Daily Papers

Editing images with diffusion models under strict training-free constraints remains a significant challenge. While recent optimisation-based methods achieve strong zero-shot edits from text, they struggle to preserve identity and capture intricate details, such as facial structure, material texture, or object-specific geometry, that exist below the level of linguistic abstraction. To address this fundamental gap, we propose Concept Distillation Sampling (CDS). To the best of our knowledge, we are the first to introduce a unified, training-free framework for target-less, multi-concept image editing. CDS overcomes the linguistic bottleneck of previous methods by integrating a highly stable distillation backbone (featuring ordered timesteps, regularisation, and negative-prompt guidance), with a dynamic weighting mechanism. This approach enables the seamless composition and control of multiple visual concepts directly within the diffusion process, utilising spatially-aware priors from pretrained LoRA adapters without spatial interference. Our method preserves instance fidelity without requiring reference samples of the desired edit. Extensive quantitative and qualitative evaluations demonstrate consistent state-of-the-art performance over existing training-free editing and multi-LoRA composition methods on the InstructPix2Pix and ComposLoRA benchmarks. Code will be made publicly available.

We introduce BézierFlow, a lightweight training approach for few-step generation with pretrained diffusion and flow models. BézierFlow achieves a 2-3x performance improvement for sampling with leq 10 NFEs while requiring only 15 minutes of training. Recent lightweight training approaches have shown promise by learning optimal timesteps, but their scope remains restricted to ODE discretizations. To broaden this scope, we propose learning the optimal transformation of the sampling trajectory by parameterizing stochastic interpolant (SI) schedulers. The main challenge lies in designing a parameterization that satisfies critical desiderata, including boundary conditions, differentiability, and monotonicity of the SNR. To effectively meet these requirements, we represent scheduler functions as Bézier functions, where control points naturally enforce these properties. This reduces the problem to learning an ordered set of points in the time range, while the interpretation of the points changes from ODE timesteps to Bézier control points. Across a range of pretrained diffusion and flow models, BézierFlow consistently outperforms prior timestep-learning methods, demonstrating the effectiveness of expanding the search space from discrete timesteps to Bézier-based trajectory transformations.

Constructing a timeline requires identifying the chronological order of events in an article. In prior timeline construction datasets, temporal orders are typically annotated by either event-to-time anchoring or event-to-event pairwise ordering, both of which suffer from missing temporal information. To mitigate the issue, we develop a new evaluation dataset, TimeSET, consisting of single-document timelines with document-level order annotation. TimeSET features saliency-based event selection and partial ordering, which enable a practical annotation workload. Aiming to build better automatic timeline construction systems, we propose a novel evaluation framework to compare multiple task formulations with TimeSET by prompting open LLMs, i.e., Llama 2 and Flan-T5. Considering that identifying temporal orders of events is a core subtask in timeline construction, we further benchmark open LLMs on existing event temporal ordering datasets to gain a robust understanding of their capabilities. Our experiments show that (1) NLI formulation with Flan-T5 demonstrates a strong performance among others, while (2) timeline construction and event temporal ordering are still challenging tasks for few-shot LLMs. Our code and data are available at https://github.com/kimihiroh/timeset.

Sequential recommender systems have demonstrated a huge success for next-item recommendation by explicitly exploiting the temporal order of users' historical interactions. In practice, user interactions contain more useful temporal information beyond order, as shown by some pioneering studies. In this paper, we systematically investigate various temporal information for sequential recommendation and identify three types of advantageous temporal patterns beyond order, including absolute time information, relative item time intervals and relative recommendation time intervals. We are the first to explore item-oriented absolute time patterns. While existing models consider only one or two of these three patterns, we propose a novel holistic temporal pattern based neural network, named HTP, to fully leverage all these three patterns. In particular, we introduce novel components to address the subtle correlations between relative item time intervals and relative recommendation time intervals, which render a major technical challenge. Extensive experiments on three real-world benchmark datasets show that our HTP model consistently and substantially outperforms many state-of-the-art models. Our code is publically available at https://github.com/623851394/HTP/tree/main/HTP-main

Continuous-time event sequences play a vital role in real-world domains such as healthcare, finance, online shopping, social networks, and so on. To model such data, temporal point processes (TPPs) have emerged as the most natural and competitive models, making a significant impact in both academic and application communities. Despite the emergence of many powerful models in recent years, there hasn't been a central benchmark for these models and future research endeavors. This lack of standardization impedes researchers and practitioners from comparing methods and reproducing results, potentially slowing down progress in this field. In this paper, we present EasyTPP, the first central repository of research assets (e.g., data, models, evaluation programs, documentations) in the area of event sequence modeling. Our EasyTPP makes several unique contributions to this area: a unified interface of using existing datasets and adding new datasets; a wide range of evaluation programs that are easy to use and extend as well as facilitate reproducible research; implementations of popular neural TPPs, together with a rich library of modules by composing which one could quickly build complex models. All the data and implementation can be found at https://github.com/ant-research/EasyTemporalPointProcess. We will actively maintain this benchmark and welcome contributions from other researchers and practitioners. Our benchmark will help promote reproducible research in this field, thus accelerating research progress as well as making more significant real-world impacts.

