AI agents are increasingly deployed to execute important tasks. While rising accuracy scores on standard benchmarks suggest rapid progress, many agents still continue to fail in practice. This discrepancy highlights a fundamental limitation of current evaluations: compressing agent behavior into a single success metric obscures critical operational flaws. Notably, it ignores whether agents behave consistently across runs, withstand perturbations, fail predictably, or have bounded error severity. Grounded in safety-critical engineering, we provide a holistic performance profile by proposing twelve concrete metrics that decompose agent reliability along four key dimensions: consistency, robustness, predictability, and safety. Evaluating 15 models across two complementary benchmarks, we find that recent capability gains have only yielded small improvements in reliability. By exposing these persistent limitations, our metrics complement traditional evaluations while offering tools for reasoning about how agents perform, degrade, and fail.

Equivariance is central to graph generative models, as it ensures the model respects the permutation symmetry of graphs. However, strict equivariance can increase computational cost due to added architectural constraints, and can slow down convergence because the model must be consistent across a large space of possible node permutations. We study this trade-off for graph generative models. Specifically, we start from an equivariant discrete flow-matching model, and relax its equivariance during training via a controllable symmetry modulation scheme based on sinusoidal positional encodings and node permutations. Experiments first show that symmetry-breaking can accelerate early training by providing an easier learning signal, but at the expense of encouraging shortcut solutions that can cause overfitting, where the model repeatedly generates graphs that are duplicates of the training set. On the contrary, properly modulating the symmetry signal can delay overfitting while accelerating convergence, allowing the model to reach stronger performance with $19\%$ of the baseline training epochs.

Deep generative models based on neural differential equations have become state-of-the-art for many generation tasks. These models rely on ODE/SDE solvers that integrate from a prior distribution to the data distribution; in many applications it is also highly desirable to integrate in the inverse direction. Standard solvers, however, accumulate discretization errors that prohibit exact inversion, an inaccuracy that is unacceptable in precision-critical applications. Existing inversion methods suffer from poor stability and low order of convergence, and are strictly limited to the ODE setting. In this work, we propose Rex, a family of reversible exponential (stochastic) Runge-Kutta solvers obtained by applying Lawson methods to convert any explicit (stochastic) Runge-Kutta scheme into an algebraically reversible one for both diffusion ODEs and SDEs. Beyond a rigorous theoretical analysis -- establishing arbitrary-order convergence and a non-zero region of linear stability -- we empirically demonstrate that Rex achieves near-machine-precision reconstruction and improves Boltzmann sampling with flow models as well as image generation and editing with diffusion models.

Recent time series modeling faces a sharp divide between numerical generation and semantic understanding, with research showing that generation models often rely on superficial pattern matching, while understanding-oriented models struggle with high-fidelity numerical output. Although unified multimodal models (UMMs) have bridged this gap in vision, their potential for time series remains untapped. We propose TimeOmni-VL, the first vision-centric framework that unifies time series understanding and generation through two key innovations: (1) Fidelity-preserving bidirectional mapping between time series and images (Bi-TSI), which advances Time Series-to-Image (TS2I) and Image-to-Time Series (I2TS) conversions to ensure near-lossless transformations. (2) Understanding-guided generation. We introduce TSUMM-Suite, a novel dataset consisting of six understanding tasks rooted in time series analytics and coupled with two generation tasks. With a calibrated Chain-of-Thought, TimeOmni-VL is the first to leverage time series understanding as an explicit control signal for high-fidelity generation. Experiments confirm that this unified approach significantly improves semantic understanding and numerical precision, establishing a new frontier for multimodal time series modeling.

Sub-bit model compression targets storage below one bit per weight; as magnitudes are aggressively compressed, the sign bit becomes a fixed-cost bottleneck. Across Transformers, CNNs, and MLPs, learned sign matrices resist low-rank approximation and are spectrally indistinguishable from an i.i.d. Rademacher baseline. This randomness gives rise to the lower bound of sub-bit model compression -- the one-bit wall. Despite this apparent randomness, most weights retain their initialization signs; flips primarily occur via rare near-zero boundary crossings, suggesting that sign-pattern randomness is largely inherited from initialization. We formalize this behavior with sign lock-in theory, a stopping-time analysis of sign flips under SGD noise. Under bounded updates and a rare re-entry condition into a small neighborhood of zero, the number of effective sign flips exhibits a geometric tail. Building on this mechanism, we introduce a from-scratch low-rank sign-template training method that prevents the emergence of this one-bit wall.

