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.
Graph-level representations are crucial tools for characterising structural differences between graphs. However, comparing graphs with different cardinalities, even when sampled from the same underlying distribution, remains challenging. Unsupervised tasks in particular require interpretable, scalable, and reliable size-aware graph representations. Our work addresses these issues by tracking the structural diversity of a graph across coarsening levels. The resulting graph embeddings, which we denote diversity curves, are interpretable by construction, efficient, and directly comparable across coarsening hierarchies. Specifically, we track the spread of graphs, a novel isometry invariant that is inherently well-suited for encoding the metric diversity and geometry of graphs. We utilise edge contraction coarsening and prove that this improves expressivity, thus leading to more powerful graph-level representations than structural descriptors alone. Demonstrating their utility over a range of baseline methods in practice, we use diversity curves to (i) cluster and visualise simulated graphs across varying sizes, (ii) distinguish the geometry of single-cell graphs, (iii) compare the structure of molecular graph datasets, and (iv) characterise geometric shapes.
Modern datasets across many disciplines increasingly consist of time-evolving, potentially infinite-dimensional random objects, such as dynamic functional data, which are naturally modeled in Hilbert spaces. In these settings, characterizing probability measures, for example, through densities, can be ill-defined or technically challenging. Motivated by clustering applications, we propose a Gaussian mixture framework for Hilbert-space-valued data based on kernel mean embeddings and develop efficient optimization algorithms for estimation. We establish theoretical guarantees showing that the proposed algorithm is well-defined and that the model yields a dense class of approximations in infinite-dimensional spaces. We evaluate the framework through extensive experiments on diverse data geometries, including $L^2$-functional data and graph signals arising in modern medical applications.
When language model agents tackle complex software engineering tasks, they often degrade over long trajectories, which we define as *agent drift*. We focus on two recurring failure modes *overthinking* and *overacting*, i.e., where the agent repeatedly reasons over information it already has, and where it issues tool calls without integrating recent observations or acquiring new evidence. In this paper, we introduce TACT (Think-Act Calibration via activation Steering), to detect and mitigate agent drift in the residual stream before it surfaces as a behavioral failure. In specific, we label trajectory steps as overthinking, overacting, or calibrated, and find that their hidden states can separate linearly along two *drift axes*, pointing from calibrated behavior toward each failure mode (AUC $\approx$ 0.9). To mitigate agent drift, we project each step's activation onto these axes at test time and pull drifted ones back toward the calibrated region. Experiments show that TACT outperforms unsteered baselines across SWE-bench Verified, Terminal-Bench 2.0, and CLAW-Eval, lifting average resolve rate by $+5.8$ pp on Qwen3.5-27B and $+4.8$ pp on Gemma-4-26B-A4B-it while cutting steps-to-resolve by up to $26\%$. These gains frame agent drift as a steerable direction in the residual stream, and position TACT as a viable handle for reliable long-horizon agents.
UAV-ground visual tracking (UGVT) aims to simultaneously track the same target from both UAV and ground views. However, existing two-stream methods suffer from isolated feature extraction and rely heavily on implicit appearance matching, which often fails to establish reliable cross-view correspondence under drastic viewpoint discrepancies, thereby leading to unstable tracking. To address these issues, we propose VL-UniTrack, a unified framework enhanced by visual-language prompts. By encoding features from both views with a single shared encoder, our method reduces feature isolation between the two views and enables sufficient cross-view interaction. To alleviate the ambiguity caused by appearance-only matching, we further design a visual-language viewpoint prompting module that fuses language descriptions with visual features to generate learnable prompts. These prompts are then injected into a prompt-guided cross-view adapter to facilitate cross-view interaction and guide the learning of view-specific feature representations. In addition, we introduce a confidence-modulated mutual distillation loss to regularize training by suppressing noise propagation. Extensive experiments demonstrate that VL-UniTrack achieves state-of-the-art performance on the latest benchmark. The code is available at https://github.com/xuboyue1999/VL-UniTrack.git.