Event sequences (ESs) arise in many practical domains including finance, retail, social networks, and healthcare. In the context of machine learning, event sequences can be seen as a special type of tabular data with annotated timestamps. Despite the importance of ESs modeling and analysis, little effort was made in adapting large language models (LLMs) to the ESs domain. In this paper, we highlight the common difficulties of ESs processing and propose a novel solution capable of solving multiple downstream tasks with little or no finetuning. In particular, we solve the problem of working with long sequences and improve time and numeric features processing. The resulting method, called ESQA, effectively utilizes the power of LLMs and, according to extensive experiments, achieves state-of-the-art results in the ESs domain.

We consider the problem of modeling high-speed flows using machine learning methods. While most prior studies focus on low-speed fluid flows in which uniform time-stepping is practical, flows approaching and exceeding the speed of sound exhibit sudden changes such as shock waves. In such cases, it is essential to use adaptive time-stepping methods to allow a temporal resolution sufficient to resolve these phenomena while simultaneously balancing computational costs. Here, we propose a two-phase machine learning method, known as ShockCast, to model high-speed flows with adaptive time-stepping. In the first phase, we propose to employ a machine learning model to predict the timestep size. In the second phase, the predicted timestep is used as an input along with the current fluid fields to advance the system state by the predicted timestep. We explore several physically-motivated components for timestep prediction and introduce timestep conditioning strategies inspired by neural ODE and Mixture of Experts. As ShockCast is the first framework for learning high-speed flows, we evaluate our methods by generating two supersonic flow datasets, available at https://huggingface.co/datasets/divelab. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS).

Understanding the abilities of LLMs to reason about natural language plans, such as instructional text and recipes, is critical to reliably using them in decision-making systems. A fundamental aspect of plans is the temporal order in which their steps needs to be executed, which reflects the underlying causal dependencies between them. We introduce CaT-Bench, a benchmark of Step Order Prediction questions, which test whether a step must necessarily occur before or after another in cooking recipe plans. We use this to evaluate how well frontier LLMs understand causal and temporal dependencies. We find that SOTA LLMs are underwhelming (best zero-shot is only 0.59 in F1), and are biased towards predicting dependence more often, perhaps relying on temporal order of steps as a heuristic. While prompting for explanations and using few-shot examples improve performance, the best F1 result is only 0.73. Further, human evaluation of explanations along with answer correctness show that, on average, humans do not agree with model reasoning. Surprisingly, we also find that explaining after answering leads to better performance than normal chain-of-thought prompting, and LLM answers are not consistent across questions about the same step pairs. Overall, results show that LLMs' ability to detect dependence between steps has significant room for improvement.

Time series classification (TSC) is dominated by a two-stage paradigm: train a feature encoder -- either from scratch on the target dataset or via pretraining on large corpora -- and then fit a task-specific classifier on top. While effective, this decoupling optimizes representation learning independently of the classification objective, requires per-dataset training, and prevents the model from exploiting label information during inference. We introduce TimEE, a 4.5M-parameter foundation model for end-to-end TSC via in-context learning. Given a labeled support set and a query time series, TimEE directly outputs a predicted class distribution in a single forward pass with no per-dataset training required. Following the prior-data fitted network (PFN) framework, TimEE is meta-trained exclusively on synthetic TSC tasks, where each task contains time series with distinct class identities arising from structured distributional shifts in the generative process. Despite seeing no real time series during pre-training, TimEE ranks first in ROC AUC (and third on accuracy) on the UCR benchmark among all compared methods, which include both foundation models and supervised deep learning baselines. To our knowledge, TimEE is the first purely synthetic-pretrained model to reach state-of-the-art performance on the UCR benchmark. These results establish end-to-end ICL with synthetic priors as a compelling, largely unexplored direction for TSC, with scaling, prior design, and richer generation mechanisms as natural avenues for improvement. Code is publicly available at http://github.com/automl/timee.