Eliciting information to reduce uncertainty about latent group-level properties from surveys and other collective assessments requires allocating limited questioning effort under real costs and missing data. Although large language models enable adaptive, multi-turn interactions in natural language, most existing elicitation methods optimize what to ask with a fixed respondent pool, and do not adapt respondent selection or leverage population structure when responses are partial or incomplete. To address this gap, we study adaptive group elicitation, a multi-round setting where an agent adaptively selects both questions and respondents under explicit query and participation budgets. We propose a theoretically grounded framework that combines (i) an LLM-based expected information gain objective for scoring candidate questions with (ii) heterogeneous graph neural network propagation that aggregates observed responses and participant attributes to impute missing responses and guide per-round respondent selection. This closed-loop procedure queries a small, informative subset of individuals while inferring population-level responses via structured similarity. Across three real-world opinion datasets, our method consistently improves population-level response prediction under constrained budgets, including a >12% relative gain on CES at a 10% respondent budget.

LLMs are widely used, yet they remain prone to factual errors that erode user trust and limit adoption in high-risk settings. One approach to mitigate this risk is to equip models with uncertainty estimation mechanisms that abstain when confidence is low. However, this binary "all-or-nothing" approach is excessively restrictive in long-form settings, often discarding valuable information. We introduce Selective Abstraction (SA), a framework that enables LLMs to trade specificity for reliability by selectively reducing the detail of uncertain content. We first formalize SA through the lenses of selective risk and coverage. We then propose Atom-wise Selective Abstraction, a claim-level instantiation that decomposes responses into atomic claims (short, self-contained statements each expressing a single fact) and replaces uncertain atoms with higher confidence, less specific abstractions. To evaluate this framework, we develop a novel end-to-end pipeline for open-ended generation that instantiates risk as factual correctness and measures coverage using an information-theoretic measure of retained information. Across six open-source models on the FactScore and LongFact-Objects benchmarks, atom-wise SA consistently outperforms existing baselines, improving the area under the risk-coverage curve (AURC) by up to 27.73% over claim removal, demonstrating that reducing specificity can boost accuracy and reliability while preserving most of their original meaning.

Segment Anything Models (SAM) achieve impressive universal segmentation performance but require massive datasets (e.g., 11M images) and rely solely on RGB inputs. Recent efficient variants reduce computation but still depend on large-scale training. We propose a lightweight RGB-D fusion framework that augments EfficientViT-SAM with monocular depth priors. Depth maps are generated with a pretrained estimator and fused mid-level with RGB features through a dedicated depth encoder. Trained on only 11.2k samples (less than 0.1\% of SA-1B), our method achieves higher accuracy than EfficientViT-SAM, showing that depth cues provide strong geometric priors for segmentation.

Self-interpretation methods prompt language models to describe their own internal states, but remain unreliable due to hyperparameter sensitivity. We show that training lightweight adapters on interpretability artifacts, while keeping the LM entirely frozen, yields reliable self-interpretation across tasks and model families. A scalar affine adapter with just $d_\text{model}+1$ parameters suffices: trained adapters generate sparse autoencoder feature labels that outperform the training labels themselves (70% vs 50% generation scoring at 70B scale), identify topics with 94% recall@1 versus 1% for untrained baselines, and decode bridge entities in multi-hop reasoning that appear in neither prompt nor response, surfacing implicit reasoning without chain-of-thought. The learned bias vector alone accounts for 85% of improvement, and simpler adapters generalize better than more expressive alternatives. Controlling for model knowledge via prompted descriptions, we find self-interpretation gains outpace capability gains from 7B to 72B parameters. Our results demonstrate that self-interpretation improves with scale, without modifying the model being interpreted.

