The forward pass of a Transformer can be seen as an interacting particle system on the unit sphere: time plays the role of layers, particles that of token embeddings, and the unit sphere idealizes layer normalization. In some weight settings the system can even be seen as a gradient flow for an explicit energy, and one can make sense of the infinite context length (mean-field) limit thanks to Wasserstein gradient flows. In this paper we study the effect of the perceptron block in this setting, and show that critical points are generically atomic and localized on subsets of the sphere.

Diffusion models cannot enforce hard constraints, yet applications in the physical sciences demand exact satisfaction of conservation laws, boundary conditions, and observational consistency. In this work, we identify a corrector kernel whose unique stationary distribution is the constrained marginal at each noise level, and approximate it by iteratively projecting through the denoiser and renoising via the forward kernel. The resulting Predict-Project-Renoise (PPR) algorithm enables sampling from pretrained diffusion models under hard constraints. Its three components are each necessary: projecting through the denoiser keeps samples close to the data manifold, while renoising and iterating drive samples toward the constrained marginal. On 2D distributions, the Kuramoto-Sivashinsky equation, and global weather forecasting with a $10^8$-dimensional atmospheric model, PPR simultaneously achieves low constraint violations and high distributional fidelity, a combination that existing methods fail to deliver.

Fine-grained and contact-rich manipulation remain challenging for robots, largely due to the underutilization of tactile feedback. To address this, we introduce TouchGuide, a novel cross-policy visuo-tactile fusion paradigm that fuses modalities within a low-dimensional action space. Specifically, TouchGuide operates in two stages to guide a pre-trained diffusion or flow-matching visuomotor policy at inference time. First, the policy produces a coarse, visually-plausible action using only visual inputs during early sampling. Second, a task-specific Contact Physical Model (CPM) provides tactile guidance to steer and refine the action, ensuring it aligns with realistic physical contact conditions. Trained through contrastive learning on limited expert demonstrations, the CPM provides a tactile-informed feasibility score to steer the sampling process toward refined actions that satisfy physical contact constraints. Furthermore, to facilitate TouchGuide training with high-quality and cost-effective data, we introduce TacUMI, a data collection system. TacUMI achieves a favorable trade-off between precision and affordability; by leveraging rigid fingertips, it obtains direct tactile feedback, thereby enabling the collection of reliable tactile data. Extensive experiments on five challenging contact-rich tasks, such as shoe lacing and chip handover, show that TouchGuide consistently and significantly outperforms state-of-the-art visuo-tactile policies.

Shapley values have emerged as a central game-theoretic tool in explainable AI (XAI). However, computing Shapley values exactly requires $2^d$ game evaluations for a model with $d$ features. Lundberg and Lee's KernelSHAP algorithm has emerged as a leading method for avoiding this exponential cost. KernelSHAP approximates Shapley values by approximating the game as a linear function, which is fit using a small number of game evaluations for random feature subsets. In this work, we extend KernelSHAP by approximating the game via higher degree polynomials, which capture non-linear interactions between features. Our resulting PolySHAP method yields empirically better Shapley value estimates for various benchmark datasets, and we prove that these estimates are consistent. Moreover, we connect our approach to paired sampling (antithetic sampling), a ubiquitous modification to KernelSHAP that improves empirical accuracy. We prove that paired sampling outputs exactly the same Shapley value approximations as second-order PolySHAP, without ever fitting a degree 2 polynomial. To the best of our knowledge, this finding provides the first strong theoretical justification for the excellent practical performance of the paired sampling heuristic.

