Daily Papers

Offline reinforcement learning learns an effective policy on offline datasets without online interaction, and it attracts persistent research attention due to its potential of practical application. However, extrapolation error generated by distribution shift will still lead to the overestimation for those actions that transit to out-of-distribution(OOD) states, which degrades the reliability and robustness of the offline policy. In this paper, we propose Contextual Conservative Q-Learning(C-CQL) to learn a robustly reliable policy through the contextual information captured via an inverse dynamics model. With the supervision of the inverse dynamics model, it tends to learn a policy that generates stable transition at perturbed states, for the fact that pertuebed states are a common kind of OOD states. In this manner, we enable the learnt policy more likely to generate transition that destines to the empirical next state distributions of the offline dataset, i.e., robustly reliable transition. Besides, we theoretically reveal that C-CQL is the generalization of the Conservative Q-Learning(CQL) and aggressive State Deviation Correction(SDC). Finally, experimental results demonstrate the proposed C-CQL achieves the state-of-the-art performance in most environments of offline Mujoco suite and a noisy Mujoco setting.

Frame-wise action-controlled image-to-video generation is a promising paradigm for interactive world simulation, where each control signal should elicit an immediate visual response. However, maintaining visual fidelity and 3D consistency over long autoregressive rollouts remains challenging. Existing 3D-aware methods often suffer from catastrophic drift due to two impediments: information loss from Latent--RGB Cycling, where generated latents are repeatedly decoded to RGB and re-encoded for future conditioning, and the training--inference gap induced by the error-free hypothesis, where clean training memory fails to match prediction-corrupted inference memory. To address these challenges, we present Robust Dreamer, a memory-augmented framework built around how to design 3D memory and how to use it robustly. First, we introduce Latent Gaussian Memory, which anchors diffusion latents inherited from the generation process to Gaussian primitives and recalls them via latent-space Gaussian splatting. This provides dense, geometry-aware, view-aligned conditioning while avoiding accumulated degradation from repeated VAE conversion. Second, we propose Deviation Learning with Dynamic Deviation Archive, which synthesizes rollout-induced latent deviations through a one-step approximation, stores them by autoregressive stage and denoising timestamp, and injects them into historical memory during training. This exposes the generator to realistic corrupted memory states and teaches internal correction before inference. Experiments on ScanNet, DL3DV, and OmniWorldGame demonstrate state-of-the-art long-horizon performance.

Reinforcement learning, including reinforcement learning with verifiable rewards (RLVR), has emerged as a powerful approach for LLM post-training. Central to these approaches is the design of the importance sampling (IS) ratio used in off-policy policy-gradient estimation. Existing methods face a fundamental bias-variance dilemma: token-level IS ratios, as adopted by PPO (Schulman et al., 2017) and GRPO (Shao et al., 2024), introduce bias by ignoring prefix state distribution mismatch; full sequence ratios provide exact trajectory-level correction but suffer from high variance due to the multiplicative accumulation of per-token ratios, while GSPO (Zheng et al., 2025) improves numerical stability via length normalization at the cost of deviating from the exact full-sequence IS correction. In this work, we identify the cumulative token IS ratio, the product of per-token ratios up to position t, as a theoretically principled solution to this dilemma. We prove that, under the token-level policy-gradient formulation, this ratio provides an unbiased prefix correction for each token-level gradient term and has strictly lower variance than the full sequence ratio. Building on this insight, we propose CTPO (Cumulative Token Policy Optimization), which combines the cumulative token IS ratio with position-adaptive clipping that scales log-space clip bounds according to the natural t growth of the cumulative log-ratio. This yields more consistent regularization across token positions. We implement and evaluate CTPO in the tool-integrated reasoning setting on several challenging mathematical reasoning benchmarks, achieving the best average performance across both model scales compared with strong GRPO and GSPO baselines. Code will be available at https://github.com/horizon-llm/CTPO.

Spatio-temporal forecasting is essential for real-world applications such as traffic management and urban computing. Although recent methods have shown improved accuracy, they often fail to account for dynamic deviations between current inputs and historical patterns. These deviations contain critical signals that can significantly affect model performance. To fill this gap, we propose ST-SSDL, a Spatio-Temporal time series forecasting framework that incorporates a Self-Supervised Deviation Learning scheme to capture and utilize such deviations. ST-SSDL anchors each input to its historical average and discretizes the latent space using learnable prototypes that represent typical spatio-temporal patterns. Two auxiliary objectives are proposed to refine this structure: a contrastive loss that enhances inter-prototype discriminability and a deviation loss that regularizes the distance consistency between input representations and corresponding prototypes to quantify deviation. Optimized jointly with the forecasting objective, these components guide the model to organize its hidden space and improve generalization across diverse input conditions. Experiments on six benchmark datasets show that ST-SSDL consistently outperforms state-of-the-art baselines across multiple metrics. Visualizations further demonstrate its ability to adaptively respond to varying levels of deviation in complex spatio-temporal scenarios. Our code and datasets are available at https://github.com/Jimmy-7664/ST-SSDL.

Training large-scale machine learning models poses distinct system challenges, given both the size and complexity of today's workloads. Recently, many organizations training state-of-the-art Generative AI models have reported cases of instability during training, often taking the form of loss spikes. Numeric deviation has emerged as a potential cause of this training instability, although quantifying this is especially challenging given the costly nature of training runs. In this work, we develop a principled approach to understanding the effects of numeric deviation, and construct proxies to put observations into context when downstream effects are difficult to quantify. As a case study, we apply this framework to analyze the widely-adopted Flash Attention optimization. We find that Flash Attention sees roughly an order of magnitude more numeric deviation as compared to Baseline Attention at BF16 when measured during an isolated forward pass. We then use a data-driven analysis based on the Wasserstein Distance to provide upper bounds on how this numeric deviation impacts model weights during training, finding that the numerical deviation present in Flash Attention is 2-5 times less significant than low-precision training.

Three of the most popular methods for training language models to reason look like three different tricks. They are not. All three adjust a single number: standard deviation, reflecting how much a prompt's sampled answers disagree. When such a model is trained, it answers each problem many times, and an automatic checker marks every answer right or wrong. The standard deviation of those marks measures the disagreement: largest when the answers split evenly between right and wrong, and zero when they all agree. Group Relative Policy Optimization (GRPO) divides by this number, GRPO Done Right (Dr. GRPO) drops the division, and Decoupled Clip and Dynamic Sampling Policy Optimization (DAPO) discards the groups where it is zero. Each is presented as its own fix, yet this paper proves they are three settings of one dial. That dial is not cosmetic: for right-or-wrong rewards, the disagreement is exactly the size of the training update, the group-standard-deviation identity. A split group teaches the most, while a unanimous group teaches nothing and falls silent. The same result says which problems deserve the most weight and how many tries each one needs. This paper confirms the intuition on a large real difficulty dataset (Big-Math) and in a controlled training run. What looks like a harmless normalization step is the dial that decides where learning happens and how strongly.

In reinforcement learning, agents collect state information and rewards through environmental interactions, essential for policy refinement. This process is notably time-consuming, especially in complex robotic simulations and real-world applications. Traditional algorithms usually re-engage with the environment after processing a single batch of samples, thereby failing to fully capitalize on historical data. However, frequently observed states, with reliable value estimates, require minimal updates; in contrast, rare observed states necessitate more intensive updates for achieving accurate value estimations. To address uneven sample utilization, we propose Novelty-guided Sample Reuse (NSR). NSR provides extra updates for infrequent, novel states and skips additional updates for frequent states, maximizing sample use before interacting with the environment again. Our experiments show that NSR improves the convergence rate and success rate of algorithms without significantly increasing time consumption. Our code is publicly available at https://github.com/ppksigs/NSR-DDPG-HER.

We propose and theoretically analyze an approach for planning with an approximate model in reinforcement learning that can reduce the adverse impact of model error. If the model is accurate enough, it accelerates the convergence to the true value function too. One of its key components is the MaxEnt Model Correction (MoCo) procedure that corrects the model's next-state distributions based on a Maximum Entropy density estimation formulation. Based on MoCo, we introduce the Model Correcting Value Iteration (MoCoVI) algorithm, and its sampled-based variant MoCoDyna. We show that MoCoVI and MoCoDyna's convergence can be much faster than the conventional model-free algorithms. Unlike traditional model-based algorithms, MoCoVI and MoCoDyna effectively utilize an approximate model and still converge to the correct value function.

Recent studies show that Large Language Models (LLMs) with safety alignment can be jail-broken by fine-tuning on a dataset mixed with harmful data. First time in the literature, we show that the jail-broken effect can be mitigated by separating states in the finetuning stage to optimize the alignment and user datasets. Unfortunately, our subsequent study shows that this simple Bi-State Optimization (BSO) solution experiences convergence instability when steps invested in its alignment state is too small, leading to downgraded alignment performance. By statistical analysis, we show that the excess drift towards consensus could be a probable reason for the instability. To remedy this issue, we propose Lazy(i) safety alignment (Lisa), which introduces a proximal term to constraint the drift of each state. Theoretically, the benefit of the proximal term is supported by the convergence analysis, wherein we show that a sufficient large proximal factor is necessary to guarantee Lisa's convergence. Empirically, our results on four downstream finetuning tasks show that Lisa with a proximal term can significantly increase alignment performance while maintaining the LLM's accuracy on the user tasks. Code is available at https://github.com/git-disl/Lisa.