We present an in-depth evaluation of LLMs' ability to negotiate, a central business task requiring strategic reasoning, theory of mind, and economic value creation. To do so, we introduce PieArena, a large-scale negotiation benchmark grounded in multi-agent interactions over realistic scenarios adapted from MBA negotiation courses at an elite business school. We evaluate language agents across three pairing regimes: mirror-play, cross-play, and human-LM play. We develop a ranking model for continuous negotiation payoffs that yields order-invariant, uncertainty-quantified leaderboards while correcting for systematic experimental asymmetries. We further study the effects of joint-intentionality agentic scaffolding and find asymmetric gains, with large improvements for mid- and lower-tier LMs and diminishing returns for frontier LMs. As calibration anchors, we collect human-human and human-LM negotiation data from trained business school students, finding that a representative frontier language agent (GPT-5) matches or exceeds this human baseline in our evaluation settings. Beyond deal outcomes, PieArena provides a multi-dimensional behavioral profile that reveals cross-model heterogeneity in instruction compliance, computation accuracy, as well as judge-assessed deception and reputation, illustrating the value of evaluation beyond outcome-only leaderboards.

We propose physics-informed spectral diffusion (PISD), a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions of partial differential equations (PDEs) conditioned on partial observations, which includes, in particular, forward and inverse PDE problems. We learn the joint distribution of PDE parameters and solutions via a diffusion process in a latent space of scaled spectral representations, where Gaussian noise corresponds to functions with controlled regularity. This spectral formulation enables significant dimensionality reduction compared to grid-based diffusion models and ensures that the induced process in function space remains within a class of functions for which the PDE operators are well defined. Building on diffusion posterior sampling, we enforce physics-informed constraints and measurement conditions during inference, applying Adam-based updates at each diffusion step. We evaluate the proposed approach on Poisson, Helmholtz, and incompressible Navier-Stokes equations, demonstrating improved accuracy and computational efficiency compared with existing diffusion-based PDE solvers, which are state of the art for sparse observations. Code is available at https://github.com/deeplearningmethods/PISD.

Integrating Large Language Models (LLMs) with external tools via multi-agent systems offers a promising new paradigm for decomposing and solving complex problems. However, training these systems remains notoriously difficult due to the credit assignment challenge, as it is often unclear which specific functional agent is responsible for the success or failure of decision trajectories. Existing methods typically rely on sparse or globally broadcast rewards, failing to capture individual contributions and leading to inefficient reinforcement learning. To address these limitations, we introduce the Shapley-based Hierarchical Attribution for Reinforcement Policy (SHARP), a novel framework for optimizing multi-agent reinforcement learning via precise credit attribution. SHARP effectively stabilizes training by normalizing agent-specific advantages across trajectory groups, primarily through a decomposed reward mechanism comprising a global broadcast-accuracy reward, a Shapley-based marginal-credit reward for each agent, and a tool-process reward to improve execution efficiency. Extensive experiments across various real-world benchmarks demonstrate that SHARP significantly outperforms recent state-of-the-art baselines, achieving average match improvements of 23.66% and 14.05% over single-agent and multi-agent approaches, respectively.

Large reasoning models achieve strong performance by scaling inference-time chain-of-thought, but this paradigm suffers from quadratic cost, context length limits, and degraded reasoning due to lost-in-the-middle effects. Iterative reasoning mitigates these issues by periodically summarizing intermediate thoughts, yet existing methods rely on supervised learning or fixed heuristics and fail to optimize when to summarize, what to preserve, and how to resume reasoning. We propose InftyThink+, an end-to-end reinforcement learning framework that optimizes the entire iterative reasoning trajectory, building on model-controlled iteration boundaries and explicit summarization. InftyThink+ adopts a two-stage training scheme with supervised cold-start followed by trajectory-level reinforcement learning, enabling the model to learn strategic summarization and continuation decisions. Experiments on DeepSeek-R1-Distill-Qwen-1.5B show that InftyThink+ improves accuracy by 21% on AIME24 and outperforms conventional long chain-of-thought reinforcement learning by a clear margin, while also generalizing better to out-of-distribution benchmarks. Moreover, InftyThink+ significantly reduces inference latency and accelerates reinforcement learning training, demonstrating improved reasoning efficiency alongside stronger performance.

