Science & Mathematics

Physics-informed neural networks (PINNs) and other residual-trained solvers judge a candidate solution by the size of its sampled PDE residual. For first-order Hamilton-Jacobi equations this is not sufficient: the same equation and boundary data admit Lipschitz almost-everywhere solutions that differ from the viscosity solution by $O(1)$ while violating the equation only on sets of measure zero. We study whether residual minimization selects such solutions in a fixed-horizon pursuit-evasion game whose Hamilton-Jacobi-Isaacs value function is known in closed form on the circle $S^1$ and on the flat tori $\mathbb{T}^{2}$ and $\mathbb{T}^{4}$. We train four neural parameterizations with ten seeds on each geometry, 120 runs in total. A standard network with periodic Fourier features converges to folded almost-everywhere solutions in all 30 runs: small residuals and the expected capture-layer gradient, yet values that are wrong over most of the domain. A network with periodicity imposed through the loss recovers the viscosity solution in one and two dimensions but becomes unreliable in four. Two parameterizations that receive the geodesic distance do substantially better: a single network fed the wrapped displacement and its distance recovers the viscosity solution in all 30 runs, while a minimum over periodic image charts succeeds in 27 of 30 and introduces a wrong-image failure mode. Finally, for the convex Hamiltonian considered here, we use the semiconcavity of the viscosity solution to build a mesh-free finite-difference test that needs only forward network evaluations; it detects the folded solutions and the harmful min-of-charts failures without access to the exact value function. A small sampled residual thus does not by itself validate a learned Hamilton-Jacobi solution; the parameterization and independent structural diagnostics can be essential for selecting the viscosity solution.

Diffusion policies with linearly composed scores have emerged as a promising approach to multitask robotic learning by combining separate factors to enable modular, task-wise adaptation, compositional generalization, and interpretable functional decomposition. However, current training objectives do not encourage factor specialization, often resulting in uninterpretable denoisers whose composed prediction is an average over identical copies, undermining their architectural premise. To address this, we propose a drop-in score-decorrelation auxiliary loss, motivated by projective composition theory. Our approach encourages specialization by penalizing overlap directly between component noise predictions, with little architectural change or computational overhead. We demonstrate across multiple benchmarks that our decorrelation loss consistently reduces measurable double-counting between components, improves task decomposition, and produces behaviorally meaningful specialization without compromising multitask performance. Website: https://al3cl1.github.io/robotics-score-decorrelation.

Dense bi-encoders and late-interaction retrievers are usually treated as alternatives, yet they fail on different queries: one vector captures what a text is about, token-level matching finds its exact entities and phrases. Using both today means two models, two indexes and a score-fusion step. We present UIBK-Embedding-v1, a 179M-parameter English encoder that produces both representations in one pass and scores them with one unmodified MaxSim. The dense embedding is written into the list of token vectors as three extra vectors, and a one-dimensional tag keeps the two kinds of vectors from matching each other, so that plain MaxSim equals the token-level MaxSim plus a weighted dense cosine. The model therefore runs in a standard late-interaction index without changes; we test it with PLAID. A shared 18-layer trunk with a separate 4-layer top per head, and a cross-encoder distilled into the fused score, turn the two heads into one retriever. On BEIR, UIBK-Embedding-v1 reaches 59.79 nDCG@10. This is 2.57 points above LateOn, the strongest model of its size, and 2.10 points above it when both models read documents of the same length; UIBK-Embedding-v1 is ahead on all 15 datasets. On a decontaminated version of BEIR it stays ahead on average (61.55 against 60.36) and on 8 of 12 datasets. Among the 156 models with complete BEIR results in the MTEB results repository, only models with at least 1.5B parameters score higher. Code, model weights, and a technical blog post are available at https://github.com/DataScienceUIBK/uibk-embedding , https://huggingface.co/DataScience-UIBK/uibk-embedding-v1 , and https://huggingface.co/blog/abdoelsayed/uibk-embedding-v1 .