Imitation-learning policies inherit the quality of the demonstrations they are trained on, and a growing set of curation metrics promise to score and filter low-quality demonstrations automatically. These metrics are each validated on different data with different protocols, so it is unclear which of them actually identify the demonstrations that harm a policy. We build a controlled testbed in which demonstration defects are injected with known type, and audit seven curation metrics along two axes: how well each separates defective from clean demonstrations, and whether training a behavior-cloning policy on each metric's curated subset improves task success. We study two defect regimes. Subtle perturbations (correlated action noise, tremor, truncation) are detectable by multivariate outlier scoring and, once removed, recover the full downstream gap. Structural errors, where the demonstration executes a wrong action at a key moment, are invisible to every action-only metric we test, and two of them are inverted: they score defective demonstrations as higher quality and, used for curation, tend to leave the policy at or below the uncurated baseline rather than above it. Only metrics that examine the state trajectory detect structural errors, and even the best of them recovers just a third of the downstream gap. High detection accuracy does not guarantee downstream improvement. We release the testbed and all curation implementations.

Kalman filter (KF) based methods for multi-object tracking (MOT) make an assumption that objects move linearly. While this assumption is acceptable for very short periods of occlusion, linear estimates of motion for prolonged time can be highly inaccurate. Moreover, when there is no measurement available to update Kalman filter parameters, the standard convention is to trust the priori state estimations for posteriori update. This leads to the accumulation of errors during a period of occlusion. The error causes significant motion direction variance in practice. In this work, we show that a basic Kalman filter can still obtain state-of-the-art tracking performance if proper care is taken to fix the noise accumulated during occlusion. Instead of relying only on the linear state estimate (i.e., estimation-centric approach), we use object observations (i.e., the measurements by object detector) to compute a virtual trajectory over the occlusion period to fix the error accumulation of filter parameters during the occlusion period. This allows more time steps to correct errors accumulated during occlusion. We name our method Observation-Centric SORT (OC-SORT). It remains Simple, Online, and Real-Time but improves robustness during occlusion and non-linear motion. Given off-the-shelf detections as input, OC-SORT runs at 700+ FPS on a single CPU. It achieves state-of-the-art on multiple datasets, including MOT17, MOT20, KITTI, head tracking, and especially DanceTrack where the object motion is highly non-linear. The code and models are available at https://github.com/noahcao/OC_SORT.

Language models (LMs) are susceptible to in-context reward hacking, where they exploit flaws in tainted or faulty written specifications or rubrics to achieve high scores without fulfilling the user's true intent. We introduce Specification Self-Correction (SSC), a novel, test-time framework that enables an LM to identify and correct flaws within its own guiding specification. SSC employs a multi-step inference process where the model first generates a response based on a potentially tainted specification, critiques its output, and then revises the specification itself to remove the exploitable loophole. A final, more robust response is then generated using this self-corrected specification. Across experiments spanning creative writing and agentic coding tasks with several LMs, we demonstrate that while models initially game tainted specifications in 50-70\% of cases, the SSC process reduces this vulnerability by over 90\%. This dynamic repair occurs at inference time, requires no weight modification, and leads to more robustly aligned model behavior. Code at https://github.com/vicgalle/specification-self-correction .

In many real-world multi-agent cooperative tasks, due to high cost and risk, agents cannot continuously interact with the environment and collect experiences during learning, but have to learn from offline datasets. However, the transition dynamics in the dataset of each agent can be much different from the ones induced by the learned policies of other agents in execution, creating large errors in value estimates. Consequently, agents learn uncoordinated low-performing policies. In this paper, we propose a framework for offline decentralized multi-agent reinforcement learning, which exploits value deviation and transition normalization to deliberately modify the transition probabilities. Value deviation optimistically increases the transition probabilities of high-value next states, and transition normalization normalizes the transition probabilities of next states. They together enable agents to learn high-performing and coordinated policies. Theoretically, we prove the convergence of Q-learning under the altered non-stationary transition dynamics. Empirically, we show that the framework can be easily built on many existing offline reinforcement learning algorithms and achieve substantial improvement in a variety of multi-agent tasks.

In this study, we investigate the DIstribution Correction Estimation (DICE) methods, an important line of work in offline reinforcement learning (RL) and imitation learning (IL). DICE-based methods impose state-action-level behavior constraint, which is an ideal choice for offline learning. However, they typically perform much worse than current state-of-the-art (SOTA) methods that solely use action-level behavior constraint. After revisiting DICE-based methods, we find there exist two gradient terms when learning the value function using true-gradient update: forward gradient (taken on the current state) and backward gradient (taken on the next state). Using forward gradient bears a large similarity to many offline RL methods, and thus can be regarded as applying action-level constraint. However, directly adding the backward gradient may degenerate or cancel out its effect if these two gradients have conflicting directions. To resolve this issue, we propose a simple yet effective modification that projects the backward gradient onto the normal plane of the forward gradient, resulting in an orthogonal-gradient update, a new learning rule for DICE-based methods. We conduct thorough theoretical analyses and find that the projected backward gradient brings state-level behavior regularization, which reveals the mystery of DICE-based methods: the value learning objective does try to impose state-action-level constraint, but needs to be used in a corrected way. Through toy examples and extensive experiments on complex offline RL and IL tasks, we demonstrate that DICE-based methods using orthogonal-gradient updates (O-DICE) achieve SOTA performance and great robustness.

How do multi-turn reasoning systems fail? The expected answer is logical contradiction, in which the system's maintained state becomes unsatisfiable. We show that the dominant mode is instead satisfiable drift, where the internal state stays consistent while the returned answer silently violates prior commitments. We build DRIFT-Bench (Decomposing Reasoning Into Failure Types), a solver-instrumented benchmark of 816 test problems across three constraint domains, and evaluate four methods on it across four open-weight models (8B-120B parameters). MUS-Repair, which feeds minimal unsatisfiable subsets back to the generator, is strongest in every setting (+1.8 to +15.0 pp over the best non-MUS baseline). But the central finding is what repair leaves behind. After structured feedback, models rarely contradict themselves. They forget. Residual errors are 98-100% satisfiable drift across all settings, while contradiction drops to near zero. Reliable multi-turn systems must separately validate that the returned answer respects the maintained state. Code is available at https://github.com/kaons-research/drift-bench.

As creative writing tasks do not have singular correct answers, large language models (LLMs) trained to perform these tasks should be able to generate diverse valid outputs. However, LLM post-training often focuses on improving generation quality but neglects to facilitate output diversity. Hence, in creative writing generation, we investigate post-training approaches to promote both output diversity and quality. Our core idea is to include deviation -- the degree of difference between a training sample and all other samples with the same prompt -- in the training objective to facilitate learning from rare high-quality instances. By adopting our approach to direct preference optimization (DPO) and odds ratio preference optimization (ORPO), we demonstrate that we can promote the output diversity of trained models while minimally decreasing quality. Our best model with 8B parameters could achieve on-par diversity as a human-created dataset while having output quality similar to the best instruction-tuned models we examined, GPT-4o and DeepSeek-R1. We further validate our approaches with a human evaluation, an ablation, and a comparison to an existing diversification approach, DivPO.

We propose a reinforcement learning (RL) framework under a broad class of risk objectives, characterized by convex scoring functions. This class covers many common risk measures, such as variance, Expected Shortfall, entropic Value-at-Risk, and mean-risk utility. To resolve the time-inconsistency issue, we consider an augmented state space and an auxiliary variable and recast the problem as a two-state optimization problem. We propose a customized Actor-Critic algorithm and establish some theoretical approximation guarantees. A key theoretical contribution is that our results do not require the Markov decision process to be continuous. Additionally, we propose an auxiliary variable sampling method inspired by the alternating minimization algorithm, which is convergent under certain conditions. We validate our approach in simulation experiments with a financial application in statistical arbitrage trading, demonstrating the effectiveness of the algorithm.

Despite rapid progress in LLM agents, performance on long-horizon, tool-using tasks remains fragile. To better understand this fragility, we ask a simple question: do all actions contribute equally to failure? Analyzing execution traces on τ-Bench (Airline/Retail) and SWE-Bench Verified, we decompose trajectories into mutating (environment-changing) vs.\ non-mutating steps and formalize decisive deviations, earliest action, level divergences that flip success to failure. A logistic regression reveals that each additional deviation in a mutating action reduces the odds of success by upto 92% on Airline and upto 96% on Retail for SoTA models. In contrast, deviations in non-mutating actions have little to no effect. Errors also grow with context length as agents drift from role and act on stale constraints. Motivated by these observations, we introduce , a model-agnostic, gradient-free, test-time safeguard that (i) adds mutation-gated verification, (ii) injects Targeted Reflection before mutating steps, and (iii) performs block-based context cleaning. delivers consistent gains, e.g., Qwen3-Thinking: +28\% relative on Airline, +11\% on Retail, and +7\% on SWE-Bench Verified; Claude: +9\%/+7\%. We further identify ceiling effects in τ-Bench, where annotation errors and underspecified tasks artificially cap model performance. To address this, we release τ-Bench Verified, which restores benchmark headroom through targeted revisions. Our results argue for action-level analysis, targeted safeguards, and reliable evaluations as prerequisites for robust multi-turn agents.