Confidence calibration is essential for making large language models (LLMs) reliable, yet existing training-free methods have been primarily studied under single-answer question answering. In this paper, we show that these methods break down in the presence of multiple valid answers, where disagreement among equally correct responses leads to systematic underestimation of confidence. To enable a systematic study of this phenomenon, we introduce MACE, a benchmark of 12,000 factual questions spanning six domains with varying numbers of correct answers. Experiments across 15 representative calibration methods and four LLM families (7B-72B) reveal that while accuracy increases with answer cardinality, estimated confidence consistently decreases, causing severe miscalibration for questions with mixed answer counts. To address this issue, we propose Semantic Confidence Aggregation (SCA), which aggregates confidence over multiple high-probability sampled responses. SCA achieves state-of-the-art calibration performance under mixed-answer settings while preserving strong calibration on single-answer questions.

With the emergence of large language models (LLMs) as a powerful class of generative artificial intelligence (AI), their use in tutoring has become increasingly prominent. Prior works on LLM-based tutoring typically learn a single tutor policy and do not capture the diversity of tutoring styles. In real-world tutor-student interactions, pedagogical intent is realized through adaptive instructional strategies, with tutors varying the level of scaffolding, instructional directiveness, feedback, and affective support in response to learners' needs. These differences can all impact dialogue dynamics and student engagement. In this paper, we explore how tutor personas embedded in human tutor-student dialogues can be used to guide LLM behavior without relying on explicitly prompted instructions. We train a steering vector using preference optimization: an activation-space direction that guides model responses toward specific tutor personas. We find that this steering vector captures tutor-specific variation across dialogue contexts, improving semantic alignment with ground-truth tutor utterances and increasing preference-based evaluations, while largely preserving lexical similarity. Analysis of the learned scaling coefficients further reveals interpretable structure across tutors, corresponding to consistent differences in tutoring behavior. These results demonstrate that activation steering offers an effective and interpretable way for controlling tutor-specific variation in LLMs using signals derived directly from human dialogue data.

Reliable uncertainty quantification (UQ) is essential for deploying large language models (LLMs) in safety-critical scenarios, as it enables them to abstain from responding when uncertain, thereby avoiding hallucinations, i.e., plausible yet factually incorrect responses. However, while semantic UQ methods have achieved advanced performance, they overlook latent semantic structural information that could enable more precise uncertainty estimates. In this paper, we propose \underline{Se}mantic \underline{S}tructural \underline{E}ntropy ({SeSE}), a principled black-box UQ framework applicable to both open- and closed-source LLMs. To reveal the intrinsic structure of the semantic space, SeSE constructs its optimal hierarchical abstraction through an encoding tree with minimal structural entropy. The structural entropy of this encoding tree thus quantifies the inherent uncertainty within LLM semantic space after optimal compression. Additionally, unlike existing methods that primarily focus on simple short-form generation, we extent SeSE to provide interpretable, granular uncertainty estimation for long-form outputs. We theoretically prove that SeSE generalizes semantic entropy, the gold standard for UQ in LLMs, and empirically demonstrate its superior performance over strong baselines across 24 model-dataset combinations.

World models offer a promising avenue for more faithfully capturing complex dynamics, including contacts and non-rigidity, as well as complex sensory information, such as visual perception, in situations where standard simulators struggle. However, these models are computationally complex to evaluate, posing a challenge for popular RL approaches that have been successfully used with simulators to solve complex locomotion tasks but yet struggle with manipulation. This paper introduces a method that bypasses simulators entirely, training RL policies inside world models learned from robots' interactions with real environments. At its core, our approach enables policy training with large-scale diffusion models via a novel decoupled first-order gradient (FoG) method: a full-scale world model generates accurate forward trajectories, while a lightweight latent-space surrogate approximates its local dynamics for efficient gradient computation. This coupling of a local and global world model ensures high-fidelity unrolling alongside computationally tractable differentiation. We demonstrate the efficacy of our method on the Push-T manipulation task, where it significantly outperforms PPO in sample efficiency. We further evaluate our approach through an ego-centric object manipulation task with a quadruped. Together, these results demonstrate that learning inside data-driven world models is a promising pathway for solving hard-to-model RL tasks in image space without reliance on hand-crafted physics simulators.

