Time Series

Long-distance depth imaging holds great promise for applications such as autonomous driving and robotics. Direct time-of-flight (dToF) imaging offers high-precision, long-distance depth sensing, yet demands ultra-short pulse light sources and high-resolution time-to-digital converters. In contrast, indirect time-of-flight (iToF) imaging often suffers from phase wrapping and low signal-to-noise ratio (SNR) as the sensing distance increases. In this paper, we introduce a novel ToF imaging paradigm, termed Burst-Encodable Time-of-Flight (BE-ToF), which facilitates high-fidelity, long-distance depth imaging. Specifically, the BE-ToF system emits light pulses in burst mode and estimates the phase delay of the reflected signal over the entire burst period, thereby effectively avoiding the phase wrapping inherent to conventional iToF systems. Moreover, to address the low SNR caused by light attenuation over increasing distances, we propose an end-to-end learnable framework that jointly optimizes the coding functions and the depth reconstruction network. A specialized double well function and first-order difference term are incorporated into the framework to ensure the hardware implementability of the coding functions. The proposed approach is rigorously validated through comprehensive simulations and real-world prototype experiments, demonstrating its effectiveness and practical applicability. The code is available at: https://github.com/ComputationalPerceptionLab/BE-ToF.

Test-time adaptation aims to improve model robustness under distribution shifts by adapting models with access to unlabeled target samples. A primary cause of performance degradation under such shifts is the model’s reliance on features that lack a direct causal relationship with the prediction target. We introduce Test-time Adaptation by Causal Trimming (TACT), a method that identifies and removes non-causal components from representations for test distributions. TACT applies data augmentations that preserve causal features while varying non-causal ones. By analyzing the changes in the representations using Principal Component Analysis, TACT identifies the highest variance directions associated with non-causal features. It trims the representations by removing their projections on the identified directions, and uses the trimmed representations for the predictions. During adaptation, TACT continuously tracks and refines these directions to get a better estimate of non-causal features. We theoretically analyze the effectiveness of this approach and empirically validate TACT on real-world out-of-distribution benchmarks. TACT consistently outperforms state-of-the-art methods by a significant margin.

Time series data in real-world applications such as healthcare, climate modeling, and finance are often irregular, multimodal, and messy, with varying sampling rates, asynchronous modalities, and pervasive missingness. However, existing benchmarks typically assume clean, regularly sampled, unimodal data, creating a significant gap between research and real-world deployment. We introduce Time-IMM, a dataset specifically designed to capture cause-driven irregularity in multimodal multivariate time series. Time-IMM represents nine distinct types of time series irregularity, categorized into trigger-based, constraint-based, and artifact-based mechanisms. Complementing the dataset, we introduce IMM-TSF, a benchmark library for forecasting on irregular multimodal time series, enabling asynchronous integration and realistic evaluation. IMM-TSF includes specialized fusion modules, including a timestamp-to-text fusion module and a multimodality fusion module, which support both recency-aware averaging and attention-based integration strategies. Empirical results demonstrate that explicitly modeling multimodality on irregular time series data leads to substantial gains in forecasting performance. Time-IMM and IMM-TSF provide a foundation for advancing time series analysis under real-world conditions. The dataset is publicly available at \url{https://github.com/blacksnail789521/Time-IMM}, and the benchmark library can be accessed at \url{https://github.com/blacksnail789521/IMM-TSF}.

Pretrained vision-language models such as CLIP achieve strong zero-shot generalization but remain vulnerable to distribution shifts caused by input corruptions. In this work, we investigate how corruptions affect CLIP’s image embeddings and uncover a consistent phenomenon we term as embedding variance collapse, where both intra-class and inter-class variances shrink as corruption severity increases. We find that this collapse is closely tied to performance degradation, with inter-class variance strongly correlated with classification accuracy. To explain this phenomenon, we analyze how corruptions alter the structure of the embedding space. Our theoretical results suggest that the visual encoder tends to encode corruption-related signals, which dilute class-discriminative features and compress the representation geometry. We further show that maximizing inter-class variance, even when estimated from pseudo-labels, can provably enhance embedding quality. Based on this insight, we propose Mint, a simple test-time adaptation method that maximizes pseudo-label-based inter-class variance on the fly using a mean accumulator and a gradient accumulator. Mint operates effectively with small batch sizes and consistently improves performance across multiple corruption benchmarks and CLIP architectures. Our code is available at https://github.com/baowenxuan/Mint.