Models of many engineering and natural systems are imperfect. The discrepancy between the mathematical representations of a true physical system and its imperfect model is called the model error. These model errors can lead to substantial differences between the numerical solutions of the model and the state of the system, particularly in those involving nonlinear, multi-scale phenomena. Thus, there is increasing interest in reducing model errors, particularly by leveraging the rapidly growing observational data to understand their physics and sources. Here, we introduce a framework named MEDIDA: Model Error Discovery with Interpretability and Data Assimilation. MEDIDA only requires a working numerical solver of the model and a small number of noise-free or noisy sporadic observations of the system. In MEDIDA, first the model error is estimated from differences between the observed states and model-predicted states (the latter are obtained from a number of one-time-step numerical integrations from the previous observed states). If observations are noisy, a data assimilation (DA) technique such as ensemble Kalman filter (EnKF) is employed to provide the analysis state of the system, which is then used to estimate the model error. Finally, an equation-discovery technique, here the relevance vector machine (RVM), a sparsity-promoting Bayesian method, is used to identify an interpretable, parsimonious, and closed-form representation of the model error. Using the chaotic Kuramoto-Sivashinsky (KS) system as the test case, we demonstrate the excellent performance of MEDIDA in discovering different types of structural/parametric model errors, representing different types of missing physics, using noise-free and noisy observations.

Self-correction is an effective technique for maintaining parallel sampling in discrete diffusion models with minimal performance degradation. Prior work has explored self-correction at inference time or during post-training; however, such approaches often suffer from limited generalization and may impair reasoning performance. GIDD pioneers pretraining-based self-correction via a multi-step BERT-style uniform-absorbing objective. However, GIDD relies on a continuous interpolation-based pipeline with opaque interactions between uniform transitions and absorbing masks, which complicates hyperparameter tuning and hinders practical performance. In this work, we propose a Self-Correcting Discrete Diffusion (SCDD) model to reformulate pretrained self-correction with explicit state transitions and learn directly in discrete time. Our framework also simplifies the training noise schedule, eliminates a redundant remasking step, and relies exclusively on uniform transitions to learn self-correction. Experiments at the GPT-2 scale demonstrate that our method enables more efficient parallel decoding while preserving generation quality.

Temporal Difference (TD) algorithms are widely used in Deep Reinforcement Learning (RL). Their performance is heavily influenced by the size of the neural network. While in supervised learning, the regime of over-parameterization and its benefits are well understood, the situation in RL is much less clear. In this paper, we present a theoretical analysis of the influence of network size and l_2-regularization on performance. We identify the ratio between the number of parameters and the number of visited states as a crucial factor and define over-parameterization as the regime when it is larger than one. Furthermore, we observe a double descent phenomenon, i.e., a sudden drop in performance around the parameter/state ratio of one. Leveraging random features and the lazy training regime, we study the regularized Least-Square Temporal Difference (LSTD) algorithm in an asymptotic regime, as both the number of parameters and states go to infinity, maintaining a constant ratio. We derive deterministic limits of both the empirical and the true Mean-Squared Bellman Error (MSBE) that feature correction terms responsible for the double descent. Correction terms vanish when the l_2-regularization is increased or the number of unvisited states goes to zero. Numerical experiments with synthetic and small real-world environments closely match the theoretical predictions.

Noise plagues many numerical datasets, where the recorded values in the data may fail to match the true underlying values due to reasons including: erroneous sensors, data entry/processing mistakes, or imperfect human estimates. We consider general regression settings with covariates and a potentially corrupted response whose observed values may contain errors. By accounting for various uncertainties, we introduced veracity scores that distinguish between genuine errors and natural data fluctuations, conditioned on the available covariate information in the dataset. We propose a simple yet efficient filtering procedure for eliminating potential errors, and establish theoretical guarantees for our method. We also contribute a new error detection benchmark involving 5 regression datasets with real-world numerical errors (for which the true values are also known). In this benchmark and additional simulation studies, our method identifies incorrect values with better precision/recall than other approaches.

Generative sequence models are often trained to plan motion in physical domains, from robotics to mechanical simulations. When constructing a dataset to train such a model, engineers may curate demonstrations to specify how trajectories should be distributed over a physical quantity like travel distance or mechanical energy. For example, a roboticist building a maze navigation agent might choose demonstrations whose travel distances cover a fixed range uniformly, hoping to constrain the agent's expected power usage. We find that standard deep learning can violate this intent: each generated trajectory can seem plausible on its own, but the aggregate distribution over the physical quantity is wrong. We call this failure physical misgeneralization, and develop an account of its mechanism. Using controlled synthetic tasks, we show that physical misgeneralization arises when local errors typical of the model class propagate through the physical measurement to shift the recovered distribution. We estimate these errors with a data deviation kernel, and we use it to predict which physical quantities gain or lose mass in both our synthetic and more applied maze navigation and double-pendulum motion tasks. Finally, our mechanistic interpretation helps identify which mitigation strategies are structurally promising, and we use it to propose a kernel-informed intervention.

Post-training quantization (PTQ) is a practical path to deploy large diffusion models, but quantization noise can accumulate over the denoising trajectory and degrade generation quality. We propose Q-Drift, a principled sampler-side correction that treats quantization error as an implicit stochastic perturbation on each denoising step and derives a marginal-distribution-preserving drift adjustment. Q-Drift estimates a timestep-wise variance statistic from calibration, in practice requiring as few as 5 paired full-precision/quantized calibration runs. The resulting sampler correction is plug-and-play with common samplers, diffusion models, and PTQ methods, while incurring negligible overhead at inference. Across six diverse text-to-image models (spanning DiT and U-Net), three samplers (Euler, flow-matching, DPM-Solver++), and two PTQ methods (SVDQuant, MixDQ), Q-Drift improves FID over the corresponding quantized baseline in most settings, with up to 4.59 FID reduction on PixArt-Sigma (SVDQuant W3A4), while preserving CLIP scores.

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 paper studies the linear model for Bitcoin price which includes regression features based on Bitcoin currency statistics, mining processes, Google search trends, Wikipedia pages visits. The pattern of deviation of regression model prediction from real prices is simpler comparing to price time series. It is assumed that this pattern can be predicted by an experienced expert. In such a way, using the combination of the regression model and expert correction, one can receive better results than with either regression model or expert opinion only. It is shown that Bayesian approach makes it possible to utilize the probabilistic approach using distributions with fat tails and take into account the outliers in Bitcoin price time series.

State Space Models (SSMs) have emerged as efficient alternatives to Transformers, mitigating their quadratic computational cost. However, the application of Parameter-Efficient Fine-Tuning (PEFT) methods to SSMs remains largely unexplored. In particular, prompt-based methods like Prompt Tuning and Prefix-Tuning, which are widely used in Transformers, do not perform well on SSMs. To address this, we propose state-based methods as a superior alternative to prompt-based methods. This new family of methods naturally stems from the architectural characteristics of SSMs. State-based methods adjust state-related features directly instead of depending on external prompts. Furthermore, we introduce a novel state-based PEFT method: State-offset Tuning. At every timestep, our method directly affects the state at the current step, leading to more effective adaptation. Through extensive experiments across diverse datasets, we demonstrate the effectiveness of our method. Code is available at https://github.com/furiosa-ai/ssm-state-tuning.

Large Language Models (LLMs) can correct their self-generated responses, but a decline in accuracy after self-correction is also witnessed. To have a deeper understanding of self-correction, we endeavor to decompose, evaluate, and analyze the self-correction behaviors of LLMs. By enumerating and analyzing answer correctness before and after self-correction, we decompose the self-correction capability into confidence (being confident to correct answers) and critique (turning wrong answers to correct) capabilities, and propose two metrics from a probabilistic perspective to measure these 2 capabilities, along with another metric for overall self-correction capability evaluation. Based on our decomposition and evaluation metrics, we conduct extensive experiments and draw some empirical conclusions. For example, we find different models can exhibit distinct behaviors: some models are confident while others are more critical. We also find the trade-off between the two capabilities (i.e. improving one can lead to a decline in the other) when manipulating model self-correction behavior by prompts or in-context learning. Further, we find a simple yet efficient strategy to improve self-correction capability by transforming Supervision Fine-Tuning (SFT) data format, and our strategy outperforms vanilla SFT in both capabilities and achieves much higher accuracy after self-correction. Our code will be publicly available on GitHub.

Post-selecting output states in measurements can effectively amplify weak signals and improve precision. However, post-selection effects may also introduce unintended biases in precision measurements. Here, we investigate the influence of post-selection in the precision spectroscopy of the 2^3S - 2^3P transition of helium (^4He) using an atomic beam. We directly observe that post-selection based on atomic positions causes a shift in the measured transition frequency, amounting to approximately -55 kHz. After accounting for this post-selection shift, we obtain a corrected frequency of 276,764,094,712.45 pm 0.86 kHz for the 2^3S_1 - 2^3P_0 transition. Combining this result with existing data for ^3He, we derive a new value for the difference in squared nuclear charge radii, δr^2 [r_{h}^{2} - r_α^{2}] = 1.0733 pm 0.0021 fm^2. This value shows a 2.8σ deviation from measurements of muonic helium ions, potentially pointing to new physics that challenges lepton universality in quantum electrodynamics.

Reinforcement learning with verifiable rewards (RLVR) has become standard for improving LLM reasoning. However, existing PPO-style trust-region mechanisms remain position-agnostic by enforcing uniform thresholds across all tokens independently. This pointwise treatment conflicts with autoregressive generation in two critical ways. First, uniform thresholds ignore autoregressive asymmetry. Early-stage deviations produce compounding sequence-level drift, causing static thresholds to under-regulate early divergence and excessively constrain late-stage exploration. Second, evaluating token-level divergence in isolation overlooks cumulative prefix drift, granting the same divergence allowance regardless of how far the conditioning history has already deviated from the rollout policy. To address this limitation, we propose CPPO (Cumulative Prefix-divergence Policy Optimization), a token-level masking rule that aligns updates with a finite-horizon policy-improvement bound via two coupled mechanisms. First, a position-weighted threshold imposes stricter limits at early positions whose effects persist longer, relaxing constraints for late-stage tokens. Second, a cumulative prefix budget tracks historical deviations, dynamically restricting further token-level deviation to prevent compounding errors along the prefix. Empirically, CPPO enhances training stability and significantly improves reasoning accuracy across various model scales.

