Science & Mathematics

Object counting in videos remains a poorly characterized capability of multimodal large language models. Counting questions are included in many existing VideoQA benchmarks, but the ground-truth count distributions in these benchmarks are heavily skewed toward small values. Across the nine benchmarks we survey, the median ground-truth count is at most five, and the three most frequent values together account for between 45% and 93% of the videos. The resulting mean accuracy is then dominated by the most frequent counts; a value-dependent bias at a rare count contributes negligibly to the average and remains invisible. We introduce CountVideoBench, a benchmark of 2,600 synthetic videos covering 26 cardinalities in the interval [5, 50] (100 videos each), grouped into six clusters of consecutive counts that span the range while enabling near-neighbor comparisons. Each video contains a single class of static objects under a controlled camera motion, removing object motion and reducing recognition as confounds. We evaluate sixteen video-language models from nine architecture families in a zero-shot setting. No model exceeds 27.6% Exact Match. The dependence of accuracy on cardinality varies across models, ranging from monotonic decline to a non-monotonic peak-and-collapse pattern, which rules out increasing difficulty with cardinality as the dominant explanation of counting failure. Every model further concentrates its predictions on its own set of preferred integers, with accuracy peaks coinciding with these values and collapsing at adjacent counts. These findings highlight the need for balanced, diagnostic counting benchmarks to reliably assess this fundamental visual capability.

In reinforcement learning, one presumes the action set to be known ahead of time, and, thus, one must know if any state-action pairs are not permissible ahead of computations. In some applications, determining this action mask is the main computational bottleneck. Isolating this problem to highlight its core properties, we study how to combine the search for an optimal policy with the learning of the mask itself, under a linear MDP model in which each attempted action reveals the exact value of a linear score determining its validity. In this framework, we first construct an algorithm based on deterministic optimistic optimization and show that it is minimax optimal, which we show is also computationally efficient. However, it is sub-optimal on non-degenerate instances, as we show. We propose an alternative, which is also computationally efficient, which plans its exploration strategy. This algorithm admits a formal interpretation as an analogue of information-directed-sampling for deterministic feedback, which may be of independent interest. Finally, we study an application of this framework to transfer learning, where the invalid action set changes over time.

Long-horizon deep search requires LLM agents to iteratively decompose complex information needs, gather evidence from external sources, and maintain a reliable research state under multiple constraints. A central challenge is that early mistakes can be amplified over the search trajectory: agents may anchor on an incorrect candidate, collect partially supporting evidence, overlook contradictions, and accumulate errors that misguide subsequent reasoning. We propose FALCA, a falsification-aware framework that formulates deep search as a propose-falsify process. FALCA adopts a collaborative Searcher-Falsifier architecture, where the Searcher proposes candidate answers or sub-answers, while independent Falsifiers actively seek counterevidence, check unmet constraints, identify conflicts, and produce concise falsification reports for research-state revision. To strengthen this loop, we introduce falsification-aware training, combining SFT warmup on falsification trajectories with agentic RL based on parallel rollouts and hierarchical credit assignment over research stages, state transitions, and actions. Experiments on five search benchmarks show that FALCA improves long-horizon deep search performance over backbone and harness ablations, while reducing confirmation bias and error accumulation through more effective falsification and research-state revision.

Navigation Among Movable Obstacles (NAMO) requires a robot to rearrange objects that block access to its goal. For a pushing robot, progress may depend on a setup push that enables a later opening without itself clearing a passage. The number of candidate sequences can grow exponentially with sequence length, making physics-based search costly. We introduce the Search-trained Push Action Ranker (SPAR), which learns to prioritize push primitives from simulated search outcomes. Searches over sequences of up to two pushes per object provide supervision that distinguishes immediate openings from setup pushes. A transformer trained with regression and ranking losses scores primitives using contact tokens conditioned on scene geometry and reachability regions. The same model guides simulator evaluations in SPAR Search and selects actions for direct execution in SPAR Policy. Both modes solve successive keyhole problems that open access to neighboring free-space regions within a NAMO planner. Across successful runs on $300$ simulated two-push keyhole problems, SPAR Search reduces median simulator calls by $7.0\times$, leading to a $3.8\times$ reduction in planning time relative to Random Search. Without retraining, the same ranker guides search on $600$ keyhole problems which have no solution within two pushes. At a depth limit of five pushes, SPAR Search achieves $50.7\%$ success within $100$ simulator calls, compared with $20.2\%$ for Random Search. These gains carry over to NAMO planning: on hard simulated scenes, SPAR Search achieves $47\%$ success within $100$ simulator calls, compared with $21\%$ for Random Search. In real-robot experiments, SPAR Policy succeeds in $37/40$ trials without a physics-based digital twin, compared with $33/40$ for SPAR Search and $27/40$ for Random Search.