Time series reasoning treats time as a first-class axis and incorporates intermediate evidence directly into the answer. This survey defines the problem and organizes the literature by reasoning topology with three families: direct reasoning in one step, linear chain reasoning with explicit intermediates, and branch-structured reasoning that explores, revises, and aggregates. The topology is crossed with the main objectives of the field, including traditional time series analysis, explanation and understanding, causal inference and decision making, and time series generation, while a compact tag set spans these axes and captures decomposition and verification, ensembling, tool use, knowledge access, multimodality, agent loops, and LLM alignment regimes. Methods and systems are reviewed across domains, showing what each topology enables and where it breaks down in faithfulness or robustness, along with curated datasets, benchmarks, and resources that support study and deployment (https://github.com/blacksnail789521/Time-Series-Reasoning-Survey). Evaluation practices that keep evidence visible and temporally aligned are highlighted, and guidance is distilled on matching topology to uncertainty, grounding with observable artifacts, planning for shift and streaming, and treating cost and latency as design budgets. We emphasize that reasoning structures must balance capacity for grounding and self-correction against computational cost and reproducibility, while future progress will likely depend on benchmarks that tie reasoning quality to utility and on closed-loop testbeds that trade off cost and risk under shift-aware, streaming, and long-horizon settings. Taken together, these directions mark a shift from narrow accuracy toward reliability at scale, enabling systems that not only analyze but also understand, explain, and act on dynamic worlds with traceable evidence and credible outcomes.

In time series editing, we aim to modify some properties of a given time series without altering others. For example, when analyzing a hospital patient's blood pressure, we may add a sudden early drop and observe how it impacts their future while preserving other conditions. Existing diffusion-based editors rely on rigid, predefined attribute vectors as conditions and produce all-or-nothing edits through sampling. This attribute- and sampling-based approach limits flexibility in condition format and lacks customizable control over editing strength. To overcome these limitations, we introduce Instruction-based Time Series Editing, where users specify intended edits using natural language. This allows users to express a wider range of edits in a more accessible format. We then introduce InstructTime, the first instruction-based time series editor. InstructTime takes in time series and instructions, embeds them into a shared multi-modal representation space, then decodes their embeddings to generate edited time series. By learning a structured multi-modal representation space, we can easily interpolate between embeddings to achieve varying degrees of edit. To handle local and global edits together, we propose multi-resolution encoders. In our experiments, we use synthetic and real datasets and find that InstructTime is a state-of-the-art time series editor: InstructTime achieves high-quality edits with controllable strength, can generalize to unseen instructions, and can be easily adapted to unseen conditions through few-shot learning.

The abundance of instructional videos and their narrations over the Internet offers an exciting avenue for understanding procedural activities. In this work, we propose to learn video representation that encodes both action steps and their temporal ordering, based on a large-scale dataset of web instructional videos and their narrations, without using human annotations. Our method jointly learns a video representation to encode individual step concepts, and a deep probabilistic model to capture both temporal dependencies and immense individual variations in the step ordering. We empirically demonstrate that learning temporal ordering not only enables new capabilities for procedure reasoning, but also reinforces the recognition of individual steps. Our model significantly advances the state-of-the-art results on step classification (+2.8% / +3.3% on COIN / EPIC-Kitchens) and step forecasting (+7.4% on COIN). Moreover, our model attains promising results in zero-shot inference for step classification and forecasting, as well as in predicting diverse and plausible steps for incomplete procedures. Our code is available at https://github.com/facebookresearch/ProcedureVRL.

Time series, characterized by a sequence of data points organized in a discrete-time order, are ubiquitous in real-world scenarios. Unlike other data modalities, time series present unique challenges due to their intricate and dynamic nature, including the entanglement of nonlinear patterns and time-variant trends. Analyzing such data is of great significance in practical applications and has been extensively studied for centuries. Recent years have witnessed remarkable breakthroughs in the time series community, with techniques shifting from traditional statistical methods to contemporary deep learning models. In this paper, we delve into the design of deep time series models across various analysis tasks and review the existing literature from two perspectives: basic modules and model architectures. Further, we develop and release Time Series Library (TSLib) as a fair benchmark of deep time series models for diverse analysis tasks. TSLib implements 30 prominent models, covers 30 datasets from different domains, and supports five prevalent analysis tasks. Based on TSLib, we thoroughly evaluate 13 advanced deep time series models across diverse tasks. Empirical results indicate that models with specific structures are well-suited for distinct analytical tasks, providing insights for research and adoption of deep time series models. Code and datasets are available at https://github.com/thuml/Time-Series-Library.

Clinical case reports encode temporal patient trajectories that are often underexploited by traditional machine learning methods relying on structured data. In this work, we introduce the forecasting problem from textual time series, where timestamped clinical findings -- extracted via an LLM-assisted annotation pipeline -- serve as the primary input for prediction. We systematically evaluate a diverse suite of models, including fine-tuned decoder-based large language models and encoder-based transformers, on tasks of event occurrence prediction, temporal ordering, and survival analysis. Our experiments reveal that encoder-based models consistently achieve higher F1 scores and superior temporal concordance for short- and long-horizon event forecasting, while fine-tuned masking approaches enhance ranking performance. In contrast, instruction-tuned decoder models demonstrate a relative advantage in survival analysis, especially in early prognosis settings. Our sensitivity analyses further demonstrate the importance of time ordering, which requires clinical time series construction, as compared to text ordering, the format of the text inputs that LLMs are classically trained on. This highlights the additional benefit that can be ascertained from time-ordered corpora, with implications for temporal tasks in the era of widespread LLM use.

