Daily Papers

Recent research-level physics-reasoning benchmarks for LLMs reveal a failure mode that lies not in knowledge or execution, but in modeling the world being reasoned about. Models often silently alter given quantities, fabricate laws, or inject unstated assumptions to force a problem into familiar patterns, and then reason inside this corrupted world. We define this premise-level divergence as modeling drift: the gap between a model's internal axiomatic world model (AWM) and the true physical world specified in the problem. Although RLVR and PRM have yielded substantial gains in mathematics and code, their reward shapes do not directly supervise world modeling in axiomatic domains such as physics. We propose Reinforcement Learning with Axiomatic World Modeling (RLAWM), which optimizes the policy by penalizing divergence between its inferred axiomatic world model and the true physics world. RLAWM probes physics reasoning at two hierarchical levels (modeling and solving), each scored by a physically grounded reward. The modeling reward targets abstract knowledge formulation, evaluating whether the model captures the true axiomatic world before attempting calculation. The solving reward targets instantiated knowledge reasoning, checking whether the model's concrete derivation remains consistent with the axiomatic world. This two-level structure separates what world the model believes it is reasoning in from how it reasons within that world. The framework operates exclusively during training, with no extra cost during inference. RLAWM improves performance by up to +12.2 points on PhysReason and +5.2 on PHYSICS over the baseline. It also generalizes zero-shot across difficulty, source, and domain, with a 2.45x gain and +10 points over the strongest baseline on olympiad-level physics and math.

Generative modeling can be formulated as learning a mapping f such that its pushforward distribution matches the data distribution. The pushforward behavior can be carried out iteratively at inference time, for example in diffusion and flow-based models. In this paper, we propose a new paradigm called Drifting Models, which evolve the pushforward distribution during training and naturally admit one-step inference. We introduce a drifting field that governs the sample movement and achieves equilibrium when the distributions match. This leads to a training objective that allows the neural network optimizer to evolve the distribution. In experiments, our one-step generator achieves state-of-the-art results on ImageNet at 256 x 256 resolution, with an FID of 1.54 in latent space and 1.61 in pixel space. We hope that our work opens up new opportunities for high-quality one-step generation.

Predictive world models enable robots to plan by imagining the outcomes of their actions, but their value for control hinges on generating many rollouts quickly. This creates a bottleneck for diffusion-based world models: multistep sampling makes each rollout expensive, limiting large-scale action search at inference time. We introduce DriftWorld, an action-conditioned world model based on drifting generative models. Rather than denoising iteratively at inference, DriftWorld learns an action-conditioned drift during training, allowing it to generate future frames from the current observation and a candidate action sequence in a single forward pass at 30+ fps, which is 17x faster on average than diffusion based baselines. We evaluate DriftWorld on standard vision-based robotic manipulation benchmarks, including Bridge-V2, RT-1, Language Table, Push-T, and Robomimic. By producing rollouts that are both accurate and fast, DriftWorld achieves state-of-the-art decision-making performance with far less inference time than diffusion-based world model baselines. Beyond online control, DriftWorld can also serve as an offline simulator for ranking real-world robot policies, with rollout-based scores correlating with ground truth at up to 0.99. These results show that drifting models are a strong fit for robot world modeling, where fast, high-quality imagination directly supports planning and policy evaluation.

This paper introduces a continuous-time stochastic dynamical framework for understanding how large language models (LLMs) may self-amplify latent biases or toxicity through their own chain-of-thought reasoning. The model posits an instantaneous "severity" variable x(t) in [0,1] evolving under a stochastic differential equation (SDE) with a drift term μ(x) and diffusion σ(x). Crucially, such a process can be consistently analyzed via the Fokker--Planck approach if each incremental step behaves nearly Markovian in severity space. The analysis investigates critical phenomena, showing that certain parameter regimes create phase transitions from subcritical (self-correcting) to supercritical (runaway severity). The paper derives stationary distributions, first-passage times to harmful thresholds, and scaling laws near critical points. Finally, it highlights implications for agents and extended LLM reasoning models: in principle, these equations might serve as a basis for formal verification of whether a model remains stable or propagates bias over repeated inferences.

Real-world datasets often exhibit temporal dynamics characterized by evolving data distributions. Disregarding this phenomenon, commonly referred to as concept drift, can significantly diminish a model's predictive accuracy. Furthermore, the presence of hyperparameters in online models exacerbates this issue. These parameters are typically fixed and cannot be dynamically adjusted by the user in response to the evolving data distribution. Gaussian Process (GP) models offer powerful non-parametric regression capabilities with uncertainty quantification, making them ideal for modeling complex data relationships in an online setting. However, conventional online GP methods face several critical limitations, including a lack of drift-awareness, reliance on fixed hyperparameters, vulnerability to data snooping, absence of a principled decay mechanism, and memory inefficiencies. In response, we propose DAO-GP (Drift-Aware Online Gaussian Process), a novel, fully adaptive, hyperparameter-free, decayed, and sparse non-linear regression model. DAO-GP features a built-in drift detection and adaptation mechanism that dynamically adjusts model behavior based on the severity of drift. Extensive empirical evaluations confirm DAO-GP's robustness across stationary conditions, diverse drift types (abrupt, incremental, gradual), and varied data characteristics. Analyses demonstrate its dynamic adaptation, efficient in-memory and decay-based management, and evolving inducing points. Compared with state-of-the-art parametric and non-parametric models, DAO-GP consistently achieves superior or competitive performance, establishing it as a drift-resilient solution for online non-linear regression.

Data drift is the change in model input data that is one of the key factors leading to machine learning models performance degradation over time. Monitoring drift helps detecting these issues and preventing their harmful consequences. Meaningful drift interpretation is a fundamental step towards effective re-training of the model. In this study we propose an end-to-end framework for reliable model-agnostic change-point detection and interpretation in large task-oriented dialog systems, proven effective in multiple customer deployments. We evaluate our approach and demonstrate its benefits with a novel variant of intent classification training dataset, simulating customer requests to a dialog system. We make the data publicly available.

Non-stationarity of an underlying data generating process that leads to distributional changes over time is a key characteristic of Data Streams. This phenomenon, commonly referred to as Concept Drift, has been intensively studied, and Concept Drift Detectors have been established as a class of methods for detecting such changes (drifts). For the most part, Drift Detectors compare regions (windows) of the data stream and detect drift if those windows are sufficiently dissimilar. In this work, we introduce the Window Dilemma, an observation that perceived drift is a product of windowing and not necessarily the underlying data generating process. Additionally, we highlight that drift detection is ill-posed, primarily because verification of drift events are implausible in practice. We demonstrate these contributions first by an illustrative example, followed by empirical comparisons of drift detectors against a variety of alternative adaptation strategies. Our main finding is that traditional batch learning techniques often perform better than their drift-aware counterparts further bringing into question the purpose of detectors in Stream Classification.

Three key properties that are desired of trustworthy machine learning models deployed in high-stakes environments are fairness, explainability, and an ability to account for various kinds of "drift". While drifts in model accuracy, for example due to covariate shift, have been widely investigated, drifts in fairness metrics over time remain largely unexplored. In this paper, we propose FEAMOE, a novel "mixture-of-experts" inspired framework aimed at learning fairer, more explainable/interpretable models that can also rapidly adjust to drifts in both the accuracy and the fairness of a classifier. We illustrate our framework for three popular fairness measures and demonstrate how drift can be handled with respect to these fairness constraints. Experiments on multiple datasets show that our framework as applied to a mixture of linear experts is able to perform comparably to neural networks in terms of accuracy while producing fairer models. We then use the large-scale HMDA dataset and show that while various models trained on HMDA demonstrate drift with respect to both accuracy and fairness, FEAMOE can ably handle these drifts with respect to all the considered fairness measures and maintain model accuracy as well. We also prove that the proposed framework allows for producing fast Shapley value explanations, which makes computationally efficient feature attribution based explanations of model decisions readily available via FEAMOE.

Large Language Models (LLMs) excel at single-turn tasks such as instruction following and summarization, yet real-world deployments require sustained multi-turn interactions where user goals and conversational context persist and evolve. A recurring challenge in this setting is context drift: the gradual divergence of a model's outputs from goal-consistent behavior across turns. Unlike single-turn errors, drift unfolds temporally and is poorly captured by static evaluation metrics. In this work, we present a study of context drift in multi-turn interactions and propose a simple dynamical framework to interpret its behavior. We formalize drift as the turn-wise KL divergence between the token-level predictive distributions of the test model and a goal-consistent reference model, and propose a recurrence model that interprets its evolution as a bounded stochastic process with restoring forces and controllable interventions. We instantiate this framework in both synthetic long-horizon rewriting tasks and realistic user-agent simulations such as in tau-Bench, measuring drift for several open-weight LLMs that are used as user simulators. Our experiments consistently reveal stable, noise-limited equilibria rather than runaway degradation, and demonstrate that simple reminder interventions reliably reduce divergence in line with theoretical predictions. Together, these results suggest that multi-turn drift can be understood as a controllable equilibrium phenomenon rather than as inevitable decay, providing a foundation for studying and mitigating context drift in extended interactions.

We study nonparametric density estimation in non-stationary drift settings. Given a sequence of independent samples taken from a distribution that gradually changes in time, the goal is to compute the best estimate for the current distribution. We prove tight minimax risk bounds for both discrete and continuous smooth densities, where the minimum is over all possible estimates and the maximum is over all possible distributions that satisfy the drift constraints. Our technique handles a broad class of drift models, and generalizes previous results on agnostic learning under drift.

In Online Continual Learning (OCL) a learning system receives a stream of data and sequentially performs prediction and training steps. Important challenges in OCL are concerned with automatic adaptation to the particular non-stationary structure of the data, and with quantification of predictive uncertainty. Motivated by these challenges we introduce a probabilistic Bayesian online learning model by using a (possibly pretrained) neural representation and a state space model over the linear predictor weights. Non-stationarity over the linear predictor weights is modelled using a parameter drift transition density, parametrized by a coefficient that quantifies forgetting. Inference in the model is implemented with efficient Kalman filter recursions which track the posterior distribution over the linear weights, while online SGD updates over the transition dynamics coefficient allows to adapt to the non-stationarity seen in data. While the framework is developed assuming a linear Gaussian model, we also extend it to deal with classification problems and for fine-tuning the deep learning representation. In a set of experiments in multi-class classification using data sets such as CIFAR-100 and CLOC we demonstrate the predictive ability of the model and its flexibility to capture non-stationarity.

Time series forecasting always faces the challenge of concept drift, where data distributions evolve over time, leading to a decline in forecast model performance. Existing solutions are based on online learning, which continually organize recent time series observations as new training samples and update model parameters according to the forecasting feedback on recent data. However, they overlook a critical issue: obtaining ground-truth future values of each sample should be delayed until after the forecast horizon. This delay creates a temporal gap between the training samples and the test sample. Our empirical analysis reveals that the gap can introduce concept drift, causing forecast models to adapt to outdated concepts. In this paper, we present Proceed, a novel proactive model adaptation framework for online time series forecasting. Proceed first estimates the concept drift between the recently used training samples and the current test sample. It then employs an adaptation generator to efficiently translate the estimated drift into parameter adjustments, proactively adapting the model to the test sample. To enhance the generalization capability of the framework, Proceed is trained on synthetic diverse concept drifts. Extensive experiments on five real-world datasets across various forecast models demonstrate that Proceed brings more performance improvements than the state-of-the-art online learning methods, significantly facilitating forecast models' resilience against concept drifts. Code is available at https://github.com/SJTU-DMTai/OnlineTSF.

A class of generative models that unifies flow-based and diffusion-based methods is introduced. These models extend the framework proposed in Albergo & Vanden-Eijnden (2023), enabling the use of a broad class of continuous-time stochastic processes called `stochastic interpolants' to bridge any two arbitrary probability density functions exactly in finite time. These interpolants are built by combining data from the two prescribed densities with an additional latent variable that shapes the bridge in a flexible way. The time-dependent probability density function of the stochastic interpolant is shown to satisfy a first-order transport equation as well as a family of forward and backward Fokker-Planck equations with tunable diffusion coefficient. Upon consideration of the time evolution of an individual sample, this viewpoint immediately leads to both deterministic and stochastic generative models based on probability flow equations or stochastic differential equations with an adjustable level of noise. The drift coefficients entering these models are time-dependent velocity fields characterized as the unique minimizers of simple quadratic objective functions, one of which is a new objective for the score of the interpolant density. We show that minimization of these quadratic objectives leads to control of the likelihood for generative models built upon stochastic dynamics, while likelihood control for deterministic dynamics is more stringent. We also discuss connections with other methods such as score-based diffusion models, stochastic localization processes, probabilistic denoising techniques, and rectifying flows. In addition, we demonstrate that stochastic interpolants recover the Schr\"odinger bridge between the two target densities when explicitly optimizing over the interpolant. Finally, algorithmic aspects are discussed and the approach is illustrated on numerical examples.

Large language models are increasingly deployed in multi-turn interactive settings where users or environments can iteratively provide lightweight feedback. Unfortunately, optimizing such behavior presents a sharp dilemma in practice: online reinforcement learning is able to effectively address multi-turn dynamics but is prohibitively expensive due to the cost of generating full correction trajectories at every update, whereas offline supervised fine-tuning (SFT) is efficient but suffers from distribution shift and behavioral collapse. To this end, we novelly propose DRIFT (Decoupled Rollouts and Importance-Weighted Fine-Tuning), a framework that operationalizes the theoretical insight that the KL-regularized RL objective is equivalent to importance-weighted supervised learning. DRIFT decouples rollout from optimization by sampling offline interaction trajectories from a fixed reference policy, deriving return-based importance weights, and optimizing the policy via weighted SFT on the resulting dataset. Empirically, we demonstrate that DRIFT matches or exceeds the performance of multi-turn reinforcement learning baselines while maintaining the training efficiency and simplicity of standard supervised fine-tuning. Code is available at https://github.com/2020-qqtcg/DRIFT.

We study inference-time scaling for diffusion models, where the goal is to adapt a pre-trained model to new target distributions without retraining. Existing guidance-based methods are simple but introduce bias, while particle-based corrections suffer from weight degeneracy and high computational cost. We introduce DriftLite, a lightweight, training-free particle-based approach that steers the inference dynamics on the fly with provably optimal stability control. DriftLite exploits a previously unexplored degree of freedom in the Fokker-Planck equation between the drift and particle potential, and yields two practical instantiations: Variance- and Energy-Controlling Guidance (VCG/ECG) for approximating the optimal drift with minimal overhead. Across Gaussian mixture models, particle systems, and large-scale protein-ligand co-folding problems, DriftLite consistently reduces variance and improves sample quality over pure guidance and sequential Monte Carlo baselines. These results highlight a principled, efficient route toward scalable inference-time adaptation of diffusion models.

