As AI becomes more personal, e.g., Agentic AI, there is an increasing need for personalizing models for various use cases. Personalized federated learning (PFL) enables each client to collaboratively leverage other clients' knowledge for better adaptation to the task of interest, without privacy risks. Despite its potential, existing PFL methods remain confined to rather simplified scenarios where data and models are the same across clients. To move towards realistic scenarios, we propose FedMosaic, a method that jointly addresses data and model heterogeneity with a task-relevance-aware model aggregation strategy to reduce parameter interference, and a dimension-invariant module that enables knowledge sharing across heterogeneous architectures without huge computational cost. To mimic the real-world task diversity, we propose a multi-modal PFL benchmark spanning 40 distinct tasks with distribution shifts over time. The empirical study shows that FedMosaic outperforms the state-of-the-art PFL methods, excelling in both personalization and generalization capabilities under challenging, realistic scenarios.

The success of teams in robotics, nature, and society often depends on the division of labor among diverse specialists; however, a principled explanation for when such diversity surpasses a homogeneous team is still missing. Focusing on multi-agent task allocation problems, we study this question from the perspective of reward design: what kinds of objectives are best suited for heterogeneous teams? We first consider an instantaneous, non-spatial setting where the global reward is built by two generalized aggregation operators: an inner operator that maps the $N$ agents' effort allocations on individual tasks to a task score, and an outer operator that merges the $M$ task scores into the global team reward. We prove that the curvature of these operators determines whether heterogeneity can increase reward, and that for broad reward families this collapses to a simple convexity test. Next, we ask what incentivizes heterogeneity to emerge when embodied, time-extended agents must learn an effort allocation policy. To study heterogeneity in such settings, we use multi-agent reinforcement learning (MARL) as our computational paradigm, and introduce Heterogeneity Gain Parameter Search (HetGPS), a gradient-based algorithm that optimizes the parameter space of underspecified MARL environments to find scenarios where heterogeneity is advantageous. Across different environments, we show that HetGPS rediscovers the reward regimes predicted by our theory to maximize the advantage of heterogeneity, both validating HetGPS and connecting our theoretical insights to reward design in MARL. Together, these results help us understand when behavioral diversity delivers a measurable benefit.

Motivated by the hypothesis that neural network representations encode abstract, interpretable features as linearly accessible, approximately orthogonal directions, sparse autoencoders (SAEs) have become a popular tool in interpretability. However, recent work has demonstrated phenomenology of model representations that lies outside the scope of this hypothesis, showing signatures of hierarchical, nonlinear, and multi-dimensional features. This raises the question: do SAEs represent features that possess structure at odds with their motivating hypothesis? If not, does avoiding this mismatch help identify said features and gain further insights into neural network representations? To answer these questions, we take a construction-based approach and re-contextualize the popular matching pursuits (MP) algorithm from sparse coding to design MP-SAE -- an SAE that unrolls its encoder into a sequence of residual-guided steps, allowing it to capture hierarchical and nonlinearly accessible features. Comparing this architecture with existing SAEs on a mixture of synthetic and natural data settings, we show: (i) hierarchical concepts induce conditionally orthogonal features, which existing SAEs are unable to faithfully capture, and (ii) the nonlinear encoding step of MP-SAE recovers highly meaningful features, helping us unravel shared structure in the seemingly dichotomous representation spaces of different modalities in a vision-language model, hence demonstrating the assumption that useful features are solely linearly accessible is insufficient. We also show that the sequential encoder principle of MP-SAE affords an additional benefit of adaptive sparsity at inference time, which may be of independent interest. Overall, we argue our results provide credence to the idea that interpretability should begin with the phenomenology of representations, with methods emerging from assumptions that fit it.

Predicting accurate future trajectories of pedestrians is essential for autonomous systems but remains a challenging task due to the need for adaptability in different environments and domains. A common approach involves collecting scenario-specific data and performing fine-tuning via backpropagation. However, the need to fine-tune for each new scenario is often impractical for deployment on edge devices. To address this challenge, we introduce TrajICL, an In-Context Learning (ICL) framework for pedestrian trajectory prediction that enables adaptation without fine-tuning on the scenario-specific data at inference time without requiring weight updates. We propose a spatio-temporal similarity-based example selection (STES) method that selects relevant examples from previously observed trajectories within the same scene by identifying similar motion patterns at corresponding locations. To further refine this selection, we introduce prediction-guided example selection (PG-ES), which selects examples based on both the past trajectory and the predicted future trajectory, rather than relying solely on the past trajectory. This approach allows the model to account for long-term dynamics when selecting examples. Finally, instead of relying on small real-world datasets with limited scenario diversity, we train our model on a large-scale synthetic dataset to enhance its prediction ability by leveraging in-context examples. Extensive experiments demonstrate that TrajICL achieves remarkable adaptation across both in-domain and cross-domain scenarios, outperforming even fine-tuned approaches across multiple public benchmarks. Project Page: https://fujiry0.github.io/TrajICL-project-page/.