In conventional natural deduction, a proof of a proposition is a derivation tree constructed out of inference rules with some number of premises and a conclusion judgement. For propositional logic, in contrast to the other connectives, the rule for disjunction elimination of $A \vee B$ involves concluding with an auxiliary formula C from $A \vdash C$ and $B \vdash C$. Not only is this asymmetry unsightly, it also introduces the need for commuting conversions across disjunction eliminations to transform between proof derivations that are morally equivalent but not $βη$-equivalent. To resolve the asymmetry, Jean-Yves Girard suggests a disjunction elimination rule with multiple conclusions A and B, but claims that "we have no way of bringing them back together". In this work, we pursue Girard's proposal using the key insight that proof derivations need not be trees, but may be directed acyclic graphs (DAGs) in general. Derivation rules are represented as nodes, premises as incoming edges, and conclusions as outgoing edges. Treating derivations as DAGs permits using the alternate rule by ensuring that the subderivations pointed at by each conclusion eventually join up at a new concluding node. Commuting conversions can then be formulated in terms of interactions with this join node. We explore ways to design a proof graph language with reduction and commutation rules such that proof simplification retains its concluding judgements, i.e. type preservation. In particular, we examine two styles of reduction rules: a local style, which only requires looking at the relevant subgraph of a whole proof but necessitates a number of extraneous constructs to satisfy type preservation; and a global style, which doesn't require all the extraneous constructs but necessitates looking at the entire proof graph as a whole.

Planetary science depends on chemical measurements made under conditions very different from those in a terrestrial laboratory. This review treats the analytical methods of planetary science as one connected chain, from orbital remote sensing through in-situ measurements by landers and rovers and sample collection and curation, to the micro-analysis of returned material on Earth. Orbital methods, including visible and near-infrared reflectance, thermal emission and gamma-ray and neutron spectroscopy, are discussed first. In-situ techniques are then reviewed, including laser-induced breakdown spectroscopy (LIBS), micro-focus X-ray fluorescence (XRF), deep-ultraviolet Raman and fluorescence spectroscopy, evolved gas analysis with gas chromatography-mass spectrometry (GC-MS) and miniaturized mass spectrometry. Contamination control and curation practices are described, followed by laboratory techniques such as secondary ion mass spectrometry (SIMS and NanoSIMS), atom probe tomography (APT), thermal ionization mass spectrometry (TIMS), synchrotron micro-XRF and X-ray absorption near-edge structure (XANES) spectroscopy. Accuracy, calibration and reference materials are discussed as the link between in-situ and laboratory data, and the role of chemometrics and data fusion is examined. Flight and laboratory instruments are compared in terms of spatial resolution, detection limit, sample consumption and throughput. Active neutron-gamma spectroscopy planned for the Dragonfly mission to Titan is also discussed. This comparison shows that in-situ and laboratory techniques are complementary. In-situ instruments provide context and select samples, while laboratory techniques provide isotopic, molecular and speciation data that cannot yet be obtained in situ.

In models of opinion dynamics, researchers typically examine how an individual's opinion on one topic is influenced by the opinions of their neighbors in a network. However, people's opinions on a topic are also influenced by their opinions and their neighbors' opinions on related topics. In an election, for example, the opinions of a voter on a variety of issues inform their opinions of electoral candidates. To consider the influence between people's opinions on multiple distinct topics, we study a multiplex extension of the traditional DeGroot consensus model. In our multiplex DeGroot model, different network layers represent distinct topics and directed interlayer edges (which are not allowed to form cycles) encode relationships between distinct topics. In our model, an individual's opinion on one topic is influenced both by the opinions of their neighbors on that topic and by their own opinions on related topics. We prove under mild conditions that our multiplex DeGroot model converges to a limit state. We also prove that strong connectedness in ``source layers'' (which represent fundamental beliefs) eventually yields a consensus opinion in each layer. In particular, we show that consensus on source layers can lead to consensus on other layers even when those layers otherwise would be polarized. By numerically simulating our multiplex DeGroot model on a two-layer network, we examine the effects on opinion dynamics of (1) different network structures and (2) different types of initial opinion data.

The Jetson AGX Orin is a common computer for robots and vehicles, yet measured accuracy, speed and energy of current depth estimators on it are hard to find. We benchmark nine model families as of October 2026: the monocular Depth Anything V2 and 3, Depth Pro, MoGe-2, Metric3D v2 and UniDepth V2, and the stereo methods libSGM, NVIDIA ESS and Fast-FoundationStereo. Every method runs on the Orin as a TensorRT FP16 engine or native CUDA code at up to three input sizes, up to the full 5.7 MP, and is scored for metric accuracy against Middlebury 2014 ground truth (non-occluded pixels of the 10 scenes whose disparity stays below 256 px), GPU time, energy and licence. Stereo is far more accurate. At 30 fps, NVIDIA's ESS reaches 0.70% AbsRel in 8.6 ms and libSGM 0.73% in 25 ms; with more compute, Fast-FoundationStereo reaches 0.33%. The best monocular models reach 12% with the true focal length (Depth Anything 3 Metric-L in 33 ms, Depth Pro in 803 ms), and 3.8-4.0% only with an oracle per-image scale (MoGe-2-L, UniDepth V2-B, Metric3D v2-L). Stereo error falls as the input resolution grows; no monocular model improves, and the metric scale of most drifts away from the truth outside their training resolution. At depth discontinuities, which AbsRel barely registers, the monocular models scatter 17-46% of the edge points between foreground and background, learned stereo 2-9% and libSGM at full resolution 1%. We give recommendations per frame-rate budget and release all code, per-scene results and engine build scripts.

