Papers

Model merging aims to consolidate multiple task-specific models without access to extra training process. However, existing subspace-based methods largely rely on a uniform treatment of task updates, overlooking their intrinsic spectral and depth-wise heterogeneity. We identify two key deviations from this assumption: different tasks require different subspace capacity and exhibit different tolerance to spectral transformation, while subspace projection introduces depth-dependent distortion. Based on these observations, we propose SADA-Merging, a spectrum-aware and depth-adaptive framework for data-free model merging. SADA-Merging allocates task-specific subspace capacity according to spectral complexity, adapts spectral preservation according to task-wise plasticity, and applies depth-dependent anchoring to compensate for projection-induced distortion. This enables the fusion process to adapt to both the intrinsic geometry of each task and its sensitivity across network depth. SADA-Merging operates directly on task updates and is applicable to both full fine-tuning and LoRA settings. Extensive experiments demonstrate consistent improvements over existing data-free merging methods across different task scales and adaptation settings.

Electricity forecasting often involves spatially related signals observed over regions, substations, and feeders, and Graph Neural Networks (GNNs) provide a natural way to represent these relations. Building a complete GNN forecasting experiment is nonetheless laborious, because graph construction, model selection, training, aggregation, and interpretation sit in incompatible tools. We present GraphToolbox, an open-source Python framework that unifies these stages in one configurationdriven pipeline built on PyTorch Geometric. It offers data-driven graph construction, an adapter that instantiates and trains 51 of the 65 PyTorch Geometric convolutions together with the recurrent cells of PyTorch Geometric Temporal, online expert aggregation, forecasting interpretability, and significance testing on cached forecasts. We evaluate the pipeline in two case studies. On French regional load, the 48 convolutions included in the complete forecasting sweep fall in a band from 1.14% to 1.60% error, online aggregation lowers this to 0.98%, and the graph models improve on classical additive and boosting baselines. On net-load, direct graph models are less accurate than a classical additive model, while forecasting each physical component separately improves them without closing that gap. Both comparisons use the same experimental interface, illustrating the role of GraphToolbox in systematic architectural evaluation.

Multi-period Repetitive Control (MPRC) can lead to amplification at non-repetitive frequencies due to the multiplication of multi-period repetitive control in their closed-loop sensitivity functions, which leads to closed-to imaginary poles. We propose a MPRC structure that eliminates such interaction. The scheme can be equivalently converted into a disturbance observer to improve robustness to frequency uncertainties. We derive an upper bound on the sensitivity function that can be optimized at either repetitive or non-repetitive frequencies. Experimental results on an active vibration isolation system show superior performance over existing robust MPRC schemes, and the capability to suppress unknown time-varying periodic disturbances.

The Lean proof assistant has a rich library of mathematical formalizations that are interesting to users of other proof assistants. To help with the translation of this library to other systems, we present a theory in the Dedukti logical framework in which one can encode Lean terms and types, and define a typability-preserving translation from some large subset of Lean to that Dedukti theory.

We report on our efforts to translate HOL-Light theorems on HOL-Light types/functions into Rocq theorems on Rocq types/functions. To this end, we developed in Rocq tactics to automate the proofs required for replacing a HOL-Light inductive type or recursive function definition by an equivalent but more idiomatic one in Rocq. We also explain how we replaced the definition of real numbers, as well as a number of mathematical notions like Rn spaces and the definition of limit, hence providing to Rocq users many definitions and theorems in logic and analysis that had not been formalized in Rocq before.

Neural Cellular Automata (NCAs) are a new type of neural network architecture which enable accurate and robust inference at extremely small model sizes. Recently, NCAs have advanced to become interesting low-resource alternatives to convolution- and attention-based architectures for various tasks such as image analysis, synthetic image generation, and simulation. The rapid development and increased research interest necessitate a comprehensive review of the emerging technology. This review provides an overview of the fundamentals of NCAs, applications to medical imaging, as well as insights into the state of the art. We analyze recent modifications to the originally proposed NCA architecture with respect to their efficiency and accuracy. Furthermore, we review practical applications in real-world scenarios with a focus on medical image analysis, segmentation, classification, registration, depth estimation, and image synthesis. Finally, we identify several advantages of NCAs, research gaps, and conclude with an analysis of future opportunities for NCAs in medical applications in confined settings or areas that have particular demands for robustness or efficient data processing.