Reasoning has substantially improved the performance of large language models (LLMs) on complicated tasks. Central to the current reasoning studies, Process Reward Models (PRMs) offer a fine-grained evaluation of intermediate reasoning steps and guide the reasoning process. However, extending PRMs to multimodal large language models (MLLMs) introduces challenges. Since multimodal reasoning covers a wider range of tasks compared to text-only scenarios, the resulting distribution shift from the training to testing sets is more severe, leading to greater generalization difficulty. Training a reliable multimodal PRM, therefore, demands large and diverse datasets to ensure sufficient coverage. However, current multimodal reasoning datasets suffer from a marked quality imbalance, which degrades PRM performance and highlights the need for an effective data selection strategy. To address the issues, we introduce DreamPRM, a domain-reweighted training framework for multimodal PRMs which employs bi-level optimization. In the lower-level optimization, DreamPRM performs fine-tuning on multiple datasets with domain weights, allowing the PRM to prioritize high-quality reasoning signals and alleviating the impact of dataset quality imbalance. In the upper-level optimization, the PRM is evaluated on a separate meta-learning dataset; this feedback updates the domain weights through an aggregation loss function, thereby improving the generalization capability of trained PRM. Extensive experiments on multiple multimodal reasoning benchmarks covering both mathematical and general reasoning show that test-time scaling with DreamPRM consistently improves the performance of state-of-the-art MLLMs. Further comparisons reveal that DreamPRM's domain-reweighting strategy surpasses other data selection methods and yields higher accuracy gains than existing test-time scaling approaches.

The coupling signal refers to a latent physiological signal that characterizes the transformation from cardiac electrical excitation, captured by the electrocardiogram (ECG), to mechanical contraction, recorded by the phonocardiogram (PCG). By encoding the temporal and functional interplay between electrophysiological and hemodynamic events, it serves as an intrinsic link between modalities and offers a unified representation of cardiac function, with strong potential to enhance multi-modal cardiovascular disease (CVD) detection. However, existing coupling signal estimation methods remain highly vulnerable to noise, particularly in real-world clinical and physiological settings, which undermines their robustness and limits practical value. In this study, we propose Noise-Robust Multi-Modal Coupling Signal Estimation (NMCSE), which reformulates coupling signal estimation as a distribution matching problem solved via optimal transport. By jointly aligning amplitude and timing, NMCSE avoids noise amplification and enables stable signal estimation. When integrated into a Temporal-Spatial Feature Extraction (TSFE) network, the estimated coupling signal effectively enhances multi-modal fusion for more accurate CVD detection. To evaluate robustness under real-world conditions, we design two complementary experiments targeting distinct sources of noise. The first uses the PhysioNet 2016 dataset with simulated hospital noise to assess the resilience of NMCSE to clinical interference. The second leverages the EPHNOGRAM dataset with motion-induced physiological noise to evaluate intra-state estimation stability across activity levels. Experimental results show that NMCSE consistently outperforms existing methods under both clinical and physiological noise, highlighting it as a noise-robust estimation approach that enables reliable multi-modal cardiac detection in real-world conditions.

Quantitative assessment of treatment response in Advanced Prostate Cancer (APC) with bone metastases remains an unmet clinical need. Whole-Body Diffusion-Weighted MRI (WB-DWI) provides two response biomarkers: Total Diffusion Volume (TDV) and global Apparent Diffusion Coefficient (gADC). However, tracking post-treatment changes of TDV and gADC from manually delineated lesions is cumbersome and increases inter-reader variability. We developed a software to automate this process. Core technologies include: (i) a weakly-supervised Residual U-Net model generating a skeleton probability map to isolate bone; (ii) a statistical framework for WB-DWI intensity normalisation, obtaining a signal-normalised b=900s/mm^2 (b900) image; and (iii) a shallow convolutional neural network that processes outputs from (i) and (ii) to generate a mask of suspected bone lesions, characterised by higher b900 signal intensity due to restricted water diffusion. This mask is applied to the gADC map to extract TDV and gADC statistics. We tested the tool using expert-defined metastatic bone disease delineations on 66 datasets, assessed repeatability of imaging biomarkers (N=10), and compared software-based response assessment with a construct reference standard (N=118). Average dice score between manual and automated delineations was 0.6 for lesions within pelvis and spine, with an average surface distance of 2mm. Relative differences for log-transformed TDV (log-TDV) and median gADC were 8.8% and 5%, respectively. Repeatability analysis showed coefficients of variation of 4.6% for log-TDV and 3.5% for median gADC, with intraclass correlation coefficients of 0.94 or higher. The software achieved 80.5% accuracy, 84.3% sensitivity, and 85.7% specificity in assessing response to treatment. Average computation time was 90s per scan.