Planning with a learned model remains a key challenge in model-based reinforcement learning (RL). In decision-time planning, state representations are critical as they must support local cost computation while preserving long-horizon structure. In this paper, we show that the Laplacian representation provides an effective latent space for planning by capturing state-space distances at multiple time scales. This representation preserves meaningful distances and naturally decomposes long-horizon problems into subgoals, also mitigating the compounding errors that arise over long prediction horizons. Building on these properties, we introduce ALPS, a hierarchical planning algorithm, and demonstrate that it outperforms commonly used baselines on a selection of offline goal-conditioned RL tasks from OGBench, a benchmark previously dominated by model-free methods.

We propose LoRA-MCL, a training scheme that extends next-token prediction in language models with a method designed to decode diverse, plausible sentence continuations at inference time. Traditional language modeling is an intrinsically ill-posed problem: given a context, multiple futures may be equally plausible. Our approach leverages Multiple Choice Learning (MCL) and the winner-takes-all loss to efficiently handle ambiguity through Low-Rank Adaptation. We provide a theoretical interpretation of applying MCL to language modeling, assuming the data is generated from a mixture of distributions. We illustrate the proposed approach using mixtures of Markov chains. We then demonstrate with experiments on audio and visual captioning, as well as machine translation, that our method achieves high diversity and relevance in generated outputs. We release the code for applying LoRA-MCL to a wide range of language models.

The quadratic computational complexity of softmax transformers has become a bottleneck in long-context scenarios. In contrast, linear attention model families provide a promising direction towards a more efficient sequential model. These linear attention models compress past KV values into a single hidden state, thereby efficiently reducing complexity during both training and inference. However, their expressivity remains limited by the size of their hidden state. Previous work proposed interleaving softmax and linear attention layers to reduce computational complexity while preserving expressivity. Nevertheless, the efficiency of these models remains bottlenecked by their softmax attention layers. In this paper, we propose Neural Attention Search Linear (NAtS-L), a framework that applies both linear attention and softmax attention operations within the same layer on different tokens. NAtS-L automatically determines whether a token can be handled by a linear attention model, i.e., tokens that have only short-term impact and can be encoded into fixed-size hidden states, or require softmax attention, i.e., tokens that contain information related to long-term retrieval and need to be preserved for future queries. By searching for optimal Gated DeltaNet and softmax attention combinations across tokens, we show that NAtS-L provides a strong yet efficient token-level hybrid architecture.

We propose causal preference elicitation, a Bayesian framework for expert-in-the-loop causal discovery that actively queries local edge relations to concentrate a posterior over directed acyclic graphs (DAGs). From any black-box observational posterior, we model noisy expert judgments with a three-way likelihood over edge existence and direction. Posterior inference uses a flexible particle approximation, and queries are selected by an efficient expected information gain criterion on the expert's categorical response. Experiments on synthetic graphs, protein signaling data, and a human gene perturbation benchmark show faster posterior concentration and improved recovery of directed effects under tight query budgets.

Quantizing LLM weights and activations is a standard approach for efficient deployment, but a few extreme outliers can stretch the dynamic range and amplify low-bit quantization errors. Prior transform-based mitigations (e.g., Hadamard rotations) are fixed and data-agnostic, and their optimality for quantization has remained unclear. We derive closed-form optimal linear blockwise transforms for joint weight-activation quantization under standard RTN AbsMax-scaled block quantizers, covering both integer and floating-point formats. The resulting construction, WUSH, combines a Hadamard backbone with a data-dependent second-moment component to form a non-orthogonal transform that is provably near-optimal for FP and INT quantizers under mild assumptions while admitting an efficient fused GPU implementation. Empirically, WUSH improves W4A4 accuracy over the strongest Hadamard-based baselines (e.g., on Llama-3.1-8B-Instruct in MXFP4, it gains +2.8 average points with RTN and +0.7 with GPTQ) while delivering up to 5.8$\times$ per-layer throughput over BF16 via FP4 MatMul. Source code is available at https://github.com/IST-DASLab/WUSH.