Crystallographic texture is an important microstructural feature that statistically describes the orientations of grains in polycrystalline materials. Conventional texture analysis relies on the orientation distribution functions and pole figures, which are essential for interpreting the texture of a given material specimen but do not, by themselves, provide a direct framework for predictive modeling of process-structure-property linkages. Data- and machine learning-based approaches offer a means to address this gap; however, a key challenge lies in developing representations and learning frameworks that account for the manifold structure of rotations. In particular, many existing machine learning techniques are designed for Euclidean data and therefore are not readily applicable to rotations in the non-Euclidean group $\text{SO}(3)$. Here we introduce TexFlow, a conditional normalizing flow framework for texture modeling that learns a probability distribution over rotations in $\text{SO}(3)$ by construction. Rotations are encoded in a six-dimensional Gram-Schmidt orthogonalization representation which is then mapped back to valid rotations $\mathbf{R}\in\text{SO}(3)$. The framework supports conditional probabilistic modeling of texture $p(\mathbf{R}|c)$, where $c$ may represent processing parameters like temperature or deformation state. To complement conventional texture-analysis visualizations, such as pole figures and sections of the orientation distribution function, we further introduce Hopf-fibration visualizations as a compact global representation of texture. TexFlow is validated on both unconditional and conditional experimental and simulated texture datasets spanning diverse material systems. We show that TexFlow can accurately capture multimodal textures and their conditional evolution, providing a data-driven framework for establishing process-texture linkages.

Local Retrieval-Augmented Generation (RAG) systems are vulnerable to indirect prompt injection and retrieval poisoning, where malicious instructions in retrieved content are mistaken for trusted input. We present nokast-secureRAG, a roughly 0.5B-parameter small language model that acts as a semantic firewall between retrieval and generation. It jointly evaluates the user query and retrieved context, classifying the pair as safe, suspicious, or malicious. The model is trained using a teacher-judge-student pipeline: a 35B teacher generates 5,233 examples across four attack families, and an independent 120B judge re-labels them, achieving 95.0% agreement before student fine-tuning. On a held-out in-distribution test set, the model achieves 0.994 detection recall at a 0.026 false-positive rate and a 0.006 attack-success-rate proxy, outperforming a regex baseline, a public prompt-injection classifier, Llama Guard 3 1B, and its untuned version. Prompt-Guard-86M reaches 0.900 recall but has a 0.690 false-positive rate. On a judgment-flip test, where the same sentence is benign or malicious depending on context, the model correctly classifies both cases 75% of the time, outperforming the compared baselines. Ablations indicate that retrieved context carries the main attack signal, while query-context consistency reduces false positives. Single-request latency is 293-404 ms, above the target of 100 ms, while amortized throughput latency is 37 ms under batching. On the external PoisonedRAG benchmark, recall falls to near zero, indicating that fluent fact-poisoning attacks lie outside the detector's instruction-consistency threat model. We report this limitation alongside the in-distribution results. The model, data-generation pipeline, and evaluation harness are released open source.

Independently trained autoregressive language models often acquire similar capabilities, but it remains unclear whether their internal representations organize behaviorally relevant information in compatible ways. We show that models do in fact organize information similarly by using specific behavioral probes that operate on compatible representations. This unlocks portable white-box monitoring: a probe developed and validated on one model can be reused when the model changes, without requiring labeled target data. To overcome incompatible native activation coordinates, we express each example through its angular distances to a shared set of anchors. We introduce a global anchored construction that summarizes information from all transformer layers and removes model-specific layer selection, so the same frozen probe can be straightforwardly applied to another model. We evaluate cross-model probe transfer across monitoring tasks on trivia datasets, safety monitoring, and mathematical reasoning. On average, transferred global anchored probes preserve at least 85% of same-model probe AUROC over chance. Anchored probes also support transfer to related datasets, remain robust across model scale and prompt changes, and retain performance better than standard probes after model updates. Transfer is nevertheless task- and target-dependent and can fail even when the monitored property remains strongly decodable in the target model. Overall, global anchoring reveals substantial task-relevant compatibility across independently trained models and provides a practical basis for portable white-box monitoring.