Causality in time series can be challenging to determine, especially in the presence of non-linear dependencies. Granger causality helps analyze potential relationships between variables, thereby offering a method to determine whether one time series can predict—Granger cause—future values of another. Although successful, Granger causal methods still struggle with capturing long-range relations between variables. To this end, we leverage the recently successful Extended Long Short-Term Memory (xLSTM) architecture and propose Granger causal xLSTMs (GC-xLSTM). It first enforces sparsity between the time series components by using a novel dynamic loss penalty on the initial projection. Specifically, we adaptively improve the model and identify sparsity candidates. Our joint optimization procedure then ensures that the Granger causal relations are recovered robustly. Our experimental evaluation on six diverse datasets demonstrates the overall efficacy of GC-xLSTM.

Due to the difficulty in collecting all unexpected abnormal patterns, One-Class Classification (OCC) has become the most popular approach to anomaly detection (AD). Reconstruction-based AD method relies on the discrepancy between inputs and reconstructed results to identify unobserved anomalies. However, recent methods trained only on normal samples may generalize to certain abnormal inputs, leading to well-reconstructed anomalies and degraded performance. To address this, we constrain reconstructions to remain on the normal manifold using a novel AD framework based on contraction mapping. This mapping guarantees that any input converges to a fixed point through iterations of this mapping. Based on this property, training the contraction mapping using only normal data ensures that its fixed point lies within the normal manifold. As a result, abnormal inputs are iteratively transformed toward the normal manifold, increasing the reconstruction error. In addition, the inherent invertibility of contraction mapping enables flow-based density estimation, where a prior distribution learned from the previous reconstruction is used to estimate the input likelihood for anomaly detection, further improving the performance. Using both mechanisms, we propose a bidirectional structure with forward reconstruction and backward density estimation. Extensive experiments on tabular data, natural image, and industrial image data demonstrate the effectiveness of our method. The code is available at URD.

Test-Time Scaling (TTS) improves the performance of Large Language Models (LLMs) by using additional inference-time computation to explore multiple reasoning paths through search. Yet how to allocate a fixed rollout budget most effectively during search remains underexplored, often resulting in inefficient use of compute at test time. To bridge this gap, we formulate test-time search as a resource allocation problem and derive the optimal allocation strategy that maximizes the probability of obtaining a correct solution under a fixed rollout budget. Within this formulation, we reveal a core limitation of existing search methods: solution-level allocation tends to favor reasoning directions with more candidates, leading to theoretically suboptimal and inefficient use of compute. To address this, we propose Direction-Oriented Resource Allocation (DORA), a provably optimal method that mitigates this bias by decoupling direction quality from candidate count and allocating resources at the direction level. To demonstrate DORA’s effectiveness, we conduct extensive experiments on challenging mathematical reasoning benchmarks including MATH500, AIME2024, and AIME2025. The empirical results show that DORA consistently outperforms strong baselines with comparable computational cost, achieving state-of-the-art accuracy. We hope our findings contribute to a broader understanding of optimal TTS for LLMs.

Multivariate time series (MTS) classification has attracted increasing attention across various domains. Existing methods either decompose MTS into separate univariate series, ignoring inter-variable dependencies, or jointly model all variables, which may lead to over-smoothing and loss of semantic structure. These limitations become particularly pronounced when dealing with complex and heterogeneous variable types. To address these challenges, we propose SwinGroupNet (SGN), which explores a novel perspective for constructing variable interaction and temporal dependency. Specifically, SGN processes multi-scale time series using (1) Variable Group Embedding (VGE), which partitions variables into groups and performs independent group-wise embedding; (2) Multi-Scale Group Window Mixing (MGWM), which reconstructs variable interactions by modeling both intra-group and inter-group dependencies while extracting multi-scale temporal features; and (3) Periodic Window Shifting and Merging (PWSM), which exploits inherent periodic patterns to enable hierarchical temporal interaction and feature aggregation. Extensive experiments on diverse benchmark datasets from multiple domains demonstrate that SGN consistently achieves state-of-the-art performance, with an average improvement of 4.2% over existing methods. We release the source code at https://anonymous.4open.science/r/SGN.