Large-scale pre-trained models (PTMs) such as BERT and GPT have recently achieved great success in Natural Language Processing and Computer Vision domains. However, the development of PTMs on healthcare time-series data is lagging behind.This underscores the limitations of the existing transformer-based architectures, particularly their scalability to handle large-scale time series and ability to capture long-term temporal dependencies. In this study, we present Timely Generative Pre-trained Transformer (TimelyGPT). TimelyGPT employs an extrapolatable position (xPos) embedding to encode trend and periodic patterns into time-series representations. It also integrates recurrent attention and temporal convolution modules to effectively capture global-local temporal dependencies. We evaluated TimelyGPT on two large-scale healthcare time series datasets corresponding to continuous biosignals and irregularly-sampled time series, respectively. Our experiments show that during pre-training, TimelyGPT excels in learning time-series representations from continuously monitored biosignals and irregularly-sampled time series data commonly observed in longitudinal electronic health records (EHRs). In forecasting continuous biosignals, TimelyGPT achieves accurate extrapolation up to 6,000 timesteps of body temperature during the sleep stage transition, given a short look-up window (i.e., prompt) containing only 2,000 timesteps. For irregularly-sampled time series, TimelyGPT with a proposed time-specific inference demonstrates high top recall scores in predicting future diagnoses using early diagnostic records, effectively handling irregular intervals between clinical records. Together, we envision TimelyGPT to be useful in a broad spectrum of health domains, including long-term patient health state forecasting and patient risk trajectory prediction.

Autoregressive models, such as the GPT family, use a fixed order, usually left-to-right, to generate sequences. However, this is not a necessity. In this paper, we challenge this assumption and show that by simply adding a positional encoding for the output, this order can be modulated on-the-fly per-sample which offers key advantageous properties. It allows for the sampling of and conditioning on arbitrary subsets of tokens, and it also allows sampling in one shot multiple tokens dynamically according to a rejection strategy, leading to a sub-linear number of model evaluations. We evaluate our method across various domains, including language modeling, path-solving, and aircraft vertical rate prediction, decreasing the number of steps required for generation by an order of magnitude.

Autoregressive models (ARMs) have become the workhorse for sequence generation tasks, since many problems can be modeled as next-token prediction. While there appears to be a natural ordering for text (i.e., left-to-right), for many data types, such as graphs, the canonical ordering is less obvious. To address this problem, we introduce a variant of ARM that generates high-dimensional data using a probabilistic ordering that is sequentially inferred from data. This model incorporates a trainable probability distribution, referred to as an order-policy, that dynamically decides the autoregressive order in a state-dependent manner. To train the model, we introduce a variational lower bound on the exact log-likelihood, which we optimize with stochastic gradient estimation. We demonstrate experimentally that our method can learn meaningful autoregressive orderings in image and graph generation. On the challenging domain of molecular graph generation, we achieve state-of-the-art results on the QM9 and ZINC250k benchmarks, evaluated using the Fr\'{e}chet ChemNet Distance (FCD).

Visualizing multiple time series presents fundamental tradeoffs between scalability and visual clarity. Time series capture the behavior of many large-scale real-world processes, from stock market trends to urban activities. Users often gain insights by visualizing them as line charts, juxtaposing or superposing multiple time series to compare them and identify trends and patterns. However, existing representations struggle with scalability: when covering long time spans, leading to visual clutter from too many small multiples or overlapping lines. We propose TiVy, a new algorithm that summarizes time series using sequential patterns. It transforms the series into a set of symbolic sequences based on subsequence visual similarity using Dynamic Time Warping (DTW), then constructs a disjoint grouping of similar subsequences based on the frequent sequential patterns. The grouping result, a visual summary of time series, provides uncluttered superposition with fewer small multiples. Unlike common clustering techniques, TiVy extracts similar subsequences (of varying lengths) aligned in time. We also present an interactive time series visualization that renders large-scale time series in real-time. Our experimental evaluation shows that our algorithm (1) extracts clear and accurate patterns when visualizing time series data, (2) achieves a significant speed-up (1000X) compared to a straightforward DTW clustering. We also demonstrate the efficiency of our approach to explore hidden structures in massive time series data in two usage scenarios.

Event sequences, characterized by irregular sampling intervals and a mix of categorical and numerical features, are common data structures in various real-world domains such as healthcare, finance, and user interaction logs. Despite advances in temporal data modeling techniques, there is no standardized benchmarks for evaluating their performance on event sequences. This complicates result comparison across different papers due to varying evaluation protocols, potentially misleading progress in this field. We introduce EBES, a comprehensive benchmarking tool with standardized evaluation scenarios and protocols, focusing on regression and classification problems with sequence-level targets. Our library simplifies benchmarking, dataset addition, and method integration through a unified interface. It includes a novel synthetic dataset and provides preprocessed real-world datasets, including the largest publicly available banking dataset. Our results provide an in-depth analysis of datasets, identifying some as unsuitable for model comparison. We investigate the importance of modeling temporal and sequential components, as well as the robustness and scaling properties of the models. These findings highlight potential directions for future research. Our benchmark aim is to facilitate reproducible research, expediting progress and increasing real-world impacts.