Speech large language models (LLMs) perform multiple tasks, including automatic speech recognition (ASR), timestamp prediction (TS), and speech translation (ST). Joint training of speech LLMs creates task trade-offs, yet standard training with fixed loss weights does not generally control the resulting trade-off according to deployment preferences. To address this, we propose Endpoint-Anchored Preference-Aware Sampling Uniformly along the Pareto Front (EA-SURF), an a priori method that adapts scalarization weights so that the resulting task trade-off reflects the desired preference. EA-SURF retains the standard weighted-loss training pipeline, tracking the current model's performance relative to each task-specific reference and adapting the scalarization weights as training proceeds. We theoretically show that EA-SURF can match a desired preference, with the update becoming stationary at the target under checkable regularity conditions. Across six three-objective speech LLM requests, EA-SURF empirically converges toward the requested targets and increases endpoint-inclusive normalized hypervolume by 17.8% over fixed loss weighting.

Large Language Models (LLMs) increasingly operate across culturally diverse settings, yet existing evaluations largely measure cultural behavior at the output level. We introduce CultureLens, a reference-grounded benchmark and mechanistic study of how LLMs use cultural information. CultureLens contains 9,261 scenarios across 75 countries and systematically varies country, value, true-norm, and contradictory-norm evidence. Across Llama-3.1-8B, Gemma-3-12B, and Qwen-3.5-27B, stating a contradictory norm lowers aligned answers by 32-47 percentage points, even when the model answers correctly from the country alone. Mechanistically, models default to Anglophone norms when no country is given. The failure under a contradictory norm is not one of missing knowledge, as blocking the norm inside the model restores the correct answer in most cases. Models accept a stated norm according to how it is presented and not whether it is true, which leaves them most exposed to errors in retrieved content. Supervised fine-tuning with contradictory-norm examples raises aligned answers under a contradictory norm to 85-93%, including on unseen countries, at a small cost under a true norm.

Class-Incremental Learning (CIL) enables models to recognize new classes over time while retaining prior knowledge, but many real-world problems are compositional, where visual concepts arise from combinations of primitives such as states (i.e., red, shiny) and objects (i.e., shoe, car). Standard CIL methods treat each composition as an independent class, ignoring shared primitives and providing no mechanism to stabilize their representations as new compositions arrive. This causes parameter updates to entangle primitives and induce drift that degrades performance on earlier compositions. Compositional Incremental Learning (composition-IL) formalizes this setting by introducing new state-object compositions across tasks. In this paper, we propose Layer-Specific Adaptation with Prototype-Anchored Adapter-Space Transport (LSA-PAST), a parameter-efficient method tailored to composition-IL. LSA integrates Low-Rank Adaptation (LoRA) into a frozen ViT with depth-specialized adapters for states, objects, and compositions. PAST then maps past, anchored prototypes into the current adapter space through a rehearsal-free affine transform fit on current-task data, enabling old prototypes to remain compatible with new adapters. Extensive experiments demonstrate that LSA-PAST achieves state-of-the-art (SOA) accuracy-forgetting trade-off performance for composition-IL.

Homomorphic encryption allows a computing service to process encrypted data, but the client must first encode and encrypt its inputs. Sharing hardware between floating-point encoding and modular encryption reduces area but requires those transform roles to execute at different times. We present a streaming FPGA architecture for CKKS encoding and encryption that computes the shared floating-point encoding transform once and performs the integer transforms for six residue moduli in parallel. Dedicated transform pipelines exchange intermediate results on chip rather than through off-chip memory. DSP Builder generates the transform RTL, and Altera HLS IP Gen compiler compiles the surrounding SYCL pipeline into IP integrated with DMA and control logic in an accelerator functional unit. At polynomial degree N = 8192, the Altera Agilex 7 implementation delivers 5,143 complete ciphertexts per second at 471 MHz. One SEAL-Embedded CPU worker on the same workstation delivers 113 ciphertexts per second for real-valued inputs using all 4,096 slots. Measurements cover prepared-input computation through complete ciphertext construction, including FPGA submission and output delivery.