We identify common challenges and requirements for verifying proofs from automated theorem provers in the Dedukti logical framework and develop a general methodology for deriving encodings of calculus rules and proof steps, including clausification. We then apply this methodology to the EP calculus for higher-order logic and integrate it into the automated theorem prover Leo-III. The resulting prototype reconstructs about 80% of generated proof steps automatically, making Leo-III the first higher-order automated theorem prover to support independently checkable proof reconstruction and providing a basis for cross-system reuse. The implementation uncovered several bugs in Leo-III.

We study the computational complexity of fundamental algorithmic problems – membership testing, separation, valid-inequality testing, and linear optimization – over polytopes and cones arising from cooperative games (also known as pseudo-Boolean functions). A central obstacle in the study of such problems is that a general cooperative game on $n$ players requires $2^n$ values, so the input size is $2^n$ for a game with $n$ players, making these computational tasks theoretically trivial. Restricting to $k$-additive games reduces the input size to $O(n^k)$, making such games a natural target for meaningful questions about the existence of efficient algorithms. On the positive side, we give an explicit extended formulation of size $O(n^k)$ for the core of $k$-additive $k$-monotone games, allowing all four problems to be solved by a single polynomial-size linear program – in particular, circumventing the ellipsoid method that is needed when building from earlier tractability results of Deng and Papadimitriou, or of Edmonds. For the cone of $k$-additive $(k{-}1)$-monotone games, we give a complete characterization of its extreme rays and derive the same $O(n^k)$ bound on extension complexity, yielding a geometry-based proof and generalization of a result of Billionnet and Minoux. On the negative side, we show that for $l \leq k-2$ the cone of $k$-additive $l$-monotone games is computationally intractable: membership testing is not in NP (unless NP\,=\,coNP), valid-inequality testing is NP-complete, and extension complexity is at least $1.5^n$. Our hardness results yield, as a special case, a result of Crama and of Gallo and Simone. Furthermore, our hardness results also explain the lack of any good characterization of the extreme rays of the cone of $k$-additive $(k{-}2)$-monotone games.

We propose a deterministic smoothed maximum a posteriori (SMAP) framework for high-dimensional multiple-input multiple-output (MIMO) detection. The discrete constellation prior is approximated by an i.i.d. Gaussian mixture, yielding a differentiable MAP objective that retains the constellation structure while enabling continuous optimization. Unlike sampling-based approaches, SMAP formulates detection as a deterministic optimization problem and can be initialized by the output of an arbitrary detector, allowing it to operate either as a standalone detector or as a refinement stage. For hard detection, we introduce SMAP-KR, which complements the continuous solution with a local $K_R$-neighbor search evaluated according to the original maximum-likelihood metric. Annealed continuation improves robustness for higher-order constellations, while a two-neighbor approximation reduces the cost of evaluating the mixture prior. We further develop a soft-output SMAP method in which a local Gaussian approximation based on the curvature of the smoothed posterior provides symbol probabilities and bit log-likelihood ratios without posterior sampling or explicit counterhypothesis lists. Numerical results for critically loaded MU-MIMO systems show that SMAP-KR provides an increasingly favorable performance-complexity tradeoff as the system dimension grows and can also effectively refine the output of existing detectors. For coded transmission, soft SMAP provides substantial block-error-rate gains over both LMMSE- and K-best-based soft detection.

Sea ice forecasts are issued several days ahead, allowing errors to accumulate while new, often sparse sea ice concentration (SIC) observations become available. We find that fixed-propagation errors concentrate near structured, high-gradient ice edges, whereas homogeneous interiors require limited propagation, suggesting that propagation distance should be state dependent. We therefore introduce ECHO (Evidence-guided Correction with Heterogeneous prOpagation), where ECHO-Scale adapts propagation distance while preserving correction geometry, and ECHO-Delta learns a bounded residual around fixed propagation. Across all 96 standard evaluation settings spanning diverse priors, observation times, sparsity levels, geometries, and noise conditions, both outperform fixed propagation. ECHO-Delta achieves the best average accuracy, while ECHO-Scale is more robust to geometry shifts. Code is available at https://github.com/yingtian22/TAKING-A-SECOND-LOOK.