In neural audio synthesis, neural vocoders and codecs are models that reconstruct waveforms from acoustic and latent representations, which are essential to the resulting audio quality. While current models are capable of generating perceptually natural speech, they still struggle with high-fidelity music and singing voice synthesis, as severe aliasing artifacts are introduced by non-linear activation functions and upsampling layers in existing architectures. Although various anti-aliasing techniques have been proposed in digital signal processing, their integration into neural vocoders and codecs remains under-explored. This paper incorporates differentiable anti-aliasing techniques into the activation and upsampling modules to bridge this gap, and thus presents Pupu-Vocoder and Pupu-Codec. We build a test signal benchmark to evaluate the anti-aliased modules, and validate our proposed models on speech, singing voice, music, and audio. Experimental results show that Pupu-Vocoder and Pupu-Codec outperform existing systems on singing voice, music, and audio, while achieving comparable performance on speech. Demos, codes, and checkpoints are available at VocodexElysium.github.io/AliasingFreeNeuralAudioSynthesis/.

Posing 3D characters is a fundamental task in computer graphics. However, existing paradigms, ranging from traditional auto-rigging to recent pose-conditioned generative models, frequently struggle with inaccurate skinning weights, fixed mesh topologies, and poor pose conformance. These challenges have become particularly pronounced with the recent explosion of AI-generated 3D assets, which often exhibit flawed structures and fused geometry. To address these issues, we introduce Make-It-Poseable, a novel feed-forward framework that reformulates character posing as a skinning-free latent-space transformation problem. By decoupling shape deformation from the constraints of fixed mesh connectivity, our method directly operates on compact latent representations to reconstruct characters in target poses. To achieve this, our framework integrates a latent posing transformer for shape manipulation, a dense pose representation for fine-grained control, and an adaptive completion module optimized via a bipartite-matched latent loss to robustly handle topological changes. Extensive experiments demonstrate that our method significantly outperforms existing baselines in posing quality. Furthermore, our skeleton-agnostic design exhibits remarkable zero-shot generalization to diverse morphologies including quadrupeds and seamlessly supports various 3D authoring applications such as part replacement and refinement.

Many state-of-the-art LLMs are trained to think before giving their answer. Reasoning can greatly improve language model capabilities, but it also makes them less interactive: given a new input, a model must stop thinking before it can respond. Real-world use cases such as voice-based or embodied assistants require an LLM agent to respond and adapt to additional information in real time, which is incompatible with sequential interactions. In contrast, humans can listen, think, and act asynchronously: we begin thinking about the problem while reading it and continue thinking while formulating the answer. In this work, we augment LLMs capable of reasoning to operate in a similar way without additional training. Our method uses the properties of positional embeddings to enable LLMs built for sequential generation to simultaneously think, listen, and write outputs. We evaluate our approach on math, commonsense, and safety reasoning: it allows models to generate accurate thinking-augmented answers while reducing time to first non-thinking token from minutes to ${\le}$ 5s and the overall delays by up to $12{\times}$.

Serving Large Language Models (LLMs) often requires choosing between stronger reasoning and lower inference cost. Model merging offers a practical way to build several models between a reasoning-oriented model and a cheaper base model, but common model-level merging methods usually control this trade-off with only one or two global knobs. We study this setting as a multi-objective optimization problem: instead of producing one merged model, the goal is to find a set of merged models that cover different accuracy--token-cost preferences. Layer-wise merging is more flexible because it can assign different merge weights to different Transformer layers. However, it introduces two practical challenges. First, the layer-wise search space is large, and existing methods often search it without using helpful signals from the source models. Second, LLM evaluations can take very different amounts of time, so synchronous batch optimization wastes GPU time while waiting for slow evaluations. We propose Asynchronous Prior-Guided Bayesian Model Merging (AP-BMM). AP-BMM uses parameter and reasoning-activation differences between the source models to suggest which layers should matter early in the search. It also uses an asynchronous Bayesian optimization loop that accounts for candidate models already being evaluated. A lightweight reranking step further spreads candidates across the accuracy--cost trade-off. Under fixed evaluation budgets, AP-BMM achieves stronger Pareto-set quality and broader trade-off coverage than synchronous layer-wise baselines and representative model-level merging baselines. Compared with the synchronous Bayesian baseline, it also reduces wall-clock time by improving GPU utilization. Code: https://github.com/MiLab-HITSZ/AP-BMM.