Data Drift is the phenomenon where the generating model behind the data changes over time. Due to data drift, any model built on the past training data becomes less relevant and inaccurate over time. Thus, detecting and controlling for data drift is critical in machine learning models. Hierarchical Temporal Memory (HTM) is a machine learning model developed by Jeff Hawkins, inspired by how the human brain processes information. It is a biologically inspired model of memory that is similar in structure to the neocortex, and whose performance is claimed to be comparable to state of the art models in detecting anomalies in time series data. Another unique benefit of HTMs is its independence from training and testing cycle; all the learning takes place online with streaming data and no separate training and testing cycle is required. In sequential learning paradigm, Sequential Probability Ratio Test (SPRT) offers some unique benefit for online learning and inference. This paper proposes a novel hybrid framework combining HTM and SPRT for real-time data drift detection and anomaly identification. Unlike existing data drift methods, our approach eliminates frequent retraining and ensures low false positive rates. HTMs currently work with one dimensional or univariate data. In a second study, we also propose an application of HTM in multidimensional supervised scenario for anomaly detection by combining the outputs of multiple HTM columns, one for each dimension of the data, through a neural network. Experimental evaluations demonstrate that the proposed method outperforms conventional drift detection techniques like the Kolmogorov-Smirnov (KS) test, Wasserstein distance, and Population Stability Index (PSI) in terms of accuracy, adaptability, and computational efficiency. Our experiments also provide insights into optimizing hyperparameters for real-time deployment in domains such as Telecom.

We develop methods for forming prediction sets in an online setting where the data generating distribution is allowed to vary over time in an unknown fashion. Our framework builds on ideas from conformal inference to provide a general wrapper that can be combined with any black box method that produces point predictions of the unseen label or estimated quantiles of its distribution. While previous conformal inference methods rely on the assumption that the data points are exchangeable, our adaptive approach provably achieves the desired coverage frequency over long-time intervals irrespective of the true data generating process. We accomplish this by modelling the distribution shift as a learning problem in a single parameter whose optimal value is varying over time and must be continuously re-estimated. We test our method, adaptive conformal inference, on two real world datasets and find that its predictions are robust to visible and significant distribution shifts.

Fine-tuning instruct models often improves target performance while inducing behavioral drift from the reference model, which can degrade existing capabilities. Rather than treating this drift as an uncontrolled consequence of optimization, we specify a behavioral drift budget before optimization and ask how to boost the target-task performance within it. Locally, behavioral drift induces a shared geometry anchored at the reference model, with the drift budget defining a boundary within this space. In this space, drift determines distance from the reference, leaving update direction as the remaining degree of freedom. Fine-tuning updates can therefore be compared through their directional efficiency, naturally reformulating fine-tuning as a direction-selection problem. This reformulation makes a concrete prediction: changing the accessible directions can qualitatively alter the outcome of fine-tuning. We test this prediction in a stringent QA-only setting, where strong instruct models are fine-tuned only on final answers but must still generate multi-step reasoning at inference. Despite this mismatch, a coarse layer-selective probe reverses the failure of QA-only fine-tuning and reveals the existence of effective directions, with multiple neighboring configurations improving target performance while preserving reasoning and general capabilities. Across Qwen3-8B and Qwen3-14B, these directions substantially improve scientific reasoning and multilingual translation. Over more than 100 languages, the resulting models match or outperform dedicated translation systems and provide a stronger initialization for subsequent reinforcement learning. Our results suggest that fine-tuning is not just about how much a model changes, but how that change is spent. https://github.com/CONE-MT/DCO and https://huggingface.co/collections/LLaMAX/dco

We propose a general methodology for recovering preference parameters from data on choices and response times. Our methods yield estimates with fast (1/n for n data points) convergence rates when specialized to the popular Drift Diffusion Model (DDM), but are broadly applicable to generalizations of the DDM as well as to alternative models of decision making that make use of response time data. The paper develops an empirical application to an experiment on intertemporal choice, showing that the use of response times delivers predictive accuracy and matters for the estimation of economically relevant parameters.

Machine learning models often experience performance degradation post-deployment due to shifts in data distribution. It is challenging to assess model's performance accurately when labels are missing or delayed. Existing proxy methods, such as drift detection, fail to measure the effects of these shifts adequately. To address this, we introduce a new method, Probabilistic Adaptive Performance Estimation (PAPE), for evaluating classification models on unlabeled data that accurately quantifies the impact of covariate shift on model performance. It is model and data-type agnostic and works for various performance metrics. Crucially, PAPE operates independently of the original model, relying only on its predictions and probability estimates, and does not need any assumptions about the nature of the covariate shift, learning directly from data instead. We tested PAPE on tabular data using over 900 dataset-model combinations created from US census data, assessing its performance against multiple benchmarks. Overall, PAPE provided more accurate performance estimates than other evaluated methodologies.

The change in data distribution over time, also known as concept drift, poses a significant challenge to the reliability of online learning methods. Existing methods typically require model retraining or drift detection, both of which demand high computational costs and are often unsuitable for real-time applications. To address these limitations, a lightweight, fast and efficient random vector functional-link network termed Lite-RVFL is proposed, capable of adapting to concept drift without drift detection and retraining. Lite-RVFL introduces a novel objective function that assigns weights exponentially increasing to new samples, thereby emphasizing recent data and enabling timely adaptation. Theoretical analysis confirms the feasibility of this objective function for drift adaptation, and an efficient incremental update rule is derived. Experimental results on a real-world safety assessment task validate the efficiency, effectiveness in adapting to drift, and potential to capture temporal patterns of Lite-RVFL. The source code is available at https://github.com/songqiaohu/Lite-RVFL.

Machine Learning models in finance are highly susceptible to model drift, where predictive performance declines as data distributions shift. This issue is especially acute in developing economies such as those in Central Asia and the Caucasus - including Tajikistan, Uzbekistan, Kazakhstan, and Azerbaijan - where frequent and unpredictable macroeconomics shocks destabilize financial data. To the best of our knowledge, this is among the first studies to examine drift mitigation methods on financial datasets from these regions. We investigate the use of synthetic outliers, a largely unexplored approach, to improve model stability against unforeseen shocks. To evaluate effectiveness, we introduce a two-level framework that measures both the extent of performance degradation and the severity of shocks. Our experiments on macroeconomic tabular datasets show that adding a small proportion of synthetic outliers generally improves stability compared to baseline models, though the optimal amount varies by dataset and model

Recently proposed Drifting Models shift iterative distribution refinement from inference to training, enabling effective one-step generation. However, their performance on complex image datasets depends strongly on the representation used to construct the drifting field: pixel-space drifting performs poorly, whereas pretrained feature spaces substantially improve sample quality for reasons that remain unclear. We trace this gap to the discriminative geometry of the representation, which determines sample weighting in kernel density estimation (KDE) and, consequently drift. We introduce persistent representation learning, which continuously learns a more discriminative representation geometry as the generator evolves across batches. We further establish a current-step gradient equivalence between the KDE ratio loss and drift regression loss under matched conditions, connecting density-ratio-based generator optimization to empirical drifting and motivating direct control of the drifting velocity. Across multiple datasets, our method learns effective discriminative representations directly from pixels and reduces FID by approximately 82-95% over the original pixel-space Drifting Models, without pretrained encoders. Adapting pretrained representations and applying velocity clipping provide further gains.

Forecasting the future anatomy of slow-evolving neurodegenerative diseases could enable earlier, more targeted intervention and improve clinical trial design, but it remains challenging because true progression signals are subtle in longitudinal MRI. In this low-signal regime, transferring modern generative sequence models directly is unreliable: training is dominated by stable baseline anatomy and confounded by dense, sample-specific nuisance variation. We first provide a theoretical analysis that explains these failures through two modes. Identity collapse occurs when optimization is driven toward reproducing the current anatomy, which prevents the model from learning faint temporal change. The continuous interpolation trap arises when standard smooth networks cannot separate localized biological drift from pervasive noise, which leads to spurious changes that diffuse across the volume. To address both issues, we propose Latent Drift, a progressive generative framework that learns change in a compressed semantic representation rather than synthesizing full-resolution anatomy. This design removes pixel-level identity from the prediction target and concentrates model capacity on progression-relevant dynamics. We further apply Finite Scalar Quantization to the learned change representation, which suppresses small, high-frequency nuisance fluctuations while preserving consistent structural drift. Experiments on longitudinal 3D brain MRI show that Latent Drift improves patient-specific neuro-forecasting over diffusion and autoregressive transformer baselines across generative fidelity and clinically relevant evaluation metrics. Project page: https://cutepkq.github.io/latent-drift{https://cutepkq.github.io/latent-drift}.

In federated learning (FL), the data distribution of each client may change over time, introducing both temporal and spatial data heterogeneity, known as concept drift. Data heterogeneity arises from three drift sources: real drift (a shift in the conditional distribution P(y|x)), virtual drift (a shift in the input distribution P(x)), and label drift (a shift in the label distribution P(y)). However, most existing FL methods addressing concept drift primarily focus on real drift. When clients experience virtual or label drift, these methods often fail to selectively retain useful historical knowledge, leading to catastrophic forgetting. A key challenge lies in distinguishing different sources of drift, as they require distinct adaptation strategies: real drift calls for discarding outdated data, while virtual or label drift benefits from retaining historical data. Without explicitly identifying the drift sources, a general adaptation strategy is suboptimal and may harm generalization. To address this challenge, we propose FedDAA, a dynamic clustered FL framework designed to adapt to multi-source concept drift while preserving valuable historical knowledge. Specifically, FedDAA integrates three modules: a cluster number determination module to find the optimal number of clusters; a real drift detection module to distinguish real drift from virtual/label drift; and a concept drift adaptation module to adapt to new data while retaining useful historical information. We provide theoretical convergence guarantees, and experiments show that FedDAA achieves 7.84% to 8.52% accuracy improvements over state-of-the-art methods on Fashion-MNIST, CIFAR-10, and CIFAR-100.

Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the denoising diffusion model in the function space which also allows us to naturally handle irregularly-sampled observations. The forward process gradually adds noise to functions, preserving their continuity, while the learned reverse process removes the noise and returns functions as new samples. To this end, we define suitable noise sources and introduce novel denoising and score-matching models. We show how our method can be used for multivariate probabilistic forecasting and imputation, and how our model can be interpreted as a neural process.

Facing climate change, the already limited availability of drinking water will decrease in the future rendering drinking water an increasingly scarce resource. Considerable amounts of it are lost through leakages in water transportation and distribution networks. Thus, anomaly detection and localization, in particular for leakages, are crucial but challenging tasks due to the complex interactions and changing demands in water distribution networks. In this work, we analyze the effects of anomalies on the dynamics of critical infrastructure systems by modeling the networks employing Bayesian networks. We then discuss how the problem is connected to and can be considered through the lens of concept drift. In particular, we argue that model-based explanations of concept drift are a promising tool for localizing anomalies given limited information about the network. The methodology is experimentally evaluated using realistic benchmark scenarios. To showcase that our methodology applies to critical infrastructure more generally, in addition to considering leakages and sensor faults in water systems, we showcase the suitability of the derived technique to localize sensor faults in power systems.

Multi-agent Large Language Model (LLM) systems have emerged as powerful architectures for complex task decomposition and collaborative problem-solving. However, their long-term behavioral stability remains largely unexamined. This study introduces the concept of agent drift, defined as the progressive degradation of agent behavior, decision quality, and inter-agent coherence over extended interaction sequences. We present a comprehensive theoretical framework for understanding drift phenomena, proposing three distinct manifestations: semantic drift (progressive deviation from original intent), coordination drift (breakdown in multi-agent consensus mechanisms), and behavioral drift (emergence of unintended strategies). We introduce the Agent Stability Index (ASI), a novel composite metric framework for quantifying drift across twelve dimensions, including response consistency, tool usage patterns, reasoning pathway stability, and inter-agent agreement rates. Through simulation-based analysis and theoretical modeling, we demonstrate how unchecked agent drift can lead to substantial reductions in task completion accuracy and increased human intervention requirements. We propose three mitigation strategies: episodic memory consolidation, drift-aware routing protocols, and adaptive behavioral anchoring. Theoretical analysis suggests these approaches can significantly reduce drift-related errors while maintaining system throughput. This work establishes a foundational methodology for monitoring, measuring, and mitigating agent drift in production agentic AI systems, with direct implications for enterprise deployment reliability and AI safety research.

We investigate diffusion approximations for a class of multivariate inhomogeneous finite-velocity random motions motivated by models of active particles. A particle alternates cyclically among prescribed velocity fields V_1,dots,V_p with random run times and evolves according to either a flight dynamics, consisting of piecewise-linear motion, or a gliding dynamics, in which the particle follows the corresponding velocity flow. Under a Kac-type scaling that couples vanishing run times with diverging particle speed, we prove weak convergence of both processes to multidimensional diffusions. It turns out that the order of successive cyclic motions affects the diffusion limit. In addition to the second-order term generated by fluctuations of the random run times, the limiting drift contains directional derivatives DV_i[V_j] of the underlying vector fields. In Stratonovich form, part of this drift is expressed through their Lie brackets [V_i,V_j]. Thus, the generic non-commutativity of the microscopic motions survives the diffusive scaling and generates a macroscopic drift which depends on the cyclic order. The limiting drift also distinguishes the flight and gliding dynamics, despite their being driven by the same vector fields and run times. Several examples, including run-and-reverse motion and cyclic dynamics generated by multiple vector fields, illustrate how the cyclic switching protocol and the geometry of the underlying velocity fields shape the limiting diffusions.

Adapting to concept drift is a challenging task in machine learning, which is usually tackled using incremental learning techniques that periodically re-fit a learning model leveraging newly available data. A primary limitation of these techniques is their reliance on substantial amounts of data for retraining. The necessity of acquiring fresh data introduces temporal delays prior to retraining, potentially rendering the models inaccurate if a sudden concept drift occurs in-between two consecutive retrainings. In communication networks, such issue emerges when performing traffic forecasting following a~failure event: post-failure re-routing may induce a drastic shift in distribution and pattern of traffic data, thus requiring a timely model adaptation. In this work, we address this challenge for the problem of traffic forecasting and propose an approach that exploits adaptive learning algorithms, namely, liquid neural networks, which are capable of self-adaptation to abrupt changes in data patterns without requiring any retraining. Through extensive simulations of failure scenarios, we compare the predictive performance of our proposed approach to that of a reference method based on incremental learning. Experimental results show that our proposed approach outperforms incremental learning-based methods in situations where the shifts in traffic patterns are drastic.

