We consider one-hidden layer neural networks trained in the feature-learning regime using gradient descent, and relate the output of the finite-width network $f_{\hat{\rho}_t^m}$ to its infinite-width counterpart $f_{\rho_t^{MF}}$, which evolves in the mean-field dynamics. While constant-time horizon bounds for $\|f_{\rho_t^{MF}} - f_{\hat{\rho}_t^m}\|$ may be obtained via standard Gr\"onwall estimates, the long-time behavior of the fluctuation is a more delicate matter. Uniform-in-time bounds often rely on (local) strong convexity in the landscape or Logarithmic Sobolev inequalities present in noisy gradient dynamics. In this work, we establish non-asymptotic weak propagation-of-chaos that holds uniformly in time, obtained by exploiting instead the convergence rate of the mean-field deterministic Wasserstein-gradient-flow dynamics. Specifically, denoting by $L_t$ the mean-field excess MSE loss at time $t$ and $m$ the number of neurons, under standard regularity assumptions and the condition $\int_0^\infty L_t^{1/2} dt =O(\log d)$, we obtain the uniform in time bound $\|f_{\rho_t^{MF}}- f_{\hat{\rho}_t^m}\|^2 \lesssim \text{poly}(d) m^{-\min(1,c/6)}$ whenever $L_t \lesssim t^{-c}$. Our result holds in a noiseless setting and does not make any assumptions on the geometry of the landscape near the optimum, and extends seamlessly to other forms of discretization, including finite number of samples and time discretization. A key takeaway of our result is that whenever the convergence rate of the mean-field, population-loss dynamics is faster than $t^{-2}$, we can attain a loss of $\epsilon$ with only $\text{poly}(d/\epsilon)$ neurons, training samples, and GD steps.
Pretrained diffusion models serve as frozen teachers for pipelines such as text-to-3D, single-step distillation, and data attribution. The teacher gradients these pipelines consume are expectations over noise levels and Gaussian noise, estimated by Monte Carlo (MC). Each MC draw requires expensive upstream work (rendering, simulation, encoding), so estimator variance dominates compute cost. We introduce CARV, a compute-aware variance-accounting framework that casts these gradients as a classical two-stage sampling problem with asymmetric per-level costs. This motivates a hierarchical MC estimator that amortizes each expensive upstream computation by reusing it across cheap diffusion draws, with within-unit variance further reduced by timestep importance sampling (IS) and stratified inverse-CDF sampling. CARV delivers 2 to 3x effective compute multipliers on text-to-3D and data attribution without changing the objective. In text-to-3D, reuse provides most of the gain and IS with stratification adds about 25%. In single-step distillation, the same techniques cut gradient variance by an order of magnitude but do not improve downstream FID, marking the regime where MC variance is no longer the bottleneck.
The aggregation of conflicting client updates remains a fundamental bottleneck in federated learning (FL) under heterogeneous data distributions. Naive averaging can produce a global update that improves the global objective while conflicting with specific clients, causing degradation for those clients. In this work, we propose CRAFT (Conflict-Resolved Aggregation for Federated Training), a new aggregation framework that treats the global update as a geometric correction problem. We formulate aggregation as finding the update closest to a reference direction while satisfying conflict-free alignment constraints. We derive a closed-form expression for the constrained optimization problem, avoiding the computational overhead of iterative solvers. Furthermore, we use a layer-wise adaptation to address conflicts at varying feature granularities. We provide a theoretical analysis showing that CRAFT promotes a common-descent structure and mitigates conflicts through its projection geometry. Extensive experiments on heterogeneous benchmarks demonstrate that CRAFT improves the accuracy of the global model while reducing performance disparity across clients compared with state-of-the-art baselines. The source code for CRAFT is available at https://github.com/tum-pbs/CRAFT.
Current end-to-end autonomous driving models are fundamentally constrained by the behavioral cloning ceiling of imitation learning. While reinforcement learning offers a path to smarter autonomy, it demands two missing pieces of infrastructure: (1) a cognitive foundation that understands traffic semantics and driving intent, and (2) a foresighted physical environment that can anticipate the consequences of candidate actions. To this end, we propose CoPhy, a CognitivePhysical reinforcement learning framework for autonomous driving. To distill to think, we distill VLM knowledge into the BEV encoder and then discard the VLM entirely, retaining cognitive ability at zero inference cost while releasing the cognitive channel as a pluggable interface for optional human language commands. To foresee to act, we build an auto-regressive BEV world model that explicitly predicts future semantic maps conditioned on candidate actions, serving as an interpretable physical sandbox from which safety metrics are directly derived. Built upon this dual infrastructure, we optimize the driving policy via GRPO with a novel dual-reward mechanism: a physical reward derived from BEV rollouts enforces hard safety constraints, while a cognitive reward from a language-aligned scorer ensures intent compliance. Extensive experiments demonstrate that CoPhy not only achieves state-of-the-art results on NAVSIM v1 and v2 benchmarks, but also enables safer driving via cognitively informed scene compliance and flexible intent control through user-defined language instructions. Project page: https://wuyang98.github.io/CoPhy/.