Cross-embodiment robot learning requires a unified action representation with consistent semantics across robot platforms. Existing representations suffer from platform-specific inconsistencies, while current solutions either maintain embodiment-specific action heads or learn latent action spaces, without fundamentally resolving the mismatch. We propose to unify robot actions in the camera frame using camera extrinsics, so that actions share consistent geometric semantics across different robot embodiments, including both single-arm and bimanual robots. However, most existing datasets lack camera extrinsic annotations, and existing offline calibration methods either suffer from local minima or require robot-specific training data. To address this gap, we present CalibAll, a training-free, robot-independent annotation pipeline that estimates camera extrinsics for offline datasets and converts heterogeneous robot actions into standardized camera-frame actions. CalibAll follows a coarse-to-fine calibration strategy: temporal PnP provides a stable initialization, followed by differentiable rendering-based refinement for high precision. Beyond extrinsics, CalibAll produces standardized TCP-pose actions and auxiliary annotations. We apply CalibAll to 16 datasets across 4 robot platforms, producing approximately 97K calibrated data episodes. Downstream simulation and real-robot experiments show that cross-embodiment pretraining with camera-frame actions achieves state-of-the-art performance.

Accurate 6D pose estimation and tracking are core capabilities for physical AI systems, yet real-world deployment remains brittle and labor-intensive. Many pipelines rely on CAD models, manual masking, or per-object adaptation, and still fail under occlusion or fast motion without a principled way to recognize failure. We propose STORM, a unified framework for reference-conditioned 6D tracking that can operate from a single reference image, with minimal manual input and improved robustness. STORM combines: (i) Hierarchical Spatial Fusion Attention (HSFA), a task-driven reference-query fusion architecture that supports both single-reference and multi-reference conditioning and can optionally use vision-language semantic conditioning to resolve instance ambiguities; and (ii) a BCE-trained tracking verifier whose continuous compatibility logit is used as an energy-like score to detect drift and trigger automatic re-initialization. Experiments on LM-O and YCB-Video show that STORM improves annotation-free pose tracking accuracy over strong baselines and recovers reliably from severe occlusions and rapid viewpoint changes with minimal overhead.

Although both data availability and the demand for accurate forecasts are increasing, collaboration between stakeholders is often constrained by data ownership and competitive interests. In contrast to recent proposals within cooperative game-theoretical frameworks, we place ourselves in a more general framework, based on prediction markets. There, independent agents trade forecasts of uncertain future events in exchange for rewards. We introduce and analyse a prediction market that (i) accounts for the historical performance of the agents, (ii) adapts to time-varying conditions, while (iii) permitting agents to enter and exit the market at will. The proposed design employs robust regression models to learn the optimal forecasts' combination whilst handling missing submissions. Moreover, we introduce a pay-off allocation mechanism that considers both in-sample and out-of-sample performance while satisfying several desirable economic properties. Case-studies using simulated and real-world data allow demonstrating the effectiveness and adaptability of the proposed market design.

This survey examines multilingual vision-language models that process text and images across languages. We review 33 models and 23 benchmarks, spanning encoder-only and generative architectures, and identify a key tension between language neutrality (consistent cross-lingual representations) and cultural awareness (adaptation to cultural contexts). Current training methods favor neutrality through contrastive learning, while cultural awareness depends on diverse data. Two-thirds of evaluation benchmarks use translation-based approaches prioritizing semantic consistency, though recent work incorporates culturally grounded content. We find discrepancies in cross-lingual capabilities and gaps between training objectives and evaluation goals.

