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.
Partial differential equation (PDE) solvers underpin modern computer graphics, geometry processing, and scientific computing. Classical Monte Carlo PDE solvers such as Walk-on-Spheres (WoS) provide mesh-free estimations that are unbiased, but with accuracy limited by sampling and numerical approximation. Learned solvers are fast but biased and brittle under distribution shift. We therefore present MC$^2$, a hybrid Neural Network-Monte Carlo PDE solver that treats a low-budget Monte Carlo solution as a structured estimator of the true field and learns a single-pass neural correction to recover a high-fidelity solution. MC$^2$ matches the accuracy of solutions using over $1000\times$ more Monte Carlo samples, outperforming all evaluated mesh-free classical, denoising, and neural-operator baselines. To enable reproducible study of finite-compute PDE solving, we additionally release PDEZoo, the largest standardized elliptic PDE benchmark to date: 2 million PDEs spanning 5 elliptic families and unlimited geometric compositions, with analytic ground truth and multi-budget Monte Carlo trajectories. Together, MC$^2$ and PDEZoo (1) empirically establish that finite-sample Monte Carlo error is structured, learnable, and correctable in a single forward pass, (2) show that we can solve PDEs $\sim$218$\times$ faster than WoS at matched accuracy and achieve a $\sim$171$\times$ reduction in inference time relative to state-of-the-art diffusion methods while attaining higher accuracy, and (3) provide the reproducible evaluation infrastructure the field has so far lacked. Code & Data: https://mc-error-correction.github.io
Unbalanced optimal transport extends classical optimal transport to measures with different total masses, but statistical guarantees for estimation of the transport map and the growth map remain limited. We study unbalanced optimal transport with quadratic cost and Kullback-Leibler marginal penalties and argue that the natural target of estimation is a transport-growth pair. Consequently, we develop two estimators for the transport-growth pair under two setups: a nearest-neighbor estimator for transporting between general densities, and a kernel-based estimator for transporting between smooth densities. We prove that the kernel-based estimator achieves the minimax optimal rate up to a logarithmic factor by deriving a matching lower bound on the minimax risk. Our main technical contribution is a reduction of estimation to a stability bound on the unbalanced optimal transport value. This bound controls the transport map and growth map risks through the duality gap of the true dual potentials for the estimated measures. These results provide a statistical foundation for estimation of the transport-growth pair in unbalanced optimal transport.
Neural scaling laws approximate a language model's loss as a power-law function of parameter count $N$ and token count $D$. Following Chinchilla-style compute-optimal training, many studies fit scaling laws from runs at one or a few fixed tokens-per-parameter (TPP) ratios $k$, with $D = kN$. We show that this collinear design, combined with the empirically common near-equality of the exponents governing $N$ and $D$, induces an inherent ill-conditioning in the Gauss-Newton least-squares problem: the condition number of the design grows as the inverse square of the gap between the $N$- and $D$-exponents. The scale coefficients become practically unidentifiable, with confidence intervals inflating by orders of magnitude, yielding a "sloppy" model whose extrapolations degrade sharply off the training ray. We prove this for four scaling-law formalisms and derive a closed-form TPP-diversity threshold that characterizes well-conditioned estimation to leading order. Empirically, in controlled experiments with 5M-77M-parameter models, non-collinear designs outperform collinear ones on held-out data with a 97.3% win rate across four laws and five corpora, and 98.7% in bfloat16. We further show the degeneracy is rooted in Jacobian geometry and is not an artifact of the loss function: any smooth objective whose Gauss-Newton weights are bounded above and away from zero inherits the same ill-conditioning.
On-policy distillation (OPD) is a powerful paradigm for LLM post-training, yet its reliance on teacher logits restricts it to white-box teachers. In this paper, we study whether rubric-based supervision can provide a text-only feedback interface for black-box OPD, and what makes it effective. Our instantiation, Rubric-based On-Policy Distillation (ROPD), induces rubrics by contrasting teacher responses with the student's current rollouts and uses them to score these rollouts for on-policy optimization. We find that, under matched settings, text-only ROPD outperforms logit-based OPD methods on four competition-math benchmarks, reaching the best AIME24 accuracy of standard logit-based OPD with 9.6x fewer training samples. Our analysis yields three findings: rubric rewards track correctness far better than teacher log-likelihood (AUC 0.90 vs. 0.35); training with them repairs more failed criteria and regresses fewer passed ones than logit-based supervision; and contrasting teacher responses with student rollouts is central to rubric quality. These results position rubric-based OPD as a flexible, black-box-compatible alternative to logit-based OPD. Our implementation is available at https://github.com/Peregrine123/ROPD_official.
As learning systems increasingly shape everyday decisions, Algorithmic Collective Action (ACA), i.e., users coordinating changes to shared data to steer model behavior, offers a complement to regulator-side policy and corporate model design. Real-world collective actions have traditionally been decentralized and fragmented into multiple collectives, despite sharing overarching objectives, with each collective differing in size, strategy, and actionable goals. However, most of the ACA literature focuses on single collective settings. To address this, we propose the first comprehensive statistical framework for ACA with multiple collectives acting on the same system. In particular, we focus on collective action in classification, studying how multiple collectives can influence a classifier's behavior. We provide quantitative statistical bounds on the success of the collectives, considering the role and the interplay of the collectives' sizes and the alignment of their goals. We make such bounds computable by each collective with only partial knowledge of other collectives' sizes and strategies. Finally, we numerically illustrate our framework on simulations inspired by interventions for climate adaptation in smart cities, demonstrating the usefulness of our bounds.
AI systems have become increasingly capable of dangerous behaviours in many domains. This raises the question: Do models sometimes choose to violate human instructions in order to perform behaviour that is more useful for certain goals? We introduce a benchmark for measuring model propensity for instrumental convergence (IC) behaviour in terminal-based agents. This is behaviour such as self-preservation that has been hypothesised to play a key role in risks from highly capable AI agents. Our benchmark is realistic and low-stakes, aiming to reduce evaluation-awareness and roleplay confounds. The suite contains seven operational tasks, each with an official workflow and a shortcut whose policy status varies by condition. An eight-variant shared framework varies monitoring, instruction clarity, stakes, permission, instrumental usefulness and blocked honest paths to support inferences regarding the factors driving IC behaviour. We evaluated ten models using deterministic environment-state scorers over 1,680 samples, with trace review employed for audit and adjudication purposes. The adjusted IC rate is 86 out of 1,680 samples (5.1%). IC behaviour is concentrated rather than uniform: two Gemini models account for 66.3% of IC cases and three tasks account for 84.9%. Conditions in which IC behaviour is indispensable for task success result in the greatest increase in the adjusted IC rate (+15.7 percentage points), whereas emphasising that task success is critical or certain framing choices do not produce comparable effects. Our findings indicate that realistic, low-nudge environments elicit IC behaviour rarely but systematically in most tested models. We conclude that it is feasible to robustly measure tendencies for dangerous behaviour in current frontier AI agents.