Personalized and continuous interactions are critical for LLM-based conversational agents, yet finite context windows and static parametric memory hinder the modeling of long-term, cross-session user states. Existing approaches, including retrieval-augmented generation and explicit memory systems, primarily operate at the fact level, making it difficult to distill stable preferences and deep user traits from evolving and potentially conflicting dialogues.To address this challenge, we propose RGMem, a self-evolving memory framework inspired by the renormalization group (RG) perspective on multi-scale organization and emergence. RGMem models long-term conversational memory as a multi-scale evolutionary process: episodic interactions are transformed into semantic facts and user insights, which are then progressively integrated through hierarchical coarse-graining, thresholded updates, and rescaling into a dynamically evolving user profile.By explicitly separating fast-changing evidence from slow-varying traits and enabling non-linear, phase-transition-like dynamics, RGMem enables robust personalization beyond flat retrieval or static summarization. Extensive experiments on the LOCOMO and PersonaMem benchmarks demonstrate that RGMem consistently outperforms SOTA memory systems, achieving stronger cross-session continuity and improved adaptation to evolving user preferences. Code is available at https://github.com/fenhg297/RGMem

We present a self-supervised machine learning framework for detecting and mapping the severity and speciation of harmful algal blooms (HABs) using multi-sensor satellite data. By fusing reflectance data from operational polar-orbiting satellite-based instruments (VIIRS, MODIS, OLCI, and OCI) with TROPOMI solar-induced fluorescence (SIF), our framework, called SIT-FUSE, generates HAB severity and speciation products without requiring per-instrument labeled datasets. The framework employs self-supervised representation learning and hierarchical deep clustering to segment phytoplankton cell abundance and species into interpretable classes, validated against in-situ data from the Gulf of Mexico and Southern California (2018-2025). Results show strong agreement with total phytoplankton, Karena brevis, and Pseudo-nitzschia spp. measurements. This work advances scalable HAB monitoring in environments where ground truth observations are limited, while enabling exploratory analysis via hierarchical embeddings - a critical step toward operationalizing self-supervised learning for global aquatic biogeochemistry.

Markov decision processes (MDPs) are a fundamental model in sequential decision making. Robust MDPs (RMDPs) extend this framework by allowing uncertainty in transition probabilities and optimizing against the worst-case realization of that uncertainty. In particular, $(s, a)$-rectangular RMDPs with $L_\infty$ uncertainty sets form a fundamental and expressive model: they subsume classical MDPs and turn-based stochastic games. We consider this model with discounted payoffs. The existence of polynomial and strongly-polynomial time algorithms is a fundamental problem for these optimization models. For MDPs, linear programming yields polynomial-time algorithms for any arbitrary discount factor, and the seminal work of Ye established strongly--polynomial time for a fixed discount factor. The generalization of such results to RMDPs has remained an important open problem. In this work, we show that a robust policy iteration algorithm runs in strongly-polynomial time for $(s, a)$-rectangular $L_\infty$ RMDPs with a constant (fixed) discount factor, resolving an important algorithmic question.

Current neural architectures lack a principled way to handle interchangeable tokens, i.e., symbols that are semantically equivalent yet distinguishable, such as bound variables. As a result, models trained on fixed vocabularies often struggle to generalize to unseen symbols, even when the underlying semantics remain unchanged. We propose a novel Transformer-based mechanism that is provably invariant to the renaming of interchangeable tokens. Our approach employs parallel embedding streams to isolate the contribution of each interchangeable token in the input, combined with an aggregated attention mechanism that enables structured information sharing across streams. Experimental results confirm the theoretical guarantees of our method and demonstrate substantial performance gains on open-vocabulary tasks that require generalization to novel symbols. Project page: https://bu-depend-lab.github.io/Symbol-Invariant-Transformer/