Traditional evaluation metrics provides numerical values but often lack comprehensibility, hindering effective differentiation of model performances. Our work addresses this challenge by introducing overlay\_dx, a novel evaluation metric measuring the performance of time series prediction models. Overlay\_dx is a visual metric that represents the percentage of predictions falling within a confidence interval around actual values. Additionally, once evaluation results are plotted, overlay\_dx computes the area under the overlay curve, providing a quantitative measure of alignment between predicted and actual values across different thresholds and predictions. Through extensive experiments, we demonstrate that our approach offers a unified evaluation framework that combines both visual and numerical assessments, enabling improved model comparison and providing valuable insights for further research and optimization efforts in time series prediction.

Various inverter-based control strategies have been proposed to improve frequency security for power systems with high renewable penetration. Among them, the grid-forming frequency shaping control is particularly promising due to its ability to shape the post-contingency aggregate system frequency dynamics into first-order with prescribed rate of change of frequency (RoCoF) and steady-state frequency deviation. Moreover, the shaped aggregate dynamics depends on the harmonic sum of all inverter transfer functions rather than on their distribution. In light of this, here we explore how to allocate shaping control resources to minimize the transient control effort needed to achieve ideal coherent dynamics. We formulate it as a constrained optimization problem by tackling two main difficulties. First, we make the squared $\mathcal{H}_2$ norm legitimate quantification of transient control cost under step power imbalances through a system transformation. Second, we simplify the $s$-domain constraint for Nadir elimination into a standard constraint that is easy to implement in optimization. The resulting non-convex optimization problem can be solved by existing successive convexification method. The effectiveness of the allocation has been verified on the modified Icelandic Power Network test case.

Event logs arise in a wide range of real-world processes, capturing not only event activities and timestamps but also multi-modal contextual information. Existing event-sequence models, including many temporal point process approaches, primarily model event activities and timestamps while overlooking heterogeneous context, such as numerical measurements, categorical attributes, textual descriptions, and metadata associated with individual events and entire traces. In this paper, we propose Universal Multi-Modal Traceformer (UMT), a unified framework for incorporating heterogeneous process context into next-event prediction. Built on a Transformer backbone, UMT introduces a universal feature encoder that maps diverse feature types into a shared representation space and handles contextual information at both the event and trace levels. UMT further develops a per-event Perceiver module that dynamically weights contextual features and adaptively integrates them into event-token representations. To accommodate the heavy-tailed and potentially multi-modal distribution of inter-arrival times, UMT represents each interval at multiple temporal scales and jointly predicts the corresponding scale-specific quantities. Experiments on 13 real-world event logs show that UMT improves both next-event activity and time prediction over existing approaches.

Modern Vision-Language Navigation (VLN) models rely mostly on pre-trained large Vision-Language Models (VLMs) to predict navigation actions. While this fusion of language instructions and visual observations allows multimodal reasoning, it obscures how information is routed across modalities or what mechanisms drive navigation decisions. Thus, it remains unclear whether VLN models ground their predictions in relevant semantic cues or can track task progress. In this work, we study the interpretability and steerability of VLN models. We use intervention-based metrics that measure how visual observations, instructions, and visual memory causally influence navigation decisions. Our results show that these navigation policies are sensitive to all input modalities and do not depend on a single one. We further show that these agents encode navigation progress and retain semantic structure from their VLM backbones, enabling concept-level steering through internal activations. Finally, we extract activation vectors for abstract behaviors to transfer them zero-shot to out-of-distribution real-world scenarios, improving performance without additional fine-tuning.