Offline reinforcement learning requires improving a policy from fixed data while avoiding out-of-distribution actions with unreliable value estimates. Diffusion and flow policies handle this trade-off by modeling the behavior distribution to regularize the RL objective, but they require iterative denoising, solver integrations, and in more efficient variants, distillation or other approximations at inference. We propose DriftQL, which combines a drift-based behavioral regularizer with critic-driven policy improvement. The value signal biases the policy toward high-value regions of the data support, while attraction and repulsion together keep generated actions near the data and prevent collapse onto a single mode. DriftQL is implemented as a single network with a unified training objective and generates actions in a single forward pass. On D4RL and OGBench, DriftQL consistently outperforms diffusion and flow methods, advancing the state of the art. Under degraded data quality, where the baselines visibly struggle, DriftQL remains close to its clean-data performance, positioning it as a promising alternative to diffusion and flow-based methods while maintaining the simplicity and efficiency of deterministic approaches. Project page: https://driftql.github.io/

Machine learning systems in fraud detection, credit scoring, and clinical risk assessment operate under delayed ground truth: outcome labels arrive days to months after the decision they evaluate. During this blind period, governance evidence degrades through mechanisms that neither drift detection methods nor governance frameworks adequately address. This paper formalizes an evidence sufficiency model with four dimensions (completeness, freshness, reliability, representativeness) and a decision-readiness gate that quantifies how label latency degrades evidence quality. The model maps three drift types to dimension-specific degradation trajectories. A complementary proxy indicator framework comprising seven measurement categories estimates sufficiency degradation without labels, with explicit coverage mapping and characterized blind spots per drift type. Evaluation on the IEEE-CIS Fraud Detection dataset (~590K transactions) with controlled drift injection shows that composite proxy monitoring detects covariate and mixed drift with 100% detection rate, while concept drift without feature change remains undetected -- consistent with the theoretical impossibility of unsupervised detection when P(X) is unchanged. Blind period simulation confirms monotone sufficiency degradation, with concept drift degrading fastest (S=0.242 at day 60 vs 0.418 for no-drift). The framework contributes a governance sufficiency monitoring instrument; its value lies in translating drift signals into auditable sufficiency assessments with characterized blind spots. Mapping sufficiency levels to governance actions requires deployment-specific calibration beyond this study's scope.

Lagrangian turbulence lies at the core of numerous applied and fundamental problems related to the physics of dispersion and mixing in engineering, bio-fluids, atmosphere, oceans, and astrophysics. Despite exceptional theoretical, numerical, and experimental efforts conducted over the past thirty years, no existing models are capable of faithfully reproducing statistical and topological properties exhibited by particle trajectories in turbulence. We propose a machine learning approach, based on a state-of-the-art diffusion model, to generate single-particle trajectories in three-dimensional turbulence at high Reynolds numbers, thereby bypassing the need for direct numerical simulations or experiments to obtain reliable Lagrangian data. Our model demonstrates the ability to reproduce most statistical benchmarks across time scales, including the fat-tail distribution for velocity increments, the anomalous power law, and the increased intermittency around the dissipative scale. Slight deviations are observed below the dissipative scale, particularly in the acceleration and flatness statistics. Surprisingly, the model exhibits strong generalizability for extreme events, producing events of higher intensity and rarity that still match the realistic statistics. This paves the way for producing synthetic high-quality datasets for pre-training various downstream applications of Lagrangian turbulence.

Enabling large language models to achieve stable self-improvement without external expert supervision remains a central challenge in complex reasoning tasks. Existing self-distillation and reinforcement learning methods lack explicit mechanisms for tracking problem-level learning progress and adapting optimization strategies accordingly. Consequently, training may over-optimize easy problems, receive weak supervision from hard problems, and fail to sufficiently explore borderline cases. To resolve these issues, we propose DRIFT, an online self-evolution policy optimization framework for large language models. DRIFT regulates the model's self-improvement process through the joint use of Difficulty Routing and Rhythm Gating. The former identifies the model's learning state at the problem level and dynamically allocates self-distillation and reinforcement learning signals, while the latter refines policy updates at the token level, concentrating exploration on critical reasoning positions. By further incorporating a success buffer and a two-stage curriculum learning strategy, DRIFT preserves high-quality historical experience while progressively guiding the model from reliable behavior acquisition toward stable policy evolution. Evaluated across five benchmarks and three model scales, DRIFT surpasses the peak performance of both GRPO and SDPO across all evaluated metrics. On the average score over the five benchmarks, DRIFT achieves 79.5%, outperforming GRPO by 9.5% and SDPO by 7.5%, establishing a new state-of-the-art result. Notably, on ToolUse, DRIFT reaches an accuracy of 79.2%, improving over GRPO by 13.5% and SDPO by 10.7%, setting a new state-of-the-art and substantially outperforming all concurrent methods.

Real-world data often exhibit extreme imbalances and out-of-distribution (OOD) instances, which significantly biases the model training. While it has been extensively studied in vision and language domains separately, the impact of long-tailed open worlds on multi-modal large language models (MLLMs) has been largely overlooked. In this paper, we first demonstrate the susceptibility and vulnerability of vision-language models to significant biases caused by tail drift and out-of-distribution (OOD) drift during both the pre-training and fine-tuning stages. To eliminate the bias from different sources, we integrate the tailed drift adaptation and OOD drift detection into a unified framework by extending the concept drift theory to multi-modal. Specifically, a T-distribution-based drift adapter is proposed to effectively mitigate the bias induced by the long-tailed problem, which also facilitates the model in distinguishing OOD data through explicit distribution modelling. Extensive experiments show significant improvements in our model's ability to adapt to tailed drift and OOD drift. Moreover, it enhances the efficiency and accuracy of image-text alignment in vision language model pre-training, particularly in the long-tail open world scenario. Furthermore, we create a set of multi-modal datasets called OpenMMlo, specifically tailored for the long-tailed open world scenario, to validate our findings. To foster the development of the multi-modal community, we have made both OpenMMlo datasets and our code publicly available at: https://github.com/Anonymous0Knight/ConceptDriftMLLMs.

In statistical modelling the biggest threat is concept drift which makes the model gradually showing deteriorating performance over time. There are state of the art methodologies to detect the impact of concept drift, however general strategy considered to overcome the issue in performance is to rebuild or re-calibrate the model periodically as the variable patterns for the model changes significantly due to market change or consumer behavior change etc. Quantitative research is the most widely spread application of data science in Marketing or financial domain where applicability of state of the art reinforcement learning for auto-learning is less explored paradigm. Reinforcement learning is heavily dependent on having a simulated environment which is majorly available for gaming or online systems, to learn from the live feedback. However, there are some research happened on the area of online advertisement, pricing etc where due to the nature of the online learning environment scope of reinforcement learning is explored. Our proposed solution is a reinforcement learning based, true self-learning algorithm which can adapt to the data change or concept drift and auto learn and self-calibrate for the new patterns of the data solving the problem of concept drift. Keywords - Reinforcement learning, Genetic Algorithm, Q-learning, Classification modelling, CMA-ES, NES, Multi objective optimization, Concept drift, Population stability index, Incremental learning, F1-measure, Predictive Modelling, Self-learning, MCTS, AlphaGo, AlphaZero

We propose Speech Enhancement based on Drifting Models (DriftSE), a novel generative framework that formulates denoising as an equilibrium problem. Rather than relying on iterative sampling, DriftSE natively achieves one-step inference by evolving the pushforward distribution of a mapping function to directly match the clean speech distribution. This evolution is driven by a Drifting Field, a learned correction vector that guides samples toward the high-density regions of the clean distribution, which naturally facilitates training on unpaired data by matching distributions rather than paired samples. We investigate the framework under two formulations: a direct mapping from the noisy observation, and a stochastic conditional generative model from a Gaussian prior. Experiments on the VoiceBank-DEMAND benchmark demonstrate that DriftSE achieves high-fidelity enhancement in a single step, outperforming multi-step diffusion baselines and establishing a new paradigm for speech enhancement.

We report the discovery of bimodal structure in the drift rate distribution of upward-drifting burst clusters from the hyperactive repeating fast radio burst FRB 20240114A. Using unsupervised machine learning (UMAP dimensionality reduction combined with HDBSCAN density-based clustering) applied to 233 upward-drifting burst clusters from the FAST telescope dataset, we identify a distinct subpopulation of 45 burst clusters (Cluster C1) with mean drift rates 2.5x higher than typical upward-drifting burst clusters (245.6 vs 98.1 MHz/ms). Gaussian mixture modeling reveals strong evidence for bimodality (delta-BIC = 296.6), with clearly separated modes (Ashman's D = 2.70 > 2) and a statistically significant gap in the distribution (11.3 sigma). Crucially, we demonstrate that this bimodality persists when restricting the analysis to single-component (U1) burst clusters only (delta-BIC = 19.9, Ashman's D = 2.71), confirming that the result is not an artifact of combining single- and multi-component burst clusters with different drift rate definitions. The extreme-drift subpopulation also exhibits systematically lower peak frequencies (-7%), shorter durations (-29%), and distinct clustering in multi-dimensional feature space. These findings are suggestive of two spatially separated emission regions in the magnetosphere, each producing upward-drifting burst clusters with distinct physical characteristics, although confirmation requires observations from additional epochs and sources.

Many modern vision-language models (VLMs) build on autoregressive decoding of discrete tokens. While text-based output interfaces enable scalable pretraining and strong zero-shot generalization across diverse tasks, they are poorly suited for problems that require precise continuous outputs, such as localizing temporal boundaries of events or generating robotic control actions. To address this challenge, we propose DRIFT, a general framework for adapting pretrained VLMs to continuous decoding tasks. DRIFT combines a base predictor, which provides a coarse estimate of the target output, with a generative refinement module based on flow matching that iteratively improves the prediction. This residual formulation transforms the generative modeling problem from learning a global output distribution to modeling a localized residual distribution around a strong prior, substantially simplifying optimization. We evaluate DRIFT on both perception and planning tasks, including visual grounding and robotic control. Across multiple tasks and architectures spanning MLLMs, VLAs, and WAMs, DRIFT consistently outperforms a strong set of regression- and generative-based solutions.

Diffusion models, initially developed for image synthesis, demonstrate remarkable generative capabilities. Recently, their application has expanded to time series forecasting (TSF), yielding promising results. Existing surveys on time series primarily focus on the application of diffusion models to time series tasks or merely provide model-by-model introductions of diffusion-based TSF models, without establishing a systematic taxonomy for existing diffusion-based TSF models. In this survey, we firstly introduce several standard diffusion models and their prevalent variants, explaining their adaptation to TSF tasks. Then, we provide a comprehensive review of diffusion models for TSF, paying special attention to the sources of conditional information and the mechanisms for integrating this conditioning within the models. In analyzing existing approaches using diffusion models for TSF, we provide a systematic categorization and a comprehensive summary of them in this survey. Furthermore, we examine several foundational diffusion models applied to TSF, alongside commonly used datasets and evaluation metrics. Finally, we discuss the progress and limitations of these approaches, as well as potential future research directions for diffusion-based TSF. Overall, this survey offers a comprehensive overview of recent progress and future prospects for diffusion models in TSF, serving as a valuable reference for researchers in the field.

Learning the distribution of data on Riemannian manifolds is crucial for modeling data from non-Euclidean space, which is required by many applications in diverse scientific fields. Yet, existing generative models on manifolds suffer from expensive divergence computation or rely on approximations of heat kernel. These limitations restrict their applicability to simple geometries and hinder scalability to high dimensions. In this work, we introduce the Riemannian Diffusion Mixture, a principled framework for building a generative diffusion process on manifolds. Instead of following the denoising approach of previous diffusion models, we construct a diffusion process using a mixture of bridge processes derived on general manifolds without requiring heat kernel estimations. We develop a geometric understanding of the mixture process, deriving the drift as a weighted mean of tangent directions to the data points that guides the process toward the data distribution. We further propose a scalable training objective for learning the mixture process that readily applies to general manifolds. Our method achieves superior performance on diverse manifolds with dramatically reduced number of in-training simulation steps for general manifolds.

Unlike conventional video game development, which relies on labor-intensive pipelines for asset production, animation, physics, and programming, video world models generate interactive environments from user inputs instantly. It enable us to create customized, explorable, and continuously evolving virtual world from text, an image, or video. Realizing this vision requires four tightly coupled capabilities: interaction, persistent spatiotemporal consistency, stable long-horizon generation, and efficient response. We present AlayaWorld, an interactive long-horizon video world model that generates 24-fps video at 540p and 720p. Built on a 15B video diffusion transformer, AlayaWorld generates short latent chunks autoregressively under camera trajectories and switchable text prompts. Its bounded visual context combines a persistent sink frame, compressed temporal history, geometry-aligned spatial memory, and recent-frame conditioning. To reduce long-term drift, the model is trained with corrupted histories and prediction residuals collected from its own roll-outs. We further introduce a discrete autoregressive distillation formulation that combines distribution-matching distillation, self-forcing++, and consistency distillation, reducing inference from approximately 30 sampling steps to four steps per chunk. On iWorld-Bench, AlayaWorld achieves the best performance over long-horizon generation. Conceived as a full-stack, open-source, and long-term project, AlayaWorld is intended to provide an extensible foundation for future research on interactive video world models.

Real-world large language model deployments (e.g., conversational AI systems, code generation assistants) naturally generate abundant implicit user dissatisfaction (DSAT) signals, as users iterate toward better answers through refinements, corrections, and expressed preferences, while explicit satisfaction (SAT) feedback is scarce. Existing preference learning approaches are poorly aligned with this data profile, as they rely on costly human annotations or assume plentiful positive responses. In this paper, we introduce DRIFT (Dissatisfaction-Refined Iterative preFerence Training), which anchors training on real-world DSAT signals and samples positives dynamically from the evolving policy. Empirically, DRIFT models trained on real-world WildFeedback datasets and synthetic UltraFeedback datasets achieve up to +6.23\% (7B) / +7.61\% (14B) on WildBench Task Score and up to +8.95\% (7B) / +12.29\% (14B) on AlpacaEval2 win rate over base models, outperforming strong baseline methods such as iterative DPO and SPIN. At larger scales, the improvements are particularly pronounced: 14B models trained with DRIFT surpass GPT-4o-mini on WildBench. Further analysis shows that DRIFT also preserves exploratory capacity, yielding more diverse high-reward solutions rather than collapsing to narrow subsets. Theoretically, we demonstrate that this design preserves preference margins and avoids the gradient degeneration. These results show that DRIFT is an effective and scalable recipe for real-world post-training that leverages the most abundant and informative signal. The code and data are available at https://github.com/cacayaya/DRIFT.git.

Continual learning treats degradation on previously seen data as evidence of failure, a convention inherited from settings with a stationary prediction target, where a correct label remains correct indefinitely. World models do not satisfy this condition. Their prediction target is the environment, which changes, so knowledge that was accurate when acquired may later become false, and discarding it is required behavior rather than a defect. Non-stationary ground truth is well studied in the concept drift literature and in the temporal factuality of language models, but has not been formulated for world models, which are distinctive in that they also encode knowledge that must never be revised. We argue that continual world models require retention stratified by invariance timescale, separating invariants such as physics and object permanence, which must never be revised, from instance-level facts that should be revised as soon as the environment changes. Standard forgetting metrics cannot distinguish a world model that has correctly revised outdated knowledge from one that has suffered catastrophic forgetting, and consequently rank a frozen model highest, while existing physical-reasoning benchmarks evaluate only frozen checkpoints. We propose differential retention, which reports invariant regression testing across the adaptation stream jointly with revision latency, without aggregation.