Query-based universal sound separation is fundamental to intelligent auditory systems, aiming to isolate specific sources from mixtures. Despite recent advances, existing methods continue to suffer from residual interference in complex acoustic scenes. This performance limitation stems largely from a data bottleneck: in-the-wild datasets contain weak labels and severe co-occurrence of events. These flaws induce models to learn spurious correlations between background noise and target categories instead of robust acoustic features. To address this, we propose an automated pipeline that eliminates co-occurrence of events by mining high-purity single-event segments from in-the-wild datasets via a semantically consistent synthesis protocol. Utilizing this pipeline, we constructed Hive, a high-quality synthetic dataset comprising 2.4k hours of raw audio. Experimental results demonstrate that, compared with the state-of-the-art model SAM-Audio which was trained on a huge dataset $\sim$500 times larger than Hive, certain open-source models trained on Hive achieve competitive separation accuracy and perceptual quality. Moreover, these models exhibited remarkable zero-shot generalization on out-of-distribution evaluation benchmarks. These findings highlight that prioritizing purity of supervised signals enables significant data efficiency, offering a new paradigm for training robust auditory foundation models with reduced computational costs. Code and dataset are available at https://cslikai.cn/Hive.

Can a diffusion model trained on bedrooms recover human faces? Diffusion models are widely used as priors for inverse problems, but standard approaches usually assume a high-fidelity model trained on data that closely match the unknown signal. In practice, one often must use a mismatched or low-fidelity diffusion prior. Surprisingly, these weak priors often perform nearly as well as full-strength, in-domain baselines. We study when and why inverse solvers are robust to weak diffusion priors. Through extensive experiments, we find that weak priors succeed when measurements are highly informative (e.g., many observed pixels), and we identify regimes where they fail. To explain this behavior, we combine Bayesian-consistency theory with local-correlation analysis: the theory gives conditions under which high-dimensional measurements make the posterior concentrate near the true signal, while the correlation analysis shows that weak and stronger natural-image priors can share similar local spatial structure. These results provide a principled justification on when weak diffusion priors can be used reliably. Code is available at https://github.com/jjia131/weak-diffusion-priors-inverse-problem.

Robot manipulation has increasingly adopted data-driven generative policy frameworks, yet the field faces a persistent trade-off: diffusion models suffer from high inference latency, while flow-based methods often require complex architectural constraints. Although in image generation domain, the MeanFlow paradigm offers a path to single-step inference, its direct application to robotics is impeded by critical theoretical pathologies, specifically spectral bias and gradient starvation in low-velocity regimes. To overcome these limitations, we propose the One-step MeanFlow Policy (OMP), a novel framework designed for high-fidelity, real-time manipulation. We introduce a lightweight directional alignment mechanism to explicitly synchronize predicted velocities with true mean velocities. Furthermore, we implement a Differential Derivation Equation (DDE) to approximate the Jacobian-Vector Product (JVP) operator, which decouples forward and backward passes to significantly reduce memory complexity. Extensive experiments on the Adroit and Meta-World benchmarks demonstrate that OMP outperforms state-of-the-art methods in success rate and trajectory accuracy, particularly in high-precision tasks, while retaining the efficiency of single-step generation.

While end-to-end self-supervised learning with backpropagation (global BP-SSL) has become central for training modern AI systems, theories of local self-supervised learning (local-SSL) have struggled to build functional representations in deep neural networks. To establish a link between global and local rules, we first develop a theory for deep linear networks: we identify conditions for local-SSL algorithms (like Forward-forward or CLAPP) to implement exactly the same weight update as a global BP-SSL. Starting from the theoretical insights, we then develop novel variants of local-SSL algorithms to approximate global BP-SSL in deep non-linear convolutional neural networks. Variants that improve the similarity between gradient updates of local-SSL with those of global BP-SSL also show better performance on image datasets (CIFAR-10, STL-10, and Tiny ImageNet). The best local-SSL rule with the CLAPP loss function matches the performance of a comparable global BP-SSL with InfoNCE or CPC-like loss functions, and improves upon state-of-the-art for local SSL on these benchmarks.