Large Language Models (LLMs) excel in natural language tasks, but less is known about their reasoning capabilities over tabular data. Prior analyses devise evaluation strategies that poorly reflect an LLM's realistic performance on tabular queries. Moreover, we have a limited understanding of the robustness of LLMs towards realistic variations in tabular inputs. Therefore, we ask: Can general-purpose LLMs reason over tabular data, really?, and focus on two questions 1) are tabular reasoning capabilities of general-purpose LLMs robust to real-world characteristics of tabular inputs, and 2) how can we realistically evaluate an LLM's performance on analytical tabular queries? Building on a recent tabular reasoning benchmark, we first surface shortcomings of its multiple-choice prompt evaluation strategy, as well as commonly used free-form text metrics such as SacreBleu and BERT-score. We show that an LLM-as-a-judge procedure yields more reliable performance insights and unveil a significant deficit in tabular reasoning performance of LLMs. We then extend the tabular inputs reflecting three common characteristics in practice: 1) missing values, 2) duplicate entities, and 3) structural variations. Experiments show that the tabular reasoning capabilities of general-purpose LLMs suffer from these variations, stressing the importance of improving their robustness for realistic tabular inputs.

Formal reasoning and automated theorem proving constitute a challenging subfield of machine learning, in which machines are tasked with proving mathematical theorems using formal languages like Lean. A formal verification system can check whether a formal proof is correct or not almost instantaneously, but generating a completely correct formal proof with large language models (LLMs) remains a formidable task. The usual approach in the literature is to prompt the LLM many times (up to several thousands) until one of the generated proofs passes the verification system. In this work, we present APOLLO (Automated PrOof repair viaLLM and Lean cOllaboration), a modular, model-agnostic agentic framework that combines the strengths of the Lean compiler with an LLM's reasoning abilities to achieve better proof-generation results at a low token and sampling budgets. Apollo directs a fully automated process in which the LLM generates proofs for theorems, a set of agents analyze the proofs, fix the syntax errors, identify the mistakes in the proofs using Lean, isolate failing sub-lemmas, utilize automated solvers, and invoke an LLM on each remaining goal with a low top-K budget. The repaired sub-proofs are recombined and reverified, iterating up to a user-controlled maximum number of attempts. On the miniF2F benchmark, we establish a new state-of-the-art accuracy of 84.9% among sub 8B-parameter models (as of August 2025) while keeping the sampling budget below one hundred. Moreover, Apollo raises the state-of-the-art accuracy for Goedel-Prover-SFT to 65.6% while cutting sample complexity from 25,600 to a few hundred. General-purpose models (o3-mini, o4-mini) jump from 3-7% to over 40% accuracy. Our results demonstrate that targeted, compiler-guided repair of LLM outputs yields dramatic gains in both efficiency and correctness, suggesting a general paradigm for scalable automated theorem proving.

The Cellular-Potts model is a powerful and ubiquitous framework for developing computational models for simulating complex multicellular biological systems. Cellular-Potts models (CPMs) are often computationally expensive due to the explicit modeling of interactions among large numbers of individual model agents and diffusive fields described by partial differential equations (PDEs). In this work, we develop a convolutional neural network (CNN) surrogate model using a U-Net architecture that accounts for periodic boundary conditions. We use this model to accelerate the evaluation of a mechanistic CPM previously used to investigate in vitro vasculogenesis. The surrogate model was trained to predict 100 computational steps ahead (Monte-Carlo steps, MCS), accelerating simulation evaluations by a factor of 590 times compared to CPM code execution. Over multiple recursive evaluations, our model effectively captures the emergent behaviors demonstrated by the original Cellular-Potts model of such as vessel sprouting, extension and anastomosis, and contraction of vascular lacunae. This approach demonstrates the potential for deep learning to serve as efficient surrogate models for CPM simulations, enabling faster evaluation of computationally expensive CPM of biological processes at greater spatial and temporal scales.