Large Language Models (LLMs) have shown strong promise for robotic task planning, particularly through the automatic generation of symbolic planning domains. However, prior work mainly treats generated domains as planning utilities. Such pipelines remain brittle under imperfect logical states and perception noise, while overlooking the potential of generated domains as scalable sources of reasoning supervision and structured reward signals. At the same time, reasoning LLMs depend on chain-of-thought (CoT) supervision, which is expensive to collect for robotic tasks, and reinforcement learning (RL) faces challenges in reward engineering. We propose Self-CriTeach, an LLM self-teaching and self-critiquing framework in which an LLM autonomously generates symbolic planning domains that serve a dual role: (1) In the self-teaching stage, generated domains are used to produce large-scale robotic planning problem--plan pairs, which are automatically converted into extended CoT trajectories for supervised fine-tuning. (2) In the self-critiquing stage, the same domains are reused as structured reward functions, providing dense feedback for reinforcement learning without manual reward engineering. This unified training pipeline yields a planning-enhanced LLM with higher planning success rates, stronger cross-task generalization, reduced inference cost, and improved resistance to imperfect logical states. GitHub Page: https://markli1hoshipu.github.io/Plan_LLM/

Training deep neural networks with noise and data heterogeneity is a major challenge. We introduce Lightweight Learnable Adaptive Weighting (LiLAW), a method that dynamically adjusts the loss weight of each training sample based on its evolving difficulty, categorized as easy, moderate, and hard, using only three global learnable scalar parameters. LiLAW learns to adaptively prioritize samples by updating these parameters with a single gradient descent step on a validation mini-batch after each training mini-batch, without requiring a clean, unbiased validation set. Experiments across general and medical imaging datasets, several noise types and levels, loss functions, and architectures with and without pretraining, including linear probing and full fine-tuning, show that LiLAW consistently improves accuracy and AUROC, especially in higher-noise settings, without requiring excessive tuning. We also obtain state-of-the-art results incorporating synthetic and augmented data from SynPAIN, GAITGen, ECG5000, and improved fairness on the Adult dataset. LiLAW is lightweight, practical, and computationally efficient, making it an effective, scalable approach to boost generalization and robustness across diverse deep learning training setups, especially in resource-constrained settings.

Low-rank architectures have become increasingly important for efficient large language model (LLM) pre-training, providing substantial reductions in both parameter complexity and memory/computational demands. Despite these advantages, current low-rank methods face three critical shortcomings: (1) compromised model performance, (2) considerable computational overhead, and (3) limited activation memory savings. To address these limitations, we propose Cross-layer Low-Rank residual Network (CR-Net), an innovative parameter-efficient framework inspired by our discovery that inter-layer activation residuals possess low-rank properties. CR-Net implements this insight through a dual-path architecture that efficiently reconstructs layer activations by combining previous-layer outputs with their low-rank differences, thereby maintaining high-rank information with minimal parameters. We further develop a specialized activation recomputation strategy tailored for CR-Net that dramatically reduces memory requirements. Extensive pre-training experiments across model scales from 60M to 7B parameters demonstrate that CR-Net consistently outperforms state-of-the-art low-rank frameworks while requiring fewer computational resources and less memory.

Recent interpretability methods have proposed to translate LLM internal representations into natural language descriptions using a second verbalizer LLM. This is intended to illuminate how the target model represents and operates on inputs. But do such activation verbalization approaches actually provide privileged knowledge about the internal workings of the target model, or do they merely convey information about the inputs provided to it? We critically evaluate popular verbalization methods and datasets used in prior work and find that one can perform well on such benchmarks without access to target model internals, suggesting that these datasets are not ideal for evaluating verbalization methods. We then run controlled experiments which reveal that verbalizations often reflect the parametric knowledge of the verbalizer LLM that generated them, rather than the knowledge of the target LLM whose activations are decoded. Taken together, our results indicate a need for targeted benchmarks and experimental controls to rigorously assess whether verbalization methods provide meaningful insights into the operations of LLMs.