Foundation models for time series analysis (TSA) have attracted significant attention. However, challenges such as training data scarcity and imbalance continue to hinder their development. Inspired by complex dynamic system theories, we design a series-symbol data generation mechanism, enabling the unrestricted creation of high-quality time series data paired with corresponding symbolic expressions. To leverage series-symbol data pairs with strong correlations, we develop SymTime, a pre-trained foundation model for enhancing time series representation using symbolic information. SymTime demonstrates competitive performance across five major TSA tasks when fine-tunes with downstream tasks, rivaling foundation models pre-trained on real-world datasets. This approach underscores the potential of series-symbol data generation and pretraining mechanisms in overcoming data scarcity and enhancing task performance. The code is available at https://github.com/wwhenxuan/SymTime.

We introduce a new interpretation of the attention matrix as a discrete-time Markov chain. Our interpretation sheds light on common operations involving attention scores such as selection, summation, and averaging in a unified framework. It further extends them by considering indirect attention, propagated through the Markov chain, as opposed to previous studies that only model immediate effects. Our key observation is that tokens linked to semantically similar regions form metastable states, i.e., regions where attention tends to concentrate, while noisy attention scores dissipate. Metastable states and their prevalence can be easily computed through simple matrix multiplication and eigenanalysis, respectively. Using these lightweight tools, we demonstrate state-of-the-art zero-shot segmentation. Lastly, we define TokenRank---the steady state vector of the Markov chain, which measures global token importance. We show that TokenRank enhances unconditional image generation, improving both quality (IS) and diversity (FID), and can also be incorporated into existing segmentation techniques to improve their performance over existing benchmarks. We believe our framework offers a fresh view of how tokens are being attended in modern visual transformers.

Open-weight large language model (LLM) zoos provide access to numerous high-quality models, but selecting the appropriate model for specific tasks remains challenging and requires technical expertise. Most users simply want factually correct, safe, and satisfying responses without concerning themselves with model technicalities, while inference service providers prioritize minimizing operating costs. These competing interests are typically mediated through service level agreements (SLAs) that guarantee minimum service quality. We introduce MESS+, a stochastic optimization algorithm for cost-optimal LLM request routing while providing rigorous SLA compliance guarantees. MESS+ learns request satisfaction probabilities of LLMs in real-time as users interact with the system, based on which model selection decisions are made by solving a per-request optimization problem. Our algorithm includes a novel combination of virtual queues and request satisfaction prediction, along with a theoretical analysis of cost optimality and constraint satisfaction. Across a wide range of state-of-the-art LLM benchmarks, MESS+ achieves an average of $2\times$ cost savings compared to existing LLM routing techniques.

Uncovering cause-effect relationships from observational time series is fundamental to understanding complex systems. While many methods infer static causal graphs, real-world systems often exhibit *dynamic causality*—where relationships evolve over time. Accurately capturing these temporal dynamics requires time-resolved causal graphs. We propose UnCLe, a novel deep learning method for scalable dynamic causal discovery. UnCLe employs a pair of Uncoupler and Recoupler networks to disentangle input time series into semantic representations and learns inter-variable dependencies via auto-regressive Dependency Matrices. It estimates dynamic causal influences by analyzing datapoint-wise prediction errors induced by temporal perturbations. Extensive experiments demonstrate that UnCLe not only outperforms state-of-the-art baselines on static causal discovery benchmarks but, more importantly, exhibits a unique capability to accurately capture and represent evolving temporal causality in both synthetic and real-world dynamic systems (e.g., human motion). UnCLe offers a promising approach for revealing the underlying, time-varying mechanisms of complex phenomena.

Recent advances in inference-time compute have significantly improved performance on complex tasks by generating long chains of thought (CoTs) using Large Reasoning Models (LRMs). However, this improved accuracy comes at the cost of high inference latency due to the length of generated reasoning sequences and the autoregressive nature of decoding. Our key insight in tackling these overheads is that LRM inference, and the reasoning that it embeds, is highly tolerant of approximations: complex tasks are typically broken down into simpler steps, each of which brings utility based on the semantic insight it provides for downstream steps rather than the exact tokens it generates. Accordingly, we introduce SpecReason, a system that automatically accelerates LRM inference by using a lightweight model to (speculatively) carry out simpler intermediate reasoning steps and reserving the costly base model only to efficiently assess (and potentially correct) the speculated outputs. Importantly, SpecReason's focus on exploiting the semantic flexibility of thinking tokens in preserving final-answer accuracy is complementary to prior speculation techniques, most notably speculative decoding, which demands token-level equivalence at each step. Across a variety of cross-domain reasoning benchmarks, SpecReason achieves 1.4-3.0$\times$ speedup over vanilla LRM inference while improving accuracy by 0.4-9.0%. Compared to speculative decoding without SpecReason, their combination yields an additional 8.8-58.0% latency reduction. We open-source SpecReason at \url{https://anonymous.4open.science/r/specreason/}.