Reinforcement learning (RL) is vital for optimizing video generation models, with a robust reward model (RM) serving as the cornerstone. However, existing video reward models often produce unstable scalar scores because they directly map complex, subjective video quality into a single score without explicit evaluation criteria. This leads to scalar drift, where the scoring scale collapses or shifts across different prompts, making the reward unreliable for RL. Drawing inspiration from professional human annotation engineering, we address this problem with RewardVerse, a rubric-based video reward framework that introduces a dynamic rubric as an intermediate representation between the evaluation query and the scorer. Instead of unconstrained direct scoring, RewardVerse first generates explicit evaluation criteria and then performs rubric-guided scoring, providing a stable semantic anchor that mitigates scalar drift. To efficiently optimize this collaborative pipeline, we propose Rubric-Guided Policy Optimization (RGPO), a two-stage training algorithm. RGPO first warms up the scorer using self-evolving seed rubrics and then jointly optimizes the rubric generator to produce query-adaptive evaluation criteria while continuously aligning the scorer with human ratings. Extensive experiments on the 16-dimensional EvalVerse benchmark and external datasets demonstrate that RewardVerse mitigates scalar drift, achieves state-of-the-art performance on both pointwise and pairwise evaluation, and provides a robust and interpretable reward signal for RL in video generation.

Auto-regressive video generation enables long video synthesis by iteratively conditioning each new batch of frames on previously generated content. However, recent work has shown that such pipelines suffer from severe temporal drift, where errors accumulate and amplify over long horizons. We hypothesize that this drift does not primarily stem from insufficient model capacity, but rather from inference-time error propagation. Specifically, we contend that drift arises from the uncontrolled reuse of corrupted latent conditioning tokens during auto-regressive inference. To correct this accumulation of errors, we propose a simple, inference-time method that mitigates temporal drift by identifying and removing unstable latent tokens before they are reused for conditioning. For this purpose, we define unstable tokens as latent tokens whose representations deviate significantly from those of the previously generated batch, indicating potential corruption or semantic drift. By explicitly removing corrupted latent tokens from the auto-regressive context, rather than modifying entire spatial regions or model parameters, our method prevents unreliable latent information from influencing future generation steps. As a result, it significantly improves long-horizon temporal consistency without modifying the model architecture, training procedure, or leaving latent space.

World foundation models aim to simulate the evolution of the real world with physically plausible behavior. Unlike prior methods that handle spatial and temporal correlations separately, we propose RAYNOVA, a geometry-agonistic multiview world model for driving scenarios that employs a dual-causal autoregressive framework. It follows both scale-wise and temporal topological orders in the autoregressive process, and leverages global attention for unified 4D spatio-temporal reasoning. Different from existing works that impose strong 3D geometric priors, RAYNOVA constructs an isotropic spatio-temporal representation across views, frames, and scales based on relative Plücker-ray positional encoding, enabling robust generalization to diverse camera setups and ego motions. We further introduce a recurrent training paradigm to alleviate distribution drift in long-horizon video generation. RAYNOVA achieves state-of-the-art multi-view video generation results on nuScenes, while offering higher throughput and strong controllability under diverse input conditions, generalizing to novel views and camera configurations without explicit 3D scene representation. Our code will be released at https://raynova-ai.github.io/.

Continual post-training enables models to absorb emerging knowledge after deployment, but repeatedly updating shared parameters can accumulate weight drift, potentially causing catastrophic forgetting and degrading general capabilities. Retrieval-augmented generation avoids such parameter drift, yet often lacks the depth of parametric knowledge integration. In this paper, we propose ReGrad (Retrievable Gradients), a new paradigm that treats gradients as retrievable units of knowledge. ReGrad pre-computes document-specific gradients offline, stores them in an indexed Gradient Bank, and retrieves only query-relevant gradients at inference time for temporary weight adaptation. However, raw language-modeling gradients are optimized for token-level document reconstruction rather than for query-driven knowledge use. We therefore introduce a bi-level meta-learning objective that reshapes document-derived gradients into generalizable adaptation signals for downstream tasks. Experiments across general and domain-specific settings show that ReGrad outperforms CPT and RAG baselines, enabling scalable and reversible parametric knowledge injection without accumulating weight drift.

Online updating of time series forecasting models aims to address the concept drifting problem by efficiently updating forecasting models based on streaming data. Many algorithms are designed for online time series forecasting, with some exploiting cross-variable dependency while others assume independence among variables. Given every data assumption has its own pros and cons in online time series modeling, we propose Online ensembling Network (OneNet). It dynamically updates and combines two models, with one focusing on modeling the dependency across the time dimension and the other on cross-variate dependency. Our method incorporates a reinforcement learning-based approach into the traditional online convex programming framework, allowing for the linear combination of the two models with dynamically adjusted weights. OneNet addresses the main shortcoming of classical online learning methods that tend to be slow in adapting to the concept drift. Empirical results show that OneNet reduces online forecasting error by more than 50% compared to the State-Of-The-Art (SOTA) method. The code is available at https://github.com/yfzhang114/OneNet.

Accurate modeling is crucial in many engineering and scientific applications, yet obtaining a reliable process model for complex systems is often challenging. To address this challenge, we propose a novel framework, reservoir computing with unscented Kalman filtering (RCUKF), which integrates data-driven modeling via reservoir computing (RC) with Bayesian estimation through the unscented Kalman filter (UKF). The RC component learns the nonlinear system dynamics directly from data, serving as a surrogate process model in the UKF prediction step to generate state estimates in high-dimensional or chaotic regimes where nominal mathematical models may fail. Meanwhile, the UKF measurement update integrates real-time sensor data to correct potential drift in the data-driven model. We demonstrate RCUKF effectiveness on well-known benchmark problems and a real-time vehicle trajectory estimation task in a high-fidelity simulation environment.

With the rapid development of speech generation technology, discrete codec representations have been widely used because they provide a stable prediction paradigm. In expressive speech generation, however, the quantization bottleneck of discrete codecs results in information gaps in fine-grained prosody, timbre, pronunciation, and frame-to-frame continuity. Continuous representations (e.g., VAE latents), by eliminating this constraint, have emerged as a more effective alternative for autoregressive modeling. Yet when continuous representations are used as autoregressive prediction targets, prediction errors can accumulate along the generation chain, causing latent drift and degrading long-form stability. To mitigate this problem, we propose SphereVAE, which constrains the VAE latent space to the unit hypersphere. SphereVAE defines a Power Spherical posterior on the hypersphere and regularizes the latent distribution toward a uniform prior, so that information is encoded mainly by directional variation, providing a bounded geometric target for autoregressive prediction and reducing the risk of norm drift. SphereVAE underperforms the standard VAE on reconstruction metrics due to reduced latent freedom. However, when integrated into VoxCPM for zero-shot TTS and long-text generation, it yields lower content error rates with comparable speaker similarity, and shows more stable long-range speaker consistency. These results indicate that an appropriate latent geometric constraint can effectively mitigate autoregressive error accumulation and drift in speech generation.

Reasoning from sequences of raw sensory data is a ubiquitous problem across fields ranging from medical devices to robotics. These problems often involve using long sequences of raw sensor data (e.g. magnetometers, piezoresistors) to predict sequences of desirable physical quantities (e.g. force, inertial measurements). While classical approaches are powerful for locally-linear prediction problems, they often fall short when using real-world sensors. These sensors are typically non-linear, are affected by extraneous variables (e.g. vibration), and exhibit data-dependent drift. For many problems, the prediction task is exacerbated by small labeled datasets since obtaining ground-truth labels requires expensive equipment. In this work, we present Hierarchical State-Space Models (HiSS), a conceptually simple, new technique for continuous sequential prediction. HiSS stacks structured state-space models on top of each other to create a temporal hierarchy. Across six real-world sensor datasets, from tactile-based state prediction to accelerometer-based inertial measurement, HiSS outperforms state-of-the-art sequence models such as causal Transformers, LSTMs, S4, and Mamba by at least 23% on MSE. Our experiments further indicate that HiSS demonstrates efficient scaling to smaller datasets and is compatible with existing data-filtering techniques. Code, datasets and videos can be found on https://hiss-csp.github.io.

Reduced-order modeling (ROM) of time-dependent and parameterized differential equations aims to accelerate the simulation of complex high-dimensional systems by learning a compact latent manifold representation that captures the characteristics of the solution fields and their time-dependent dynamics. Although high-fidelity numerical solvers generate the training datasets, they have thus far been excluded from the training process, causing the learned latent dynamics to drift away from the discretized governing physics. This mismatch often limits generalization and forecasting capabilities. In this work, we propose Physics-informed ROM (Φ-ROM) by incorporating differentiable PDE solvers into the training procedure. Specifically, the latent space dynamics and its dependence on PDE parameters are shaped directly by the governing physics encoded in the solver, ensuring a strong correspondence between the full and reduced systems. Our model outperforms state-of-the-art data-driven ROMs and other physics-informed strategies by accurately generalizing to new dynamics arising from unseen parameters, enabling long-term forecasting beyond the training horizon, maintaining continuity in both time and space, and reducing the data cost. Furthermore, Φ-ROM learns to recover and forecast the solution fields even when trained or evaluated with sparse and irregular observations of the fields, providing a flexible framework for field reconstruction and data assimilation. We demonstrate the framework's robustness across various PDE solvers and highlight its broad applicability by providing an open-source JAX implementation that is readily extensible to other PDE systems and differentiable solvers, available at https://phi-rom.github.io.

Credit risk modeling relies extensively on Weight of Evidence (WoE) and Information Value (IV) for feature engineering, and Population Stability Index (PSI) for drift monitoring, yet their theoretical foundations remain disconnected. We establish a unified information-theoretic framework revealing these industry-standard metrics as instances of classical information divergences. Specifically, we prove that IV exactly equals PSI (Jeffreys divergence) computed between good and bad credit outcomes over identical bins. Through the delta method applied to WoE transformations, we derive standard errors for IV and PSI, enabling formal hypothesis testing and probabilistic fairness constraints for the first time. We formalize credit modeling's inherent performance-fairness trade-off as maximizing IV for predictive power while minimizing IV for protected attributes. Using automated binning with depth-1 XGBoost stumps, we compare three encoding strategies: logistic regression with one-hot encoding, WoE transformation, and constrained XGBoost. All methods achieve comparable predictive performance (AUC 0.82-0.84), demonstrating that principled, information-theoretic binning outweighs encoding choice. Mixed-integer programming traces Pareto-efficient solutions along the performance-fairness frontier with uncertainty quantification. This framework bridges theory and practice, providing the first rigorous statistical foundation for widely-used credit risk metrics while offering principled tools for balancing accuracy and fairness in regulated environments.

Evolving borrower behaviors, shifting economic conditions, and changing regulatory landscapes continuously reshape the data distributions underlying modern credit-scoring systems. Conventional explainability techniques, such as SHAP, assume static data and fixed background distributions, making their explanations unstable and potentially unfair when concept drift occurs. This study addresses that challenge by developing adaptive explanation frameworks that recalibrate interpretability and fairness in dynamically evolving credit models. Using a multi-year credit dataset, we integrate predictive modeling via XGBoost with three adaptive SHAP variants: (A) per-slice explanation reweighting that adjusts for feature distribution shifts, (B) drift-aware SHAP rebaselining with sliding-window background samples, and (C) online surrogate calibration using incremental Ridge regression. Each method is benchmarked against static SHAP explanations using metrics of predictive performance (AUC, F1), directional and rank stability (cosine, Kendall tau), and fairness (demographic parity and recalibration). Results show that adaptive methods, particularly rebaselined and surrogate-based explanations, substantially improve temporal stability and reduce disparate impact across demographic groups without degrading predictive accuracy. Robustness tests, including counterfactual perturbations, background sensitivity analysis, and proxy-variable detection, confirm the resilience of adaptive explanations under real-world drift conditions. These findings establish adaptive explainability as a practical mechanism for sustaining transparency, accountability, and ethical reliability in data-driven credit systems, and more broadly, in any domain where decision models evolve with population change.

Pose-Free Feed-forward 3D Gaussian Splatting (3DGS) has recently emerged as a powerful paradigm for fast scene reconstruction. However, its performance degrades significantly in long image sequences due to cumulative camera pose estimation drift, which propagates errors into geometric modeling and severely limits rendering fidelity. In this work, we revisit the long-sequence bottleneck and identify pose drift as the primary factor restricting reconstruction quality. Furthermore, while SfM-based pseudo ground-truth poses introduce sensor noise, purely rendering-based supervision often leads to optimization instability and local minima due to the entangled optimization of geometry and pose. To address the challenges, we propose a synergistic pose-free framework that explicitly couples geometry and appearance via a Raymap-Guided Coupling Module (RGC). Concretely, we anchor Gaussian centers to raymap-induced geometry and jointly optimize RGB reconstruction, raymap consistency, and camera regularization under a unified objective, yielding a bidirectional feedback loop: stronger geometry improves rendering, and appearance supervision in turn refines geometry and pose. To further stabilize learning across wide temporal ranges, we introduce a Dual-Frequency Viewpoint Scheduling strategy that combines easy-to-hard interval expansion with replay of short-interval pairs. Extensive experiments across in-domain and cross-domain datasets show consistent gains in both rendering and pose estimation, with notably improved robustness on long sequences. Ablation studies validate our central insight: explicitly designed geometry-appearance synergy is the key to scalable and drift-robust pose-free feed-forward 3D reconstruction.

Modern generative models typically rely on an adversarial critic, a prescribed noise-to-data path, or an autoregressive factorization. Instead, we show that a proper distributional energy can induce sample-level motion and provide direct regression supervision for a one-step generator. Three-Body Scattering Modeling (TBSM) for generation turns the energy distance into a constant-size per-projectile interaction: each projectile is attracted toward one real source and repelled from one independently generated source. Conditioned on the projectile and its condition, its expectation equals the 2-Wasserstein gradient-flow velocity of frac12D_E^2(P_θ,Q). A batch of B frozen-target events yields O(B) sample-level losses, each using one reference for its condition instead of the minibatch-wide all-pairs field used by methods such as Drifting Models. Tracking this conditional expectation online can reduce field noise. Using scattering in frozen image features, TBSM trains one-step generators on ImageNet-256, achieving FID{}=2.23 with pixel-space PixelDiT-XL and FID{}=1.63 with latent-space DiT-XL at NFE{}=1. We provide a design map relating diffusion-related supervision, Drift-like dynamics, and GAN-like objectives. These results establish tracked scattering as a route to high-dimensional one-step generation. Code: https://github.com/sp12138/TBSM.