Foundation models like the Segment Anything Model (SAM) demonstrate impressive zero-shot generalization but frequently degrade under diverse real-world illumination, particularly for instance segmentation. In this work, we address this limitation by developing Lighting Convolutional-Attention (LCA), an adapter module that enhances segmentation robustness without fine-tuning the heavy backbone. LCA employs a dual-branch architecture to process RGB features alongside contrast maps, enabling physically motivated sensitivity to structural changes rather than illumination artifacts. We optimize LCA through a pairwise training strategy, introducing a targeted loss term that explicitly penalizes discrepancies between clean images and their corresponding illumination variants. To evaluate and support this architecture, we conduct a comprehensive empirical study across multiple existing benchmarks and present a novel Unity-based synthetic dataset specifically designed to accurately replicate complex real-world lighting conditions. Extensive experimental results demonstrate that our approach successfully bridges the domain gap, delivering superior lighting-robust segmentation.
We study post-hoc Learning to Defer (L2D) through the lens of ideal distributions: divergence-regularized reweightings of the data distribution under which a model attains low task loss. We define deferral via the density-ratio between a model's and an expert's ideals. Using the reduction from density-ratio estimation to class-probability estimation, we derive the DR CPE losses for post-hoc L2D scorers. Deferral decisions are then made by thresholding the scorer. For KL-based ideal distributions, our deferral rule recovers Chow's rule under the original distribution and a connection to an expert-tilted Bayes posterior---which incorporates the expert's performance---depending on if the ideal distributions are marginal or joint distributions. This leads to two variants of the DR CPE losses, with the joint variant being computationally convenient in practice. We establish consistency properties of the joint DR CPE losses when considering the zero-one task loss and strongly proper composite CPE losses. Experimentally, our approach is competitive compared to common baselines and is more robust across dataset settings. More broadly, our results cast post-hoc L2D as density-ratio estimation between ideal distributions, bridging Chow-style rules, expert comparison, and elucidating connections to related learning settings including anomaly detection.
Stochastic gradient descent (SGD) is a fundamental optimization algorithm widely used in modern machine learning. In this paper, we propose Factor-Augmented SGD (FSGD), a new optimization method that leverages latent factor representations in high-dimensional learning tasks. Unlike standard two-stage dimension reduction approaches that rely on offline representation learning and full data storage, a key novelty of FSGD is that it operates purely on streaming data, making it scalable to large-scale and high-dimensional problems. Furthermore, we establish the first theoretical framework that explicitly incorporates latent factor estimation error into the analysis of SGD, and provide moment convergence in $\ell^s$ norm under decaying step sizes and mini-batch updates. Our results provide a new foundation for employing SGD reliably and scalably in high-dimensional machine learning systems.
Graph Retrieval-Augmented Generation (GraphRAG) faces significant challenges in complex relational retrieval tasks, particularly in densely connected knowledge graphs where the number of possible paths grows rapidly with reasoning depth. Existing GraphRAG retrieval algorithms either rely on rigid, predefined heuristics to identify relevant graph context or employ costly LLM-based reasoning to guide graph traversal. To address these limitations, we propose DotRAG, a lightweight, training-free GraphRAG retrieval algorithm that uses large language model (LLM) reasoning to narrow the search space and recover task-relevant relational paths. During indexing, DotRAG constructs an entity-relation knowledge graph, generates a graph-wide overview summarizing its contents, and leverages graph reachability indexing to avoid expensive online graph traversals. At query time, the LLM uses this overview to identify promising graph regions and hypothesizes relationship sequences connecting graph information to the query. The LLM then performs targeted relational searches, using graph constraints to restrict the candidate pool progressively. On MetaQA 2-hop queries, DotRAG achieves 97.78% retrieval recall and 51.27% F1, compared to the best baseline scores of 34.74% and 6.33%, respectively. On STaRK-MAG, DotRAG achieves 85.07% recall on 2-hop queries while demonstrating greater computational efficiency than reasoning-based GraphRAG baselines, with 12.2x lower retrieval latency than HopRAG.