We study the problem of denoising observations \(Y_i=X_i+Z_i\), where the latent variables \(X_i\) are sampled from a low-dimensional manifold in \(\mathbb{R}^n\) and the noise variables \(Z_i\) are isotropic Gaussian. We propose a convex-relaxation estimator that first reduces dimension by principal component analysis and then projects the observations onto the convex hull of the projected latent manifold. We construct a statistical oracle that estimates its supporting hyperplanes from empirical Gaussian tail probabilities of the noisy sample. Under a lower-mass condition on the latent distribution, we prove finite-sample guarantees for the oracle and derive error bounds for the resulting denoiser. The analysis combines risk bounds for least-squares projection under convex constraints (due to Chatterjee) with entropy bounds for the manifold. We also verify the assumptions of the framework for a Cryo-Electron Microscopy observation model by establishing suitable covering number and Lipschitz estimates for the associated group action and imaging operators.
Understanding human actions from visual observations is essential for human-robot interaction, particularly when semantic interpretation of unfamiliar or hard-to-annotate actions is required. For rapid or less common activities, collecting sufficient labeled data for supervised learning is challenging, making zero-shot approaches a practical alternative for semantic understanding without task-specific training. While recent advances in large-scale pre-trained models enable such zero-shot reasoning, the impact of temporal resolution, especially for rapid and fine-grained motions, remains underexplored. In this study, we investigate temporal-resolution conditions for zero-shot semantic understanding of high-speed human actions. Using kendo as a representative case of rapid and subtle motion patterns, we propose a training-free pipeline that combines a pre-trained video-language model for semantic representation with large language model-based reasoning for pairwise action comparison. Our primary experiment evaluates full-observation raw videos from 10 to 120 Hz in 10-Hz increments. Nearest class prototype (NCP) accuracy is highest at 120 Hz, and the mean over 70-120 Hz is higher than that over 10-60 Hz. The corresponding mean prototype margin changes from -5.74 to +2.52 similarity-score points between these two halves and is also highest at 120 Hz. Secondary experiments show that tracking overlays reduce mean full-observation performance but improve mean partial-observation performance. These findings provide preliminary evidence that retaining high-temporal-resolution visual information can benefit training-free semantic understanding of rapid human actions.
Optical chemical structure recognition (OCSR) translates molecular images into machine-readable representations such as SMILES strings or molecular graphs, but remains challenging in real-world documents due to wide variations in chemical structures, shorthand conventions, and scanning artifacts. Most existing deep learning approaches rely on teacher forcing with token-level Maximum Likelihood Estimation (MLE). This training paradigm suffers from exposure bias, as models are trained under ground-truth prefixes but must condition on their own previous predictions during inference. Moreover, token-level MLE objectives hinder the optimization towards molecular-level evaluation criteria such as chemical validity and structural similarity. Here we introduce Minimum Risk Training (MRT) to OCSR and propose COMO (Closed-loop Optical Molecule recOgnition), a framework that mitigates exposure bias by directly optimizing over molecule-level, non-differentiable objectives. Experiments on ten benchmarks, including synthetic and real-world chemical diagrams from patent and scientific literature, demonstrate that COMO substantially outperforms existing rule-based and learning-based methods with less training data, consistently achieving superior performance across both reproduced baselines and previously reported results. Ablation studies further show that MRT is architecture-agnostic, demonstrating its potential for broad application to end-to-end OCSR systems.
