have shown that N2 annealing produces Zni, VO+, and shallow-donor centers, whereas Zni, VO+, and Hi-related centers are observed after annealing the ZnO microparticles in an air atmosphere. The resolved paramagnetic centers exhibit distinctly different behavior over 5-297 K. The shallow-donor and Hi signals are rapidly quenched below approximately 50 K, while the Zni contribution shows a nonmonotonic temperature dependence. In contrast, the VO+ signal persists up to room temperature and increases with temperature, consistent with charge redistribution among donor-related defects involving deep oxygen-vacancy states. The cavity Q-factor generally decreases with increasing temperature for both annealed samples, indicating atmosphere-dependent changes in the microwave losses. These results show that the annealing atmosphere controls the paramagnetic defect population, the temperature dependence of donor-related centers, and the associated electronic response of ZnO microparticles.

Many supervised dimensionality reduction methods promote intra-class compactness and inter-class separation but do not explicitly constrain class geometry, leading to variability in the relative arrangement of classes across independent runs. Such variability limits the reproducibility and interpretability of low-dimensional embeddings. We propose the Isometric Centroid-Encoder (ICE), a supervised dimensionality reduction framework in which class centroids are learned directly in the latent space while preserving a prescribed pairwise class-centroid geometry. Unlike existing centroid- or prototype-based methods that primarily encourage intra-class compactness, ICE explicitly regularizes the relative arrangement of latent class centroids. Unlike multidimensional scaling and many metric-learning approaches that preserve sample-level relationships, ICE operates on class centroids, preserving inter-class geometry without requiring large numbers of sample-pair or triplet constraints. We further show that the intrinsic dimensionality required to represent the centroid-distance configuration of $M$ classes is at most $M-1$, explaining the observed saturation of distance-preservation measures as the latent dimensionality increases. To quantify embedding reproducibility, we introduce the Centroid Neighborhood Stability (CNS) metric, which measures the consistency of class-level neighborhood topology across independent runs and complements existing embedding quality measures. Experiments on image and biological datasets demonstrate that ICE produces stable embeddings with improved preservation of class-centroid geometry while remaining computationally efficient. Additional analyses of optimization dynamics, sensitivity, and preprocessing further provide practical insights into latent dimensionality and explicit geometry modeling for supervised dimensionality reduction.

Many agent tasks recur with new data or small changes, yet agents regenerate their reasoning and actions on each run, producing different results. Distilling a prior run into a skill helps the agent avoid earlier mistakes, but it still re-runs the full process each time, so runs can vary and incur that cost. We compile a successful agent run into a reusable neuro-symbolic program (NSP) with a set of guidelines we call FlashScript. Actions and data transformations become code, instance-specific values become parameters, and decisions that need model judgment become LLM calls. We identify three layers where these calls belong and three techniques that replace most of them with code. The compilation does not remove nondeterminism; it localizes it, so the deterministic program and its neural calls can be reviewed and tested separately. Across 120 WorkBench analytics tasks with Claude Haiku 4.5, the NSPs were correct and made identical tool calls on every run, using about 70 times fewer input tokens and a third of the runtime of a skill-guided agent whose runs were inconsistent. In a composite version of the tasks, the skill-guided agent's accuracy fell to 23%, and its output inconsistency increased, while the NSPs remained correct and identical across all runs. The NSPs successfully generalized to all 108 unseen instances of the same templates. Our findings suggest that NSPs from agent trajectories can be considered cumulative software assets for end-users to test, maintain, and reuse in their recurring workflows.

Catastrophic forgetting in continual learning (CL) manifests not only as accuracy degradation but also as \emph{explanation drift}: models maintain predictive accuracy while silently shifting attention from diagnostic features to spurious correlations. This work identifies and resolves a previously overlooked structural flaw in explanation-aware CL: pixel-level saliency regularization derives supervision targets from the model's own frozen saliency maps, creating a \emph{self-referential drift loop} that actively reinforces spurious attention across tasks. We introduce \textbf{C$^3$L} (Concept-Consistent Continual Learning), which breaks this loop by anchoring regularization to class-consistent semantic concepts (e.g., ``curved beak'', ``striped pattern'') discovered offline, independent of model state, providing (i) target independence from model drift, and (ii) cross-instance semantic consistency across every instance of a class. We identify that our concept-based objective, combined with approximate LRP relevance conservation, induces a \emph{crowding-out effect}: since concept and background regions compete for the relevance of the same prediction, enforcing high relevance within concept regions implicitly suppresses spurious background correlations without explicit penalization. \method does not require human-annotated concept sets, as it employs a fully automated concept discovery and spatial grounding. Extensive evaluation across five benchmarks and over 20 baselines demonstrates state-of-the-art performance in accuracy, forgetting, explanation quality, spurious correlation mitigation, and out-of-distribution robustness.