Three-dimensional scene reconstruction from sparse-view satellite images is a long-standing and challenging task. While 3D Gaussian Splatting (3DGS) and its variants have recently attracted attention for its high efficiency, existing methods remain unsuitable for satellite images due to incompatibility with rational polynomial coefficient (RPC) models and limited generalization capability. Recent advances in generalizable 3DGS approaches show potential, but they perform poorly on multi-temporal sparse satellite images due to limited geometric constraints, transient objects, and radiometric inconsistencies. To address these limitations, we propose SkySplat, a novel self-supervised framework that integrates the RPC model into the generalizable 3DGS pipeline, enabling more effective use of sparse geometric cues for improved reconstruction. SkySplat relies only on RGB images and radiometric-robust relative height supervision, thereby eliminating the need for ground-truth height maps. Key components include a Cross-Self Consistency Module (CSCM), which mitigates transient object interference via consistency-based masking, and a multi-view consistency aggregation strategy that refines reconstruction results. Compared to per-scene optimization methods, SkySplat achieves an 86 times speedup over EOGS with higher accuracy. It also outperforms generalizable 3DGS baselines, reducing MAE from 13.18 m to 1.80 m on the DFC19 dataset significantly, and demonstrates strong cross-dataset generalization on the MVS3D benchmark. The is available at https://github.com/NanCheng2001/SkySplat-main

Graph neural networks (GNNs) are increasingly often employed in high-stakes applications, such as fraud detection or healthcare, but are susceptible to adversarial attacks. A number of techniques have been proposed to provide adversarial robustness guarantees, but support for commonly used aggregation functions in message-passing GNNs is lacking. In this paper, we develop an exact (sound and complete) verification method for GNNs to compute guarantees against attribute and structural perturbations that involve edge addition or deletion, subject to budget constraints. Our method employs constraint solving with bound tightening, and iteratively solves a sequence of relaxed constraint satisfaction problems while relying on incremental solving capabilities of solvers to improve efficiency. We implement GNNev, a versatile exact verifier for message-passing neural networks, which supports three aggregation functions -- sum, max and mean -- with the latter two considered here for the first time. Extensive experimental evaluation of GNNev on real-world fraud datasets (Amazon and Yelp) and biochemical datasets (MUTAG and ENZYMES) demonstrates its usability and effectiveness, as well as superior performance on node classification and competitiveness on graph classification compared to existing exact verification tools on sum-aggregated GNNs.

Adapting language models to new data distributions by simple finetuning is challenging. This is due to the rigidity of their subword tokenizers, which typically remain unchanged during adaptation. This inflexibility often leads to inefficient tokenization, causing overfragmentation of text in out-of-distribution domains, unseen languages, or scripts. In this work, we develop byte-level LMs with learnable tokenizers to make tokenization adaptive. Our models include a submodule that learns to predict boundaries given the input byte sequence, encoding it into variable-length segments. Most tokenizer-free methods train this boundary predictor using an auxiliary loss that enforces a fixed compression rate across the training corpus, introducing a new kind of rigidity. We propose FLEXITOKENS, a simplified training objective that enables significantly greater flexibility during adaptation. Evaluating across multiple multilingual benchmarks, morphologically diverse tasks, and domains, we demonstrate that FLEXITOKENS consistently reduces token over-fragmentation and achieves up to 10% point improvements on token classification and generative tasks compared to BPE and other gradient-based tokenizer baselines. We validate our findings using models of varying sizes, and our method demonstrates consistent improvements across scales. Code and data for our experiments will be released at https://github.com/skai-research/flexitokens

Large language models (LLMs) have achieved remarkable success across a wide range of natural language processing tasks, yet their performance remains heavily biased toward high-resource languages. Tibetan, despite its cultural significance and large speaker population, is still substantially underrepresented. In this work, we present a comprehensive pipeline for advancing Tibetan language modeling through large-scale data curation and continual pre-training. We construct a 72 GB high-quality Tibetan corpus, the largest to date, and adapt Qwen2.5-7B through balanced multilingual continual pre-training with Tibetan, Chinese, and English, followed by multilingual instruction tuning. To further scale capacity efficiently, we extend the dense model to a 50B-A10B Mixture-of-Experts architecture. Due to the absence of standardized Tibetan benchmarks, we build multiple evaluation datasets via high-quality translation and human verification. Experimental results show that both dense and MoE models consistently outperform existing open-source and Tibetan-focused models of similar scale across diverse tasks. Our work advances Tibetan-centric LLM research and provides transferable insights for extending LLMs to other low-resource languages. We will release the model weights, evaluation benchmarks, and detailed data processing documentation in the follow-up.