Issues faced when using software are reported in the form of bug reports. However, many bug reports are invalid, meaning they do not require code changes, and are resolved with a no-code fix. Manually determining the root cause of the invalid bug reports and providing actionable resolutions by the customer support causes a serious waste of resources. Our goal is to introduce a standardized taxonomy for root-cause oriented invalid bug report subclassification, and perform experiments to test the accuracy of various approaches on invalid subclassification and no-code fix generation. We study how different configurations perform on a gold-standard benchmark we have created. Using a manually curated benchmark for higher quality analysis, we experimented with vanilla LLMs, Retrieval Augmented Generation, and agentic web search to identify invalid subclasses and generate no-code fixes. We evaluated the results against manually labeled ground truth data that includes the invalid subclass and no-code fixes from the original bug reports. We measured subclass detection performance with weighted F1-Score, and assessed no-code fix suggestions using BERTScore and Judge LLM success rates. For subclassification, retrieval augmented generation achieves the highest overall performance with 0.66 weighted F1, slightly outperforming vanilla LLMs at 0.65 and agentic web search at 0.64. At the subclass level, performance peaks at 0.85 F1 for Non-reproducibility and 0.79 for Feature Request and Question, while Wrong Version remains the most challenging with scores between 0.00 and 0.29. For no-code fix generation, agentic web search achieves the highest overall Judge LLM success rate at 68.9%, compared to 64.4% for RAG applications and 64.9% for vanilla LLMs, with subclass-level peaks of 87.4% for Working as Designed and 72.2% for Question.
Training tool-calling agents requires large-scale trajectory data with verifiable labels, yet existing approaches either synthesize environments that diverge from real API behavior or generate tasks without ground-truth outcomes for verification. We present FireFly, a pipeline for generating verified tool-call data from real-world MCP servers. Our key insight is to invert the standard synthesis pipeline: rather than generating tasks and hoping they are solvable, we first let a strong LLM explore real APIs along graph-guided DAG structures, then synthesize tasks backward from observed outcomes, guaranteeing label correctness by construction. To handle the scale of real-world tool spaces (${\sim}$1,000 tools), we build a pairwise tool graph and sample sub-DAGs to focus exploration on semantically coherent workflows. To address environment drift in live APIs, we construct a retrieval-augmented simulator that caches all exploration results and replays them during training and evaluation, enabling fully offline and reproducible RL. Applying this pipeline yields 5,144 verified tasks spanning 240 servers and 993 tools. A 4B-parameter model trained with GRPO on FireFly matches Claude Sonnet 4.6 on our held-out test set and shows improvements on multiple tool-calling benchmarks including Tau2-Bench, MCPMark, and MCP-Atlas.
Generative artificial intelligence (AI) is increasingly integrated into the online platforms where humans exchange opinions; large language models (LLMs) have been polishing users' posts on LinkedIn and providing context for content shared on X. While prior work has shown that AI can express biased opinions and shape individuals' opinions during human-AI interactions, less attention has been paid to its influence on collective opinion formation when mediating human-to-human communication. We address this gap via a combination of empirical and theoretical analyses. We show empirically that LLMs from multiple popular families introduce directional biases when instructed to edit human-written texts on contested topics, for example, nudging texts in favor of gun control and against atheism. Building on this observation, we introduce a mathematical model of opinion dynamics in which an AI system sits between users on a social network, transforming the opinions they express and perceive. By analytically characterizing the equilibrium of this model and performing simulations on real social network data, we show that biases introduced by AI in human-to-human communication can be amplified through the network and shift collective opinion in their direction. In light of these findings, we investigate whether such biases are controllable by online platforms. We audit the "Explain this post" feature on X and find evidence of pro-life bias in Grok's outputs on abortion-related content, which we trace back to specific design choices. We conclude with a discussion of the broader implications of our findings in relation to ongoing legislative efforts in the European Union.
As LLM-based agents increasingly browse the web on users' behalf, a natural question arises: can websites passively identify which underlying model powers an agent? Doing so would represent a significant security risk, enabling targeted attacks tailored to known model vulnerabilities. Across 14 frontier LLMs and four web environments spanning information retrieval and shopping tasks, we show that an agent's actions and interaction timings, captured via a passive JavaScript tracker, are sufficient to identify the underlying model with up to 96\% F1 within a fixed harness. Although fingerprints are harness-specific, with cross-harness transfer falling to near chance, pooling traces across harnesses recovers model identification at 0.74 to 0.81 Macro-F1. We further show that strong classifiers can be trained from roughly one third of the available traces, and that identification improves steadily as more events are observed. Injecting randomised timing delays between actions substantially degrades classifier performance, but does not provide robust protection: a classifier retrained on delayed traces largely recovers performance. We release our code and a labelled corpus of agent traces at https://github.com/KabakaWilliam/known_actions.
