Science & Mathematics

Over-fitted Gaussian mixtures can contain many parameter configurations with nearly the same density, making the order of density cancellation central to their parameter-learning rates. Ho and Nguyen encoded these cancellations in a polynomial system and conjectured its exact order as a function of cluster size. The key to resolving the conjecture is a common positive-variance shift that turns the coefficient equations into Gaussian moment matching. For every cluster size $\Mhn\ge2$, we prove that the real, nonzero-weight system has order $2\Mhn$: a sharp sign-change bound forces rigidity at that order, while positive Gauss--Hermite quadrature constructs a non-trivial solution through order $2\Mhn-1$. Population-density calculations at 110-digit working precision recover the predicted leading term for two to six components; finite multistart searches recover the same observed powers for two to five components, with smaller finite-scale constants for three to five components. For parameter learning, the exact order gives an explicit pointwise maximum-likelihood exponent and an exact local minimax order on specified shrinking neighbourhoods of a fixed known mixing measure. The same coefficient viewpoint separates high-order cancellation from exact parameter symmetries in mixtures of experts. Synchronized replication preserves the conditional density while keeping the corresponding parameter losses positive in two broad standard-softmax classes, showing why statistical rate arguments must account for exact parameter symmetries.

Preference labels align model training, but the judgments behind them are difficult to inspect or verify. In this paper, we examine how preference construction can be checked when intermediate decisions are recorded, and which of them remain uncertain. We present Symbolic Preference Labeling, a method in which a pretrained language model classifies predefined attributes of prompts and responses. Explicit rules assign response verdicts, and a fixed verdict ranking determines the preference label. Each preference label has a recorded derivation: the response verdicts and preference label can be recomputed from the stored attribute assignments, rules, and verdict ranking without rerunning the language model. On 200 prompts annotated by human raters, the language model produces valid structured outputs for 192 prompts. All eight parsing failures occur in the subset of self-harm prompts marked as harmful. Using 465 preference pairs, we train one policy model with direct preference optimization across five training seeds. Mean measured benign refusal is 40.82 percent on 1,319 benign prompts that resemble unsafe ones, and mean measured toxic refusal is 84.98 percent on 655 toxic prompts. This study distinguishes the reproducibility of preference labels from attribute correctness. The recorded derivations make preference construction open to inspection, while attribute correctness and semantic safety require separate validation.

With the widespread adoption of large language models (LLMs) across languages and domains, AI safety has emerged as a critical global concern. However, due to resource constraints, research and development efforts tend to prioritize a limited number of high-resource languages, leaving many others, especially those spoken in Africa, underrepresented. While existing research on language "resource-ness" has largely examined whether sufficient resources are available to develop language technologies, the question of whether languages are adequately represented in AI safety research has received attention only more recently. This report examines the readiness of African languages for inclusion in AI safety discussions, drawing on existing literature and data. It considers four factors: the availability of AI-relevant resources, including text data; national AI policy support; performance on established text benchmarks; and speaker population. Based on these factors, languages are grouped into four readiness categories: fully ready, mostly ready, emerging, and foundational support needed. This classification is intended to inform the inclusion of African languages in AI safety benchmarks, highlight varying levels of preparedness, and guide strategic investment in data development, policy, and community engagement for underrepresented languages.

Producing synthetic data for comparison testing a migrated COBOL application is a major challenge that agentic migrations face today. Our prior paper, the Agentic Method for Deterministic Validation of Legacy Code Migration, presents a deterministic oracle to facilitate such migrations, the Locksmith Loop. We now propose a novel method for achieving high branch and paragraph coverage through generated synthetic end-to-end test cases, by means of entry-replay test-case certification by observing the code execution trace on a surrogate COBOL program that mocks external interactions via a chronological external-operation tape. We applied our method to a very large COBOL program with 33,429 lines of code to generate 849 synthetic end-to-end test cases covering 2,973/3,806 source branches (78.1%) and 989/1,033 main-AST paragraphs (95.7%). Using the Locksmith Loop's projected-agreement validation, the generated Java code matched the COBOL surrogate on the specified observations across all 849 certified synthetic end-to-end test cases. During the campaign we detected 61 defects and fixed the Java generator accordingly. To test whether the coding agent could silently introduce business logic bugs, we seeded 450 defects into the Java code, such as deleted writes, deleted paragraph calls, and altered rounding, to verify how many of these would be detected by the gating methodology. The gate detected 47.6%, including all deleted writes and paragraph calls in executed code, but was unable to detect the rounding and precision defects.