Federated Learning (FL) faces inherent challenges in balancing model performance, privacy preservation, and communication efficiency, especially in non-IID decentralized environments. Recent approaches either sacrifice formal privacy guarantees, incur high overheads, or overlook quantum-enhanced expressivity. We introduce AdeptHEQ-FL, a unified hybrid classical-quantum FL framework that integrates (i) a hybrid CNN-PQC architecture for expressive decentralized learning, (ii) an adaptive accuracy-weighted aggregation scheme leveraging differentially private validation accuracies, (iii) selective homomorphic encryption (HE) for secure aggregation of sensitive model layers, and (iv) dynamic layer-wise adaptive freezing to minimize communication overhead while preserving quantum adaptability. We establish formal privacy guarantees, provide convergence analysis, and conduct extensive experiments on the CIFAR-10, SVHN, and Fashion-MNIST datasets. AdeptHEQ-FL achieves a $\approx 25.43\%$ and $\approx 14.17\%$ accuracy improvement over Standard-FedQNN and FHE-FedQNN, respectively, on the CIFAR-10 dataset. Additionally, it reduces communication overhead by freezing less important layers, demonstrating the efficiency and practicality of our privacy-preserving, resource-aware design for FL.

Novel view synthesis for underwater scene reconstruction presents unique challenges due to complex light-media interactions. Optical scattering and absorption in water body bring inhomogeneous medium attenuation interference that disrupts conventional volume rendering assumptions of uniform propagation medium. While 3D Gaussian Splatting (3DGS) offers real-time rendering capabilities, it struggles with underwater inhomogeneous environments where scattering media introduces artifacts and inconsistent appearance. In this study, we propose a physics-based framework that disentangles object appearance from water medium effects through tailored Gaussian modeling. Our approach introduces appearance embeddings, which are explicit medium representations for backscatter and attenuation, enhancing scene consistency. In addition, we propose a depth-guided optimization strategy that leverages pseudo-depth maps as supervision with depth regularization and scale penalty terms to improve geometric fidelity. By integrating the proposed appearance and medium modeling components via an underwater imaging model, our approach achieves both high-quality novel view synthesis and physically accurate scene restoration. Experiments demonstrate our significant improvements in rendering quality and restoration accuracy over existing methods. The project page is available at https://bilityniu.github.io/3D-UIR.

Multimodal Large Language Models (MLLMs) have achieved significant advances in integrating visual and linguistic information, yet their ability to reason about complex and real-world scenarios remains limited. The existing benchmarks are usually constructed in the task-oriented manner without guarantee that different task samples come from the same data distribution, thus they often fall short in evaluating the synergistic effects of lower-level perceptual capabilities on higher-order reasoning. To lift this limitation, we contribute Lens, a multi-level benchmark with 3.4K contemporary images and 60K+ human-authored questions covering eight tasks and 12 daily scenarios, forming three progressive task tiers, i.e., perception, understanding, and reasoning. One feature is that each image is equipped with rich annotations for all tasks. Thus, this dataset intrinsically supports to evaluate MLLMs to handle image-invariable prompts, from basic perception to compositional reasoning. In addition, our images are manully collected from the social media, in which 53% were published later than Jan. 2025. We evaluate 15+ frontier MLLMs such as Qwen2.5-VL-72B, InternVL3-78B, GPT-4o and two reasoning models QVQ-72B-preview and Kimi-VL. These models are released later than Dec. 2024, and none of them achieve an accuracy greater than 60% in the reasoning tasks. Project page: https://github.com/Lens4MLLMs/lens. ICCV 2025 workshop page: https://lens4mllms.github.io/mars2-workshop-iccv2025/