In this paper, we introduce TimeGPT, the first foundation model for time series, capable of generating accurate predictions for diverse datasets not seen during training. We evaluate our pre-trained model against established statistical, machine learning, and deep learning methods, demonstrating that TimeGPT zero-shot inference excels in performance, efficiency, and simplicity. Our study provides compelling evidence that insights from other domains of artificial intelligence can be effectively applied to time series analysis. We conclude that large-scale time series models offer an exciting opportunity to democratize access to precise predictions and reduce uncertainty by leveraging the capabilities of contemporary advancements in deep learning.

Self-supervised learning has garnered increasing attention in time series analysis for benefiting various downstream tasks and reducing reliance on labeled data. Despite its effectiveness, existing methods often struggle to comprehensively capture both long-term dynamic evolution and subtle local patterns in a unified manner. In this work, we propose TimeDART, a novel self-supervised time series pre-training framework that unifies two powerful generative paradigms to learn more transferable representations. Specifically, we first employ a causal Transformer encoder, accompanied by a patch-based embedding strategy, to model the evolving trends from left to right. Building on this global modeling, we further introduce a denoising diffusion process to capture fine-grained local patterns through forward diffusion and reverse denoising. Finally, we optimize the model in an autoregressive manner. As a result, TimeDART effectively accounts for both global and local sequence features in a coherent way. We conduct extensive experiments on public datasets for time series forecasting and classification. The experimental results demonstrate that TimeDART consistently outperforms previous compared methods, validating the effectiveness of our approach. Our code is available at https://github.com/Melmaphother/TimeDART.

Recent work on the sequence universality of State Space Models (SSMs) has introduced efficient, maximally expressive continuous-time approaches for time-series modelling. While these works focus on discriminative settings, we extend this perspective to generative time-series modelling by proving that maximally expressive Structured Linear Controlled Differential Equations (SLiCEs) are universal time-series generators, in the sense that they can approximate the induced path laws of continuous causal pushforwards on compact latent sets in W_infty. Building on these theoretical results, we propose Generative SLiCEs (G-SLiCEs), a maximally expressive continuous-time model for flow matching on path-space. Empirically, we show that expressivity improves performance in probabilistic forecasting and downstream tasks, while retaining the advantages of continuous-time models such as generalising to arbitrary observation grids. This is particularly beneficial for irregular grids, where fixed-grid models often struggle.

Autoregressive patch-based image generation has recently shown competitive results in terms of image quality and scalability. It can also be easily integrated and scaled within Vision-Language models. Nevertheless, autoregressive models require a defined order for patch generation. While a natural order based on the dictation of the words makes sense for text generation, there is no inherent generation order that exists for image generation. Traditionally, a raster-scan order (from top-left to bottom-right) guides autoregressive image generation models. In this paper, we argue that this order is suboptimal, as it fails to respect the causality of the image content: for instance, when conditioned on a visual description of a sunset, an autoregressive model may generate clouds before the sun, even though the color of clouds should depend on the color of the sun and not the inverse. In this work, we show that first by training a model to generate patches in any-given-order, we can infer both the content and the location (order) of each patch during generation. Secondly, we use these extracted orders to finetune the any-given-order model to produce better-quality images. Through our experiments, we show on two datasets that this new generation method produces better images than the traditional raster-scan approach, with similar training costs and no extra annotations.

Time series modeling is a well-established problem, which often requires that methods (1) expressively represent complicated dependencies, (2) forecast long horizons, and (3) efficiently train over long sequences. State-space models (SSMs) are classical models for time series, and prior works combine SSMs with deep learning layers for efficient sequence modeling. However, we find fundamental limitations with these prior approaches, proving their SSM representations cannot express autoregressive time series processes. We thus introduce SpaceTime, a new state-space time series architecture that improves all three criteria. For expressivity, we propose a new SSM parameterization based on the companion matrix -- a canonical representation for discrete-time processes -- which enables SpaceTime's SSM layers to learn desirable autoregressive processes. For long horizon forecasting, we introduce a "closed-loop" variation of the companion SSM, which enables SpaceTime to predict many future time-steps by generating its own layer-wise inputs. For efficient training and inference, we introduce an algorithm that reduces the memory and compute of a forward pass with the companion matrix. With sequence length ell and state-space size d, we go from O(d ell) na\"ively to O(d + ell). In experiments, our contributions lead to state-of-the-art results on extensive and diverse benchmarks, with best or second-best AUROC on 6 / 7 ECG and speech time series classification, and best MSE on 14 / 16 Informer forecasting tasks. Furthermore, we find SpaceTime (1) fits AR(p) processes that prior deep SSMs fail on, (2) forecasts notably more accurately on longer horizons than prior state-of-the-art, and (3) speeds up training on real-world ETTh1 data by 73% and 80% relative wall-clock time over Transformers and LSTMs.