Reconstruction-based methods are competitive choices for multivariate time series anomaly detection (MTS AD). However, one challenge these methods may suffer is over generalization, where abnormal inputs are also well reconstructed. In addition, balancing robustness and sensitivity is also important for final performance, as robustness ensures accurate detection in potentially noisy data, while sensitivity enables early detection of subtle anomalies. To address these problems, inspired by idempotent generative network, we take the view from the manifold and propose a novel module named **I**dempotent **G**eneration for **A**nomaly **D**etection (IGAD) which can be flexibly combined with a reconstruction-based method without introducing additional trainable parameters. We modify the manifold to make sure that normal time points can be mapped onto it while tightening it to drop out abnormal time points simultaneously. Regarding the latest findings of AD metrics, we evaluated IGAD on various methods with four real-world datasets, and they achieve visible improvements in VUS-PR than their predecessors, demonstrating the effective potential of IGAD for further improvements in MTS AD tasks. Our instructions on integrating IGAD into customized models and example codes are available at https://github.com/ProEcho1/Idempotent-Generation-for-Anomaly-Detection-IGAD.

Deep State Space Models (SSMs) reignite physics-grounded compute paradigms, as RNNs could natively be embodied into dynamical systems. This calls for dedicated learning algorithms obeying to core physical principles, with efficient techniques to simulate these systems and guide their design. We propose \emph{Recurrent Hamiltonian Echo Learning} (RHEL), an algorithm which provably computes loss gradients as finite differences of physical trajectories of non-dissipative, \emph{Hamiltonian systems}. In ML terms, RHEL only requires three ``forward passes'' irrespective of model size, without explicit Jacobian computation, nor incurring any variance in the gradient estimation. Motivated by the potential to implement our algorithm in non-digital physical systems, we first introduce RHEL in \emph{continuous time} and demonstrate its formal equivalence with the continuous adjoint state method. To facilitate the simulation of Hamiltonian systems trained by RHEL, we propose a \emph{discrete-time} version of RHEL which is equivalent to Backpropagation Through Time (BPTT) when applied to a class of recurrent modules which we call \emph{Hamiltonian Recurrent Units} (HRUs). This setting allows us to demonstrate the scalability of RHEL by generalizing these results to hierarchies of HRUs, which we call \emph{Hamiltonian SSMs} (HSSMs). We apply RHEL to train HSSMs with linear and nonlinear dynamics on a variety of time-series tasks ranging from mid-range to long-range classification and regression with sequence length reaching $\sim 50k$. We show that RHEL consistently matches the performance of BPTT across all models and tasks. This work opens new doors for the design of scalable, energy-efficient physical systems endowed with self-learning capabilities for sequence modelling.

Loss of plasticity (LoP) is the primary cause of cognitive decline in normal aging brains next to cell loss. Recent works show that similar LoP also plagues neural networks during deep continual learning (DCL). While it has been shown that random perturbations of learned weights can alleviate LoP, its underlying mechanisms remain insufficiently understood. Here we offer a unique view of LoP and dissect its mechanisms through the lenses of an innovative framework combining the theory of neural collapse and finite-time Lyapunov exponents (FTLE) analysis. We show that LoP actually consists of two contrasting types: (i) type-1 LoP is characterized by highly negative FTLEs, where the network is prevented from learning due to the collapse of representations; (ii) while type-2 LoP is characterized by excessively positive FTLEs, where the network can train well but the growingly chaotic behaviors reduce its test accuracy. Based on these understandings, we introduce Generalized Mixup, designed to relax the representation space for prolonged DCL and demonstrate its superior efficacy vs. existing methods.

