arXiv:2506.01544v2 Announce Type: replace Abstract: We introduce Temporal Variational Implicit Neural Representations (TV-INRs), a probabilistic framework for modeling irregular multivariate time series that enables efficient and accurate individualized imputation and forecasting. By integrating implicit neural representations with latent variable models, TV-INRs learn distributions over time-continuous generator functions conditioned on signal-specific covariates. Unlike existing INR approaches that require extensive training, fine-tuning or meta-learning, our method achieves accurate individualized predictions through a single forward pass. Our experiments demonstrate that with a single TV-INRs instance, we can accurately solve diverse imputation and forecasting tasks, offering a computationally efficient and scalable solution for real-world applications. TV-INRs performs particularly well in low-data regimes, where on several datasets it achieves substantially lower imputation error, including order-of-magnitude improvements.
Science Journals
arXiv:2607.05407v1 Announce Type: new Abstract: Modern artificial intelligence (AI) systems present profound new risks to child safety. AI is increasingly being misused to create AI-generated child sexual abuse material, facilitate child sexual exploitation, and reduce barriers to harm. In this paper, we argue that protecting children from AI-facilitated sexual abuse requires new approaches to AI safety. Existing safety techniques assume data accessibility, transparency, and evaluation practices that are incompatible with the ethical and legal constraints surrounding child sexual abuse material. We examine how these constraints create new technical challenges, such as limitations on dataset auditing, red teaming, and fine-tuning prevention. In turn, we outline *15 open problems* in online child sexual exploitation and abuse across the AI development lifecycle, from dataset curation and model design to deployment and long-term maintenance. We propose targeted recommendations for researchers, developers, and policymakers to bridge the gap between theoretical AI safety and the realities of child protection. Our work aims to reframe preventing AI-facilitated child sexual abuse as a central, safety-critical dimension for AI research, motivating work that translates responsible AI principles into concrete safeguards against the exploitation of children.
arXiv:2607.05409v1 Announce Type: new Abstract: Introductory programming instruction relies on hands-on practice and short learning activities to support mastery of foundational concepts. Although many such learning resources exist, organizing and linking these items in instructionally meaningful ways is challenging without time-intensive expert curation. This study investigates the use of pattern-based Knowledge Components (KCs) to automatically identify code-based learning resources targeting similar concepts. In our approach, pattern-based KCs are extracted from each code sample, and related activities are identified by measuring similarity between the KC sets associated with each activity. By leveraging alignment at the level of semantically important programming patterns, this method supports contextually appropriate and pedagogically useful recommendations. We evaluate our approach on an expert-organized corpus of introductory Python materials in which instructors grouped items into bundles based on conceptual similarity. Results show that our pattern-based KC approach retrieves resources that align with this expert organization, and outperformed representative KC- and embedding-based baselines across standard ranking evaluations. Overall, the framework supports targeted, concept-oriented guidance for programming learners and can help instructors organize, bundle, and recommend instructional content at scale.
arXiv:2607.04990v2 Announce Type: replace Abstract: This work delivers two key contributions: one to efficient feature selection in reinforcement learning (RL), the other to the theory of non-monotone inclusions. On the RL side, the estimation bias inherent in conventional regularization schemes is addressed by augmenting classical least-squares temporal-difference (LSTD) policy evaluation with the sparsity-inducing, non-convex projected minimax concave (PMC) penalty. Because the PMC penalty is weakly convex, the resulting fixed-point problem is no longer monotone; instead, it falls under a broader class of non-monotone inclusions involving the sum of a monotone Lipschitz operator and a hypomonotone operator. On the theory side, novel convergence conditions are developed for the forward-reflected-backward splitting (FRBS) method applied to this broader class of non-monotone inclusion problems. Under mild conditions, Lyapunov stability and the existence of a limit point of the sequence of FRBS iterates are established; alternatively, under the weak Minty variational inequality assumption, exact convergence is guaranteed. Numerical tests on benchmark datasets show that the proposed FRBS iterates, applied to the non-convexly regularized LSTD problem, substantially outperform state-of-the-art feature-selection methods, especially when many noisy features are present.