We give a bounded-error quantum polynomial-time algorithm for finding hidden parabolic subgroups of $\mathrm{GL}_n(R)$ over any effectively presented finite chain ring $R$. We call auxiliary group elements or subgroups used to extract information through oracle queries \emph{probes}. For chain length at least two, elementary abelian socle probes first recover the complete flag modulo the maximal ideal. When the residue field has size $q\ge3$, we reconstruct the flag recursively, lifting rank-one terminal members one digit at a time. The intermediate digits reduce to abelian hidden subgroup problems, while the final digit is a finite-field multiple-shift problem solved using learning from subset and Fourier sampling. For $q=2$, where distinct flags can have the same stabilizer, we instead lift the conjugate parabolic subgroup through the congruence filtration. A final linear system determines it modulo normalizer directions. The algorithm outputs generators with probability at least $1-ε$ in time $\mathrm{poly}(n,\log|R|,\log(1/ε))$. Consequences include $\mathrm{GL}_n(\mathbb{Z}/N\mathbb{Z})$ for every $N\ge2$ and, with an explicit maximal-order presentation, $\mathrm{GL}_n(\mathcal{O}_K/N\mathcal{O}_K)$ for number fields $K$.

A growing body of work proposes dynamic expert-skipping methods for Mixture-of-Experts (MoE) models that adjust the number of experts activated per token during inference, aiming to preserve model quality while further reducing the number of active parameters. These methods have added calibrated importance scores, inter-expert similarity metrics, or learned per-token allocators in order to identify experts to skip. However, different calibration regimes, different reductions in the effective number of experts, and evaluation suites make comparisons difficult. We classify four representative prior methods into a unified taxonomy and benchmark them against a natural, simple baseline: statically reducing the number of experts $k$ (i.e., same reduced $k$ across all layers and tokens). We provide a fair comparison of these methods at matched expert-compute budget, on two modern MoEs (Gemma4-26B-A4B and Qwen3-30B-A3B) in a text-only setting and a contemporary vision-language model (Qwen3-VL) in a multimodal setting. Surprisingly, we find that the simple baseline is hard to outperform consistently across models, modalities, benchmarks, and calibration settings. The methods we benchmark often underperform the baseline and achieved gains, when present, are minor. We further find that the effective $k$ achieved (or optimized for) in calibration can diverge from the effective $k$ in testing, resulting in over- or under-estimating the compute at inference time. Based on these findings, we recommend a calibration-free per-modality static $k$ reduction and validate this on a held-out model and modality. We further argue that a static control at matched measured compute is the baseline any dynamic skipping method must beat.

Homotopy type theory (HoTT) provides a natural setting for studying the metatheory of type theory, as it comes with additional extensionality principles compared to ordinary Martin-Löf type theory. In particular, it is especially suitable for developing semantics of type theory, where one distinguishes two kinds of models: strict models, which give us sound interpretations, and pseudomodels. Pseudomodels are useful as they occur prevalently and can be turned into strict models by constructions called strictifications. However, the commonly used strictifications do not translate well to HoTT, as they require assumptions that are generally not satisfied by concrete examples of models. We show how to carry out the universe model construction, due to Voevodsky, in HoTT. Under this construction, every pseudomodel together with a universe type closed under enough type formers gives rise to a strict model. We also show how to interpret type formers in the resulting model assuming that the universe is closed under them. Finally, we demonstrate that this construction generalises existing instances of strict set models in the literature, and we apply it to more examples, yielding presheaf models and assembly models of type theory in HoTT. Our results are formalised in Rocq using the UniMath library.

Electrical substation equipment is commonly interconnected by busbars and flexible conductors. Such interconnected infrastructures exhibit complex dynamic interactions, where the response of each component is influenced by local structural properties, mechanical coupling, system topology, and transient excitation. High-fidelity FE models can capture some of these effects, but their computational cost limits their use for real-time prediction. Purely data-driven models offer faster inference, yet they struggle to generalize, requiring additional simulations and retraining for each new configuration. This work presents a ROM embedded Graph Neural Network (ROMeGNN) for topology-aware seismic digital twins of interconnected structural systems. The system is represented as a graph, where structural components are treated as nodes and mechanical interconnections as edges. Each high-fidelity component model is first reduced to a reduced-order modal representation, which forms a differentiable dynamics operator within the GNN. Rather than learning the full response directly, the GNN estimates topology-dependent interaction forces that enter the differentiable ROM solver as coupling inputs for modal state advancement. This hybrid formulation preserves the known component-level physics and uses data-driven message passing to learn complex inter-component forces across varying system layouts. The framework is demonstrated on interconnected electrical substation equipment subjected to randomized seismic inputs. It delivers rapid predictions of response quantities relevant to seismic damage assessment while remaining applicable across varying layouts, component combinations, and excitation scenarios. These results highlight the potential of embedding physics within graph learning architectures for real-time, interpretable, topology-adaptive seismic digital twins of interconnected engineering systems.