Modern robots face challenges shared by humans, where machines must learn multiple sensorimotor skills and express them adaptively. Equipping robots with a human-like memory of how it feels to do multiple stereotypical movements can make robots more aware of normal operational states and help develop self-preserving safer robots. Associative Skill Memories (ASMs) aim to address this by linking movement primitives to sensory feedback, but existing implementations rely on hard-coded libraries of individual skills. A key unresolved problem is how a single neural network can learn a repertoire of skills while enabling fault detection and context-aware execution. Here we introduce Neural Associative Skill Memories (ASMs), a framework that utilises self-supervised predictive coding for temporal prediction to unify skill learning and expression, using biologically plausible learning rules. Unlike traditional ASMs which require explicit skill selection, Neural ASMs implicitly recognize and express skills through contextual inference, enabling fault detection across learned behaviours without an explicit skill selection mechanism. Compared to recurrent neural networks trained via backpropagation through time, our model achieves comparable qualitative performance in skill memory expression while using local learning rules and predicts a biologically relevant speed-accuracy trade-off during skill memory expression. This work advances the field of neurorobotics by demonstrating how predictive coding principles can model adaptive robot control and human motor preparation. By unifying fault detection, reactive control, skill memorisation and expression into a single energy-based architecture, Neural ASMs contribute to safer robotics and provide a computational lens to study biological sensorimotor learning.

Formal program specifications in the form of preconditions, postconditions, and class invariants have several benefits for the construction and maintenance of programs. They not only aid in program understanding due to their unambiguous semantics but can also be enforced dynamically (or even statically when the language supports a formal verifier). However, synthesizing high-quality specifications in an underlying programming language is limited by the expressivity of the specifications or the need to express them in a declarative manner. Prior work has demonstrated the potential of large language models (LLMs) for synthesizing high-quality method pre/postconditions for Python and Java, but does not consider class invariants. In this work, we describe ClassInvGen, a method for co-generating executable class invariants and test inputs to produce high-quality class invariants for a mainstream language such as C++, leveraging LLMs' ability to synthesize pure functions. We show that ClassInvGen outperforms a pure LLM-based technique to generate specifications (from code) as well as prior data-driven invariant inference techniques such as Daikon. We contribute a benchmark of standard C++ data structures along with a harness that can help measure both the correctness and completeness of generated specifications using tests and mutants. We also demonstrate its applicability to real-world code by performing a case study on several classes within a widely used and high-integrity C++ codebase.

The perspective of developing trustworthy AI for critical applications in science and engineering requires machine learning techniques that are capable of estimating their own uncertainty. In the context of regression, instead of estimating a conditional mean, this can be achieved by producing a predictive interval for the output, or to even learn a model of the conditional probability $p(y|x)$ of an output $y$ given input features $x$. While this can be done under parametric assumptions with, e.g. generalized linear model, these are typically too strong, and non-parametric models offer flexible alternatives. In particular, for scalar outputs, learning directly a model of the conditional cumulative distribution function of $y$ given $x$ can lead to more precise probabilistic estimates, and the use of proper scoring rules such as the weighted interval score (WIS) and the continuous ranked probability score (CRPS) lead to better coverage and calibration properties. This paper introduces novel algorithms for learning probabilistic regression trees for the WIS or CRPS loss functions. These algorithms are made computationally efficient thanks to an appropriate use of known data structures - namely min-max heaps, weight-balanced binary trees and Fenwick trees. Through numerical experiments, we demonstrate that the performance of our methods is competitive with alternative approaches. Additionally, our methods benefit from the inherent interpretability and explainability of trees. As a by-product, we show how our trees can be used in the context of conformal prediction and explain why they are particularly well-suited for achieving group-conditional coverage guarantees.