The proliferation of 3D printing raises new security and forensic challenges, including the risk of unauthorized fabrication of untraceable firearms and other regulated items. To enable traceability, we consider single-fragment forensic coding, in which a unique identifier is embedded into a printed object and must be recoverable from any fragment containing an axis-parallel box of prescribed minimum volume and coordinatewise thickness, even in the presence of substitution errors. To address this problem, we introduce and study multidimensional cyclically permutable codes (CPCs), for which every cyclic translate uniquely determines both the original codeword and the applied translation. By applying periodic lifting to a CPC base array, every complete period contained in a fragment corresponds to an unknown cyclic translate of a codeword, thereby reducing the forensic alignment problem to multidimensional cyclic synchronization. We establish theoretical bounds and develop explicit constructions in both the noiseless and substitution-error settings. For fixed dimension $d$ and alphabet size $q$, we obtain the optimal redundancy $d\log_q k+o(1)$ for noiseless $d$-dimensional CPCs of side length $k$. For fixed $t$, the optimal redundancy of $t$-substitution-correcting $d$-dimensional CPCs lies between $(t+1)d\log_q k+O(1)$ and $(2t+1)d\log_q k+O(1)$. For binary alphabets and $d\geq2$, an explicit robust row-anchor construction achieves $(t+1)d\log_2 k+O(\log\log k)$ redundancy, matching the optimal leading term. In the thick-fragment regime $h=cM^{1/d}$, where $M$ and $h$ lower-bound the volume and the side lengths of a box contained in the fragment, periodic lifting yields single-fragment forensic codes of rate $c^d-o(1)$. In particular, the rate approaches one when $c=1-o(1)$.

Computational social science increasingly relies on large language models for text annotation, and the validity of published findings now rests on the labels generated by such models. Decision models, a new model class built for categorical question answering, answer typed questions with a choice, a probability distribution over the label set, and a confidence score rather than free text, at a small fraction of frontier inference prices. Whether their answers are accurate, and whether that stated confidence can be trusted on social science constructs, are unknown. Here, we mirror the evaluation of Ziems et al. (2024) on 18 computational social science classification tasks (7,977 items), comparing the first commercial decision model and two open-weight counterparts against 19 frontier and open-weight language models under the same zero-shot protocol, and extending the decision-model comparison to eleven open-weight systems released in the week after it. The decision model trails the per-task best LLM on 14 of 15 evaluation tasks, with a median deficit of 11.6 macro-F1 points, at a median 44 times lower measured cost. Its confidence is better calibrated than the verbalized confidence of 16 of the 19 LLMs, yet three frontier models show lower median calibration error (0.157 against 0.066). While items above 0.9 confidence are typically labeled accurately (median accuracy 0.815), on one task, empathy in peer-support dialogues, the model reports high confidence while performing near chance. Nonetheless, our results suggest that decision models are useful as a first step in the annotation pipeline: routing low-confidence items to an LLM matches or exceeds the LLM alone at a quarter to half of its cost.

Over the past decade, a growing body of research has shown that $\gamma$-weak submodularity broadly arises in numerous subset selection tasks, including feature selection, neural network pruning, and video summarization. Despite its prevalence, maximizing a $\gamma$-weakly submodular function subject to a general matroid constraint remains challenging. To date, the only known approximation guarantee is the conservative $(1+1/\gamma)^{-2}$ factor established by \citet{chen2018weakly}. To improve upon this result, this paper proposes a novel algorithm called \MGPE, which repeatedly performs maximum-gain local exchanges through careful control of a non-homogeneous Poisson clock, and proves that this \MGPE\ can attain an approximation ratio arbitrarily close to $\rho_\gamma=1-\left(\gamma/(2-\gamma)\right)^{ \frac{\gamma^2}{2(1-\gamma)} }$. In sharp contrast to the previous guarantee, our obtained factor $\rho_\gamma$ not only strictly improves upon $(1+1/\gamma)^{-2}$ for every $\gamma\in(0,1]$, but also can asymptotically approach the optimal $(1-1/e)$-approximation for submodular maximization as $\gamma\to1$. Furthermore, we surprisingly find that when the matroid constraint reduces to a cardinality or the objective satisfies the stronger notion of $\alpha$-weak DR-submodularity, \MGPE\ can automatically recover the tight approximation ratios of $1-e^{-\gamma}$ and $1-e^{-\alpha}$, respectively. Here, $\alpha\in(0,1]$ denotes the DR ratio.