Kernelized Stein discrepancy (KSD) is a score-based discrepancy widely used in goodness-of-fit tests. It can be applied even when the target distribution has an unknown normalising factor, such as in Bayesian analysis. We show theoretically and empirically that the KSD test can suffer from low power when the target and the alternative distributions have the same well-separated modes but differ in mixing proportions. We propose to perturb the observed sample via Markov transition kernels, with respect to which the target distribution is invariant. This allows us to then employ the KSD test on the perturbed sample. We provide numerical evidence that with suitably chosen transition kernels the proposed approach can lead to substantially higher power than the KSD test.

Moments when a time series changes its behaviour are called change points. Detection of such points is a well-known problem, which can be found in many applications: quality monitoring of industrial processes, failure detection in complex systems, health monitoring, speech recognition and video analysis. Occurrence of change point implies that the state of the system is altered and its timely detection might help to prevent unwanted consequences. In this paper, we present two online change-point detection approaches based on neural networks. These algorithms demonstrate linear computational complexity and are suitable for change-point detection in large time series. We compare them with the best known algorithms on various synthetic and real world data sets. Experiments show that the proposed methods outperform known approaches.

When an LLM agent reads a confidential file, then writes a summary, then emails it externally, no single step is unsafe, but the sequence is a data leak. We call this safety drift: individually safe actions compounding into violations. Prior work has measured this problem; we predict it. SafetyDrift models agent safety trajectories as absorbing Markov chains, computing the probability that a trajectory will reach a violation within a given number of steps via closed form absorption analysis. A consequence of the monotonic state design is that every agent will eventually violate safety if left unsupervised (absorption probability 1.0 from all states), making the practical question not if but when, and motivating our focus on finite horizon prediction. Across 357 traces spanning 40 realistic tasks in four categories, we discover that "points of no return" are sharply task dependent: in communication tasks, agents that reach even a mild risk state have an 85% chance of violating safety within five steps, while in technical tasks the probability stays below 5% from any state. A lightweight monitor built on these models detects 94.7% of violations with 3.7 steps of advance warning at negligible computational cost, outperforming both keyword matching (44.7% detection, 55.9% false positive rate) and per step LLM judges (52.6% detection, 38.2% false positive rate) while running over 60,000x faster.

This article presents an experiment in fine-tuning a pretrained causal language model (Meta's Llama 3.1 8B Instruct) for aiding in three fundamental tasks of philological research: chronological and geographic attribution as well as text restoration in ancient Greek inscriptions and documentary papyri. Using a prompt-based instruct approach, the fine-tuned models surpass the state of the art in key metrics. For inscriptions, the models achieve a lower average character error rate (CER) of 22.5% (vs. 26.3%), while closely matching top-1 accuracy (60.9% vs. 61.8%) and top-20 accuracy (77.5% vs. 78.3%) for sequences up to 10 characters. They also provide a practical advantage by ignoring spaces during reconstruction, aligning better with the scriptio continua typically used in ancient written artifacts. In geographic attribution, the model outperforms previous benchmarks with a top-1 accuracy of 75.0% (vs. 70.8%) and a top-3 accuracy of 83.7% (vs. 82.1%). For dating, it achieves an average deviation of 26.2 years (vs. 29.3) and a median deviation of 1 year (vs. 3) from the actual date range. The models also set new baselines for documentary papyri, with a CER of 16.3%, a top-1 accuracy of 71.3%, and top-20 of 85.0% in text reconstruction; a top-1 accuracy of 66.4% and top-3 of 79.9% in geographic attribution; and, in chronological attribution, a deviation of 21.7 years from the actual termini post/ante quem, with a median deviation of 0 years.

Conformal prediction(CP) has become a cornerstone of distribution-free uncertainty quantification, conventionally evaluated by its coverage and interval length. This work critically examines the sufficiency of these standard metrics. We demonstrate that the interval length might be deceptively improved through a counter-intuitive approach termed Prejudicial Trick(PT), while the coverage remains valid. Specifically, for any given test sample, PT probabilistically returns an interval, which is either null or constructed using an adjusted confidence level, thereby preserving marginal coverage. While PT potentially yields a deceptively lower interval length, it introduces practical vulnerabilities: the same input can yield completely different prediction intervals across repeated runs of the algorithm. We formally derive the conditions under which PT achieves these misleading improvements and provide extensive empirical evidence across various regression and classification tasks. Furthermore, we introduce a new metric interval stability which helps detect whether a new CP method implicitly improves the length based on such PT-like techniques. Code is available at https://github.com/benben-cd/PT-Conformal-Prediction.

Reinforcement Learning with Verifiable Rewards (RLVR) trains policies against automated verifiers to avoid costly human labeling. To reduce vulnerability to verifier hacking, many RLVR systems collapse rewards to binary {0,1} during training. This choice carries a cost: it introduces false negatives (rejecting correct answers, FNs) and false positives (accepting incorrect ones, FPs). For instance, a rule-based checker may mark the correct fraction 12{36} as wrong when compared against the canonical 1{3} due to brittle parsing/equivalence rules (FN), while a large language model (LLM) judges can be gamed by superficial cues or even a single adversarial token, yielding inflated correctness for wrong solutions (FP). We formalize verifier unreliability by modeling the verifier as a stochastic reward channel with asymmetric noise rates. From this abstraction, we derive two correction algorithms for verifier errors. The first is a backward correction that de-biases the observed binary reward to recover an unbiased estimator of the clean policy gradient. The second is a forward correction that reweights score-function terms so that the expected update direction aligns with the clean gradient; notably, it requires only the FN rate. We implement both as lightweight hooks in a group relative policy optimization (GRPO)-based RLVR pipeline and evaluate them on math-reasoning models and benchmarks. Across models and datasets, both corrections improve over uncorrected training; the forward variant converges faster and remains stable under heavier noise. Finally, we show a practical appeal mechanism in which a lightweight LLM verifier estimates the FN rate online by rechecking rule-based negatives, obtaining outperformance compared with other state-of-the-art contenders.

Benchmarks measure whether a model is correct. They do not measure whether a model is reliable. This distinction is largely academic for single-shot inference, but becomes critical for agentic AI systems, where a single rephrased prompt can trigger cascading failures in multi-step execution. Yet this form of instability is not captured by existing evaluations. Hallucinations live in variance: they arise when semantically equivalent prompts activate inconsistent internal pathways, producing divergent outputs. Consistent but incorrect outputs reflect bias or missing knowledge; confident guessing reflects calibration failure. Neither constitutes hallucination under this definition. When error is variance-dominated, reducing redundant pathways improves reliability without adding knowledge. We formalize this through Semantic Stability (SS), measured via Paraphrase Consistency (PC@k): generate k paraphrases, greedy decode each, compute mode agreement. SS is a diagnostic for variance-driven unreliability, not a method for improving correctness. We show that a dense Qwen3-0.6B agrees with itself only 23.8% of the time; at 32% sparsity, agreement jumps to 55.9%. A phase diagram reveals the sweet spot where variance reduction outpaces bias accumulation, and regimes where stability collapses onto wrong answers.

Reinforcement learning for large language models suffers from high-variance token-level importance sampling (IS) ratios, which would destabilize policy optimization at scale. To improve stability, recent methods typically use a fixed sequence-level IS ratio for all tokens in a sequence or adjust each token's IS ratio separately, thereby neglecting temporal off-policy derivation across tokens in a sequence. In this paper, we first empirically identify that local off-policy deviation is structurally inconsistent at the token level, which may distort policy-gradient updates across adjacent tokens and lead to training collapse. To address the issue, we propose Online Causal Kalman Filtering for stable and effective Policy Optimization (KPO). Concretely, we model the desired IS ratio as a latent state that evolves across tokens and apply a Kalman filter to update this state online and autoregressively based on the states of past tokens, regardless of future tokens. The resulting filtered IS ratios preserve token-wise local structure-aware variation while strongly smoothing noise spikes, yielding more stable and effective policy updates. Experimentally, KPO achieves superior results on challenging math reasoning datasets compared with state-of-the-art counterparts.

Spiking Neural Networks (SNNs) can achieve competitive performance by converting already existing well-trained Artificial Neural Networks (ANNs), avoiding further costly training. This property is particularly attractive in Reinforcement Learning (RL), where training through environment interaction is expensive and potentially unsafe. However, existing conversion methods perform poorly in continuous control, where suitable baselines are largely absent. We identify error amplification as the key cause: small action approximation errors become temporally correlated across decision steps, inducing cumulative state distribution shift and severe performance degradation. To address this issue, we propose Cross-Step Residual Potential Initialization (CRPI), a lightweight gradient-free mechanism that carries over residual membrane potentials across decision steps to suppress temporally correlated errors. Experiments on continuous control benchmarks with both vector and visual observations demonstrate that CRPI can be integrated into existing conversion pipelines and substantially recovers lost performance. Our results highlight continuous control as a critical and challenging benchmark for ANN-to-SNN conversion, where small errors can be strongly amplified and impact performance. Code is available at https://github.com/xuzijie32/ANN2SNN-CRPI.

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.