arXiv:2603.23916v4 Announce Type: replace Abstract: Multimodal deception detection aims to identify deceptive behavior by analyzing audiovisual cues for forensics and security. In these high-stakes settings, investigators need verifiable evidence connecting audiovisual cues to final decisions, along with reliable generalization across domains and cultural contexts. However, existing benchmarks provide only binary labels without intermediate reasoning cues. Datasets are also small with limited scenario coverage, leading to shortcut learning. We address these issues through three contributions. First, we construct reasoning datasets by augmenting existing benchmarks with structured cue-level descriptions and reasoning chains, enabling models to output auditable reports. Second, we release T4-Deception, a multicultural dataset based on the unified ``To Tell the Truth'' television format implemented across four countries. With 1695 samples, it is the largest non-laboratory deception detection dataset. Third, we propose two modules for robust learning under small-data conditions. Stabilized Individuality-Commonality Synergy (SICS) refines multimodal representations by combining learnable global priors with sample-adaptive residuals and applying polarity-aware recalibration. Distilled Modality Consistency (DMC) aligns modality-specific predictions with the fused multimodal predictions via knowledge distillation to prevent unimodal shortcut learning. Experiments on three established benchmarks and our novel dataset demonstrate that our method achieves state-of-the-art performance in both in-domain and cross-domain scenarios, while exhibiting superior transferability across diverse cultural contexts. The datasets and code are available at this link.
arXiv:2607.05176v2 Announce Type: replace Abstract: Small object detection (SOD) remains a challenging task in real-world applications. Despite recent advances, existing detectors remain limited by rigid processing that entangle spatial aggregation with implicit frequency aliasing and truncation, leading to inadequate preservation of high-frequency components for SOD. To tackle these limitations, we propose a Frequency-Spatial Domain Collaborative Detection Transformer (FSDC-DETR), a novel collaborative framework that explicitly models complementary spatial and frequency representations. Specifically, we first introduce Dual-Branch Frequency-Spatial Adaptive Fusion (DBFSAF) to enhance frequency diversity and adaptively capture frequency-spatial domain discriminative representations. Building on these representations, a frequency-spatial interaction scheme is further explored within the hybrid encoder to enable progressive feature propagation to the decoder. In particular, structure-aware frequency-spatial aggregation is achieved through Shunt Frequency-Spatial Feature Fusion (SFS-FF), establishing bidirectional interaction and progressive cross-scale propagation between frequency and spatial representations for coherent discriminative modeling. Meanwhile, informative high-frequency responses are preserved during scale transitions through Frequency-Spatial Dynamic Downsampling (FSD-Down), thereby minimizing frequency degradation throughout multi-scale fusion for the precise SOD. Experimental results demonstrate that FSDC-DETR achieves state-of-the-art performance, improving AP by 6.4 on VisDrone-DET2019 and 6.6 on AITODv2, with gains of 6.8 and 6.9 AP for small objects. The code is available at github.com/nevereverinsomnia/FSDC-DETR.
arXiv:2607.05683v1 Announce Type: new Abstract: Battery charging of Autonomous Mobile Robots (AMRs) in warehouses is a critical operational challenge that heavily impacts both order processing times and throughput. In this study, we address the dynamic AMR charging problem under stochastic order arrivals, where robots must learn optimal charging decisions. Traditional fixed-rule heuristics often prove suboptimal in dynamic environments and fail to account for multi-AMR coordination, leading to severe resource inefficiencies. To overcome these limitations, we propose a Proximal Policy Optimization (PPO)-based Deep Reinforcement Learning (DRL) framework designed for multi-block warehouses with fixed charging stations. Our model dynamically learns two key decisions: charging station selection and optimal charging duration, explicitly accounting for anticipated queuing times at the stations. Extensive numerical experiments benchmark the proposed model against state-of-the-art DRL and traditional heuristic approaches. Results demonstrate that our PPO framework increases order-completion rates by up to 6\% compared to the strongest baseline, while significantly reducing the total time dedicated to recharging operations. Furthermore, we validate the model's robustness across diverse warehouse configurations and stochastic arrival rates. Finally, we interpret the learned DRL policy, offering valuable operational insights into its superiority over standard benchmarks.