We prove that a bounded shortened region initiates decoding throughout multidimensional spatially coupled regular LDPC and MacKay–Neal (MN) codes over the binary erasure channel (BEC). In every fixed finite dimension, uniform hypercube coupling permits the coupling width and shortened region to be chosen independently of the total number $V$ of spatial positions. At fixed widths and dimension $d>1$, replacing a shortened slab by a bounded hypercube reduces the shortening fraction from order $V^{-1/d}$ to order $V^{-1}$, with the same improvement in the shortening term of the check-count rate bound. Regular LDPC codes decode below their uncoupled potential threshold. MN codes achieve capacity for every integer degree choice $\ell>r\geq2$, $g\geq2$: their actual transmitted rates tend to $r/\ell$ and their average bit-erasure probabilities under sum-product decoding vanish below $1-r/\ell$. The proof combines an endpoint-potential identity, removal of an auxiliary constraint, finite-time estimates uniform in direction, and a curvature comparison that transfers flat-boundary progress to expanding balls. For MN codes, elementary inequalities establish fixed-point positivity for all these degrees. Two-dimensional density-evolution examples illustrate the dependence on the initial shortened region; the general sufficient constants are not evaluated numerically.

A connectome-constrained model of the fly visual system, optimized for motion and then frozen, can be driven over architectural drawings by prescribed motion and used as a texture representation. We compare it with information-matched baselines that see the same 721 photoreceptor samples. On clean synthetic data the frozen model transfers but loses to task training: 0.857 area-weighted accuracy in one-shot hatch matching versus 0.959 for a 5,888-parameter CNN, and 0.619 IoU in wall segmentation versus 0.905 for a matched network. Under scan noise and thickened strokes, the trained networks lose up to 0.188 accuracy while the frozen pipeline loses 0.030. On fourteen production sheets, opened once, a 1,876-parameter fly model reaches 0.505 average precision versus 0.415 for a network two hundred times larger. A preregistered held-out split confirms the clean-data ordering: 0.835 for the circuit, 0.894 for receptors only, and 0.971-0.980 for trained CNNs. Rewiring the connectome while preserving degrees or type pairs and transmitter signs costs 0.271-0.356 accuracy across three seeds, so the exact wiring is load-bearing. Yet the intact circuit does not beat its moving retina, and T4/T5 silencing leaves both tasks intact. Longer observations reverse the circuit-receptor ordering once the stimulus spans a period, but not through T4/T5. Thus active sampling and exact structure matter, while clean-data practical performance remains dominated by task-trained networks and the useful transfer margin is largely retinal.

CLIP, a foundational vision-language model, has emerged as a powerful tool for open-vocabulary semantic segmentation. While freezing CLIP's text encoder is known to preserve its generalization capability, recent studies show that fine-tuning both CLIP's text and image encoders jointly significantly enhances segmentation performance, especially for classes from open sets. In this work, we explain this phenomenon from the perspective of hierarchy alignment, since during fine-tuning, the hierarchical level of image embeddings shifts from image-level to pixel-level. We achieve this by leveraging hyperbolic space, which naturally encodes hierarchical structures. Our key observation is that, during fine-tuning, the hyperbolic radius of CLIP's text embeddings decreases, facilitating better alignment with the pixel-level granularity of visual data. Building on this, we propose HyperCLIP++, a novel and parameter-efficient adaptation strategy. HyperCLIP++ directly adjusts the hyperbolic radius of CLIP's embeddings via scaling transformations to achieve a hierarchy alignment to the target task, i.e., segmentation. To ensure this hierarchy alignment is effected consistently across both modalities and preserves their cross-modal alignment during training, HyperCLIP++ integrates a Dual Cross-Relation Communication (DCRC) module that synchronizes these adjustments between the vision and text pathways. Our experiments show that HyperCLIP++ achieves state-of-the-art performance across three benchmarks while fine-tuning only approximately 5% of CLIP's total parameters. More importantly, we observe that after adjustment, CLIP's text embeddings exhibit a relatively fixed hyperbolic radius across datasets, suggesting that the hierarchical level required for this segmentation task might be quantified using the hyperbolic radius.