Vision-language-action (VLA) models are effective as end-to-end motion planners, but can be brittle when evaluated in closed-loop settings due to being trained under traditional imitation learning framework. Existing closed-loop supervision approaches lack scalability and fail to completely model a reactive environment. We propose MAPLE, a novel framework for reactive, multi-agent rollout of a dynamic driving scenario in the latent space of the VLA model. The ego vehicle and nearby traffic agents are independently controlled over multi-step horizons, while being reactive to other agents in the scene, enabling closed-loop training. MAPLE consists of two training stages: (1) supervised fine-tuning on the latent rollouts based on ground-truth trajectories, followed by (2) reinforcement learning with global and agent -specific rewards that encourage safety, progress, and interaction realism. We further propose diversity rewards that encourage the model to generate planning behaviors that may not be present in logged driving data. Notably, our closed-loop training framework is scalable and does not require external simulators, which can be computationally expensive to run and have limited visual fidelity to the real-world. MAPLE achieves state-of-the-art driving performance on Bench2Drive and demonstrates scalable, closed-loop multi-agent play for robust E2E autonomous driving systems.
Classical planners can effectively solve very large deterministic MDPs represented in STRIPS or PDDL where states are sets of atoms over objects and relations, and lifted action schemas add or delete these atoms. This compact representation yields strong search heuristics and provides an ideal setting for structural generalization, since lifted relations and action schemas give rise to infinitely many domain instances. A central challenge is to learn these relations and action schemas from data, and recent approaches have addressed this problem using different types of observations. In this work, we develop a novel neural network architecture for learning action schemas from traces where states are fully observed but action arguments are unobserved. The problem is a simplification but an important step towards learning planning domains from sequences of images and action labels, and we aim to solve this simplification in a nearly perfect manner. The challenge lies in learning the action schemas while simultaneously identifying the action arguments from observed state changes. Our approach yields a robust differentiable component that can then be integrated into larger neuro-symbolic models. We evaluate the architecture on various planning domains, where the learned lifted action schemas must recover the ground-truth structure. Additionally, we report experiments on robustness to observation noise, on component ablations, and on a variation related to slot-based dynamics models.
Post-training a language model can induce surprising behavioral changes far beyond the intended training target. We study two particularly striking examples: emergent misalignment (EM), where fine-tuning on a narrow dataset leads to misaligned behavior in unrelated contexts, and subliminal learning (SL), where a student model inherits a teacher's misalignment through seemingly benign training data. We examine how the training data, evaluation data, and training method shape where and how strongly misalignment transfers between data and models. We characterize the data by the domain of a prompt (its topical context) and its task (the function the model performs), and we build natural-language and synthetic datasets organized as domain-task grids. We find that EM transfers more strongly to prompts that share the task of the fine-tuning data than to prompts that share its domain. In the synthetic setting, tasks that the model has learned well spread misalignment more broadly. For SL, we go beyond SFT (supervised fine-tuning) to off-policy distillation on the teacher's full next-token distribution and, to our knowledge for the first time, on-policy distillation, where the teacher only scores tokens sampled by the student. Misalignment transfers even under on-policy distillation, more strongly than under SFT and at a level comparable to off-policy distillation. Unlike SFT, where the teacher both generates the data and supervises the student, distillation lets us separate the two. With the teacher fixed, the data change how much misalignment the student inherits, but the teacher determines to which domains and tasks it transfers most strongly. Together, these results show how data and training influence the extent and patterns of emergent and subliminal misalignment.
Predictive Coding (PC) is an influential account of cortical learning. Much of recent work has focused on comparing PC to Backpropagation (BP) to find whether PC offers any advantages. Small scale experiments show that PC enables learning that is more sample efficient and effective in many contexts, though a thorough theoretical understanding of the phenomena remains elusive. To address this, we quantify the efficiency of learning in BP and PC through a metric called ``target alignment'', which measures how closely the change in the output of the network is aligned to the output prediction error. We then derive and empirically validate analytical expressions for target alignment in Deep Linear Networks. We show that learning in PC is more efficient than BP, which is especially pronounced in deep, narrow and pre-trained networks. We also derive exact conditions for guaranteed optimal target alignment in PC and validate our findings through experiments. We study full training trajectories of linear and non-linear models, and find the predicted benefits of PC persist in practice even when some assumptions are violated. Overall, this work provides a mechanistic understanding of the higher learning efficiency observed for PC over BP in previous works, and can guide how PC should be parametrised to learn most effectively.