arXiv:2607.06244v1 Announce Type: cross Abstract: Pulse-echo speed-of-sound (SoS) imaging based on minute misalignments between consecutively acquired ultrasound images traditionally relies on images beamformed on Cartesian grids. Existing SoS imaging developments do not allow for real-time imaging and typically do not prioritize feasibility in conventional ultrasound systems that have limited resources and rigid processing structures. In this work, we propose a resource-efficient approach based on radial beamforming with virtual source transmits for implementation within an on-the-fly beamformer. We also introduce alternating transmissions with fast pair-alternating beamforming for motion-robust displacement tracking with typical line-based beamformers. We tested these methods comparatively on numerical simulations, tissue-mimicking phantom experiments, and in vivo data from breast lesion examinations. We demonstrate that the proposed radial grid beamforming approach performs comparably to a Cartesian grid approach, while allowing implementation on standard hardware for beamforming. Our proposed sequences would allow for SoS data acquisition frame rates of more than 20 fps in parallel to conventional B-mode imaging. The proposed speckle-shift based radial approach with fast alternation between congruent beamforming lines is a major step towards real-time SoS imaging on standard ultrasound systems with moderate resources.
arXiv:2607.05187v2 Announce Type: replace Abstract: As CMOS technology scales into the deep nanometer regime, digital circuit reliability is increasingly threatened by the combined stochastic effects of Bias Temperature Instability (BTI) and Process Variation (PV). Traditional reliability analysis methods, which rely on computationally intensive simulations or extensive lookup tables, fail to scale efficiently for large designs, creating a critical bottleneck in design space exploration. To address this, we propose SMART, a novel framework that integrates Machine Learning (ML) with Monte Carlo simulation to enable rapid, high-fidelity reliability analysis. SMART employs Random Forest regression to predict gate delay distributions directly, bypassing time-consuming atomic model parameter extractions. Crucially, the model utilizes Bayesian Optimization for automated hyperparameter tuning, ensuring maximum predictive robustness across diverse libraries. Experimental validation on ISCAS85 benchmark circuits demonstrates that SMART achieves a 94.54% reduction in analysis time compared to state-of-the-art methods, while maintaining a remarkable average accuracy error of just 1.63%. By shifting computational complexity to an offline training phase, the proposed framework offers a scalable, accurate solution for designing resilient, reliability-aware digital systems.
arXiv:2607.05253v2 Announce Type: replace Abstract: Large-scale Vision-Language Models like CLIP have demonstrated impressive open-set localization capabilities at the image level. However, adapting this capability to pixel-level dense prediction poses challenges due to global feature biases. In this paper, we introduce CLIPix, a simple yet effective framework that repurposes CLIP to perform pixel-level localization. By tracing back CLIP's classification process, CLIPix identifies object-specific attentive regions and repurposes them as pixel-level localization cues. To address noise introduced by global biases, we propose a Noise-Resistant Correction strategy, refining these cues for more precise segmentation. Additionally, we introduce a Localization Embedding strategy to integrate both localization and enriched detail information, enabling accurate, high-resolution segmentation. Our approach preserves CLIP's generalization strength and unlocks its potential for segmenting arbitrary objects. Extensive experiments on the PASCAL and COCO datasets demonstrate that CLIPix achieves state-of-the-art performance, underscoring its effectiveness.
arXiv:2112.02353v3 Announce Type: replace Abstract: Hierarchical classification aims to sort the object into a hierarchical structure of categories. For example, a bird can be categorized according to a three-level hierarchy of order, family, and species. Existing methods commonly address hierarchical classification by decoupling it into a series of multi-class classification tasks. However, such a multi-task learning strategy fails to fully exploit the correlation among various categories across different levels of the hierarchy. In this paper, we propose Label Hierarchy Transition (LHT), a unified probabilistic framework based on deep learning, to address the challenges of hierarchical classification. The LHT framework consists of a transition network and a confusion loss. The transition network focuses on explicitly learning the label hierarchy transition matrices, which has the potential to effectively encode the underlying correlations embedded within class hierarchies. The confusion loss encourages the classification network to learn correlations across different label hierarchies during training. The proposed framework can be readily adapted to any existing deep network with only minor modifications. We experiment with a series of public benchmark datasets for hierarchical classification problems, and the results demonstrate the superiority of our approach beyond current state-of-the-art methods. Furthermore, we extend our proposed LHT framework to the skin lesion diagnosis task and validate its great potential in computer-aided diagnosis. The code of our method is available at \href{https://github.com/renzhenwang/label-hierarchy-transition}{https://github.com/renzhenwang/label-hierarchy-transition}.