Adapting visuomotor policies to new manipulation tasks often requires substantial manual engineering or teleoperated data collection. Simulation can provide task-specific data at scale, but constructing the scene, designing expert behavior, and configuring data generation still require significant per-task effort. We present ARSTAG, an agentic Real2Sim2Real system that turns a single RGB image and a natural-language instruction directly into robot policy-learning data. A hierarchy of language agents constructs a task-scoped simulation scene, generates robot-feasible demonstrations, and expands the training distribution through task-consistent randomization, while a coordinator agent manages cross-stage feedback and recovery. Across seven manipulation tasks spanning grasping, placement, and stacking, the ARSTAG-generated demonstrations enable sim-to-real transfer of three visuomotor policy architectures to a dual-arm robot, with pi0.5 achieving an average real-world success rate of 74.6%. Ablations show that task-consistent randomization substantially improves robustness, and policy performance increases with generated dataset size. Project webpage: https://boweili666.github.io/ARSTAG/.

Confocal Laser Endomicroscopy (CLE) provides real-time, cellular-resolution optical biopsy but has a narrow field of view, which image mosaicing can extend to provide anatomical context. Because of line-by-line acquisition, probe motion, and probe-tissue interaction, frame alignment generally requires a non-linear transformation whose accuracy is difficult to quantify: flexible transformation models can fit intensity features and noise, so appearance-based metrics such as Normalized Cross-Correlation (NCC) can improve without a genuine gain in geometric accuracy. We therefore establish a dataset of 132 frame pairs across fourteen pCLE sequences from 4 patients with manually annotated landmark correspondences, so that Target Registration Error (TRE) can serve as a geometrically grounded complement to NCC. We assess the effect of progressively increasing the transformation model's degrees of freedom, from translation to Thin Plate Spline (TPS), and of six feature-matching backends spanning classical (Shi-Tomasi, Lucas-Kanade) and learned (SuperPoint, SuperGlue, LightGlue, LoFTR, RoMa) approaches. Translation and rigid models prove insufficient under tissue deformation, while TPS with random sampling achieves the strongest landmark-derived alignment of the evaluated configurations; among the learned matchers, used without fine-tuning, only RoMa offers a robust, if modest, advantage over other methods. At the sequence level, pairwise registration quality proved an unreliable predictor of final mosaic quality, so mosaic quality must be evaluated directly rather than inferred from pairwise metrics.

We present $t_0$, a family of open-weights foundation models for forecasting with multivariate context. We release its first two members: $\texttt{t0-alpha}$ and $\texttt{t0-beta}$, respectively 102M and 256M parameters. Both condition their forecasts on target history, past covariates, and known-future covariates, without task-specific retraining. Their transformer layers alternate attention along time and across variates. They produce probabilistic forecasts through quantile predictions. Pretraining combines curated public data with synthetic generator families constructed to contain covariate-to-target dependencies. On GIFT-Eval, $\texttt{t0-alpha}$ reaches an aggregate CRPS of 0.4941, and $\texttt{t0-beta}$ a CRPS of 0.4738 and a MASE of 0.6865, third on both and within 4.0% of the best zero-shot TSFM. On fev-bench they score 42.2 and 46.7 in skill, the latter third again and 2.0 points behind the leader. We analyze $\texttt{t0-alpha}$ in depth. Known-future covariates raise its skill by 6.3 percentage points across 30 tasks. The report also examines its calibration, its rollout strategy on long horizons, and its robustness to missing data. On the Victoria electricity-demand benchmark, $\texttt{t0-beta}$ is among the most accurate models with a context of nearly a year. In an independent Macrocosm evaluation of hourly ERCOT prices over 29 months, both cut the MAE of the lagged-price baseline by 38%.