Despite the success of adaptive time-stepping in ODE simulation, it has so far seen few applications for Stochastic Differential Equations (SDEs). To simulate SDEs adaptively, methods such as the Virtual Brownian Tree (VBT) have been developed, which can generate Brownian motion (BM) non-chronologically. However, in most applications, knowing only the values of Brownian motion is not enough to achieve a high order of convergence; for that, we must compute time-integrals of BM such as int_s^t W_r , dr. With the aim of using high order SDE solvers adaptively, we extend the VBT to generate these integrals of BM in addition to the Brownian increments. A JAX-based implementation of our construction is included in the popular Diffrax library (https://github.com/patrick-kidger/diffrax). Since the entire Brownian path produced by VBT is uniquely determined by a single PRNG seed, previously generated samples need not be stored, which results in a constant memory footprint and enables experiment repeatability and strong error estimation. Based on binary search, the VBT's time complexity is logarithmic in the tolerance parameter varepsilon. Unlike the original VBT algorithm, which was only precise at some dyadic times, we prove that our construction exactly matches the joint distribution of the Brownian motion and its time integrals at any query times, provided they are at least varepsilon apart. We present two applications of adaptive high order solvers enabled by our new VBT. Using adaptive solvers to simulate a high-volatility CIR model, we achieve more than twice the convergence order of constant stepping. We apply an adaptive third order underdamped or kinetic Langevin solver to an MCMC problem, where our approach outperforms the No U-Turn Sampler, while using only a tenth of its function evaluations.

Interpreting time series models is uniquely challenging because it requires identifying both the location of time series signals that drive model predictions and their matching to an interpretable temporal pattern. While explainers from other modalities can be applied to time series, their inductive biases do not transfer well to the inherently challenging interpretation of time series. We present TimeX, a time series consistency model for training explainers. TimeX trains an interpretable surrogate to mimic the behavior of a pretrained time series model. It addresses the issue of model faithfulness by introducing model behavior consistency, a novel formulation that preserves relations in the latent space induced by the pretrained model with relations in the latent space induced by TimeX. TimeX provides discrete attribution maps and, unlike existing interpretability methods, it learns a latent space of explanations that can be used in various ways, such as to provide landmarks to visually aggregate similar explanations and easily recognize temporal patterns. We evaluate TimeX on eight synthetic and real-world datasets and compare its performance against state-of-the-art interpretability methods. We also conduct case studies using physiological time series. Quantitative evaluations demonstrate that TimeX achieves the highest or second-highest performance in every metric compared to baselines across all datasets. Through case studies, we show that the novel components of TimeX show potential for training faithful, interpretable models that capture the behavior of pretrained time series models.

We study the challenging problem of simultaneously localizing a sequence of queries in the form of instructional diagrams in a video. This requires understanding not only the individual queries but also their interrelationships. However, most existing methods focus on grounding one query at a time, ignoring the inherent structures among queries such as the general mutual exclusiveness and the temporal order. Consequently, the predicted timespans of different step diagrams may overlap considerably or violate the temporal order, thus harming the accuracy. In this paper, we tackle this issue by simultaneously grounding a sequence of step diagrams. Specifically, we propose composite queries, constructed by exhaustively pairing up the visual content features of the step diagrams and a fixed number of learnable positional embeddings. Our insight is that self-attention among composite queries carrying different content features suppress each other to reduce timespan overlaps in predictions, while the cross-attention corrects the temporal misalignment via content and position joint guidance. We demonstrate the effectiveness of our approach on the IAW dataset for grounding step diagrams and the YouCook2 benchmark for grounding natural language queries, significantly outperforming existing methods while simultaneously grounding multiple queries.

Time series forecasting with limited data is a challenging yet critical task. While transformers have achieved outstanding performances in time series forecasting, they often require many training samples due to the large number of trainable parameters. In this paper, we propose a training technique for transformers that prepares the training windows through random sampling. As input time steps need not be consecutive, the number of distinct samples increases from linearly to combinatorially many. By breaking the temporal order, this technique also helps transformers to capture dependencies among time steps in finer granularity. We achieve competitive results compared to the state-of-the-art on real-world datasets.