arXiv:2210.16286v2 Announce Type: replace Abstract: To understand the training dynamics of neural networks, prior studies have considered the mean-field limit of two-layer neural networks as the width tends to infinity, establishing theoretical guarantees for its convergence under gradient flow training as well as approximation and generalization capabilities. In this work, we study the infinite-width limit of a type of three-layer neural network where the first-layer weights are randomly sampled and untrained. To rigorously define the limiting model, we extend the mean-field theory by lifting the representation of neurons from Euclidean to functional spaces. This allows us to establish the mean-field training dynamics as a functional gradient flow with a time-varying kernel that remains positive-definite under suitable assumptions, thus proving a linear-rate convergence of its training loss. Furthermore, we define novel function spaces that contain the solutions obtained through the mean-field training dynamics and prove Rademacher complexity bounds for these spaces. Notably, our analysis applies to a range of scaling choices of the model, resulting in two distinct regimes of the mean-field limit that both exhibit feature learning through training.
arXiv:2607.06564v1 Announce Type: new Abstract: Recently, Vision-Language-Action (VLA) models have demonstrated strong generalization across diverse tasks. However, effective robotic manipulation in physical environments fundamentally requires geometric understanding and spatial reasoning. While some VLA approaches attempt to incorporate 3D information, they are constrained by limited data availability and geometric information loss in current 3D encoding pipelines, and fail to jointly capture 3D geometry and temporally structured actions in dynamic environments. To address these limitations, we introduce Lift3D-VLA, a unified VLA framework that equips models with explicit 3D point cloud reasoning and enables temporally coherent action generation. First, building upon our previous work Lift3D, an enhanced 2D model-lifting strategy is proposed to geometrically align 3D points with pretrained 2D positional embeddings. This design enables direct point-cloud encoding within the VLA vision encoder while minimizing spatial information loss. Based on explicit 3D inputs, we propose Geometry-Centric Masked Autoencoding (GC-MAE), a dual-objective self-supervised framework that reconstructs the current point cloud while predicting its future geometric evolution. This formulation allows the 2D vision encoder to internalize both 3D structure and physical dynamics. To fully exploit 3D representations, we further design layer-wise temporal action modeling, which leverages multiple layers of the LLM to collaboratively predict action chunks, enabling temporally consistent predictions. Across 22 simulated tasks and 8 real-world manipulation tasks, Lift3D-VLA achieves 10.8% and 11.1% higher mean success rates on MetaWorld and RLBench than the best-performing prior VLA methods, and outperforms the strongest real-world baseline by 4 percentage points, while exhibiting stronger generalization to out-of-distribution perturbations.
arXiv:2502.15631v2 Announce Type: replace Abstract: Large language models have demonstrated remarkable progress in mathematical reasoning, leveraging chain-of-thought and reinforcement learning. However, many open questions remain regarding the interplay between reasoning token usage and accuracy gains. In particular, when comparing models across generations, it is unclear whether improved performance results from longer reasoning chains or more efficient reasoning. We systematically analyze reasoning chain length across o1-mini and o3-mini variants on the Omni-MATH benchmark, finding that o3-mini (m) achieves superior accuracy without requiring longer reasoning chains than o1-mini. Moreover, we show that accuracy generally declines as reasoning chains grow across all models and compute settings, even when controlling for difficulty of the questions. This accuracy drop is significantly smaller in more proficient models, suggesting that new generations of reasoning models use test-time compute more effectively. Finally, we highlight that while o3-mini (h) achieves a marginal accuracy gain over o3-mini (m), it does so by allocating substantially more reasoning tokens across all problems, even the ones that o3-mini (m) can already solve. These findings provide new insights into the relationship between model capability and reasoning length, with implications for efficiency, scaling, and evaluation methodologies.