Asynchronous reinforcement learning improves rollout throughput for large language model agents by decoupling sample generation from policy optimization, but it also introduces a critical failure mode for PPO-style off-policy correction. In heterogeneous training systems, the total importance ratio should ideally be decomposed into two semantically distinct factors: a training--inference discrepancy term that aligns inference-side and training-side distributions at the same behavior-policy version, and a policy-staleness term that constrains the update from the historical policy to the current policy. We show that practical asynchronous pipelines with delayed updates and partial rollouts often lose the required historical training-side logits, or old logits. This missing-old-logit problem entangles discrepancy repair with staleness correction, breaks the intended semantics of decoupled correction, and makes clipping and masking thresholds interact undesirably. To address this issue, we study both exact and approximate correction routes. We propose three exact old-logit acquisition strategies: snapshot-based version tracking, a dedicated old-logit model, and synchronization via partial rollout interruption, and compare their system trade-offs. From the perspective of approximate correction, we focus on preserving the benefits of decoupled correction through a more appropriate approximate policy when exact old logits cannot be recovered at low cost, without incurring extra system overhead. Following this analysis, we adopt a revised PPO-EWMA method, which achieves significant gains in both training speed and optimization performance. Code at https://github.com/millioniron/ROLL.

Self-correction is a highly desirable capability of large language models (LLMs), yet it has consistently been found to be largely ineffective in modern LLMs. Existing approaches for training self-correction either require multiple models or rely on a more capable model or other forms of supervision. To this end, we develop a multi-turn online reinforcement learning (RL) approach, SCoRe, that significantly improves an LLM's self-correction ability using entirely self-generated data. To build SCoRe, we first show that variants of supervised fine-tuning (SFT) on offline model-generated correction traces are insufficient for instilling self-correction behavior. In particular, we observe that training via SFT either suffers from a distribution mismatch between the training data and the model's own responses or implicitly prefers only a certain mode of correction behavior that is often not effective at test time. SCoRe addresses these challenges by training under the model's own distribution of self-generated correction traces and using appropriate regularization to steer the learning process into learning a self-correction strategy that is effective at test time as opposed to simply fitting high-reward responses for a given prompt. This regularization prescribes running a first phase of RL on a base model to generate a policy initialization that is less susceptible to collapse and then using a reward bonus to amplify self-correction during training. When applied to Gemini 1.0 Pro and 1.5 Flash models, we find that SCoRe achieves state-of-the-art self-correction performance, improving the base models' self-correction by 15.6% and 9.1% respectively on the MATH and HumanEval benchmarks.

Foundation models, specifically Large Language Models (LLMs), have lately gained wide-spread attention and adoption. Reinforcement Learning with Human Feedback (RLHF) involves training a reward model to capture desired behaviors, which is then used to align LLM's. These reward models are additionally used at inference-time to estimate LLM responses' adherence to those desired behaviors. However, there is little work measuring how robust these reward models are to distribution shifts. In this work, we evaluate how reward model performance - measured via accuracy and calibration (i.e. alignment between accuracy and confidence) - is affected by distribution shift. We show novel calibration patterns and accuracy drops due to OOD prompts and responses, and that the reward model is more sensitive to shifts in responses than prompts. Additionally, we adapt an OOD detection technique commonly used in classification to the reward model setting to detect these distribution shifts in prompts and responses.

On-policy distillation (OPD) has shown strong potential for transferring reasoning ability from frontier or domain-specific models to smaller students. While effective on static single-turn tasks, its behavior in multi-turn agent settings remains underexplored. In this work, we identify a key limitation of vanilla OPD in such settings, which we term Trajectory-Level KL Instability. Specifically, we observe that KL divergence increases together with a drop in success rate, and even after convergence, the KL remains high, leading to unstable training. This instability arises from inter-turn error compounding: as errors accumulate, the student is driven beyond the teacher's effective support, rendering the supervision signal unreliable. To address this, we propose TCOD (Temporal Curriculum On-Policy Distillation), a simple yet effective framework that controls the trajectory depth exposed to the student and progressively expands it from short to long with a curriculum schedule.Experimental results across four student-teacher pairs on three multi-turn agent benchmarks (ALFWorld, WebShop, ScienceWorld) show that TCOD mitigates KL escalation and enhances KL stability throughout training, improving agent performance by up to 18 points over vanilla OPD. Further evaluations show that TCOD can even surpass the teacher's performance and generalize to tasks on which the teacher fails.

The intrinsic probabilistic nature of quantum systems makes error correction or mitigation indispensable for quantum computation. While current error-correcting strategies focus on correcting errors in quantum states or quantum gates, these fine-grained error-correction methods can incur significant overhead for quantum algorithms of increasing complexity. We present a first step in achieving error correction at the level of quantum algorithms by combining a unified perspective on modern quantum algorithms via quantum signal processing (QSP). An error model of under- or over-rotation of the signal processing operator parameterized by epsilon < 1 is introduced. It is shown that while Pauli Z-errors are not recoverable without additional resources, Pauli X and Y errors can be arbitrarily suppressed by coherently appending a noisy `recovery QSP.' Furthermore, it is found that a recovery QSP of length O(2^k c^{k^2} d) is sufficient to correct any length-d QSP with c unique phases to k^{th}-order in error epsilon. Allowing an additional assumption, a lower bound of Omega(cd) is shown, which is tight for k = 1, on the length of the recovery sequence. Our algorithmic-level error correction method is applied to Grover's fixed-point search algorithm as a demonstration.

In this paper, we explore a novel approach to 3D anomaly detection (AD) that goes beyond merely identifying anomalies based on structural characteristics. Our primary perspective is that most anomalies arise from unpredictable defective forces originating from both internal and external sources. To address these anomalies, we seek out opposing forces that can help correct them. Therefore, we introduce the Mechanics Complementary Model-based Framework for the 3D-AD task (MC4AD), which generates internal and external corrective forces for each point. We first propose a Diverse Anomaly-Generation (DA-Gen) module designed to simulate various types of anomalies. Next, we present the Corrective Force Prediction Network (CFP-Net), which uses complementary representations for point-level analysis to simulate the different contributions from internal and external corrective forces. To ensure the corrective forces are constrained effectively, we have developed a combined loss function that includes a new symmetric loss and an overall loss. Notably, we implement a Hierarchical Quality Control (HQC) strategy based on a three-way decision process and contribute a dataset titled Anomaly-IntraVariance, which incorporates intraclass variance to evaluate our model. As a result, the proposed MC4AD has been proven effective through theory and experimentation. The experimental results demonstrate that our approach yields nine state-of-the-art performances, achieving optimal results with minimal parameters and the fastest inference speed across five existing datasets, in addition to the proposed Anomaly-IntraVariance dataset. The source is available at https://github.com/hzzzzzhappy/MC4AD

Counterfactual explanations are attracting significant attention due to the flourishing applications of machine learning models in consequential domains. A counterfactual plan consists of multiple possibilities to modify a given instance so that the model's prediction will be altered. As the predictive model can be updated subject to the future arrival of new data, a counterfactual plan may become ineffective or infeasible with respect to the future values of the model parameters. In this work, we study the counterfactual plans under model uncertainty, in which the distribution of the model parameters is partially prescribed using only the first- and second-moment information. First, we propose an uncertainty quantification tool to compute the lower and upper bounds of the probability of validity for any given counterfactual plan. We then provide corrective methods to adjust the counterfactual plan to improve the validity measure. The numerical experiments validate our bounds and demonstrate that our correction increases the robustness of the counterfactual plans in different real-world datasets.

While self-correction has shown promise in improving LLM outputs in terms of style and quality (e.g. Chen et al., 2023; Madaan et al., 2023), recent attempts to self-correct logical or reasoning errors often cause correct answers to become incorrect, resulting in worse performances overall (Huang et al., 2023). In this paper, we break down the self-correction process into two core components: mistake finding and output correction. For mistake finding, we release BIG-Bench Mistake, a dataset of logical mistakes in Chain-of-Thought reasoning traces. We provide benchmark numbers for several state-of-the-art LLMs, and demonstrate that LLMs generally struggle with finding logical mistakes. For output correction, we propose a backtracking method which provides large improvements when given information on mistake location. We construe backtracking as a lightweight alternative to reinforcement learning methods, and show that it remains effective with a reward model at 60-70% accuracy.

Active reasoning requires large language model (LLM) agents to interact with external sources and strategically gather information to solve problems in multiple turns. Central to this process is belief tracking: maintaining an accurate representation of the underlying state and uncertainty in understanding and solving the problem. However, due to limited reasoning capabilities, LLM-based agents often suffer belief deviation: their internal beliefs drift from the true problem state, leading to loss of state awareness and uninformative or repetitive actions. Once this happens, errors compound in the trajectories used for reinforcement learning (RL), leading to misattributed credits and limited exploration. To address this issue, we propose to track belief deviation and develop T^3, a simple yet principled method that detects excessive deviation and truncates training trajectories to suppress uninformative tail effects. Hence, T^3 preserves credits for informative prefixes and systematically improves policy optimization. Across 5 challenging tasks, T^3 consistently enhances training stability and yields performance gains of up to 30 points while cutting token cost by up to 34%. These results highlight belief control as a key principle for building robust LLM agents capable of active reasoning.

Many political science theories relate to latent variables, but such quantities cannot be observed directly and must instead be estimated from data with inherent uncertainty. In regression models, when a variable is measured with error, its slope coefficient is known to be biased toward zero. We show how measurement error interacts with unique aspects of latent variable estimation, identification restrictions in particular, and demonstrate how common error adjustment strategies can worsen bias. We introduce a method for adjusting coefficients on latent predictors, which reduces bias and typically increases the magnitude of estimated coefficients, often dramatically. We illustrate these dynamics using several different estimation strategies for the latent predictors. Corrected estimates using our proposed method show stronger relationships -- sometimes up to 50% larger -- than those from naive regression. Our findings highlight the importance of considering measurement error in latent predictors and the inadequacy of many commonly used approaches for dealing with this issue.