Web agents are typically evaluated on English-language interfaces, leaving their ability to operate across the world's multilingual websites largely unexplored. This gap is especially significant for low-resource languages, where standardized resources for evaluating web agents remain limited. To address this gap, we introduce Low-Resource Web Agent Benchmark (LoWAgent), a benchmark for evaluating web agents across different low-resource languages (LRLs) in comparison to the default, English. LoWAgent evaluates web agents across English and four LRLs: Hindi, Bengali, Urdu, and Amharic. The benchmark comprises of six fully localized websites, instantiated across five languages to yield 3,000 task instances. We evaluate three closed-source and five open-source models across all five languages on all six websites. Our findings show that both closed-source and open-source models experience performance degradation for LRLs compared to English, with substantially greater performance drops observed among the open-source model agents. We further evaluate the robustness of the models on realistic interface disruptions, such as cookie notices and advertisement pop-ups, and find that these further degrade agentic performance. Finally, we show that post-training on a small subset of LoWAgent traces can significantly improve low-resource language agentic task performance, demonstrating the usefulness of our benchmark.

We study the sample complexity of estimating Ornstein--Uhlenbeck diffusion scores in $\mathbb R^d$ using denoising score matching (DSM) with finite-width shallow ReLU networks, and its implications for reverse-process sampling. Under weak differentiability and polynomial-growth conditions on normalized derivatives of the initial density, we combine complementary estimates from the Gaussian transition kernel and the initial density to obtain explicit Sobolev bounds that are uniform in time on each fixed ball. Combining these bounds with existing shallow-network approximation theory gives explicit control of the approximation error and a sufficient path-norm budget. We then use truncation and localized Rademacher complexity to establish high-probability risk bounds for path-norm-constrained empirical DSM minimizers with unbounded inputs and labels. Under additional bounded-density and sub-Gaussian assumptions, suitable choices of network width and path-norm budget yield squared $L^2(P_t)$ score risk $\widetilde O(n^{-(d+3)/(2d+3)})$ at each fixed time $t>0$, where $n$ is the number of independent training samples and $P_t$ is the forward marginal. The nonasymptotic bounds retain explicit dependence on diffusion time and the regularity and tail parameters of the initial distribution. Aggregating the score errors over a time grid and applying existing sampling theory together with an early-stopping bound yields a high-probability total-variation error $\widetilde O(n^{-(d+3)/(4d+6)})$ between the generated and original data distributions under suitable sampling parameters. Here $\widetilde O$ suppresses logarithmic factors for fixed dimension, confidence level, and initial distribution.

We investigate quasi-2D active-passive colloidal mixtures with electric field-mediated non-identical interactions: unlike species attract and like species repel. Mapping the steady states across total area fraction and active particle area fraction identifies the regime of active percolated network formation among active fluid and clustered states. Within the percolated network regime, relaxation speeds up with increasing density, contrary to expectations for dense particulate gels. Particle-resolved dynamics and microstructure link this acceleration to activity-driven rearrangements enabled by asymmetric interactions.

Deep neural networks have achieved remarkable success on vision benchmarks, yet they continue to struggle with many generalization challenges. Supervised vision training relies on one-hot labels, which provide limited information about semantic structure and shared attributes between classes. This limited supervision can leave visual representations vulnerable to distribution shifts, spurious correlations, texture bias, adversarial perturbations, and forgetting in sequential learning settings. We study whether pretrained language models can serve as lightweight auxiliary supervision for vision training without requiring paired image-text data, prompt engineering, or contrastive objectives. Specifically, we evaluate two forms of language guidance, Explicit Language Guidance (ExLG) and Implicit Language Guidance (ImLG). We conduct a comprehensive evaluation across six generalization regimes, including in-distribution, out-of-distribution generalization, shortcut and spurious correlation resistance, texture and shape bias, adversarial robustness, and continual learning. Our analyses show that the two mechanisms have complementary strengths, with explicit guidance consistently benefiting in-distribution, low-data performance, and continual learning retention, while implicit guidance is often more useful in shortcut-sensitive settings and under stronger adversarial perturbations. Importantly, both are lightweight and add minimal parameters and training overhead. The analyses characterize when language-derived structure helps supervised vision training and provides a practical roadmap for using off-the-shelf pretrained models from another modality as auxiliary supervision.