arXiv:2504.01759v4 Announce Type: replace Abstract: Practical online inference in dynamic environments requires a lightweight filtering mechanism that remains adaptive to state changes while retaining reliable information from past noisy observations. To address this challenge, we propose the $\alpha\beta$-HMM, an interpretable low-parameter hidden Markov filtering framework that replaces the full transition matrix with an equal-exit surrogate governed by an exit-probability parameter $\alpha$, and introduces a step-size parameter $\beta$ through a generalized measurement update to regulate the influence of observational evidence. A central feature of the proposed method is that it preserves the nonlinear log-belief-ratio dynamics of HMM-type filtering, which turn out to be critical for strong performance. To analyze this nonlinear recursion, we develop a dynamical-systems framework and a deterministic reference system, through which we characterize adaptation capability, learning performance, and practical guidance for selecting the two proposed parameters. In parallel, we study the approximation error induced by the equal-exit surrogate and show that the resulting low-parameter filter remains competitive with the oracle HMM across a broad range of environments. These results reveal an explicit learning-adaptation trade-off induced by the two proposed parameters, provide principled guidance for parameter tuning, and show that strong filtering performance can be achieved within a tractable and interpretable low-parameter framework.
arXiv:2607.06221v1 Announce Type: new Abstract: We present a succinct encoding of planar graphs that supports executing a breadth-first search directly on the encoding. The succinct encoding can be constructed in expected $O(n)$ time using $O(n)$ bits during construction; a compact variant can be constructed in deterministic $O(n)$ time using $O(n)$ bits. Once the encoding is constructed, a BFS from any start vertex can be computed in $O(n)$ time using $o(n)$ additional bits, including the space needed to represent the BFS tree. The resulting BFS tree $T$ remains available for standard tree operations, such as traversal, parent and child queries, layer queries, and lowest common ancestor queries, in constant time per query or output element. The encoding also supports standard graph queries. For plane graphs $G=(V, E)$, we provide traversal of the interdigitating tree $\hat T$, i.e., the spanning tree of the dual graph whose edges correspond to $E \setminus E(T)$. As our main application, we implement the well-known planar separator theorem in a space-efficient way. For biconnected plane graphs, our encoding allows us to compute a balanced separator of size $O(\sqrt n)$ in $O(n)$ time using $o(n)$ additional bits. Along the way, we show that biconnected plane graphs encoded by our representation can be triangulated in expected $O(n)$ time and $o(n)$ bits in the succinct variant, or in deterministic $O(n)$ time using $O(n)$ bits in the compact variant. Further applications include computation of a tree decomposition of width $O(d)$ where $d$ is the diameter of the plane graph at hand and testing for bipartiteness. Finally, all results that do not rely on a plane embedding generalize to separable graph classes.
arXiv:2607.06222v1 Announce Type: new Abstract: Extreme subsea environments often cause severe feature de-gradation and estimator divergence in underwater visual-inertial SLAM. Although sensors like Doppler Velocity Logs (DVL) and pressure gauges provide auxiliary constraints, robust multi-sensor fusion during intermittent visual failure remains challenging. To address this, we present APVI-SLAM, a real-time multi-sensor fusion SLAM system that achieves both accurate underwater localization and photorealistic mapping. Our approach introduces a reliability-aware localization framework that dynamically reweights sensor estimators and employs a sliding-window freezing strategy to recover from tracking failures, substantially enhancing system robustness. Furthermore, for high-fidelity scenes reconstruction, we propose an efficient quadtree-guided mapping module that facilitates incremental water-medium modeling and 3D Gaussian optimization. Recognizing the lack of benchmark for underwater mapping evaluation, we also contribute a coral reef surveying dataset with synchronized multi-modality data. Extensive experiments on public and our proposed benchmarks demonstrate that APVI-SLAM achieves state-of-the-art localization and reconstruction quality at real-time speeds.