Principal Component Analysis (PCA) minimises aggregate reconstruction error, which can inadvertently represent majority subgroups with substantially higher fidelity than minority subgroups. Fairness-aware extensions of PCA correct this disparity but require group labels as input. We address the logically prior question: given only a data matrix, which binary partition of the data suffers the greatest representational disparity under a shared PCA projection? We formalise this as the max-disparity partition problem and propose a greedy local-search algorithm, grounded in the Fiduccia-Mattheyses bipartitioning framework, that discovers the disparity-maximising partition without any predefined group labels. Two benchmark algorithms, a fixed-projection sorting baseline and a simulated-annealing variant, confirm that the greedy solution is empirically near-optimal. Having identified the partition, we attribute the disparity to specific features via PCA loading scores and association rule mining, enabling a practitioner to assess whether the disadvantaged group corresponds to a human-meaningful minority. On the Predict Students' Dropout and Academic Success dataset, representational disparity is driven predominantly by institutional and programmatic proxies for socioeconomic disadvantage, with gender emerging as a secondary but consistent contributor within the disadvantaged group. The discovered partition is then passed directly to Fair PCA, completing a detect-explain-mitigate pipeline.

We introduce the Endless Exam, a benchmark spanning fourteen parameterised families of mathematical construction problems, with verifiable scores that distinguish progress before and beyond published mathematical frontiers. Each submitted object is checked automatically for validity and assigned a relative quality score against a published frontier or construction baseline, without capping improvements at 1. The benchmark draws long-term challenges from open mathematical problems and generates larger instances by varying their parameters. Compact certificates allow large constructions to be verified without listing every element. Across nine models evaluated on 69 distinct instances, continuous quality scores distinguish performance even though none of the 30 published-frontier references is surpassed. Size-quality curves show how construction quality changes as problem size increases. We release the generators, verifiers, references, model responses and analysis to support continued measurement before and beyond human frontiers.

Concepts are commonly defined as abstract, compact representations of knowledge and treated as basic units of intelligent behavior. Yet, cognition, psychology, and AI lack a shared mathematical language for them. Modern systems represent concepts as vectors, distributions, symbols, graphs, and other structures, but these formalisms are typically treated as competing rather than as solutions to a common problem. We propose an operation-based view that evaluates mathematical frameworks by the conceptual operations they support, identifying thirteen operations (including similarity, composition, generalization, and grounding) that recur across cognition, psychology, and AI. We show that ten frameworks embody distinct commitments to concepts as self-contained content, relational structure, or evolving process, and that these commitments determine which operations each supports naturally. For example, vector-based models facilitate graded similarity and generalization but struggle with explicit composition, whereas symbolic models support composition but offer but generalize poorly. No single framework we examined naturally supports all operations without extension. We test this account empirically using categorization as a case study, operationalizing nine theories on the same items against human judgments. Despite addressing the same conceptual question, the theories produce different procedures and results, demonstrating that mathematical commitment shapes what a theory can explain. We call for hybrid formalisms that treat content, relation, and process as jointly primary.

Embodied AI systems, particularly humanoid robots deployed in real world scenarios require whole-body control policies that are both task-responsive and physically smooth. However, smoothness is not uniform across the body: lower body must remain sufficiently reactive, while the upper body must be tightly regulated to preserve stability. Existing reinforcement learning approaches typically impose smoothness through auxiliary terms in the reward function, which compete with task objectives, treating the body as uniform and provide no direct control over the physical quantities responsible for smooth behavior. We introduce DeCap (Decoupled Constraint-aware policy), a constrained reinforcement learning algorithm that decouples whole-body smoothness into separate upper- and lower-body constraint groups, each formulates smoothness as explicit constraints on physical motion limits. To improve constraint satisfaction near feasibility boundaries, DeCap incorporates a bounded barrier penalty that activates proactively as limits are approached and remains bounded at the constraint limit. On real-world humanoid whole-body control task, DeCap reduces upper-body action rate by 2.50x and acceleration by 2.18x relative to reward-based smoothness policies, while also improving lower-body smoothness and reducing transient motion. We demonstrate that a fixed set of smoothness constraints transfers across diverse terrains, alleviating the need of extensive reward tuning.