Analog circuit design relies heavily on reusing existing intellectual property (IP), yet searching across heterogeneous representations such as SPICE netlists, schematics, and functional descriptions remains challenging. Existing methods are largely limited to exact matching within a single modality, failing to capture cross-modal semantic relationships. To bridge this gap, we present AnalogRetriever, a unified tri-modal retrieval framework for analog circuit search. We first build a high-quality dataset on top of Masala-CHAI through a two-stage repair pipeline that raises the netlist compile rate from 22.0\% to 99.97\%. Built on this foundation, AnalogRetriever encodes schematics and descriptions with a vision-language model and netlists with a port-aware relational graph convolutional network, mapping all three modalities into a shared embedding space via curriculum contrastive learning. Experiments show that AnalogRetriever achieves an average Recall@1 of 75.2\% across all six cross-modal retrieval directions, significantly outperforming existing baselines. When integrated into the AnalogCoder agentic framework as a retrieval-augmented generation module, it consistently improves functional pass rates and enables previously unsolved tasks to be completed.
Quantization has become a standard tool for efficient LLM deployment, especially for local inference, where models are now routinely served at 2-3 bits per parameter. The state of the art is currently split into simple scalar quantization techniques, such as GPTQ or AWQ, which are widely deployed but plateau in accuracy at 3-4 bits per parameter (bpp), and "second-generation" vector- or trellis-quantized methods, such as QTIP, GPTVQ and AQLM, which push the accuracy frontier but are notoriously hard to implement and to scale. In this paper, we ask whether this gap is fundamental, or whether a carefully optimized $\textit{scalar}$ quantizer can recover most of it. We answer in the affirmative, by introducing GSQ (Gumbel-Softmax Quantization), a post-training scalar quantization method which jointly learns the per-coordinate grid assignments and the per-group scales using a Gumbel-Softmax relaxation of the discrete grid. GSQ matches the cardinality of the relaxation to the small number of levels available in the target bit-width regime (e.g., 3-8 levels for ternary and 3 bpp, respectively), making optimization tractable. Practically, on the standard Llama-3.1-8B/70B-Instruct models, GSQ closes most of the gap between scalar quantization and the QTIP frontier at 2 and 3 bits, while using a symmetric scalar grid with group-wise quantization, and thus remains compatible with existing scalar inference kernels. We further show that the same discrete-assignment optimization can be applied to practical GGUF K-Quant checkpoints: starting from publicly released GGUF models, GSQ improves accuracy while projecting the result back into the same deployment format. Finally, GSQ scales to trillion-scale Mixture-of-Experts models such as Kimi-K2.5, where vector-quantized methods are difficult to apply. The source code is publicly available at https://github.com/IST-DASLab/GSQ.
Power has become a central bottleneck for AI inference. This problem is becoming more urgent as agentic AI emerges as a major workload class, yet prior power-management techniques focus almost entirely on single-turn LLM serving. Our analysis shows that agentic serving behaves fundamentally differently: each request carries long-lived context that evolves across tool-interleaved turns, and lowering GPU frequency can push the system into a thrashing regime where memory pressure sharply worsens both performance and power efficiency. These observations show that power optimization for agentic serving requires rethinking. We present KAIROS, a context-aware power optimization system for agentic AI serving. KAIROS uses agent context as a first-class control signal to jointly manage GPU frequency, per-instance concurrency, and multi-instance request placement. This enables KAIROS to save power when memory headroom exists while avoiding thrashing and preserving performance targets. At a high level, KAIROS tracks requests at agent granularity, adapts local control to context growth and agent progress, and routes agents across instances to jointly improve power efficiency and memory stability. Evaluated across diverse software and data engineering agentic tasks, KAIROS achieves an average of 27% (up to 39.8%) power reduction while meeting the performance targets.
Exploratory analysis of high-dimensional data relies on embedding the data into a low-dimensional space, based on which a visualization plot is produced to uncover meaningful structures and to communicate geometric and distributional data characteristics. Finding a suitable embedding algorithm configuration, particularly the hyperparameter setting, to produce a visualization plot that faithfully represents the underlying reality and encourages pattern discovery is labor-intensive and requires domain knowledge. To ease this burden, we propose an agentic AI pipeline that integrates rigorous quantitative assessment with large language model (LLM) based approximation of qualitative human judgment and insight. By treating visualization evaluation and hyperparameter optimization as a semantic task, our system generates a multi-faceted report that contextualizes quantitative metrics with descriptive summaries, and suggests actionable recommendations of algorithm configuration for refining data visualization. Through an iterative refinement loop, the system rapidly produces a high-quality visualization plot in full automation.