We study the problem of learning optimal policies in finite-horizon Markov Decision Processes (MDPs) using low-rank reinforcement learning (RL) methods. In finite-horizon MDPs, the policies, and therefore the value functions (VFs) are not stationary. This aggravates the challenges of high-dimensional MDPs, as they suffer from the curse of dimensionality and high sample complexity. To address these issues, we propose modeling the VFs of finite-horizon MDPs as low-rank tensors, enabling a scalable representation that renders the problem of learning optimal policies tractable. Our approach focuses on VF approximation within a policy iteration framework, where low-rank policy evaluation is combined with greedy policy improvement to compute near-optimal policies. We introduce an optimization-based framework for solving the Bellman equations with low-rank constraints, along with block-coordinate descent (BCD) and block-coordinate gradient descent (BCGD) algorithms, both with theoretical convergence guarantees. We further establish that bounded low-rank policy evaluation error translates into bounded policy improvement in the finite-horizon setting. For scenarios where the system dynamics are unknown, we adapt the proposed BCGD method to estimate the VFs using sampled trajectories. Numerical experiments further demonstrate that the proposed framework reduces computational demands in controlled synthetic scenarios and more realistic resource allocation problems, while achieving competitive policy performance in terms of attained returns.

Sequential Monte Carlo (SMC), or particle filtering, is widely used in nonlinear state-space systems, but its performance often suffers from poorly approximated proposal and state-transition distributions. This work introduces a differentiable particle filter that leverages the unsupervised variational SMC objective to parameterize the proposal and transition distributions with a neural network, designed to learn from high-dimensional observations. Experimental results demonstrate that our approach outperforms established baselines in tracking the challenging Lorenz attractor from high-dimensional and partial observations. Furthermore, an evidence lower bound based evaluation indicates that our method offers a more accurate representation of the posterior distribution.

Generating overtaking trajectories in high-speed scenarios is typically addressed through hierarchical planning, which often suffers from local optima due to single initial solutions and low computational efficiency during numerical optimization. To overcome these limitations, this paper proposes a Spatio-temporal topology and Reachable set analysis enhanced Overtaking trajectory Planning framework (SROP). Specifically, by introducing topological classes to represent distinct overtaking behaviors, the upper-layer planner performs a spatio-temporal search to extract diverse initial paths, effectively preventing local optima. Subsequently, a lower-layer planner conducts parallel trajectory evaluation using reachable sets, which decouples vehicle kinematic constraints from the optimization process to ensure feasibility and significantly accelerate computation. Numerical experiments demonstrate that SROP improves trajectory smoothness by 66.8% and reduces computation time by 62.9% compared to state-of-the-art methods. Furthermore, by seamlessly integrating the method into the F1TENTH autonomous racing simulation platform, a 100-lap sensitivity analysis demonstrates high overtaking success rates in challenging scenarios, thereby validating its practical utility, real-time efficiency, and robustness.

Data scarcity poses a serious threat to modern machine learning and artificial intelligence, as their practical success typically relies on the availability of big datasets. One effective strategy to mitigate the issue of insufficient data is to first harness information from other data sources possessing certain similarities in the study design stage, and then employ the multi-task or meta learning framework in the analysis stage. In this paper, we focus on multi-task (or multi-source) linear models whose coefficients across tasks share an invariant low-rank component, a popular structural assumption considered in the recent multi-task or meta learning literature. Under this assumption, we propose a new algorithm, called Meta Subspace Pursuit (abbreviated as Meta-SP), that provably learns this invariant subspace shared by different tasks. Under this stylized setup for multi-task or meta learning, we establish both the algorithmic and statistical guarantees of the proposed method. Extensive numerical experiments are conducted, comparing Meta-SP against several competing methods, including popular, off-the-shelf model-agnostic meta learning algorithms such as ANIL. These experiments demonstrate that Meta-SP achieves superior performance over the competing methods in various aspects.