Explorable image-to-scene generation is essential for applications in gaming, robotics, and virtual reality. Existing methods based on video diffusion model (VDM) commonly rely on incomplete conditioning signals such as sparse point clouds or 2D panoramas, leading to stochastic hallucinations, long-term drifts and suboptimal 3D consistency. We present SpatialCrafter, a novel two-stage framework that addresses these issues by introducing a global 3D proxy for high-fidelity image-to-scene generation. Specifically, we decompose the generation process into global proxy generation and appearance refinement. For proxy generation, we propose a Point-anchored Sparse Structure~(PaSS) Flow module that predicts a spatially aligned and geometrically consistent 3D proxy. For appearance refinement, we re-frame the VDM as a Generative Deferred Refiner which synthesizes high-frequency photorealistic details upon proxy-defined scene geometry. To better integrate the proxy with the pre-trained VDM, we introduce Parallel Geometry Injection and Proxy-Aware Corruption training strategies, which improve robustness to proxy artifacts without disrupting the pretrained generative manifold. Furthermore, as no suitable dataset exists for this explorable scene generation task, we construct a new large-scale dataset of 115K scenes. To the best of our knowledge, it is the first hybrid dataset for image-to-scene generation. Extensive experiments on both synthetic and real-world datasets show that SpatialCrafter outperforms state-of-the-art methods, mitigates long-term drift, and remains robust and consistent under rapid camera motion and extreme viewpoint changes. Our project page: https://fangchuan.github.io/SpatialCrafter/{fangchuan.github.io/SpatialCrafter/}

The evolution of linguistic style in conversations is an underexplored issue in NLP. Most style-control datasets focus on sentences or assume a static style throughout, missing the dynamic shifts that occur as user preferences change during interactions. We introduce ConvoDrift, a dataset designed to model progressive stylistic conversational tone drift under fixed semantic intent. It is built on 15,727 shared multi-turn conversational structures for adaptation and persona-conditioned alignment methods. It consists of six prompt-response pairs per conversation, each with the annotation of style drift and style direction labels. These pairs cover a range of communication genres. We further derive a complementary pairwise dataset by pairing semantically equivalent but stylistically distinct responses and annotating persona-conditioned preferences using five distinct style communication personas, enabling the controlled study of personalisation and pluralistic alignment in language tone. In addition to dataset construction, we conduct a comprehensive evaluation involving human validation, LLM-as-judge assessment, and automatic lexical and semantic evaluations. Across seven Likert criteria annotated by three human annotators, the average Krippendorff's alpha is 0.88, and our lexical and semantic analyses show that drift events induce lexical changes while preserving semantic similarity.

Closed-loop human-AI systems generate high-dimensional behavioural trajectories whose collective dynamics remain obscure. Using 297,915 learners' adaptive-tutoring histories, we define semantic order variables before model fitting and test them in user-disjoint cohorts. The state exhibits reproducible basin-like flow and operationally defined, state-heterogeneous metastable-like kinetics. A construction-matched null distinguishes normalised-memory relaxation from a reproducible excess field. A four-term conditional mechanism recovers population drift (r = 0.946; learner-bootstrap 95% CI, 0.935-0.955). Predictive event-level self-supervised learning recovers the state and learned-plane flow; null-referenced corrections retain directional, partial-amplitude excess-field structure without full calibration. Shuffled-order training reverses learned-plane flow on ordered trajectories; support-alignment randomisation selectively reduces inward transport. Both axes remain linearly accessible without state supervision. Without cross-model fitting, the models share leading population drift (r = 0.866; learner-bootstrap 95% CI, 0.857-0.875) and persistence ordering; residual directions remain model-specific. These results identify an externally anchored leading-order effective field linking empirical dynamics, an interpretable mechanism and neural computation.

Autonomous driving requires reasoning about how the environment evolves and planning actions accordingly. Existing world-model-based approaches typically predict future scenes first and plan afterwards, resulting in open-loop imagination that may drift from the actual decision process. In this paper, we present Uni-World VLA, a unified vision-language-action (VLA) model that tightly interleaves future frame prediction and trajectory planning. Instead of generating a full world rollout before planning, our model alternates between predicting future frames and ego actions step by step, allowing planning decisions to be continuously conditioned on the imagined future observations. This interleaved generation forms a closed-loop interaction between world modeling and control, enabling more adaptive decision-making in dynamic traffic scenarios. In addition, we incorporate monocular depth information into frames to provide stronger geometric cues for world modeling, improving long-horizon scene prediction. Experiments on the NAVSIM benchmark show that our approach achieves competitive closed-loop planning performance while producing high-fidelity future frame predictions. These results demonstrate that tightly coupling world prediction and planning is a promising direction for scalable VLA driving systems.

This monograph presents the core principles that have guided the development of diffusion models, tracing their origins and showing how diverse formulations arise from shared mathematical ideas. Diffusion modeling starts by defining a forward process that gradually corrupts data into noise, linking the data distribution to a simple prior through a continuum of intermediate distributions. The goal is to learn a reverse process that transforms noise back into data while recovering the same intermediates. We describe three complementary views. The variational view, inspired by variational autoencoders, sees diffusion as learning to remove noise step by step. The score-based view, rooted in energy-based modeling, learns the gradient of the evolving data distribution, indicating how to nudge samples toward more likely regions. The flow-based view, related to normalizing flows, treats generation as following a smooth path that moves samples from noise to data under a learned velocity field. These perspectives share a common backbone: a time-dependent velocity field whose flow transports a simple prior to the data. Sampling then amounts to solving a differential equation that evolves noise into data along a continuous trajectory. On this foundation, the monograph discusses guidance for controllable generation, efficient numerical solvers, and diffusion-motivated flow-map models that learn direct mappings between arbitrary times. It provides a conceptual and mathematically grounded understanding of diffusion models for readers with basic deep-learning knowledge.

This paper presents WorldPlay, a streaming video diffusion model that enables real-time, interactive world modeling with long-term geometric consistency, resolving the trade-off between speed and memory that limits current methods. WorldPlay draws power from three key innovations. 1) We use a Dual Action Representation to enable robust action control in response to the user's keyboard and mouse inputs. 2) To enforce long-term consistency, our Reconstituted Context Memory dynamically rebuilds context from past frames and uses temporal reframing to keep geometrically important but long-past frames accessible, effectively alleviating memory attenuation. 3) We also propose Context Forcing, a novel distillation method designed for memory-aware model. Aligning memory context between the teacher and student preserves the student's capacity to use long-range information, enabling real-time speeds while preventing error drift. Taken together, WorldPlay generates long-horizon streaming 720p video at 24 FPS with superior consistency, comparing favorably with existing techniques and showing strong generalization across diverse scenes. Project page and online demo can be found: https://3d-models.hunyuan.tencent.com/world/ and https://3d.hunyuan.tencent.com/sceneTo3D.

LLM agents increasingly operate through multi-turn tool use and environment interaction, where safety risks often emerge from intermediate steps long before they surface in the final outcome. Reactive auditing is therefore insufficient: post-hoc diagnosis frequently misses the chance to flag risks while they are unfolding. We propose TRACES, a representation-based proactive auditor that learns prefix-level trajectory risk states from the hidden representations of an observer LLM. TRACES induces latent mechanism features from step representations and models their temporal evolution to estimate whether a partial trajectory is drifting toward unsafe behavior. To sidestep the cost and ambiguity of step-level risk annotation, TRACES is trained with weak trajectory-level supervision while still producing dense prefix-level risk estimates. Across multiple agent safety benchmarks, TRACES improves both full-trajectory safety prediction and proactive risk discrimination. Our analyses further suggest that these risk states can help train a safer agent, highlighting the broader potential of proactive auditing for long-horizon agent safety.

Score-based diffusion models generate samples from an unknown target distribution using a time-reversed diffusion process. While such models represent state-of-the-art approaches in industrial applications such as artificial image generation, it has recently been noted that their performance can be further improved by considering injection noise with heavy tailed characteristics. Here, I present a generalization of generative diffusion processes to a wide class of non-Gaussian noise processes. I consider forward processes driven by standard Gaussian noise with super-imposed Poisson jumps representing a finite activity Levy process. The generative process is shown to be governed by a generalized score function that depends on the jump amplitude distribution and can be estimated by minimizing a simple MSE loss as in conventional Gaussian models. Both probability flow ODE and SDE formulations are derived using basic technical effort. A detailed implementation for a pure jump process with Laplace distributed amplitudes yields a generalized score function in closed analytical form and is shown to outperform the equivalent Gaussian model in specific parameter regimes.

Score-based diffusion models are a class of generative models whose dynamics is described by stochastic differential equations that map noise into data. While recent works have started to lay down a theoretical foundation for these models, an analytical understanding of the role of the diffusion time T is still lacking. Current best practice advocates for a large T to ensure that the forward dynamics brings the diffusion sufficiently close to a known and simple noise distribution; however, a smaller value of T should be preferred for a better approximation of the score-matching objective and higher computational efficiency. Starting from a variational interpretation of diffusion models, in this work we quantify this trade-off, and suggest a new method to improve quality and efficiency of both training and sampling, by adopting smaller diffusion times. Indeed, we show how an auxiliary model can be used to bridge the gap between the ideal and the simulated forward dynamics, followed by a standard reverse diffusion process. Empirical results support our analysis; for image data, our method is competitive w.r.t. the state-of-the-art, according to standard sample quality metrics and log-likelihood.

Diffusion models are a class of generative models that learn to synthesize samples by inverting a diffusion process that gradually maps data into noise. While these models have enjoyed great success recently, a full theoretical understanding of their observed properties is still lacking, in particular, their weak sensitivity to the choice of noise family and the role of adequate scheduling of noise levels for good synthesis. By identifying a correspondence between diffusion models and a well-known paradigm in cognitive science known as serial reproduction, whereby human agents iteratively observe and reproduce stimuli from memory, we show how the aforementioned properties of diffusion models can be explained as a natural consequence of this correspondence. We then complement our theoretical analysis with simulations that exhibit these key features. Our work highlights how classic paradigms in cognitive science can shed light on state-of-the-art machine learning problems.

Image generation models now produce high-quality static images, yet their ability to represent how a visual world changes over time remains poorly understood. Practical workflows such as storyboarding, step-by-step illustration, reference-guided editing, and video previsualization require models to preserve identities, objects, spatial relations, and causal order across multiple visual states. Existing evaluations largely measure single-image correctness, compositional alignment, or video quality, leaving open whether an image model can coherently imagine a temporally ordered process. We introduce ImageTime, a diagnostic benchmark that uses spatiotemporal consistency as a behavioral probe of visual world modeling in image generation. Given an action instruction, and optionally a reference image specifying the initial state, a model must generate one image containing four ordered key states: initial state, action onset, transition state, and final state. This four-keyframe protocol is more temporally demanding than single-image generation while avoiding the confounds of dense video dynamics. ImageTime organizes tasks with a progressive capability hierarchy and decomposes each scenario into stage-wise state predicates, cross-frame temporal constraints, and forbidden causal violations. GPT-5.5 scores all generated images under a structured VLM-as-judge protocol, producing interpretable capability scores, diagnostic subscores, and failure labels. Through multi-family benchmarking, ImageTime reveals where current image generation systems succeed, fail, and drift when asked to maintain coherent visual world states over time.

Consistency models (CMs) offer faster sampling than traditional diffusion models, but their training is resource-intensive. For example, as of 2024, training a state-of-the-art CM on CIFAR-10 takes one week on 8 GPUs. In this work, we propose an effective scheme for training CMs that largely improves the efficiency of building such models. Specifically, by expressing CM trajectories via a particular differential equation, we argue that diffusion models can be viewed as a special case of CMs. We can thus fine-tune a consistency model starting from a pretrained diffusion model and progressively approximate the full consistency condition to stronger degrees over the training process. Our resulting method, which we term Easy Consistency Tuning (ECT), achieves vastly reduced training times while improving upon the quality of previous methods: for example, ECT achieves a 2-step FID of 2.73 on CIFAR10 within 1 hour on a single A100 GPU, matching Consistency Distillation trained for hundreds of GPU hours. Owing to this computational efficiency, we investigate the scaling laws of CMs under ECT, showing that they obey the classic power law scaling, hinting at their ability to improve efficiency and performance at larger scales. Our code (https://github.com/locuslab/ect) is publicly available, making CMs more accessible to the broader community.

Process analytics is an umbrella of data-driven techniques which includes making predictions for individual process instances or overall process models. At the instance level, various novel techniques have been recently devised, tackling next activity, remaining time, and outcome prediction. At the model level, there is a notable void. It is the ambition of this paper to fill this gap. To this end, we develop a technique to forecast the entire process model from historical event data. A forecasted model is a will-be process model representing a probable future state of the overall process. Such a forecast helps to investigate the consequences of drift and emerging bottlenecks. Our technique builds on a representation of event data as multiple time series, each capturing the evolution of a behavioural aspect of the process model, such that corresponding forecasting techniques can be applied. Our implementation demonstrates the accuracy of our technique on real-world event log data.

Diffusion models have achieved state-of-the-art performance in generative modeling tasks across various domains. Prior works on time series diffusion models have primarily focused on developing conditional models tailored to specific forecasting or imputation tasks. In this work, we explore the potential of task-agnostic, unconditional diffusion models for several time series applications. We propose TSDiff, an unconditionally trained diffusion model for time series. Our proposed self-guidance mechanism enables conditioning TSDiff for downstream tasks during inference, without requiring auxiliary networks or altering the training procedure. We demonstrate the effectiveness of our method on three different time series tasks: forecasting, refinement, and synthetic data generation. First, we show that TSDiff is competitive with several task-specific conditional forecasting methods (predict). Second, we leverage the learned implicit probability density of TSDiff to iteratively refine the predictions of base forecasters with reduced computational overhead over reverse diffusion (refine). Notably, the generative performance of the model remains intact -- downstream forecasters trained on synthetic samples from TSDiff outperform forecasters that are trained on samples from other state-of-the-art generative time series models, occasionally even outperforming models trained on real data (synthesize).

Risk decision systems in fraud detection and credit scoring operate under structural label absence: ground truth arrives weeks to months after decisions are made. During this blind period, model performance may degrade silently, eroding the governance evidence that justifies automated decisions. Existing drift detection methods either require labels (supervised detectors) or detect statistical change without distinguishing harmful degradation from benign distributional evolution (unsupervised detectors). No existing framework integrates drift detection with governance evidence assessment and operational response. This paper presents a label-free governance monitoring extension to the Governance Drift Toolkit that produces governance alerts rather than statistical alarms. The monitoring architecture applies composite multi-proxy monitoring across four proxy monitors (score distribution, feature drift, prediction entropy, confidence distribution), with governance-calibrated thresholds. Empirical evaluation on the Lending Club credit scoring dataset (1.37M loans, 11 years) demonstrates three findings. First, raw proxy metrics (Feature PSI delta up to 1.84, Score PSI delta up to 0.92) distinguish injected covariate degradation from natural temporal drift in an offline evaluation setting. Second, pure concept drift in P(Y|X) produces exactly zero delta across all proxy metrics in all windows, confirming the irreducible blind spot of label-free monitoring as a structural verification. Third, the composite score provides monotonic severity progression as more monitors trigger (0.583 to 0.833 to 1.000), enabling graduated governance response. Cross-domain comparison with IEEE-CIS fraud detection results shows the detectable/undetectable boundary is consistent across both domains. The toolkit and evaluation code are available as open-source artifacts.