We describe an iterative procedure for optimizing policies, with guaranteed monotonic improvement. By making several approximations to the theoretically-justified procedure, we develop a practical algorithm, called Trust Region Policy Optimization (TRPO). This algorithm is similar to natural policy gradient methods and is effective for optimizing large nonlinear policies such as neural networks. Our experiments demonstrate its robust performance on a wide variety of tasks: learning simulated robotic swimming, hopping, and walking gaits; and playing Atari games using images of the screen as input. Despite its approximations that deviate from the theory, TRPO tends to give monotonic improvement, with little tuning of hyperparameters.

Uncertainty quantification (UQ) is vital for trustworthy deep learning, yet existing methods are either computationally intensive, such as Bayesian or ensemble methods, or provide only partial, task-specific estimates, such as single-forward-pass techniques. In this paper, we propose a post-hoc single-forward-pass framework that jointly captures aleatoric and epistemic uncertainty without modifying or retraining pretrained models. Our method applies Split-Point Analysis (SPA) to decompose predictive residuals into upper and lower subsets, computing Mean Absolute Residuals (MARs) on each side. We prove that, under ideal conditions, the total MAR equals the harmonic mean of subset MARs; deviations define a novel Self-consistency Discrepancy Score (SDS) for fine-grained epistemic estimation across regression and classification. For regression, side-specific quantile regression yields prediction intervals with improved empirical coverage, which are further calibrated via SDS. For classification, when calibration data are available, we apply SPA-based calibration identities to adjust the softmax outputs and then compute predictive entropy on these calibrated probabilities. Extensive experiments on diverse regression and classification benchmarks demonstrate that our framework matches or exceeds several state-of-the-art UQ methods while incurring minimal overhead. Our source code is available at https://github.com/zzz0527/SPC-UQ.

The current state of machine learning scholarship in Timeseries Anomaly Detection (TAD) is plagued by the persistent use of flawed evaluation metrics, inconsistent benchmarking practices, and a lack of proper justification for the choices made in novel deep learning-based model designs. Our paper presents a critical analysis of the status quo in TAD, revealing the misleading track of current research and highlighting problematic methods, and evaluation practices. Our position advocates for a shift in focus from solely pursuing novel model designs to improving benchmarking practices, creating non-trivial datasets, and critically evaluating the utility of complex methods against simpler baselines. Our findings demonstrate the need for rigorous evaluation protocols, the creation of simple baselines, and the revelation that state-of-the-art deep anomaly detection models effectively learn linear mappings. These findings suggest the need for more exploration and development of simple and interpretable TAD methods. The increment of model complexity in the state-of-the-art deep-learning based models unfortunately offers very little improvement. We offer insights and suggestions for the field to move forward. Code: https://github.com/ssarfraz/QuoVadisTAD

Training a model to predict the next step in a concurrent program is harder than it looks: two runs of the same program from the same trace prefix can produce different next events, both valid, because the scheduler is nondeterministic. A model trained against a single label is learning to guess one outcome of a random process. We turn this around and use the nondeterminism as a training signal. We run each program many times, aggregate the observed next events into an empirical distribution, and fine-tune a 7B model to match that distribution with a KL objective. On 798 held-out predictions drawn from real production Go bugs (CockroachDB, Kubernetes, gRPC, etcd), fine-tuning on fewer than a thousand traces reaches 36.2% accuracy, ahead of Gemini 3.5 Flash used zero-shot (34.8%) and the same model without fine-tuning (28.6%). Distribution training matches cross-entropy on accuracy (35.8% vs. 36.2%) while reducing Expected Calibration Error from 0.205 to 0.169. We also derive a formal goroutine-leak signature for a class of select-blocked goroutines where P(GoUnblock)=0 holds by scheduler semantics, not by learning. We release the dataset, trained adapters, and all tooling.

Distilled autoregressive diffusion models facilitate real-time short video synthesis but suffer from severe error accumulation during long-sequence generation. While existing Test-Time Optimization (TTO) methods prove effective for images or short clips, we identify that they fail to mitigate drift in extended sequences due to unstable reward landscapes and the hypersensitivity of distilled parameters. To overcome these limitations, we introduce Test-Time Correction (TTC), a training-free alternative. Specifically, TTC utilizes the initial frame as a stable reference anchor to calibrate intermediate stochastic states along the sampling trajectory. Extensive experiments demonstrate that our method seamlessly integrates with various distilled models, extending generation lengths with negligible overhead while matching the quality of resource-intensive training-based methods on 30-second benchmarks.

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.

Earth system models suffer from various structural and parametric errors in their representation of nonlinear, multi-scale processes, leading to uncertainties in their long-term projections. The effects of many of these errors (particularly those due to fast physics) can be quantified in short-term simulations, e.g., as differences between the predicted and observed states (analysis increments). With the increase in the availability of high-quality observations and simulations, learning nudging from these increments to correct model errors has become an active research area. However, most studies focus on using neural networks, which while powerful, are hard to interpret, are data-hungry, and poorly generalize out-of-distribution. Here, we show the capabilities of Model Error Discovery with Interpretability and Data Assimilation (MEDIDA), a general, data-efficient framework that uses sparsity-promoting equation-discovery techniques to learn model errors from analysis increments. Using two-layer quasi-geostrophic turbulence as the test case, MEDIDA is shown to successfully discover various linear and nonlinear structural/parametric errors when full observations are available. Discovery from spatially sparse observations is found to require highly accurate interpolation schemes. While NNs have shown success as interpolators in recent studies, here, they are found inadequate due to their inability to accurately represent small scales, a phenomenon known as spectral bias. We show that a general remedy, adding a random Fourier feature layer to the NN, resolves this issue enabling MEDIDA to successfully discover model errors from sparse observations. These promising results suggest that with further development, MEDIDA could be scaled up to models of the Earth system and real observations.

Large Language Models (LLMs) have exhibited strong mathematical reasoning and computational prowess, tackling tasks ranging from basic arithmetic to advanced competition-level problems. However, frequently occurring subtle errors, such as miscalculations or incorrect substitutions, limit the models' full mathematical potential. Existing studies to improve mathematical ability typically involve distilling reasoning skills from stronger LLMs or applying preference learning to step-wise response pairs. Although these methods leverage samples of varying granularity to mitigate reasoning errors, they overlook the frequently occurring subtle errors. A major reason is that sampled preference pairs involve differences unrelated to the errors, which may distract the model from focusing on subtle errors. In this work, we propose a novel preference learning framework called eRror-Injected Self-Editing (RISE), which injects predefined subtle errors into partial tokens of correct solutions to construct hard pairs for error mitigation. In detail, RISE uses the model itself to edit a small number of tokens in the solution, injecting designed subtle errors. Then, pairs composed of self-edited solutions and their corresponding correct ones, along with pairs of correct and incorrect solutions obtained through sampling, are used together for subtle error-aware DPO training. Compared with other preference learning methods, RISE further refines the training objective to focus on predefined errors and their tokens, without requiring fine-grained sampling or preference annotation. Extensive experiments validate the effectiveness of RISE, with preference learning on Qwen2-7B-Instruct yielding notable improvements of 3.0% on GSM8K and 7.9% on MATH.

In this paper, we propose feedback designs for manipulating a quantum state to a target state by performing sequential measurements. In light of Belavkin's quantum feedback control theory, for a given set of (projective or non-projective) measurements and a given time horizon, we show that finding the measurement selection policy that maximizes the probability of successful state manipulation is an optimal control problem for a controlled Markovian process. The optimal policy is Markovian and can be solved by dynamical programming. Numerical examples indicate that making use of feedback information significantly improves the success probability compared to classical scheme without taking feedback. We also consider other objective functionals including maximizing the expected fidelity to the target state as well as minimizing the expected arrival time. The connections and differences among these objectives are also discussed.

Given a stationary state-space model that relates a sequence of hidden states and corresponding measurements or observations, Bayesian filtering provides a principled statistical framework for inferring the posterior distribution of the current state given all measurements up to the present time. For example, the Apollo lunar module implemented a Kalman filter to infer its location from a sequence of earth-based radar measurements and land safely on the moon. To perform Bayesian filtering, we require a measurement model that describes the conditional distribution of each observation given state. The Kalman filter takes this measurement model to be linear, Gaussian. Here we show how a nonlinear, Gaussian approximation to the distribution of state given observation can be used in conjunction with Bayes' rule to build a nonlinear, non-Gaussian measurement model. The resulting approach, called the Discriminative Kalman Filter (DKF), retains fast closed-form updates for the posterior. We argue there are many cases where the distribution of state given measurement is better-approximated as Gaussian, especially when the dimensionality of measurements far exceeds that of states and the Bernstein-von Mises theorem applies. Online neural decoding for brain-computer interfaces provides a motivating example, where filtering incorporates increasingly detailed measurements of neural activity to provide users control over external devices. Within the BrainGate2 clinical trial, the DKF successfully enabled three volunteers with quadriplegia to control an on-screen cursor in real-time using mental imagery alone. Participant "T9" used the DKF to type out messages on a tablet PC.