In this paper, we introduce FITS, a lightweight yet powerful model for time series analysis. Unlike existing models that directly process raw time-domain data, FITS operates on the principle that time series can be manipulated through interpolation in the complex frequency domain. By discarding high-frequency components with negligible impact on time series data, FITS achieves performance comparable to state-of-the-art models for time series forecasting and anomaly detection tasks, while having a remarkably compact size of only approximately 10k parameters. Such a lightweight model can be easily trained and deployed in edge devices, creating opportunities for various applications. The code is available in: https://github.com/VEWOXIC/FITS

The task of video generation requires synthesizing visually realistic and temporally coherent video frames. Existing methods primarily use asynchronous auto-regressive models or synchronous diffusion models to address this challenge. However, asynchronous auto-regressive models often suffer from inconsistencies between training and inference, leading to issues such as error accumulation, while synchronous diffusion models are limited by their reliance on rigid sequence length. To address these issues, we introduce Auto-Regressive Diffusion (AR-Diffusion), a novel model that combines the strengths of auto-regressive and diffusion models for flexible, asynchronous video generation. Specifically, our approach leverages diffusion to gradually corrupt video frames in both training and inference, reducing the discrepancy between these phases. Inspired by auto-regressive generation, we incorporate a non-decreasing constraint on the corruption timesteps of individual frames, ensuring that earlier frames remain clearer than subsequent ones. This setup, together with temporal causal attention, enables flexible generation of videos with varying lengths while preserving temporal coherence. In addition, we design two specialized timestep schedulers: the FoPP scheduler for balanced timestep sampling during training, and the AD scheduler for flexible timestep differences during inference, supporting both synchronous and asynchronous generation. Extensive experiments demonstrate the superiority of our proposed method, which achieves competitive and state-of-the-art results across four challenging benchmarks.

Prior-data fitted networks (PFNs) have emerged as powerful foundation models for tabular causal inference, yet their extension to time series remains limited by the absence of synthetic data generators that provide interventional targets. Existing time series benchmarks generate observational data with ground-truth causal graphs but lack the interventional data required for training causal foundation models. To address this, we propose CausalTimePrior, a principled framework for generating synthetic temporal structural causal models (TSCMs) with paired observational and interventional time series. Our prior supports configurable causal graph structures, nonlinear autoregressive mechanisms, regime-switching dynamics, and multiple intervention types (hard, soft, time-varying). We demonstrate that PFNs trained on CausalTimePrior can perform in-context causal effect estimation on held-out TSCMs, establishing a pathway toward foundation models for time series causal inference.

We present a constraint-based algorithm for learning causal structures from observational time-series data, in the presence of latent confounders. We assume a discrete-time, stationary structural vector autoregressive process, with both temporal and contemporaneous causal relations. One may ask if temporal and contemporaneous relations should be treated differently. The presented algorithm gradually refines a causal graph by learning long-term temporal relations before short-term ones, where contemporaneous relations are learned last. This ordering of causal relations to be learnt leads to a reduction in the required number of statistical tests. We validate this reduction empirically and demonstrate that it leads to higher accuracy for synthetic data and more plausible causal graphs for real-world data compared to state-of-the-art algorithms.

Deep neural networks, including transformers and convolutional neural networks, have significantly improved multivariate time series classification (MTSC). However, these methods often rely on supervised learning, which does not fully account for the sparsity and locality of patterns in time series data (e.g., diseases-related anomalous points in ECG). To address this challenge, we formally reformulate MTSC as a weakly supervised problem, introducing a novel multiple-instance learning (MIL) framework for better localization of patterns of interest and modeling time dependencies within time series. Our novel approach, TimeMIL, formulates the temporal correlation and ordering within a time-aware MIL pooling, leveraging a tokenized transformer with a specialized learnable wavelet positional token. The proposed method surpassed 26 recent state-of-the-art methods, underscoring the effectiveness of the weakly supervised TimeMIL in MTSC. The code will be available at https://github.com/xiwenc1/TimeMIL.

Time series play a fundamental role in many domains, capturing a plethora of information about the underlying data-generating processes. When a process generates multiple synchronized signals we are faced with multidimensional time series. In this context a fundamental problem is that of motif mining, where we seek patterns repeating twice with minor variations, spanning some of the dimensions. State of the art exact solutions for this problem run in time quadratic in the length of the input time series. We provide a scalable method to find the top-k motifs in multidimensional time series with probabilistic guarantees on the quality of the results. Our algorithm runs in time subquadratic in the length of the input, and returns the exact solution with probability at least 1-δ, where δ is a user-defined parameter. The algorithm is designed to be adaptive to the input distribution, self-tuning its parameters while respecting user-defined limits on the memory to use. Our theoretical analysis is complemented by an extensive experimental evaluation, showing that our algorithm is orders of magnitude faster than the state of the art.