Learning the tail behavior of a distribution is a notoriously difficult problem. By definition, the number of samples from the tail is small, and deep generative models, such as normalizing flows, tend to concentrate on learning the body of the distribution. In this paper, we focus on improving the ability of normalizing flows to correctly capture the tail behavior and, thus, form more accurate models. We prove that the marginal tailedness of an autoregressive flow can be controlled via the tailedness of the marginals of its base distribution. This theoretical insight leads us to a novel type of flows based on flexible base distributions and data-driven linear layers. An empirical analysis shows that the proposed method improves on the accuracy -- especially on the tails of the distribution -- and is able to generate heavy-tailed data. We demonstrate its application on a weather and climate example, in which capturing the tail behavior is essential.

Drifting Models generate a sample with a single function evaluation, making them attractive for fast parallel language generation, but their one-step formulation does not support iterative refinement. We propose Recurrent Language Generation via Drifting (ReLaDrift), which uses a shared Drifting Model to generate an initial draft from noise and iteratively refine it in a continuous latent space. We train this recurrence by sampling the number of rounds and applying the drifting loss only at the final round, stopping gradients through preceding rounds so that only one round requires backpropagation. Unlike the one-step Drifting Model, whose accuracy does not improve when iterated, ReLaDrift enables a trade-off between test-time computation and generation quality, as diffusion and flow language models do. On Sudoku Hard and GSM8K, it achieves competitive or superior performance compared with these iterative-generation approaches across a range of inference budgets. Our code is available at https://github.com/Yuki-Ots/ReLaDrift

Irregularly sampled time series data arise naturally in many application domains including biology, ecology, climate science, astronomy, and health. Such data represent fundamental challenges to many classical models from machine learning and statistics due to the presence of non-uniform intervals between observations. However, there has been significant progress within the machine learning community over the last decade on developing specialized models and architectures for learning from irregularly sampled univariate and multivariate time series data. In this survey, we first describe several axes along which approaches to learning from irregularly sampled time series differ including what data representations they are based on, what modeling primitives they leverage to deal with the fundamental problem of irregular sampling, and what inference tasks they are designed to perform. We then survey the recent literature organized primarily along the axis of modeling primitives. We describe approaches based on temporal discretization, interpolation, recurrence, attention and structural invariance. We discuss similarities and differences between approaches and highlight primary strengths and weaknesses.

We introduce a new family of physics-inspired generative models termed PFGM++ that unifies diffusion models and Poisson Flow Generative Models (PFGM). These models realize generative trajectories for N dimensional data by embedding paths in N{+}D dimensional space while still controlling the progression with a simple scalar norm of the D additional variables. The new models reduce to PFGM when D{=}1 and to diffusion models when D{to}infty. The flexibility of choosing D allows us to trade off robustness against rigidity as increasing D results in more concentrated coupling between the data and the additional variable norms. We dispense with the biased large batch field targets used in PFGM and instead provide an unbiased perturbation-based objective similar to diffusion models. To explore different choices of D, we provide a direct alignment method for transferring well-tuned hyperparameters from diffusion models (D{to} infty) to any finite D values. Our experiments show that models with finite D can be superior to previous state-of-the-art diffusion models on CIFAR-10/FFHQ 64{times}64 datasets, with FID scores of 1.91/2.43 when D{=}2048/128. In class-conditional setting, D{=}2048 yields current state-of-the-art FID of 1.74 on CIFAR-10. In addition, we demonstrate that models with smaller D exhibit improved robustness against modeling errors. Code is available at https://github.com/Newbeeer/pfgmpp

Mixed-precision post-training quantization needs a per-module sensitivity signal; for a text embedder the obvious one -- the retrieval quality a module costs when quantized -- needs relevance labels that deployments rarely have. We measure a label-free substitute: quantization-induced representation drift, obtained by quantizing one module, re-encoding the corpus, and recording how far the output embeddings moved from their full-precision positions. What is specific is the observable: the deployed output representation a dense retriever ranks with. Across five development embedders, configuration-level drift orders sampled mixed-precision plans against held-out retrieval quality at a macro Spearman of 0.911, the sensitivity transports across calibration corpora and retrieval domains in the usable regime, module drifts compose rank-consistently but not numerically, and relevance-derived sensitivity adds no consistent value. The method is one additive allocation under a hard packed-byte budget, with no labels and no search. On three embedders held untouched until method, baselines and hypotheses were frozen and sealed, the pre-registered directional hypothesis against the prior LieQ criterion holds (3/3 at the main budget, no collapse) and drift scores above a two-sided LieQ steelman in 2/3; but at the main budget drift is numerically lower than same-budget uniform precision on all three (-0.99, -0.85, -1.01 points), having reduced module and whole-model drift as designed. Output drift is thus a robust coarse sensitivity signal, not a universally optimal allocation objective: it avoids the catastrophic failures of the transferred signed-geometry adaptation and can remain usable at stressed budgets where uniform collapses, but fine-grained redistribution around a strong uniform operating point remains unresolved.

Automated Machine Learning (AutoML) systems have been shown to efficiently build good models for new datasets. However, it is often not clear how well they can adapt when the data evolves over time. The main goal of this study is to understand the effect of data stream challenges such as concept drift on the performance of AutoML methods, and which adaptation strategies can be employed to make them more robust. To that end, we propose 6 concept drift adaptation strategies and evaluate their effectiveness on different AutoML approaches. We do this for a variety of AutoML approaches for building machine learning pipelines, including those that leverage Bayesian optimization, genetic programming, and random search with automated stacking. These are evaluated empirically on real-world and synthetic data streams with different types of concept drift. Based on this analysis, we propose ways to develop more sophisticated and robust AutoML techniques.

Catastrophic forgetting remains a central obstacle for continual learning in neural models. Popular approaches -- replay and elastic weight consolidation (EWC) -- have limitations: replay requires a strong generator and is prone to distributional drift, while EWC implicitly assumes a shared optimum across tasks and typically uses a diagonal Fisher approximation. In this work, we study the gradient geometry of diffusion models, which can already produce high-quality replay data. We provide theoretical and empirical evidence that, in the low signal-to-noise ratio (SNR) regime, per-sample gradients become strongly collinear, yielding an empirical Fisher that is effectively rank-1 and aligned with the mean gradient. Leveraging this structure, we propose a rank-1 variant of EWC that is as cheap as the diagonal approximation yet captures the dominant curvature direction. We pair this penalty with a replay-based approach to encourage parameter sharing across tasks while mitigating drift. On class-incremental image generation datasets (MNIST, FashionMNIST, CIFAR-10, ImageNet-1k), our method consistently improves average FID and reduces forgetting relative to replay-only and diagonal-EWC baselines. In particular, forgetting is nearly eliminated on MNIST and FashionMNIST and is more than halved on ImageNet-1k. These results suggest that diffusion models admit an approximately rank-1 Fisher. With a better Fisher estimate, EWC becomes a strong complement to replay: replay encourages parameter sharing across tasks, while EWC effectively constrains replay-induced drift.

Consistency models have been proposed for fast generative modeling, achieving results competitive with diffusion and flow models. However, these methods exhibit inherent instability and limited reproducibility when training from scratch, motivating subsequent work to explain and stabilize these issues. While these efforts have provided valuable insights, the explanations remain fragmented, and the theoretical relationships remain unclear. In this work, we provide a theoretical examination of consistency models by analyzing them from a flow map-based perspective. This joint analysis clarifies how training stability and convergence behavior can give rise to degenerate solutions. Building on these insights, we revisit self-distillation as a practical remedy for certain forms of suboptimal convergence and reformulate it to avoid excessive gradient norms for stable optimization. We further demonstrate that our strategy extends beyond image generation to diffusion-based policy learning, without reliance on a pretrained diffusion model for initialization, thereby illustrating its broader applicability.

The integration of extensive, dynamic knowledge into Large Language Models (LLMs) remains a significant challenge due to the inherent entanglement of factual data and reasoning patterns. Existing solutions, ranging from non-parametric Retrieval-Augmented Generation (RAG) to parametric knowledge editing, are often constrained in practice by finite context windows, retriever noise, or the risk of catastrophic forgetting. In this paper, we propose DRIFT, a novel dual-model architecture designed to explicitly decouple knowledge extraction from the reasoning process. Unlike static prompt compression, DRIFT employs a lightweight knowledge model to dynamically compress document chunks into implicit fact tokens conditioned on the query. These dense representations are projected into the reasoning model's embedding space, replacing raw, redundant text while maintaining inference accuracy. Extensive experiments show that DRIFT significantly improves performance on long-context tasks, outperforming strong baselines among comparably sized models. Our approach provides a scalable and efficient paradigm for extending the effective context window and reasoning capabilities of LLMs. Our code is available at https://github.com/Lancelot-Xie/DRIFT.

While diffusion models can successfully generate data and make predictions, they are predominantly designed for static images. We propose an approach for efficiently training diffusion models for probabilistic spatiotemporal forecasting, where generating stable and accurate rollout forecasts remains challenging, Our method, DYffusion, leverages the temporal dynamics in the data, directly coupling it with the diffusion steps in the model. We train a stochastic, time-conditioned interpolator and a forecaster network that mimic the forward and reverse processes of standard diffusion models, respectively. DYffusion naturally facilitates multi-step and long-range forecasting, allowing for highly flexible, continuous-time sampling trajectories and the ability to trade-off performance with accelerated sampling at inference time. In addition, the dynamics-informed diffusion process in DYffusion imposes a strong inductive bias and significantly improves computational efficiency compared to traditional Gaussian noise-based diffusion models. Our approach performs competitively on probabilistic forecasting of complex dynamics in sea surface temperatures, Navier-Stokes flows, and spring mesh systems.

Temporal point processes are the dominant paradigm for modeling sequences of events happening at irregular intervals. The standard way of learning in such models is by estimating the conditional intensity function. However, parameterizing the intensity function usually incurs several trade-offs. We show how to overcome the limitations of intensity-based approaches by directly modeling the conditional distribution of inter-event times. We draw on the literature on normalizing flows to design models that are flexible and efficient. We additionally propose a simple mixture model that matches the flexibility of flow-based models, but also permits sampling and computing moments in closed form. The proposed models achieve state-of-the-art performance in standard prediction tasks and are suitable for novel applications, such as learning sequence embeddings and imputing missing data.

The objective of this study is to evaluate the potential for History Matching (HM) to tune a climate system with multi-scale dynamics. By considering a toy climate model, namely, the two-scale Lorenz96 model and producing experiments in perfect-model setting, we explore in detail how several built-in choices need to be carefully tested. We also demonstrate the importance of introducing physical expertise in the range of parameters, a priori to running HM. Finally we revisit a classical procedure in climate model tuning, that consists of tuning the slow and fast components separately. By doing so in the Lorenz96 model, we illustrate the non-uniqueness of plausible parameters and highlight the specificity of metrics emerging from the coupling. This paper contributes also to bridging the communities of uncertainty quantification, machine learning and climate modeling, by making connections between the terms used by each community for the same concept and presenting promising collaboration avenues that would benefit climate modeling research.

This survey delves into the application of diffusion models in time-series forecasting. Diffusion models are demonstrating state-of-the-art results in various fields of generative AI. The paper includes comprehensive background information on diffusion models, detailing their conditioning methods and reviewing their use in time-series forecasting. The analysis covers 11 specific time-series implementations, the intuition and theory behind them, the effectiveness on different datasets, and a comparison among each other. Key contributions of this work are the thorough exploration of diffusion models' applications in time-series forecasting and a chronologically ordered overview of these models. Additionally, the paper offers an insightful discussion on the current state-of-the-art in this domain and outlines potential future research directions. This serves as a valuable resource for researchers in AI and time-series analysis, offering a clear view of the latest advancements and future potential of diffusion models.

Recent years have witnessed significant progress in developing efficient training and fast sampling approaches for diffusion models. A recent remarkable advancement is the use of stochastic differential equations (SDEs) to describe data perturbation and generative modeling in a unified mathematical framework. In this paper, we reveal several intriguing geometric structures of diffusion models and contribute a simple yet powerful interpretation to their sampling dynamics. Through carefully inspecting a popular variance-exploding SDE and its marginal-preserving ordinary differential equation (ODE) for sampling, we discover that the data distribution and the noise distribution are smoothly connected with an explicit, quasi-linear sampling trajectory, and another implicit denoising trajectory, which even converges faster in terms of visual quality. We also establish a theoretical relationship between the optimal ODE-based sampling and the classic mean-shift (mode-seeking) algorithm, with which we can characterize the asymptotic behavior of diffusion models and identify the score deviation. These new geometric observations enable us to improve previous sampling algorithms, re-examine latent interpolation, as well as re-explain the working principles of distillation-based fast sampling techniques.

Generating continuous-time, continuous-space stochastic processes (e.g., videos, weather forecasts) conditioned on partial observations (e.g., first and last frames) is a fundamental challenge. Existing approaches, (e.g., diffusion models), suffer from key limitations: (1) noise-to-data evolution fails to capture structural similarity between states close in physical time and has unstable integration in low-step regimes; (2) random noise injected is insensitive to the physical process's time elapsed, resulting in incorrect dynamics; (3) they overlook conditioning on arbitrary subsets of states (e.g., irregularly sampled timesteps, future observations). We propose ABC: Any-Subset Autoregressive Models via Non-Markovian Diffusion Bridges in Continuous Time and Space. Crucially, we model the process with one continual SDE whose time variable and intermediate states track the real time and process states. This has provable advantages: (1) the starting point for generating future states is the already-close previous state, rather than uninformative noise; (2) random noise injection scales with physical time elapsed, encouraging physically plausible dynamics with similar time-adjacent states. We derive SDE dynamics via changes-of-measure on path space, yielding another advantage: (3) path-dependent conditioning on arbitrary subsets of the state history and/or future. To learn these dynamics, we derive a path- and time-dependent extension of denoising score matching. Our experiments show ABC's superiority to competing methods on multiple domains, including video generation and weather forecasting.

Reliable traffic data are essential for understanding urban mobility and developing effective traffic management strategies. This study introduces the DRone-derived Intelligence For Traffic analysis (DRIFT) dataset, a large-scale urban traffic dataset collected systematically from synchronized drone videos at approximately 250 meters altitude, covering nine interconnected intersections in Daejeon, South Korea. DRIFT provides high-resolution vehicle trajectories that include directional information, processed through video synchronization and orthomap alignment, resulting in a comprehensive dataset of 81,699 vehicle trajectories. Through our DRIFT dataset, researchers can simultaneously analyze traffic at multiple scales - from individual vehicle maneuvers like lane-changes and safety metrics such as time-to-collision to aggregate network flow dynamics across interconnected urban intersections. The DRIFT dataset is structured to enable immediate use without additional preprocessing, complemented by open-source models for object detection and trajectory extraction, as well as associated analytical tools. DRIFT is expected to significantly contribute to academic research and practical applications, such as traffic flow analysis and simulation studies. The dataset and related resources are publicly accessible at https://github.com/AIxMobility/The-DRIFT.