Evaluating anomaly detection algorithms in time series data is critical as inaccuracies can lead to flawed decision-making in various domains where real-time analytics and data-driven strategies are essential. Traditional performance metrics assume iid data and fail to capture the complex temporal dynamics and specific characteristics of time series anomalies, such as early and delayed detections. We introduce Proximity-Aware Time series anomaly Evaluation (PATE), a novel evaluation metric that incorporates the temporal relationship between prediction and anomaly intervals. PATE uses proximity-based weighting considering buffer zones around anomaly intervals, enabling a more detailed and informed assessment of a detection. Using these weights, PATE computes a weighted version of the area under the Precision and Recall curve. Our experiments with synthetic and real-world datasets show the superiority of PATE in providing more sensible and accurate evaluations than other evaluation metrics. We also tested several state-of-the-art anomaly detectors across various benchmark datasets using the PATE evaluation scheme. The results show that a common metric like Point-Adjusted F1 Score fails to characterize the detection performances well, and that PATE is able to provide a more fair model comparison. By introducing PATE, we redefine the understanding of model efficacy that steers future studies toward developing more effective and accurate detection models.

Decoders for quantum error correction (QEC) experiments rely on detector error models (DEMs), which encode, for each error, its probability and the detectors and logical observables it flips. Here we show that estimating DEM event probabilities from experimental syndromes is feasible, avoids independent device benchmarking, and produces useful decoder priors for estimating and reducing decoded logical error probabilities. We evaluate our methods using open-source data from surface-code memory experiments performed on Google's Willow chip, and we carry out analogous surface-code experiments on IBM's ibm\_miami processor. Despite the different physical error scales of the Google and IBM devices, in both cases our estimated DEMs improve logical error probabilities relative to baseline device-informed DEMs, typically at the 5%-10% level and with larger gains in some IBM cases, without additional calibration circuits, decoder fine-tuning, or supervised fitting to logical outcomes.

The progress in modelling time series and, more generally, sequences of structured data has recently revamped research in anomaly detection. The task stands for identifying abnormal behaviors in financial series, IT systems, aerospace measurements, and the medical domain, where anomaly detection may aid in isolating cases of depression and attend the elderly. Anomaly detection in time series is a complex task since anomalies are rare due to highly non-linear temporal correlations and since the definition of anomalous is sometimes subjective. Here we propose the novel use of Hyperbolic uncertainty for Anomaly Detection (HypAD). HypAD learns self-supervisedly to reconstruct the input signal. We adopt best practices from the state-of-the-art to encode the sequence by an LSTM, jointly learned with a decoder to reconstruct the signal, with the aid of GAN critics. Uncertainty is estimated end-to-end by means of a hyperbolic neural network. By using uncertainty, HypAD may assess whether it is certain about the input signal but it fails to reconstruct it because this is anomalous; or whether the reconstruction error does not necessarily imply anomaly, as the model is uncertain, e.g. a complex but regular input signal. The novel key idea is that a detectable anomaly is one where the model is certain but it predicts wrongly. HypAD outperforms the current state-of-the-art for univariate anomaly detection on established benchmarks based on data from NASA, Yahoo, Numenta, Amazon, and Twitter. It also yields state-of-the-art performance on a multivariate dataset of anomaly activities in elderly home residences, and it outperforms the baseline on SWaT. Overall, HypAD yields the lowest false alarms at the best performance rate, thanks to successfully identifying detectable anomalies.

Self-improving AI agents are designed to learn from their mistakes. We show they can also hallucinate mistakes that never happened. We study this failure mode in automated harness optimization, where an LLM-based proposer edits an agent's scaffold, including prompts, parsers, filters, validators and guardrails, to eliminate observed failures. But this process rarely asks first: was there a real failure to fix? We introduce the Counterfactual Fabrication Lab, a deterministic micro-lab where the correct action is known: do nothing. The lab plants a candidate guardrail for a failure class that provably never occurs, presents only legal episodes, and uses a byte-exact oracle to check every cited violation. The proposer behaves as expected on real violations and abstains on featureless legal input. Yet when the legal input contains a harmless pattern resembling a familiar game rule, it invents a failure: in 15/60 runs, versus 0/60 on featureless input, it enables the nonexistent-rule guardrail and cites a violation the oracle refutes. The effect is structured, not indiscriminate. In single-shot proposals it appears only when three conditions coincide: a rule-shaped pattern, an open-ended rule set and an instruction that presupposes failures. Removing any of these conditions eliminates the fabrication. Because the invented guardrail changes no true outcome and cannot improve an already-perfect suppression score, the phenomenon is neither reward hacking nor over-refusal. It is a phantom guardrail: a fix for a failure that never happened, invisible to suppression-only acceptance. Inside an add-only accept loop it re-enters even without the failure-presupposing instruction, the loop's keep-adding role supplying the demand the instruction supplied in single shot, and once in it stays. We present the Counterfactual Fabrication Lab for measuring fabricated failures in self-improving agent harnesses.

Unsupervised anomaly detection (UAD) in brain imaging is crucial for identifying pathologies without the need for labeled data. However, accurately localizing anomalies remains challenging due to the intricate structure of brain anatomy and the scarcity of abnormal examples. In this work, we introduce REFLECT, a novel framework that leverages rectified flows to establish a direct, linear trajectory for correcting abnormal MR images toward a normal distribution. By learning a straight, one-step correction transport map, our method efficiently corrects brain anomalies and can precisely localize anomalies by detecting discrepancies between anomalous input and corrected counterpart. In contrast to the diffusion-based UAD models, which require iterative stochastic sampling, rectified flows provide a direct transport map, enabling single-step inference. Extensive experiments on popular UAD brain segmentation benchmarks demonstrate that REFLECT significantly outperforms state-of-the-art unsupervised anomaly detection methods. The code is available at https://github.com/farzad-bz/REFLECT.

Reinforcement learning (RL) fine-tuning of large language models (LLMs) often suffers from instability due to the numerical mismatch between the training and inference policies. While prior work has attempted to mitigate this issue through algorithmic corrections or engineering alignments, we show that its root cause lies in the floating point precision itself. The widely adopted BF16, despite its large dynamic range, introduces large rounding errors that breaks the consistency between training and inference. In this work, we demonstrate that simply reverting to FP16 effectively eliminates this mismatch. The change is simple, fully supported by modern frameworks with only a few lines of code change, and requires no modification to the model architecture or learning algorithm. Our results suggest that using FP16 uniformly yields more stable optimization, faster convergence, and stronger performance across diverse tasks, algorithms and frameworks. We hope these findings motivate a broader reconsideration of precision trade-offs in RL fine-tuning.

The ambition of harnessing the quantum for computation is at odds with the fundamental phenomenon of decoherence. The purpose of quantum error correction (QEC) is to counteract the natural tendency of a complex system to decohere. This cooperative process, which requires participation of multiple quantum and classical components, creates a special type of dissipation that removes the entropy caused by the errors faster than the rate at which these errors corrupt the stored quantum information. Previous experimental attempts to engineer such a process faced an excessive generation of errors that overwhelmed the error-correcting capability of the process itself. Whether it is practically possible to utilize QEC for extending quantum coherence thus remains an open question. We answer it by demonstrating a fully stabilized and error-corrected logical qubit whose quantum coherence is significantly longer than that of all the imperfect quantum components involved in the QEC process, beating the best of them with a coherence gain of G = 2.27 pm 0.07. We achieve this performance by combining innovations in several domains including the fabrication of superconducting quantum circuits and model-free reinforcement learning.

In real-world applications of reinforcement learning, it is often challenging to obtain a state representation that is parsimonious and satisfies the Markov property without prior knowledge. Consequently, it is common practice to construct a state larger than necessary, e.g., by concatenating measurements over contiguous time points. However, needlessly increasing the dimension of the state may slow learning and obfuscate the learned policy. We introduce the notion of a minimal sufficient state in a Markov decision process (MDP) as the subvector of the original state under which the process remains an MDP and shares the same reward function as the original process. We propose a novel SEquEntial Knockoffs (SEEK) algorithm that estimates the minimal sufficient state in a system with high-dimensional complex nonlinear dynamics. In large samples, the proposed method achieves selection consistency. As the method is agnostic to the reinforcement learning algorithm being applied, it benefits downstream tasks such as policy learning. Empirical experiments verify theoretical results and show the proposed approach outperforms several competing methods regarding variable selection accuracy and regret.

Popular guidance for denoising diffusion probabilistic model (DDPM) linearly combines distinct conditional models together to provide enhanced control over samples. However, this approach overlooks nonlinear effects that become significant when guidance scale is large. To address this issue, we propose characteristic guidance, a guidance method that provides first-principle non-linear correction for classifier-free guidance. Such correction forces the guided DDPMs to respect the Fokker-Planck (FP) equation of diffusion process, in a way that is training-free and compatible with existing sampling methods. Experiments show that characteristic guidance enhances semantic characteristics of prompts and mitigate irregularities in image generation, proving effective in diverse applications ranging from simulating magnet phase transitions to latent space sampling.

Mechanical defects in real situations affect observation values and cause abnormalities in multivariate time series, such as sensor values or network data. To perceive abnormalities in such data, it is crucial to understand the temporal context and interrelation between variables simultaneously. The anomaly detection task for time series, especially for unlabeled data, has been a challenging problem, and we address it by applying a suitable data degradation scheme to self-supervised model training. We define four types of synthetic outliers and propose the degradation scheme in which a portion of input data is replaced with one of the synthetic outliers. Inspired by the self-attention mechanism, we design a Transformer-based architecture to recognize the temporal context and detect unnatural sequences with high efficiency. Our model converts multivariate data points into temporal representations with relative position bias and yields anomaly scores from these representations. Our method, AnomalyBERT, shows a great capability of detecting anomalies contained in complex time series and surpasses previous state-of-the-art methods on five real-world benchmarks. Our code is available at https://github.com/Jhryu30/AnomalyBERT.