arXiv:2607.06262v1 Announce Type: new Abstract: Diffusion and flow policies have recently demonstrated remarkable performance in robotic applications by accurately capturing multimodal robot trajectory distributions, especially in the context of vision language action (VLA) models. However, high quality policy performance also requires fast inference and high quality demonstrations, which are often hard to get. Lack of these leads to suboptimal policy behaviors and failure under distribution shifts. In this work we address the problem of fine-tuning and accelerating suboptimal flow-based policies using the robot's experience through RL post-training. We introduce Optimal Transport Q-Learning (OTQL), a new method for finetuning flow policies using advantage weighted conditional optimal transport flow matching. OTQL can finetune and accelerate flows with an interaction budget of 50-60 episodes while avoiding computationally expensive distillation in simulation and real-world robot tasks. Our results show that OTQL post-trains flow policies using the robot's own experience, increasing average success percentage of single-task policies from 36% to 86% and of a pre-trained VLA from 38% to 76% while reducing the number of inference steps per action generation by 70%.
arXiv:2607.06265v1 Announce Type: new Abstract: Similarly to Thomson, we consider the thermoelectric generator at open circuit as a classical heat engine. It is shown that, as long as the Thomson coefficient is nonzero, the operation generates entropy and is therefore irreversible. By expanding Thomson's approach we show that the voltage produced can be described by the usual Guy--Stodola equation for classical heat engines.
arXiv:2607.02289v2 Announce Type: replace-cross Abstract: Three-dimensional superconducting radio-frequency (SRF) cavities provide exceptionally long-lived electromagnetic modes and, when coupled to nonlinear elements such as transmon qubits, become promising architectures for bosonic quantum information processing. The inverse design of such systems, i.e., recovering device geometries that produce specified electromagnetic and coupling targets, is generally a one-to-many problem. The qubit-cavity coupling strength depends sensitively on both the transmon geometry and its position within the cavity's electromagnetic field. As these systems scale up and their design parameter spaces grow, the cost of conventional iterative simulation becomes prohibitive. We present two deep neural network (DNN) approaches that address this inverse-design problem at complementary levels of the design stack. The first proposes SRF cavity geometries that produce target cavity observables. The second proposes transmon qubit designs that produce target qubit-cavity parameters - the coupling rate, qubit frequency, and anharmonicity $(g, \nu_q, \alpha)$. The recovered candidate designs match the targets to within ~5% (cavity) and ~2% (transmon), confirmed by end-to-end re-simulation. Both approaches map desired device behavior directly to candidate designs, a fast alternative to the iterative simulation studies usually required.
arXiv:2607.06252v1 Announce Type: cross Abstract: Many problems in science and engineering are difficult to model accurately, either due to unknown physical mechanisms, poorly quantified measurement uncertainty, or prohibitive computational costs of high-fidelity simulations. These challenges limit the applicability of classical probabilistic inference methods such as Markov chain Monte Carlo, especially in high-dimensional Bayesian inverse problems. As data from scientific experiments become increasingly available, machine learning methods offer a flexible alternative to explicit parametric modelling. We study neural likelihood approximation, where the goal is to learn the likelihood function directly from data without explicit knowledge of the underlying data-generating process. A common approach trains likelihood surrogates by minimizing the Kullback-Leibler divergence between the true posterior and an approximate posterior, which is equivalent to minimizing the expected negative log-likelihood. This work improves the theoretical foundations of neural likelihood approximation by alleviating limitations of restrictive model classes: we show that, by working with un-normalized potentials and folding normalization into the training objective, the resulting learning problem is strictly convex. We show that empirical minimizers of the resulting data-driven objective converge to the true likelihood as the sample size grows. Numerical experiments for the neural likelihood approximation are conducted for a deblurring and a non-linear PDE based imaging problem.