Reward-based fine-tuning of diffusion models has largely inherited likelihood-based policy optimization developed for autoregressive large language models (LLMs). Diffusion models, however, are natively trained through velocity regression and do not directly provide the likelihood of a generated sample. Existing methods address this using transition likelihoods along stochastic denoising trajectories or evidence lower bounds (ELBOs) to approximate generated-sample likelihoods. These approximations arise from applying likelihood-based updates to models whose native training and generation operate through velocity fields. We instead take velocity matching as the starting point for reward fine-tuning. We propose reward-based velocity matching (RVM), which weights the velocity-matching loss by reward with an additional anchor regression term, requiring neither likelihood estimation nor likelihood ratios. RVM recovers Reinforce Adjoint Matching at the update level and contains DiffusionNFT as a special case, while ELBO-based methods are closely related through the same velocity-regression structure. This unified view isolates reward design and anchor velocity as principal design choices in velocity-based fine-tuning. Across text-to-image, text-to-video, and image-to-video generation, RVM matches or outperforms the evaluated trajectory-based methods. On Wan2.1-T2V-1.3B, it achieves the highest VBench Overall among the evaluated methods, with substantially lower estimated training costs than the trajectory-based approaches. For video fine-tuning, we introduce a dynamic-tracking reward that provides explicit motion feedback and improves both Dynamic Degree and overall VBench performance.

We introduce Diffusion World Model (DWM), a conditional diffusion model capable of predicting multistep future states and rewards concurrently. As opposed to traditional one-step dynamics models, DWM offers long-horizon predictions in a single forward pass, eliminating the need for recursive quires. We integrate DWM into model-based value estimation, where the short-term return is simulated by future trajectories sampled from DWM. In the context of offline reinforcement learning, DWM can be viewed as a conservative value regularization through generative modeling. Alternatively, it can be seen as a data source that enables offline Q-learning with synthetic data. Our experiments on the D4RL dataset confirm the robustness of DWM to long-horizon simulation. In terms of absolute performance, DWM significantly surpasses one-step dynamics models with a 44% performance gain, and achieves state-of-the-art performance.

We develop a framework for non-asymptotic analysis of deterministic samplers used for diffusion generative modeling. Several recent works have analyzed stochastic samplers using tools like Girsanov's theorem and a chain rule variant of the interpolation argument. Unfortunately, these techniques give vacuous bounds when applied to deterministic samplers. We give a new operational interpretation for deterministic sampling by showing that one step along the probability flow ODE can be expressed as two steps: 1) a restoration step that runs gradient ascent on the conditional log-likelihood at some infinitesimally previous time, and 2) a degradation step that runs the forward process using noise pointing back towards the current iterate. This perspective allows us to extend denoising diffusion implicit models to general, non-linear forward processes. We then develop the first polynomial convergence bounds for these samplers under mild conditions on the data distribution.

In recent years, generative pre-trained paradigms such as Large Language Models (LLMs) and Large Vision Models (LVMs) have achieved revolutionary advancements and widespread real-world applications. Particularly, the emergence of pre-trained LLMs-based temporal works, compared to previous deep model approaches, has demonstrated superior generalization and robustness, showcasing the potential of generative pre-trained paradigms as foundation models for time series. However, those LLMs-based works mainly focus on cross-modal research, i.e., leveraging the language capabilities of LLMs in time series contexts. Although they have achieved impressive performance, there still exist the issues of concept drift caused by differences in data distribution and inflexibility caused by misalignment of dimensions. To this end, inspired by recent work on LVMs, we reconsider the paradigm of time series modeling. In this paper, we comprehensively explore, for the first time, the effectiveness and superiority of the Generative Pre-trained Diffusion (GPD) paradigm in real-world multivariate time series forecasting (TSF). Specifically, to mitigate performance bias introduced by sophisticated networks, we propose a straightforward MLP diffusion network for unconditional modeling of time series. Then we employ a zero-shot and tuning-free method to predict (generate) future data using historical data as prompts. The GPD paradigm is established on the time series modality, effectively preventing the phenomenon of concept drift, and enabling flexible forecasting of arbitrary lengths. We demonstrate that the GPD paradigm achieves comprehensive performance and generalization comparable to current SOTA LLM-based and deep model paradigms on mainstream benchmarks and various TSF tasks. Extensive experiments validate the potential of the GPD paradigm and its assistance in future related research.

The friction coefficient of a particle can depend on its position as it does when the particle is near a wall. We formulate the dynamics of particles with such state-dependent friction coefficients in terms of a general Langevin equation with multiplicative noise, whose evaluation requires the introduction of specific rules. Two common conventions, the Ito and the Stratonovich, provide alternative rules for evaluation of the noise, but other conventions are possible. We show the requirement that a particle's distribution function approach the Boltzmann distribution at long times dictates that a drift term must be added to the Langevin equation. This drift term is proportional to the derivative of the diffusion coefficient times a factor that depends on the convention used to define the multiplicative noise. We explore the consequences of this result in a number examples with spatially varying diffusion coefficients. We also derive path integral representations for arbitrary interpretation of the noise, and use it in a perturbative study of correlations in a simple system.

We present a straightforward statistical test to detect certain violations of the assumption that the data are Independent and Identically Distributed (IID). The specific form of violation considered is common across real-world applications: whether the examples are ordered in the dataset such that almost adjacent examples tend to have more similar feature values (e.g. due to distributional drift, or attractive interactions between datapoints). Based on a k-Nearest Neighbors estimate, our approach can be used to audit any multivariate numeric data as well as other data types (image, text, audio, etc.) that can be numerically represented, perhaps with model embeddings. Compared with existing methods to detect drift or auto-correlation, our approach is both applicable to more types of data and also able to detect a wider variety of IID violations in practice. Code: https://github.com/cleanlab/cleanlab

Diffusion models are a class of probabilistic generative models that have been widely used as a prior for image processing tasks like text conditional generation and inpainting. We demonstrate that these models can be adapted to make predictions and provide uncertainty quantification for chaotic dynamical systems. In these applications, diffusion models can implicitly represent knowledge about outliers and extreme events; however, querying that knowledge through conditional sampling or measuring probabilities is surprisingly difficult. Existing methods for conditional sampling at inference time seek mainly to enforce the constraints, which is insufficient to match the statistics of the distribution or compute the probability of the chosen events. To achieve these ends, optimally one would use the conditional score function, but its computation is typically intractable. In this work, we develop a probabilistic approximation scheme for the conditional score function which provably converges to the true distribution as the noise level decreases. With this scheme we are able to sample conditionally on nonlinear userdefined events at inference time, and matches data statistics even when sampling from the tails of the distribution.

Coarse-guided visual generation, which synthesizes fine visual samples from degraded or low-fidelity coarse references, is essential for various real-world applications. While training-based approaches are effective, they are inherently limited by high training costs and restricted generalization due to paired data collection. Accordingly, recent training-free works propose to leverage pretrained diffusion models and incorporate guidance during the sampling process. However, these training-free methods either require knowing the forward (fine-to-coarse) transformation operator, e.g., bicubic downsampling, or are difficult to balance between guidance and synthetic quality. To address these challenges, we propose a novel guided method by using the h-transform, a tool that can constrain stochastic processes (e.g., sampling process) under desired conditions. Specifically, we modify the transition probability at each sampling timestep by adding to the original differential equation with a drift function, which approximately steers the generation toward the ideal fine sample. To address unavoidable approximation errors, we introduce a noise-level-aware schedule that gradually de-weights the term as the error increases, ensuring both guidance adherence and high-quality synthesis. Extensive experiments across diverse image and video generation tasks demonstrate the effectiveness and generalization of our method.

Large language model (LLM) post-training enhances latent skills, unlocks value alignment, improves performance, and enables domain adaptation. Unfortunately, post-training is known to induce forgetting, especially in the ubiquitous use-case of leveraging third-party pre-trained models, which is typically understood as a loss of parametric or factual knowledge. We argue that this accuracy-centric view is insufficient for modern foundation models and instead define forgetting as systematic model drift that degrades behavior and user experience. In this context, we introduce CapTrack, a capability-centric framework for analyzing forgetting in LLMs that combines a behavioral taxonomy with an evaluation suite built on established benchmarks and targeted adaptations. Using CapTrack, we conduct a large-scale empirical study across post-training algorithms, domains, and model families, including models up to 80B parameters. We find that forgetting extends beyond parametric knowledge, with pronounced drift in robustness and default behaviors. Instruction fine-tuning induces the strongest relative drift, while preference optimization is more conservative and can partially recover lost capabilities. Differences across model families persist, and no universal mitigation emerges.

Irregular sampling intervals and missing values in real-world time series data present challenges for conventional methods that assume consistent intervals and complete data. Neural Ordinary Differential Equations (Neural ODEs) offer an alternative approach, utilizing neural networks combined with ODE solvers to learn continuous latent representations through parameterized vector fields. Neural Stochastic Differential Equations (Neural SDEs) extend Neural ODEs by incorporating a diffusion term, although this addition is not trivial, particularly when addressing irregular intervals and missing values. Consequently, careful design of drift and diffusion functions is crucial for maintaining stability and enhancing performance, while incautious choices can result in adverse properties such as the absence of strong solutions, stochastic destabilization, or unstable Euler discretizations, significantly affecting Neural SDEs' performance. In this study, we propose three stable classes of Neural SDEs: Langevin-type SDE, Linear Noise SDE, and Geometric SDE. Then, we rigorously demonstrate their robustness in maintaining excellent performance under distribution shift, while effectively preventing overfitting. To assess the effectiveness of our approach, we conduct extensive experiments on four benchmark datasets for interpolation, forecasting, and classification tasks, and analyze the robustness of our methods with 30 public datasets under different missing rates. Our results demonstrate the efficacy of the proposed method in handling real-world irregular time series data.

Diffusion models are generative models that have recently demonstrated impressive performances in terms of sampling quality and density estimation in high dimensions. They rely on a forward continuous diffusion process and a backward continuous denoising process, which can be described by a time-dependent vector field and is used as a generative model. In the original formulation of the diffusion model, this vector field is assumed to be the score function (i.e. it is the gradient of the log-probability at a given time in the diffusion process). Curiously, on the practical side, most studies on diffusion models implement this vector field as a neural network function and do not constrain it be the gradient of some energy function (that is, most studies do not constrain the vector field to be conservative). Even though some studies investigated empirically whether such a constraint will lead to a performance gain, they lead to contradicting results and failed to provide analytical results. Here, we provide three analytical results regarding the extent of the modeling freedom of this vector field. {Firstly, we propose a novel decomposition of vector fields into a conservative component and an orthogonal component which satisfies a given (gauge) freedom. Secondly, from this orthogonal decomposition, we show that exact density estimation and exact sampling is achieved when the conservative component is exactly equals to the true score and therefore conservativity is neither necessary nor sufficient to obtain exact density estimation and exact sampling. Finally, we show that when it comes to inferring local information of the data manifold, constraining the vector field to be conservative is desirable.

We introduce ensembles within score-based sampling methods to develop gradient-free approximate sampling techniques that leverage the collective dynamics of particle ensembles to compute approximate reverse diffusion drifts. We introduce the underlying methodology, emphasizing its relationship with generative diffusion models and the previously introduced F\"ollmer sampler. We demonstrate the efficacy of ensemble strategies through various examples, ranging from low- to medium-dimensionality sampling problems, including multi-modal and highly non-Gaussian probability distributions, and provide comparisons to traditional methods like NUTS. Our findings highlight the potential of ensemble strategies for modeling complex probability distributions in situations where gradients are unavailable. Finally, we showcase its application in the context of Bayesian inversion problems within the geophysical sciences.

Modeling Lagrangian turbulence remains a fundamental challenge due to its multiscale, intermittent, and non-Gaussian nature. Recent advances in data-driven diffusion models have enabled the generation of realistic Lagrangian velocity trajectories that accurately reproduce statistical properties across scales and capture rare extreme events. This study investigates three key aspects of diffusion-based modeling for Lagrangian turbulence. First, we assess architectural robustness by comparing a U-Net backbone with a transformer-based alternative, finding strong consistency in generated trajectories, with only minor discrepancies at small scales. Second, leveraging a deterministic variant of diffusion model formulation, namely the deterministic denoising diffusion implicit model (DDIM), we identify structured features in the initial latent noise that align consistently with extreme acceleration events. Third, we explore accelerated generation by reducing the number of diffusion steps, and find that DDIM enables substantial speedups with minimal loss of statistical fidelity. These findings highlight the robustness of diffusion models and their potential for interpretable, scalable modeling of complex turbulent systems.

Multimodal large language models (MLLMs) are rapidly advancing, yet their reasoning ability often lags behind that of strong text-only counterparts. Existing methods to bridge this gap rely on supervised fine-tuning over large-scale multimodal reasoning data or reinforcement learning, both of which are resource-intensive. A promising alternative is model merging, which interpolates parameters between reasoning-enhanced LLMs and multimodal variants. However, our analysis shows that naive merging is not always a "free lunch": its effectiveness varies drastically across model families, with some (e.g., LLaVA, Idefics) benefiting while others (e.g., Qwen) suffer performance degradation. To address this, we propose Directional Reasoning Injection for Fine-Tuning (DRIFT) MLLMs, a lightweight method that transfers reasoning knowledge in the gradient space, without destabilizing multimodal alignment. DRIFT precomputes a reasoning prior as the parameter-space difference between reasoning and multimodal variants, then uses it to bias gradients during multimodal fine-tuning. This approach preserves the simplicity of standard supervised fine-tuning pipelines while enabling efficient reasoning transfer. Extensive experiments on multimodal reasoning benchmarks, including MathVista and MathVerse, demonstrate that DRIFT consistently improves reasoning performance over naive merging and supervised fine-tuning, while matching or surpassing training-heavy methods at a fraction of the cost.

We address the problem of learning the dynamics of an unknown non-parametric system linking a target and a feature time series. The feature time series is measured on a sparse and irregular grid, while we have access to only a few points of the target time series. Once learned, we can use these dynamics to predict values of the target from the previous values of the feature time series. We frame this task as learning the solution map of a controlled differential equation (CDE). By leveraging the rich theory of signatures, we are able to cast this non-linear problem as a high-dimensional linear regression. We provide an oracle bound on the prediction error which exhibits explicit dependencies on the individual-specific sampling schemes. Our theoretical results are illustrated by simulations which show that our method outperforms existing algorithms for recovering the full time series while being computationally cheap. We conclude by demonstrating its potential on real-world epidemiological data.