Walking without vision requires timely, unambiguous guidance, yet many wearable aids encode directions as audio or vibrotactile signals that users must translate into movement. We present XoNav, a four-actuator hip exoskeleton that renders guidance cues directly at the hip joints. It renders an Advance cue and two-level Braking cues through sagittal-plane actuators and two-level Steering cues through frontal-plane actuators. A bilateral LSTM-based gait-state classifier uses two thigh-mounted IMUs to identify gait states, enabling haptic cues to be delivered in coordination with the wearer's gait while suppressing them during standing. The classifier generalized to unseen users with recalls of 95.2-97.9%, with mean detection delays of 38.6 and 63.1 ms for stance-to-swing and swing-to-stance transitions, respectively. Constrained human-in-the-loop Bayesian optimization personalized Braking for minimum resistance and Steering for maximum comfort while ensuring detectability and safety. All participants reliably distinguished between grades of their personalized cues and the firmest Braking cue remained below 53% of the safety limit. In blindfolded Wizard-of-Oz navigation trials along three paths, the participants kept 98.8% of the walked distance within a 0.75 m wide passage, with a 4.9% increase in mean progression speed per trial. A body-worn camera, RTAB-Map and Nav2 further enabled a feasibility study of autonomous navigation and detours around previously unmapped obstacles.

Multi-vector retrieval models such as ColBERT often outperform single-vector models of comparable scale by matching queries and documents at the token level. However, retaining a vector for every token substantially increases storage requirements and slows retrieval compared to single-vector bi-encoders, limiting their scalability. We introduce FLINT (Fixed-budget Late INTeraction), an architecture that uses attention-based pooling to represent each query and document with a fixed number of embedding vectors. Unlike architectures that pool only document representations while retaining token-level queries, FLINT applies pooling symmetrically to both sides, limiting document storage and the number of vector comparisons needed during retrieval. FLINT achieves comparable ranking effectiveness to the closest baselines on BEIR and outperforms them on several benchmarks with longer and more complex queries, including BrowseComp+, CRUMB, and TREC Tip-of-the-Tongue 2025. We demonstrate that FLINT's effectiveness-efficiency benefits extend across encoder architectures, testing it on two separate backbones (BERT and ModernBERT). On long-query corpora, FLINT delivers 1.5-2.8 times faster end-to-end retrieval than ConstBERT, the closest baseline. FLINT also reduces index size by 5.3-9.3 times relative to token-level late-interaction models such as ColBERTv2.

Maximum clique and maximum consensus are widely used formulations for robust point cloud registration in robotics. Maximum consensus seeks one transformation that aligns as many matches as possible, while maximum clique selects matches through pairwise distance tests. Maximum clique is often used as a substitute for or an approximation to maximum consensus, with empirical evidence suggesting a close relationship. However, how closely the two formulations agree is not fully understood. We study this relationship theoretically. We show that a maximum clique can have arbitrarily large alignment error and be arbitrarily larger than the maximum consensus set at any fixed positive tolerance, and derive geometric conditions that bound this error. When rotation is fixed, we derive sharp error bounds and tests that exactly characterize maximum consensus for the translation subproblem. Finally, we study group-$k$ consistency, which tests groups of $k$ matches, and determine the smallest group sizes that guarantee alignment error bounds independent of point cloud scale and geometry. These are $d+1$ for rotations and translations and $d+2$ when reflections are allowed, in dimensions $d\ge 2$. Interactive examples and proof verification using the Lean theorem prover are available at https://ariarobotics.github.io/mc-vs-mc-registration/.