arXiv:2607.06382v1 Announce Type: cross Abstract: A persistent empirical observation is that trained neural networks outperform their neural tangent kernel (NTK) limit on tasks with compositional structure, yet a quantitative account of $\textbf{when}$ and $\textbf{by how much}$ has been lacking. Working on the unit circle, we give such an account through a dichotomy between two complexity measures of the target: its $\textbf{Fourier complexity}$, which controls NTK kernel regression, and its $\textbf{architectural complexity}$, which controls learning over depth-$L$, width-$w$ ReLU networks with the variation norm of the weights bounded by $R$. We first characterize the minimax rate of the architecture class $\mathcal{C}_{L,w,R}$, pinning it down up to a single factor of $L$: between $\Omega(Lw^2R^2/n)$ and $\tilde{O}(L^2w^2R^2/n)$. We then show the NTK estimator sits $\textbf{exponentially}$ above this floor whenever the two complexities decouple: for the depth-$L$ iterated sawtooth, NTK regression needs $\Omega(4^L)$ samples while the minimax floor is polynomial in $L$. Numerical experiments confirm the theoretical claims: on bandlimited smooth targets, the NTK is competitive or better, while on the hypercube sparse-parity model, a standard two-layer network beats the NTK by four to six orders of magnitude in test error. The gap is thus a function-space property, a mismatch between the kernel's smoothness bias and the target's compositional structure, rather than a generic kernel-versus-network phenomenon.
arXiv:2607.06348v1 Announce Type: new Abstract: We introduce a physics-informed framework for learning finite-dimensional embeddings of solution families of partial differential equations. The method uses a multihead Physics-Informed Neural Network in which a shared body learns a latent manifold representing the solution space, while linear heads reconstruct individual solutions associated with different initial conditions. A head-orthogonalization penalty removes degeneracies in the latent representation and stabilizes the principal-component spectrum across training realizations. Because the initial condition is built into the network output by construction, these principal components measure the additional variability the network learns on top of the initial profile, not the full solution itself. We apply the method to the one-dimensional viscous Burgers equation, with the heat and wave equations as robustness checks. For a latent dimension $n_b=20$, the learned manifolds exhibit pronounced effective dimensional reduction: for Burgers dynamics, only $2$-$4$ principal components capture about $95\%$ of the latent-space variance, while $4$-$7$ capture about $99\%$, depending on the initial-condition family; the same qualitative compression holds for the heat and wave equations. We also split the wavenumber axis into bands (``Fourier shells'') and measure how much each band contributes to every principal component. The resulting frequency profile is invariant under the change-of-basis freedom that the orthogonalization penalty leaves in the latent space, and is therefore reproducible across independent training runs. More broadly, this establishes the learned spectral profiles and principal components as robust observables of solution-manifold geometry.
arXiv:2607.06349v1 Announce Type: new Abstract: Building sensors are embedded in physical topology, spatial hierarchy, and operational context, yet existing forecasters often treat them as isolated time series or rely on fixed covariate sets. We present TopoBrick, a training-free framework for zero-shot building IoT (Internet-of-Things) forecasting. TopoBrick uses building knowledge graphs to construct a compact structural skeleton and employs an agentic topology sampler to select target-specific exogenous variables. The selected variables are organized by deployment-time availability, separating past-known sensor states from future-known calendar, schedule, and meteorological exogenous variables. Across three real-world buildings, TopoBrick outperforms strong zero-shot foundation-model baselines and remains competitive with fully trained building-specific models. Ablations show that topology-aware sampling is more reliable than random, ontology-only, or fixed-hop selection, especially for physically coupled HVAC and weather-driven sensing variables.
arXiv:2606.30611v2 Announce Type: replace Abstract: Understanding facial expressions in videos requires modeling subtle and localized facial dynamics under unconstrained conditions. Although recent Vision Transformer (ViT)-based video models have shown strong performance through large-scale self-supervised pretraining, their attention mechanisms often emphasize dominant global motions and coarse temporal dynamics, limiting sensitivity to fine-grained facial variations. To address this limitation, we propose MiRA (Marginal-induced Attention Redistribution), a plug-in frame-marginal attention redistribution framework for ViT backbones that enhances spatio-temporal selectivity toward subtle facial dynamics without introducing additional trainable parameters. MiRA derives frame-level confidence and intra-frame concentration statistics from self-attention maps to estimate frame-wise marginal importance and redistribute attention toward spatiotemporally localized facial cues. We first introduce a principled exact mode based on post-softmax attention redistribution. To further improve efficiency, we propose flashLite mode, a lightweight pre-softmax approximation that integrates frame-marginal redistribution into FlashAttention kernels while preserving the effectiveness of the exact formulation. Experimental results on challenging Facial Expression Recognition (FER) benchmarks demonstrate consistent improvements over strong ViT baselines.