The security of the modern web depends on the correctness of JavaScript (JS) engines, yet these complex systems remain vulnerable to high-impact bugs. A critical limitation of state-of-the-art fuzzers is the coverage plateau: once a fuzzer saturates the control-flow graph, edge coverage loses its ability to guide discovery. Because complex engine behaviors, such as JIT optimization tiers and hidden class transitions, often share identical edge coverage, standard coverage metrics are blind to the distinct internal states required to trigger deep errors. To bridge this gap, we present StateLens, a framework that employs Large Language Models (LLM) to automate the discovery of deep internal states. Blindly placing instrumentation probes at all states is infeasible due to the vast state space and the high runtime overhead. StateLens introduces a novel agent-based reasoning pipeline that emulates the intuition of a security researcher. By iteratively traversing code and developer comments, our agents intelligently select high-value instrumentation targets, effectively separating logic-driving state variables from irrelevant data. This results in synthesizable, high-signal feedback probes that map the engine's hidden configurations. This instrumentation feeds a dual-feedback mechanism, effectively guiding the fuzzer toward unexplored engine semantics. Our evaluation confirms that StateLens significantly outperforms state-of-the-art fuzzers and uncovering 68 new bugs.

% !TEX root = ../main.tex Real-time embodied companion interaction requires a robot to infer user intent from streaming speech, generate timely responses, and execute expressive, interruptible motions. Existing systems typically decouple dialogue orchestration from gesture synthesis, relying on offline motion generation from complete audio. This separation leaves open how a deployed robot can dynamically synchronize response content, prosodic timing, and physical safety under incremental inputs and uncertain turn boundaries. We present MIRA, a unified framework for real-time full-duplex embodied companion interaction. Given streaming user speech, dialogue history, and vocal affect, MIRA predicts both the response text and an explicit embodiment cue that routes the response to the appropriate physical behavior. Discrete social behaviors (\eg listening and greeting) are mapped to validated robot trajectories, while speaking responses are accompanied by streaming, generative co-speech motion. For co-speech motion generation, we propose ROSCO, a prefix-conditioned diffusion model for streaming audio-to-joint motion generation. We further design RHPC, an inference scheme that maintains a sufficiently long temporal context for motion prediction while bounding physical commitment to a short, interruptible prefix. At the interaction level, we design CORTEX, a dual-timescale interaction policy that combines low-latency barge-in preemption and streaming response generation with deliberative turn decisions, backed by a robot-side execution layer that enforces physical safety constraints during execution. MIRA is deployed on an Astribot S1 humanoid robot. Quantitative evaluations demonstrate competitive audio-motion alignment relative to state-of-the-art motion-generation baselines, while real-robot deployment measurements characterize streaming responsiveness and interruption handling.

Multi-modal object Re-Identification (ReID) benefits from complementary information across heterogeneous imaging modalities. To further enrich semantic representation, text descriptions have recently been incorporated as an additional modality. However, recent vision-language approaches often treat text descriptions as clean, deterministic signals and overlook their inherent noise, including modality-mismatched phrases and semantically ambiguous expressions. Moreover, prevailing methods lack explicit mechanisms to reconcile fine-grained structural discrepancies between modalities, even after high-level semantic alignment. To address these challenges, we propose a novel framework centered on Positive-Incentive Noise ({\pi}-noise) and structured prompt modulation. First, the Semantic Cross-Modal Modulator harnesses task-aware {\pi}-noise, sampled from a distribution conditioned on both visual and text inputs, to perturb global tokens and enable semantics-guided cross-modal compensation. Second, the Structure-Aware Prompt Adapter injects learnable geometric priors via prompts to enhance spatial consistency. Third, the Context-Aware Sparse Fusion module distills structural context to guide adaptive fusion while shielding identity features from noisy local details. Experiments on three multi-modal ReID benchmarks demonstrate the effectiveness and robustness of our approach. The code is available at https://github.com/zw-absin/INSPI.