Video face restoration aims to enhance degraded face videos into high-quality results with realistic facial details, stable identity, and temporal coherence. Recent diffusion-based methods have brought strong generative priors to restoration and enabled more realistic detail synthesis. However, existing approaches for face videos still rely heavily on generic diffusion priors and multi-step sampling, which limit both facial adaptation and inference efficiency. These limitations motivate the use of one-step diffusion for video face restoration, yet achieving faithful facial recovery alongside temporally stable outputs remains challenging. In this paper, we propose, DVFace, a one-step diffusion framework for real-world video face restoration. Specifically, we introduce a spatio-temporal dual-codebook design to extract complementary spatial and temporal facial priors from degraded videos. We further propose an asymmetric spatio-temporal fusion module to inject these priors into the diffusion backbone according to their distinct roles. Evaluation on various benchmarks shows that DVFace delivers superior restoration quality, temporal consistency, and identity preservation compared to recent methods. Code: https://github.com/zhengchen1999/DVFace.
Artificial intelligence provides low-cost predictions for many analytics tasks, but their reliability and the value of another human label vary across tasks. We study how to allocate a shared human-validation budget when task-level uncertainty is unknown and each acquired label informs both estimation and subsequent allocation. For known difficulty levels, the benchmark follows a cost-adjusted Neyman rule that accounts for task importance and label cost. Within our Tuned Rectification-Difficulty framework, we develop an upper-confidence-bound policy that jointly learns the correction coefficients of tuned prediction-powered inference and the resulting difficulties from paired human labels and predictions, and establish an allocation-regret guarantee for the confidence-radius policy. In synthetic experiments and a real digital-twin survey with 68 tasks and over 2,000 respondents, our method closes most of the gap to the oracle on the allocation objective. It matches the estimation error of uniform allocation with up to 22.7% and 4.5% fewer human labels, respectively. The same allocation structure extends beyond scalar means to vector-valued decision models, including regression and choice/conjoint estimation, by replacing the scalar residual variance with a scalarized sandwich covariance. The value of AI depends not only on model accuracy but also on the operational policy that targets human oversight where it matters most.
A recent line of work initiated by Chiesa and Gur and further developed by Herman and Rothblum investigates the sample and communication complexity of verifying properties of distributions with the assistance of a powerful, knowledgeable, but untrusted prover. In this work, we initiate the study of differentially private distribution property verification. After all, if we do not trust the prover to help us with verification, why should we trust it with our sensitive sample? We map a landscape of differentially private verification of properties of distributions. In the non-private case it is known that one-round private-coin protocols can have substantially lower complexity than public-coin (AM) protocols. In contrast, the possibility for improvement in differentially private interactive proofs depends on the privacy parameter regime and model. Drawing on connections between privacy and replicability and privacy amplification techniques in the literature we show: 1. There exists a reduction from any one-round $(\varepsilon,\delta)$-differentially private private-coin protocol to a differentially private AM protocol for the parameter regime $\varepsilon = O(1/\sqrt{s})$ and $\delta= O(1/s^{5/2})$ with approximately the same privacy and sample and communication complexities. In the local model, this is relaxed to $\varepsilon = O(1/\sqrt{\log s})$ 2. However, when the privacy guarantee is very relaxed ($\varepsilon \in \Omega(\log s)$), private coins indeed reduce sample and communication complexities. We also obtain a computationally efficient Merlin-Arthur proof for privately testing whether samples are drawn from a product distribution and prove that its sample complexity is optimal up to a $polylog N$ factor by reducing uniformity testing to independence testing with Boolean attributes and appealing to known lower bounds on sample complexity for private uniformity testing.