Diffusion models have achieved remarkable success as generative models. However, even a well-trained model can accumulate errors throughout the generation process. These errors become particularly problematic when arbitrary guidance is applied to steer samples toward desired properties, which often breaks sample fidelity. In this paper, we propose a general solution to address the off-manifold phenomenon observed in diffusion models. Our approach leverages a time predictor to estimate deviations from the desired data manifold at each timestep, identifying that a larger time gap is associated with reduced generation quality. We then design a novel guidance mechanism, `Temporal Alignment Guidance' (TAG), attracting the samples back to the desired manifold at every timestep during generation. Through extensive experiments, we demonstrate that TAG consistently produces samples closely aligned with the desired manifold at each timestep, leading to significant improvements in generation quality across various downstream tasks.

We study how to learn ε-optimal strategies in zero-sum imperfect information games (IIG) with trajectory feedback. In this setting, players update their policies sequentially based on their observations over a fixed number of episodes, denoted by T. Existing procedures suffer from high variance due to the use of importance sampling over sequences of actions (Steinberger et al., 2020; McAleer et al., 2022). To reduce this variance, we consider a fixed sampling approach, where players still update their policies over time, but with observations obtained through a given fixed sampling policy. Our approach is based on an adaptive Online Mirror Descent (OMD) algorithm that applies OMD locally to each information set, using individually decreasing learning rates and a regularized loss. We show that this approach guarantees a convergence rate of mathcal{O}(T^{-1/2}) with high probability and has a near-optimal dependence on the game parameters when applied with the best theoretical choices of learning rates and sampling policies. To achieve these results, we generalize the notion of OMD stabilization, allowing for time-varying regularization with convex increments.

Accurate state estimation in Unmanned Aerial Vehicles (UAVs) is crucial for ensuring reliable and safe operation, as anomalies occurring during mission execution may induce discrepancies between expected and observed system behaviors, thereby compromising mission success or posing potential safety hazards. It is essential to continuously monitor and detect such conditions in order to ensure a timely response and maintain system reliability. In this work, we focus on UAV state estimation anomalies and provide a large-scale real-world UAV dataset to facilitate research aimed at improving the development of anomaly detection. Unlike existing datasets that primarily rely on injected faults into simulated data, this dataset comprises 1396 real flight logs totaling over 52 hours of flight time, collected across diverse indoor and outdoor environments using a collection of PX4-based UAVs equipped with a variety of sensor configurations. The dataset comprises both normal and anomalous flights without synthetic manipulation, making it uniquely suitable for realistic anomaly detection tasks. A structured classification is proposed that categorizes UAV state estimation anomalies into four classes: mechanical and electrical, external position, global position, and altitude anomalies. These classifications reflect collective, contextual, and outlier anomalies observed in multivariate sensor data streams, including IMU, GPS, barometer, magnetometer, distance sensors, visual odometry, and optical flow, that can be found in the PX4 logging mechanism. It is anticipated that this dataset will play a key role in the development, training, and evaluation of anomaly detection and isolation systems to address the critical gap in UAV reliability research.

The accurate modeling of dynamics in interactive environments is critical for successful long-range prediction. Such a capability could advance Reinforcement Learning (RL) and Planning algorithms, but achieving it is challenging. Inaccuracies in model estimates can compound, resulting in increased errors over long horizons. We approach this problem from the lens of Koopman theory, where the nonlinear dynamics of the environment can be linearized in a high-dimensional latent space. This allows us to efficiently parallelize the sequential problem of long-range prediction using convolution while accounting for the agent's action at every time step. Our approach also enables stability analysis and better control over gradients through time. Taken together, these advantages result in significant improvement over the existing approaches, both in the efficiency and the accuracy of modeling dynamics over extended horizons. We also show that this model can be easily incorporated into dynamics modeling for model-based planning and model-free RL and report promising experimental results.

Time series anomalies can offer information relevant to critical situations facing various fields, from finance and aerospace to the IT, security, and medical domains. However, detecting anomalies in time series data is particularly challenging due to the vague definition of anomalies and said data's frequent lack of labels and highly complex temporal correlations. Current state-of-the-art unsupervised machine learning methods for anomaly detection suffer from scalability and portability issues, and may have high false positive rates. In this paper, we propose TadGAN, an unsupervised anomaly detection approach built on Generative Adversarial Networks (GANs). To capture the temporal correlations of time series distributions, we use LSTM Recurrent Neural Networks as base models for Generators and Critics. TadGAN is trained with cycle consistency loss to allow for effective time-series data reconstruction. We further propose several novel methods to compute reconstruction errors, as well as different approaches to combine reconstruction errors and Critic outputs to compute anomaly scores. To demonstrate the performance and generalizability of our approach, we test several anomaly scoring techniques and report the best-suited one. We compare our approach to 8 baseline anomaly detection methods on 11 datasets from multiple reputable sources such as NASA, Yahoo, Numenta, Amazon, and Twitter. The results show that our approach can effectively detect anomalies and outperform baseline methods in most cases (6 out of 11). Notably, our method has the highest averaged F1 score across all the datasets. Our code is open source and is available as a benchmarking tool.

Driving on roads is restricted by various traffic rules, aiming to ensure safety for all traffic participants. However, human road users usually do not adhere to these rules strictly, resulting in varying degrees of rule conformity. Such deviations from given rules are key components of today's road traffic. In autonomous driving, robotic agents can disturb traffic flow, when rule deviations are not taken into account. In this paper, we present an approach to derive the distribution of degrees of rule conformity from human driving data. We demonstrate our method with the Waymo Open Motion dataset and Safety Distance and Speed Limit rules.

A content-moderation system can score well on every standard accuracy metric and still cause real harm, if its mistakes fall on the few users who connect otherwise separate communities. We show this in an agent-based model where N=240 learning agents on a community-structured network each post harmless, productive, or dangerous content, and a regulator removes or penalizes whatever a noisy classifier flags. Overall usefulness barely moves as the noise changes (one-way ANOVA, p=0.96): by aggregate measures, nothing looks wrong. The damage instead concentrates on these bridge users, whose useful posts are wrongly suppressed and whose dangerous posts are wrongly spared. A governance loss (L_gov) that prices these two mistakes separately from the cost of enforcement more than doubles under false-positive-heavy noise. Aggregate accuracy hides who is harmed, and the cheap quantity to audit is how many connections a user has (degree), a near-perfect proxy for the betweenness that defines a bridge (r=0.96).

Large language models (LLMs) can call tools effectively, yet they remain brittle in multi-turn execution: following a tool call error, smaller models often degenerate into repetitive invalid re-invocations, failing to interpret error feedback and self-correct. This brittleness hinders reliable real-world deployment, where the execution errors are inherently inevitable during tool interaction procedures. We identify a key limitation of current approaches: standard reinforcement learning (RL) treats errors as sparse negative rewards, providing no guidance on how to recover, while pre-collected synthetic error-correction datasets suffer from distribution mismatch with the model's on-policy error modes. To bridge this gap, we propose Fission-GRPO, a framework that converts execution errors into corrective supervision within the RL training loop. Our core mechanism fissions each failed trajectory into a new training instance by augmenting it with diagnostic feedback from a finetuned Error Simulator, then resampling recovery rollouts on-policy. This enables the model to learn from the precise errors it makes during exploration, rather than from static, pre-collected error cases. On the BFCL v4 Multi-Turn, Fission-GRPO improves the error recovery rate of Qwen3-8B by 5.7% absolute, crucially, yielding a 4% overall accuracy gain (42.75% to 46.75%) over GRPO and outperforming specialized tool-use agents.

This research enhances linear regression models by integrating a Kalman filter and analysing curve areas to minimize loss. The goal is to develop an optimal linear regression equation using stochastic gradient descent (SGD) for weight updating. Our approach involves a stepwise process, starting with user-defined parameters. The linear regression model is trained using SGD, tracking weights and loss separately and zipping them finally. A Kalman filter is then trained based on weight and loss arrays to predict the next consolidated weights. Predictions result from multiplying input averages with weights, evaluated for loss to form a weight-versus-loss curve. The curve's equation is derived using the two-point formula, and area under the curve is calculated via integration. The linear regression equation with minimum area becomes the optimal curve for prediction. Benefits include avoiding constant weight updates via gradient descent and working with partial datasets, unlike methods needing the entire set. However, computational complexity should be considered. The Kalman filter's accuracy might diminish beyond a certain prediction range.

This paper studies the original discrete-time denoising diffusion probabilistic model (DDPM) from a probabilistic point of view. We present three main theoretical results. First, we show that the time-dependent score function associated with the forward diffusion process admits a characterization as the backward component of a forward--backward stochastic differential equation (FBSDE). This result provides a structural description of the score function and clarifies how score estimation errors propagate along the reverse-time dynamics. As a by-product, we also obtain a system of semilinear parabolic PDEs for the score function. Second, we use tools from Schrödinger's problem to relate distributional errors arising in reverse time to corresponding errors in forward time. This approach allows us to control the reverse-time sampling error in a systematic way. Third, combining these results, we derive an explicit upper bound for the total variation distance between the sampling distribution of the discrete-time DDPM algorithm and the target data distribution under general finite noise schedules. The resulting bound separates the contributions of the learning error and the time discretization error. Our analysis highlights the intrinsic probabilistic structure underlying discrete-time DDPMs and provides a clearer understanding of the sources of error in their sampling procedure.