Safety alignment of Large Language Models (LLMs) is extremely fragile, as fine-tuning on a small number of benign samples can erase safety behaviors learned from millions of preference examples. Existing studies attempt to explain this phenomenon by comparing parameters and hidden states before and after fine-tuning, but overlook their dynamic evolution during fine-tuning. In this paper, we uncover a critical mechanism underlying safety degradation by analyzing parameter dynamics, where benign fine-tuning causes parameters to cumulatively drift toward danger-aligned directions, progressively undermining the model's safety. This finding suggests that samples contributing more to this drift has greater fine-tuning risks. Based on this insight, we propose a method of Sample-Level Quantification of Safety Degradation (SQSD), which quantifies the influence of each training sample on safety degradation. Specifically, SQSD computes continuous risk scores to samples by measuring their induced parameter updates' projection difference between danger and safety directions. Extensive experiments across multiple models and datasets demonstrate that SQSD effectively quantifies sample-level fine-tuning risks and exhibits strong transferability across model architectures, parameter scales, and parameter-efficient methods.

Diffusion models have achieved remarkable performance in generative modeling, yet their theoretical foundations are often intricate, and the gap between mathematical formulations in papers and practical open-source implementations can be difficult to bridge. Existing tutorials primarily focus on deriving equations, offering limited guidance on how diffusion models actually operate in code. To address this, we present a concise implementation of approximately 300 lines that explains diffusion models from a code-execution perspective. Our minimal example preserves the essential components -- including forward diffusion, reverse sampling, the noise-prediction network, and the training loop -- while removing unnecessary engineering details. This technical report aims to provide researchers with a clear, implementation-first understanding of how diffusion models work in practice and how code and theory correspond. Our code and pre-trained models are available at: https://github.com/disanda/GM/tree/main/DDPM-DDIM-ClassifierFree.

Given a dataset on actions and resulting long-term rewards, a direct estimation approach fits value functions that minimize prediction error on the training data. Temporal difference learning (TD) methods instead fit value functions by minimizing the degree of temporal inconsistency between estimates made at successive time-steps. Focusing on finite state Markov chains, we provide a crisp asymptotic theory of the statistical advantages of this approach. First, we show that an intuitive inverse trajectory pooling coefficient completely characterizes the percent reduction in mean-squared error of value estimates. Depending on problem structure, the reduction could be enormous or nonexistent. Next, we prove that there can be dramatic improvements in estimates of the difference in value-to-go for two states: TD's errors are bounded in terms of a novel measure - the problem's trajectory crossing time - which can be much smaller than the problem's time horizon.

The prevailing inference framework for diffusion models formulates generation fundamentally as a problem of numerical integration. This perspective casts the model as an exact estimator, neglecting the inherent statistical uncertainty of the denoising process. In this work, we propose Forward-Process Aligned Diffusion prediction (DiFA), a training-free framework that reframes inference-time data prediction refinement as a sequential state estimation problem. Rather than reusing past outputs solely for numerical integration, DiFA treats iterative data predictions along the reverse trajectory as correlated observations to build a forward-aligned temporal consensus. Inspired by Kalman filtering, this consensus aggregates historical predictions according to structural consistency and noise-level compatibility. To counteract the over-smoothing tendency of temporal consensus, we introduce a deviation guidance mechanism to adaptively preserve residual details. Empirically, DiFA yields significant improvements on CIFAR-10 and ImageNet across the evaluated metrics, including FID, IS, and FD-DINOv2, demonstrating that aligning inference with the forward statistical structure substantially improves generative fidelity.

Multimodal learning systems often struggle in non-stationary environments due to concept drift, where changing data distributions can degrade performance. Modality-specific drifts and the lack of mechanisms for continuous, stable adaptation compound this challenge. This paper introduces LS-OGD, a novel adaptive control framework for robust multimodal learning in the presence of concept drift. LS-OGD uses an online controller that dynamically adjusts the model's learning rate and the fusion weights between different data modalities in response to detected drift and evolving prediction errors. We prove that under bounded drift conditions, the LS-OGD system's prediction error is uniformly ultimately bounded and converges to zero if the drift ceases. Additionally, we demonstrate that the adaptive fusion strategy effectively isolates and mitigates the impact of severe modality-specific drift, thereby ensuring system resilience and fault tolerance. These theoretical guarantees establish a principled foundation for developing reliable and continuously adapting multimodal learning systems.

Diffusion language models generate tokens in parallel, but still require multiple sampling steps to produce high-quality text. In this paper, we investigate whether a model can learn to generate an entire sequence in a single forward pass. We propose Seq-Drifting, a framework that applies drifting to sequences of continuous token representations and directly learns a map from Gaussian noise to text. Unlike existing DLMs that derive the supervision at each position directly from the observed token in a training sequence, Seq-Drifting builds a drift field whose position-wise targets adapt to the current generated context. At each position, attraction guides each output toward a set of contextually plausible token representations, while repulsion discourages collapse across samples and repetition within sequences. The generator learns from this drift field during training and produces all tokens jointly in one pass at inference. Empirically, Seq-Drifting achieves a generative perplexity of 36.01 on LM1B in one step and performs competitively in both unconditional and conditional generation. Experiments on translation, summarization, and reasoning further demonstrate the applicability of the framework beyond open-ended generation. These results suggest that drifting over token sequences offers a promising path toward effective one-step text generation. Our code is available at https://github.com/jyliu-ai/Seq-Drifting.

Diffusion (score-based) generative models have been widely used for modeling various types of complex data, including images, audios, and point clouds. Recently, the deep connection between forward-backward stochastic differential equations (SDEs) and diffusion-based models has been revealed, and several new variants of SDEs are proposed (e.g., sub-VP, critically-damped Langevin) along this line. Despite the empirical success of the hand-crafted fixed forward SDEs, a great quantity of proper forward SDEs remain unexplored. In this work, we propose a general framework for parameterizing the diffusion model, especially the spatial part of the forward SDE. An abstract formalism is introduced with theoretical guarantees, and its connection with previous diffusion models is leveraged. We demonstrate the theoretical advantage of our method from an optimization perspective. Numerical experiments on synthetic datasets, MINIST and CIFAR10 are also presented to validate the effectiveness of our framework.

Split conformal prediction has recently sparked great interest due to its ability to provide formally guaranteed uncertainty sets or intervals for predictions made by black-box neural models, ensuring a predefined probability of containing the actual ground truth. While the original formulation assumes data exchangeability, some extensions handle non-exchangeable data, which is often the case in many real-world scenarios. In parallel, some progress has been made in conformal methods that provide statistical guarantees for a broader range of objectives, such as bounding the best F_1-score or minimizing the false negative rate in expectation. In this paper, we leverage and extend these two lines of work by proposing non-exchangeable conformal risk control, which allows controlling the expected value of any monotone loss function when the data is not exchangeable. Our framework is flexible, makes very few assumptions, and allows weighting the data based on its relevance for a given test example; a careful choice of weights may result on tighter bounds, making our framework useful in the presence of change points, time series, or other forms of distribution drift. Experiments with both synthetic and real world data show the usefulness of our method.

Deep-research agents solve tasks through long trajectories of search, tool use, evidence inspection, and answer synthesis. Evaluation based on final answers shows whether an agent succeeds, but not which parts of the trajectory make the answer unreliable. We study span-level error localization for deep-research agents. We collect 2,790 real trajectories from two agent frameworks, three backbone models, and three benchmarks, convert raw logs into semantic spans, and annotate harmful error spans through LLM-assisted expert review. From these annotations, we build TELBench, a 1,000-instance benchmark for identifying error spans among normal exploration, failed searches, tentative hypotheses, and harmless noise. We further propose DRIFT, a claim-centric auditing framework that tracks agent claims, checks their support in trajectory evidence, and marks spans where unsupported or conflicting claims affect the answer path. Experiments across model families and auditing frameworks show that DRIFT improves span-level error localization and first-error accuracy by up to 30 percentage points. Our work provides a process-level view of reliability in deep-research agents.

We introduce a novel framework for efficient sampling from complex, unnormalised target distributions by exploiting multiscale dynamics. Traditional score-based sampling methods either rely on learned approximations of the score function or involve computationally expensive nested Markov chain Monte Carlo (MCMC) loops. In contrast, the proposed approach leverages stochastic averaging within a slow-fast system of stochastic differential equations (SDEs) to estimate intermediate scores along a diffusion path without training or inner-loop MCMC. Two algorithms are developed under this framework: MultALMC, which uses multiscale annealed Langevin dynamics, and MultCDiff, based on multiscale controlled diffusions for the reverse-time Ornstein-Uhlenbeck process. Both overdamped and underdamped variants are considered, with theoretical guarantees of convergence to the desired diffusion path. The framework is extended to handle heavy-tailed target distributions using Student's t-based noise models and tailored fast-process dynamics. Empirical results across synthetic and real-world benchmarks, including multimodal and high-dimensional distributions, demonstrate that the proposed methods are competitive with existing samplers in terms of accuracy and efficiency, without the need for learned models.

Autoregressive video diffusion models enable streaming generation but often degrade over long rollouts: static scene layouts drift, while mechanisms that improve spatial stability tend to suppress motion, causing natural flows such as water, fire, or smoke to stagnate. We study this stability-motion trade-off in fixed-camera long-horizon nature video generation, where the two failure modes can be more clearly separated than in moving-camera settings. We propose Steady-Forcing, a memory and training framework combining a persistent visual anchor (V-Sink), an exponential moving-average motion memory (EMA-Sink), block-relative temporal encoding, periodic cache purification, and distillation from a Wan2.1-14B teacher with motion-rewarded priors under task-focused configurations. Together, these components are designed to preserve background identity while sustaining visually plausible fluid dynamics over multi-minute autoregressive rollouts. Evaluations across seven baselines show that Steady-Forcing improves long horizon background consistency and imaging quality, while a blind user study indicates stronger perceived stability and motion continuity. The benchmark evaluation further suggest that generic VBench aggregate scores under-penalize fixed-camera artifacts as well as rewarding drift-induced optical flow as Dynamic Degree while not directly penalizing texture hardening or flow stagnation - motivating future task-specific benchmarks for static-camera nature-flow evaluation. Project page: https://minar09.github.io/steadyforcing/

Diffusion models have recently been increasingly applied to temporal data such as video, fluid mechanics simulations, or climate data. These methods generally treat subsequent frames equally regarding the amount of noise in the diffusion process. This paper explores Rolling Diffusion: a new approach that uses a sliding window denoising process. It ensures that the diffusion process progressively corrupts through time by assigning more noise to frames that appear later in a sequence, reflecting greater uncertainty about the future as the generation process unfolds. Empirically, we show that when the temporal dynamics are complex, Rolling Diffusion is superior to standard diffusion. In particular, this result is demonstrated in a video prediction task using the Kinetics-600 video dataset and in a chaotic fluid dynamics forecasting experiment.

Recurrent reasoning models have attracted growing attention for scaling test-time computation, typically by iteratively refining latent states with shared parameters. However, these models apply each learned update with a fixed unit scale, which can be conservative when updates make persistent progress and overly aggressive when they fluctuate, limiting the benefit of additional loops. To understand how the scale should vary along the trajectory, we first analyze the sensitivity of terminal loss to recurrent update scale. We show that its temporal average admits an exact decomposition into persistent-progress and centered-fluctuation contributions. Based on this, we introduce the Trajectory Adaptive Progress-Fluctuation Scheduler (TAPS), which tracks their balance across recurrent updates and adapts the step size online. Theoretically, we establish sufficient conditions under which TAPS reduces expected terminal loss and reaches a target quality in fewer recurrent loops. Empirically, we show that TAPS improves terminal accuracy across structured reasoning tasks without retraining. By further incorporating the progress-fluctuation principle into training, TAPS yields additional accuracy gains with up to 1.56 times wall-clock speedup at matched baseline accuracy. The broad applicability of TAPS is supported by its effectiveness across diverse recurrent architectures and inference strategies. Together, these results establish update scale as complementary control axis of recurrent inference alongside architecture and depth.

Colloquially speaking, image generation models based upon diffusion processes are frequently said to exhibit "hallucinations," samples that could never occur in the training data. But where do such hallucinations come from? In this paper, we study a particular failure mode in diffusion models, which we term mode interpolation. Specifically, we find that diffusion models smoothly "interpolate" between nearby data modes in the training set, to generate samples that are completely outside the support of the original training distribution; this phenomenon leads diffusion models to generate artifacts that never existed in real data (i.e., hallucinations). We systematically study the reasons for, and the manifestation of this phenomenon. Through experiments on 1D and 2D Gaussians, we show how a discontinuous loss landscape in the diffusion model's decoder leads to a region where any smooth approximation will cause such hallucinations. Through experiments on artificial datasets with various shapes, we show how hallucination leads to the generation of combinations of shapes that never existed. Finally, we show that diffusion models in fact know when they go out of support and hallucinate. This is captured by the high variance in the trajectory of the generated sample towards the final few backward sampling process. Using a simple metric to capture this variance, we can remove over 95% of hallucinations at generation time while retaining 96% of in-support samples. We conclude our exploration by showing the implications of such hallucination (and its removal) on the collapse (and stabilization) of recursive training on synthetic data with experiments on MNIST and 2D Gaussians dataset. We release our code at https://github.com/locuslab/diffusion-model-hallucination.

As AI model size grows, neural scaling laws have become a crucial tool to predict the improvements of large models when increasing capacity and the size of original (human or natural) training data. Yet, the widespread use of popular models means that the ecosystem of online data and text will co-evolve to progressively contain increased amounts of synthesized data. In this paper we ask: How will the scaling laws change in the inevitable regime where synthetic data makes its way into the training corpus? Will future models, still improve, or be doomed to degenerate up to total (model) collapse? We develop a theoretical framework of model collapse through the lens of scaling laws. We discover a wide range of decay phenomena, analyzing loss of scaling, shifted scaling with number of generations, the ''un-learning" of skills, and grokking when mixing human and synthesized data. Our theory is validated by large-scale experiments with a transformer on an arithmetic task and text generation using the large language model Llama2.

We present an online post-hoc calibration method, called Online Platt Scaling (OPS), which combines the Platt scaling technique with online logistic regression. We demonstrate that OPS smoothly adapts between i.i.d. and non-i.i.d. settings with distribution drift. Further, in scenarios where the best Platt scaling model is itself miscalibrated, we enhance OPS by incorporating a recently developed technique called calibeating to make it more robust. Theoretically, our resulting OPS+calibeating method is guaranteed to be calibrated for adversarial outcome sequences. Empirically, it is effective on a range of synthetic and real-world datasets, with and without distribution drifts, achieving superior performance without hyperparameter tuning. Finally, we extend all OPS ideas to the beta scaling method.

We study a space-time Brownian motion with drift B(t)=(t_0+t,y_0+W(t)+t) killed at the moving boundary of the cone {(t,x):0<x<t}. This article determines the parabolic Martin boundary and all harmonic functions associated with this process. To that end, the asymptotics of Green's functions are determined along all directions. We also find the exit probabilities at the edges, the probability of remaining in the cone forever and the laws of the exit point and exit time. From this, we derive an explicit formula for the transition kernel of the process. These results arise from two different methods initially introduced to study random walks. An analytical approach, developed in the 1970s by Malyshev and based on the steepest descent method on a Riemann surface, is used to determine the asymptotics of the Green's functions. A recursive compensation approach, inspired by the method developed in the 1990s by Adan, Wessels and Zijm, is used to determine the harmonic functions.