Vision-language-action (VLA) models are sensitive to visual corruptions, but knowing that a corruption is typically harmful does not establish whether removing it would benefit the current episode. Furthermore, when several corruptions co-occur, deciding what to correct requires understanding which ones contribute to failure risk and how much their removal would help. We define this problem as failure attribution. Detecting corruption presence alone cannot answer this question, as corruptions can be present but relatively harmless, while directly measuring removal benefits requires costly paired policy rollouts with and without the corruption present. To address this, we introduce a factorized risk model that learns separate representations of the scene and corruptions, allowing us to estimate removal benefits through latent intervention from the current image and task instruction, without paired clean images or additional counterfactual rollouts. We evaluate our approach on OpenVLA and $π_{0.5}$ in simulation and $π_{0.5}$-DROID on a Franka robot. Our method outperforms monolithic and vision-language-model (VLM) baselines, including achieving approximately 3x lower attribution error than frontier VLMs. We also demonstrate our method adapts to execution context and corruption intensity, and can be used for online failure monitoring on hardware.

The development of embodied models of animal behavior is a major goal of the neuro-AI community. Embodied models will enhance our ability to make direct comparisons between biological and artificial agents. To make such comparisons effective, though, we need embodied models that actually move like animals. Previous work has developed virtual animal bodies and techniques for training realistic motion through imitation. However, to date, there is no system for embodied animal modeling that produces natural movements both during trained goal-directed behavior, and during exploration driven by random generation. Here, we introduce Simulated Control via Augmented Motor Priors for Embodied Reinforcement learning (SCAMPER), a system for training an embodied virtual rat model, enabling natural movements during both goal-directed behavior and random exploration. SCAMPER uses a variational architecture with two distinct priors, a motion prior for control and a behavior prior for exploration. We show that combining both of these priors allows SCAMPER to generate realistic behavior during exploration and exploit the task structure effectively. SCAMPER can also learn from sparse rewards as a result of the diverse movements induced by the behavior prior, allowing the system to model realistic sparse-reward tasks from experimental neuroscience. Altogether, SCAMPER provides the neuro-AI community with an effective new system for training embodied models of rodents on realistic tasks.

Offline goal-conditioned reinforcement learning enables skill acquisition by reaching any goal from any state without dense rewards. Model-based methods allow for planning by scaling test-time compute to solve complex tasks. Combining both holds appealing promise for pre-training on suboptimal demonstrations and zero-shot adaptation via goal specification and planning. Yet existing methods assume effective planning requires accurate next-state prediction in pixel or latent space. In this work, we show that value prediction is more useful for planning, whereas accurate state prediction is often unnecessary. Our key insight is that offline goal reaching naturally admits a closed-form Monte Carlo return, enabling value regression to replace temporal-difference bootstrapping. We use this return as the sole supervision for latent world models: imagined latents are trained to predict goal-reaching value rather than match future states, implicitly preventing representation collapse. These planning-oriented representations let imperfect world models imagine on the level sets of value field beyond dataset transitions. We then present VPFlow, a value-predictive planner that pairs the world models with a one-step flow policy and plans in its noise space via evolutionary search. It enables policy improvement with imagined generalized advantage and reduces out-of-distribution queries common in action-space planning. On 30 state and pixel OGBench datasets, VPFlow surpasses model-free baselines by at least 30.3 and 10.1 percentage points in success rate, respectively, and outperforms latent planners LeWorldModel, PLDM, and TD-MPC2. It achieves this despite a latent prediction error orders of magnitude larger than with state prediction, while minimizing this error lowers success rate. This demonstrates that value-predictive representations, not exact state prediction, are what offline planning requires.

Effective detection of hate content is essential for maintaining healthy online communities, yet performance can vary substantially across languages. This work investigates a core practical question: Can training data from one language support hate-speech detection in another language with comparable performance? To answer this question, we conduct a large-scale study across 14 languages. \change{We observe consistent patterns in which certain language pairs transfer more effectively than others. Among the factors we measure, linguistic similarity is the strongest predictor of these patterns, with temporal overlap and dataset-size difference playing smaller roles. These measurable factors do not fully explain the observed patterns; a complementary qualitative analysis suggests that shared cultural cues and communicative norms may be associated with some of the remaining cases, particularly within several clusters. We present this cultural interpretation as a hypothesis from qualitative inspection rather than a measured cause.}{} Our analysis includes low-resource languages, offering practical insights into when cross-lingual transfer can support them and where its limitations emerge. These findings inform the design of more reliable multilingual hate-detection systems.