Agent harnesses are executable code that specifies the prompts, tools, and control flow around a language model. A single global harness can struggle with heterogeneous tasks that require different execution strategies. In this work, we introduce Object-Oriented Harness (OO-Harness), a harness optimization framework that evolves a hierarchy of executable harness classes using object-oriented design. During training, an evolution agent uses execution records to create a family of specialized harnesses, each implemented as a subclass of the base or an existing specialized harness via inheritance. At test time, a harness router uses routing lessons accumulated during training to select a specific harness for each task. Across three long-horizon benchmarks spanning business workflows, workspace tasks, and tool use, OO-Harness achieves the best performance among the compared methods, with an absolute improvement of up to 15% over the base. Extensive ablation studies examine the contributions of its core components.

Reasoning about safety is essential for embodied agents powered by large language models (LLMs). We introduce the Contextual Action and Plan Safety benchmark (CAPSafe), designed to evaluate safety reasoning at two levels: (1) an action-level dataset that tests whether a single action is safe given its environmental context, and (2) a plan-level dataset that evaluates whether agents can generate safe long-horizon plans for complex hazardous household tasks. CAPSafe models safety conditions where hazards are situational (inferred from object properties), multiple hazards can co-occur within the same environment, and each is annotated with a relative severity level for fine-grained analysis. Evaluating nine closed and open-source LLMs reveals a substantial gap between hazard recognition and safe long-horizon planning. Several models achieve high accuracy in recognizing unsafe actions (exceeding 90% in the best cases), yet safe long-horizon planning remains substantially harder. Gemini-3-pro achieves the highest safe success rate (78.19%), while other models remain below 65%. These results highlight that robust safety reasoning over long action sequences remains an open challenge.

Training multimodal search agents requires tasks that make visually grounded search necessary for determining the answer. Textual identity clues and unused target evidence allow shortcuts in synthetic questions, weakening supervision for visual search and evidence integration. We propose RACE, an image-conditioned task synthesis framework that constructs dependencies from images to targets and from target-specific evidence to answers. Referential Abstraction (RA) replaces identity-revealing text with specific visual references or ambiguous relational references resolved by searching among depicted candidates. Compositional Evidence (CE) links retrieved facts about multiple entities in one image or entities from different images into joint questions whose answers require every designated contribution. Both operations also apply to images found during search, allowing new visual observations to determine subsequent search targets or supply answer evidence. Fine-tuning Qwen3.5-27B on only 12K teacher-generated trajectories from RACE raises average accuracy across ten multimodal benchmarks from 53.5 to 56.0, a relative improvement of approximately 4.7% over the matched base agent. Our code, data, and model will be publicly available.

Head-dimension compression can reduce the memory required by the key-value (KV) cache, but existing methods often reconstruct full-dimensional representations during inference, adding significant decoding FLOPs overhead. We formalize the design considerations for converting pretrained attention into a natively reduced-dimensional form that reduces both KV-cache storage and attention computation using a calibration set. Specifically, we consider reductions that (1) apply a shared projection to queries and keys so that they remain in a common reduced feature space, (2) derive this projection jointly from query and key activations to better preserve their interaction, and (3) are compatible with the pretrained RoPE transformation. To obtain a reconstruction-free realization of this reduction, we restrict it to coordinate selection and theoretically show that RoPE compatibility then holds if and only if complete rotary pairs are retained. Building on this characterization, we introduce RACE, a post-training method that selects rotary pairs using their joint query-key activation energy. We theoretically show that this criterion minimizes a separable, calibration-dependent upper bound on post-RoPE query-key product approximation error. The resulting reductions are folded into the model weights and require neither runtime reconstruction nor specialized kernels. Across three model families and different compression levels, RACE outperforms structured pruning and remains competitive with reconstruction-based methods on language-modeling, zero-shot, and long-context tasks. At 50% KV-cache retention and 256K context, RACE reduces total inference FLOPs by 47.8%, yielding 1.79x higher throughput, 43.2% lower time-to-first-token (TTFT), and 28.1% lower allocated GPU memory in comparison to an uncompressed model.