Times series foundation models (TSFMs) have emerged as a promising paradigm for time series analysis and forecasting, showing remarkable generalization performance across different domains. While efforts have been made on hallucinations of foundation models, the hallucinations of TSFMs have been underexplored. In this paper, we formally define TSFM hallucinations in the zero-shot forecasting setting by examining whether a generated forecast exhibits different dynamics from those of the context. Our study reveals that TSFM hallucinations primarily stem from the loss of context information in hidden states during forward propagation. As such, we propose methodologies to identify signal subspaces in TSFMs and magnify their information through intervention. Extensive experiments demonstrate that our proposed intervention approach effectively mitigates hallucinations and improves forecasting performance. Furthermore, the signal strength measure we compute from signal subspaces has strong predictive power of hallucinations and forecasting performance of the model. Our work contributes to deeper understanding of TSFM trustworthiness that could foster future research in this direction.

Sampling efficiently from a target unnormalized probability density remains a core challenge, with relevance across countless high-impact scientific applications. A promising approach towards this challenge is the design of amortized samplers that borrow key ideas, such as probability path design, from state-of-the-art generative diffusion models. However, all existing diffusion-based samplers remain unable to draw samples from distributions at the scale of even simple molecular systems. In this paper, we propose Progressive Inference-Time Annealing (PITA) a novel framework to learn diffusion-based samplers that combines two complementary interpolation techniques: I.) Annealing of the Boltzmann distribution and II.) Diffusion smoothing. PITA trains a sequence of diffusion models from high to low temperatures by sequentially training each model at progressively higher temperatures, leveraging engineered easy access to samples of the temperature-annealed target density. In the subsequent step, PITA enables simulating the trained diffusion model to *procure training samples at a lower temperature* for the next diffusion model through inference-time annealing using a novel Feynman-Kac PDE combined with Sequential Monte Carlo. Empirically, PITA enables, for the first time, equilibrium sampling of $N$-body particle systems, Alanine Dipeptide, and tripeptides in Cartesian coordinates with dramatically lower energy function evaluations.

Anomaly detection is a crucial task in data mining, focusing on identifying data points that deviate significantly from the main patterns in the data. This paper introduces Anomaly Detection by an Ensemble of Random Pairs of Hyperspheres (ADERH), a new isolation-based technique leveraging two key observations: (i) anomalies are comparatively rare, and (ii) they typically deviate more strongly from general patterns than normal data points. Drawing on a delta-separation argument, ADERH constructs an ensemble of multi-scale hyperspheres built upon randomly paired data points to identify anomalies. To address inevitable overlaps between anomalous and normal regions in the feature space, ADERH integrates two complementary concepts: Pitch, which highlights points near hypersphere boundaries, and NDensity, which down-weights hyperspheres centered on sparse (and often anomalous) regions. By averaging these local, density-adjusted ``isolation'' indicators across many random subsets, ADERH yields robust anomaly scores that clearly separate normal from abnormal samples. Extensive experiments on diverse real-world datasets show that ADERH consistently outperforms state-of-the-art methods while maintaining linear runtime scalability and stable performance across varying hyperparameter settings.

In-context learning, the ability of large language models to perform tasks using only examples provided in the prompt, has recently been adapted for time series forecasting. This paradigm enables zero-shot prediction, where past values serve as context for forecasting future values, making powerful forecasting tools accessible to non-experts and increasing the performance when training data are scarce. Most existing zero-shot forecasting approaches rely on transformer architectures, which, despite their success in language, often fall short of expectations in time series forecasting, where recurrent models like LSTMs frequently have the edge. Conversely, while LSTMs are well-suited for time series modeling due to their state-tracking capabilities, they lack strong in-context learning abilities. We introduce *TiRex* that closes this gap by leveraging xLSTM, an enhanced LSTM with competitive in-context learning skills. Unlike transformers, state-space models, or parallelizable RNNs such as RWKV, TiRex retains state tracking, a critical property for long-horizon forecasting. To further facilitate its state-tracking ability, we propose a training-time masking strategy called CPM. TiRex sets a new state of the art in zero-shot time series forecasting on the Hugging Face benchmarks *GiftEval* and *Chronos-ZS*, outperforming significantly larger models including *TabPFN-TS* (Prior Labs), *Chronos Bolt* (Amazon), *TimesFM* (Google), and *Moirai* (Salesforce) across both short- and long-term forecasts.