The WebView interface in Android (hybrid) applications enables the native side (e.g., Java) to exchange data with the Web (e.g., JavaScript). This creates cross-language information flow channels that existing single-language analyzers cannot analyze. Existing hybrid app analyses address only part of the problem: some build bridge-aware call graphs but provide limited information-flow analysis, some rely on coarse assumptions, and some focus only on web vulnerabilities. We present MifDroid, a static-analysis- guided dynamic-analysis framework with a lifecycle-aware per-WebView call graph, a bridge-aware type-and-effect system, and a modular JavaScript analysis engine. We evaluated MifDroid on 338 apps from the F-Droid repository (out of 4,126 total) that use addJavascriptInterface, enabling active communication between Java and JavaScript. Our guided dynamic phase adds 662 entries to the 444 produced by static analysis, raising the resolution rate from 36.5% to 74.5%, produces the resolved bridge-related entries for 115 apps that static analysis leaves empty. MifDroid reported 14 vulnerable cross-language information flows, five of which have been accepted and fixed by the maintainers.

In Cluster Editing, we are given a graph $G$ and an integer $k$ and ask whether at most $k$ edge insertions and deletions turn $G$ into a disjoint union of cliques. Komusiewicz and Niedermeier asked in 2012 at MFCS whether Cluster Editing is fixed-parameter tractable with respect to the number $\ell$ of edge deletions, a parameter based on the solution rather than on the structure of the input graph. We answer this question negatively: Cluster Editing with at most $k$ edits, at most $\ell$ of which are deletions, is W[1]-hard with respect to $\ell$, even when combined with the pathwidth and the feedback edge set number of the input graph. The hardness extends to editing towards $H$-free graphs for every graph $H$ that is a clique minus one edge on at least four vertices. On the positive side, we show that the problem becomes fixed-parameter tractable when $\ell$ is combined with the excess $μ$ of $k$ over the lower bound given by a packing of modification-disjoint induced paths on three vertices, a lower bound that state-of-the-art solvers use. Each of the two parameters alone leads to intractability, but together they admit an $O(4^{μ+\ell}\cdot(n+m+μ))$-time algorithm and a problem kernel with $O((\ell+μ)^2)$ vertices. Both results extend to packings of stars and the algorithm extends to $H$-free editing.

Test-case generation is critical but remains challenging for language models. Existing test-time scaling methods either isolate candidates or aggregate traces, which do not scale to long-horizon tasks. We present TEX, a collaborative test-time scaling framework based on execution-driven cross-validation. TEX parallelizes agents to generate tests and patches, cross-executing each test against every patch to form a $K \times K$ feedback matrix. Agents use their matrix slices for refinement, enabling objective validation without verbose trace sharing. On SWT-Bench Verified, TEX achieves 86.4%, establishing a new state-of-the-art and improving +9.0% over single-agent baselines. Moreover, even random selection from TEX outputs (84.4%) surpasses the previous SOTA (84.0%), showing collaborative execution feedback improves solution quality, not just best-case samples. Our results highlight execution-grounded feedback as an effective scaling mechanism for long-horizon agentic tasks.

This letter jointly optimizes fluid-antenna port selection, fixed-cardinality reconfigurable intelligent surface (RIS) element activation, and 1-bit reflection phases through an exact angular event sweep that extends full-activation divide-and-sort geometry to subset selection. We establish deterministic gain bounds and activation monotonicity, derive exact single-element outage expressions and high signal-to-noise ratio (SNR) asymptotics for independent RIS branches with correlated receiving ports, and prove diversity order equal to the RIS element count for fixed positive-definite RIS covariance. With perfect instantaneous channel state information, a quality-of-service aware policy activates the minimum number of elements required to meet a target SNR while preserving full-activation outage probability. An explicit overhead condition identifies when reduced activation improves net energy efficiency. Correlated-channel benchmarks illustrate subset-selection gains, aperture effects, and overhead-dependent energy-efficiency tradeoffs.