Tree ensembles such as random forests (RFs) and gradient boosting machines (GBMs) are among the most widely used supervised learners, yet their theoretical properties remain incompletely understood. We adopt a spectral perspective on these algorithms, with two main contributions. First, we derive minimax-optimal convergence for RF regression, showing that, under mild regularity conditions on tree growth, the eigenvalue decay of the induced kernel operator governs the statistical rate. Second, we exploit this spectral viewpoint to develop compression schemes for tree ensembles. For RFs, leading eigenfunctions of the kernel operator capture the dominant predictive directions; for GBMs, leading singular vectors of the smoother matrix play an analogous role. Learning nonlinear maps for these spectral representations yields distilled models that are orders of magnitude smaller than the originals while maintaining competitive predictive performance. Our methods compare favorably to state of the art algorithms for forest pruning and rule extraction, with applications to resource constrained computing.
We study posterior contraction rates for sparse Bayesian Kolmogorov-Arnold networks (KANs) over anisotropic Besov spaces, providing a statistical foundation for KANs from a Bayesian point of view. We show that sparse Bayesian KANs equipped with spike-and-slab-type sparsity priors attain a near-minimax posterior contraction rate. In particular, the contraction rate depends on the intrinsic anisotropic smoothness of the underlying function. Moreover, by placing a hyperprior on a single model-size parameter, the resulting posterior adapts to unknown anisotropic smoothness and still achieves the corresponding near-minimax rate. A distinctive feature of our results, compared with those for standard multilayer perceptrons, is that the KAN depth can be kept fixed: owing to the expressive power of learnable spline edge functions, the required approximation complexity is controlled through the network width, the range and size of the spline grid, and parameter sparsity. Our analysis develops theoretical tools tailored to sparse spline-edge architectures, including approximation and complexity bounds for Bayesian KANs. We then extend to compositional Besov spaces and show that the contraction rates depend on layerwise smoothness and effective dimension of the underlying compositional structure, thereby effectively avoiding the curse of dimensionality. Together, these results advance the theoretical understanding of Bayesian neural networks and establish rigorous Bayesian guarantees for KANs.
Probabilistic linear solvers (PLSs) return probability distributions that quantify uncertainty due to limited computation in the solution of linear systems. The literature has traditionally distinguished between Bayesian PLSs, which condition a prior on information obtained from projections of the linear system, and probabilistic iterative methods (PIMs), which lift classical iterative solvers to probability space. In this work we show this dichotomy to be false: Bayesian PLSs are a special case of non-stationary affine PIMs. In addition, we prove that any realistic affine PIM is calibrated. These results motivate a focus on (non-stationary) affine PIMs, but their practical adoption has been limited by the significant manual effort required to implement them. To address this, we introduce affine tracing, an algorithmic framework that automatically constructs a PIM from a standard implementation of an affine iterative method by passing symbolic tracers through the computation to build an affine computational graph. We show how this graph can be transformed to compute posterior covariances, and how equality saturation can be used to perform algebraic simplifications required for computation under specific prior choices. We demonstrate the framework by automatically generating a probabilistic multigrid solver and evaluate its performance in the context of Gaussian process approximation.
AI systems can now cheaply generate plausible scientific artifacts such as papers, reviews, and surveys. This creates a risk of \emph{epistemic pollution} in our scientific systems, where unreliable but plausible-looking artifacts can accumulate faster than the system can filter them out. The problem is structural: the epistemic infrastructure of science was calibrated to a world where producing a plausible artifact required substantial expertise, labor, and time, so generation cost itself served as a rough filter; AI weakens that filter without comparably lowering verification cost. This position paper argues that \textbf{AI-era science should rebalance the costs of generating and verifying scientific artifacts by redesigning epistemic infrastructure at the level of the artifact}. The current paper-centered system makes verification expensive: papers compress long-context scientific logic into prose, forcing reviewers, human or AI, to reconstruct underlying argument structure before they can evaluate it. As one step in this direction, we propose \textbf{blueprints}: structured, decomposed research artifacts that represent claims, evidence, assumptions, and definitions as typed graph components. Blueprints complement rather than replace papers---the paper remains the narrative interface, the blueprint becomes the verification interface---and are designed to trade an upfront generation cost for cheaper, more local, more distributed verification downstream. We also instantiate the proposal in a proof-of-concept prototype.