Variable-order Markov models generate sequences over a finite alphabet by conditioning each symbol on the longest available suffix of the generated history. Regular constraints, by contrast, describe finite-horizon control requirements by an automaton: fixed positions, forced endings, metrical patterns, and forbidden copied fragments are all special cases. Existing exact methods already handle regular constraints with belief propagation for first-order Markov chains. The contribution here is the variable-order extension: identifying the state space on which the existing BP-regular machinery must be run when the generator is a variable-order/backoff model. A first-order constraint layer can enforce useful support conditions, but it computes future mass after merging histories that a variable-order generator deliberately keeps distinct. We formalize this mismatch and give the sparse construction obtained by replacing the first-order Markov state with the observed context state, then taking the standard product with the regular constraint automaton. For a fixed trained context graph and automaton, inference is linear in the sequence horizon; in general it is polynomial in the number of reachable product edges. This gives the correct variable-order distribution conditioned on regular constraints without expanding to all K-tuples. The same finite-source interface supports reversible data augmentation by inverse count lookup, matching materialized transposition augmentation without storing transformed corpora. We also separate exact BP inference from generation-time backoff policies, such as singleton avoidance, whose stochastic semantics must be made explicit if exactness is claimed.

The Sequential Recommendation modeling paradigm is shifting from Transformer to Mamba architecture, which comprises two generations: Mamba1, based on the State Space Model (SSM), and Mamba2, based on State Space Duality (SSD). Although SSD offers superior computational efficiency compared to SSM, it suffers performance degradation in sequential recommendation tasks, especially in low-dimensional scenarios that are critical for these tasks. Considering that time-aware enhancement methods are commonly employed to mitigate performance loss, our analysis reveals that the performance decline of SSD can similarly be fundamentally compensated by leveraging mechanisms in time-aware methods. Thus, we propose integrating time-awareness into the SSD framework to address these performance issues. However, integrating current time-aware methods, modeled after TiSASRec, into SSD faces the following challenges: 1) the complexity of integrating these transformer-based mechanisms with the SSD architecture, and 2) the computational inefficiency caused by the need for dimensionality expansion of time-difference modeling. To overcome these challenges, we introduce a novel Time-aware Structured Masked Matrix that efficiently incorporates time-aware capabilities into SSD. Building on this, we propose Time-Aware Mamba for Recommendation (TiM4Rec), which mitigates performance degradation in low-dimensional SSD contexts while preserving computational efficiency. This marks the inaugural application of a time-aware enhancement method specifically tailored for the Mamba architecture within the domain of sequential recommendation. Extensive experiments conducted on three real-world datasets demonstrate the superiority of our approach. The code for our model is accessible at https://github.com/AlwaysFHao/TiM4Rec.

A central problem in learning from sequential data is representing cumulative history in an incremental fashion as more data is processed. We introduce a general framework (HiPPO) for the online compression of continuous signals and discrete time series by projection onto polynomial bases. Given a measure that specifies the importance of each time step in the past, HiPPO produces an optimal solution to a natural online function approximation problem. As special cases, our framework yields a short derivation of the recent Legendre Memory Unit (LMU) from first principles, and generalizes the ubiquitous gating mechanism of recurrent neural networks such as GRUs. This formal framework yields a new memory update mechanism (HiPPO-LegS) that scales through time to remember all history, avoiding priors on the timescale. HiPPO-LegS enjoys the theoretical benefits of timescale robustness, fast updates, and bounded gradients. By incorporating the memory dynamics into recurrent neural networks, HiPPO RNNs can empirically capture complex temporal dependencies. On the benchmark permuted MNIST dataset, HiPPO-LegS sets a new state-of-the-art accuracy of 98.3%. Finally, on a novel trajectory classification task testing robustness to out-of-distribution timescales and missing data, HiPPO-LegS outperforms RNN and neural ODE baselines by 25-40% accuracy.

Recent advances in multimodal time series learning underscore a paradigm shift from analytics centered on basic patterns toward advanced time series understanding and reasoning. However, existing multimodal time series datasets mostly remain at the level of surface alignment and question answering, without reaching the depth of genuine reasoning. The absence of well-defined tasks that genuinely require time series reasoning, along with the scarcity of high-quality data, has limited progress in building practical time series reasoning models (TSRMs). To this end, we introduce Time Series Reasoning Suite (TSR-Suite), which formalizes four atomic tasks that span three fundamental capabilities for reasoning with time series: (1) perception, acquired through scenario understanding and causality discovery; (2) extrapolation, realized via event-aware forecasting; and (3) decision-making, developed through deliberation over perception and extrapolation. TSR-Suite is the first comprehensive time series reasoning suite that supports not only thorough evaluation but also the data pipeline and training of TSRMs. It contains more than 23K samples, of which 2.3K are carefully curated through a human-guided hierarchical annotation process. Building on this foundation, we introduce TimeOmni-1, the first unified reasoning model designed to address diverse real-world problems demanding time series reasoning. The model is trained in multiple stages, integrating a mixture of task scenarios, novel reward functions, and tailored optimizations. Experiments show that TimeOmni-1 delivers strong out-of-distribution generalization across all tasks and achieves a high rate of valid responses. It significantly improves causality discovery accuracy (64.0% vs. 35.9% with GPT-4.1) and raises the valid response rate by over 6% compared to GPT-4.1 on the event-aware forecasting task.

Recent explainable artificial intelligence (XAI) methods for time series primarily estimate point-wise attribution magnitudes, while overlooking the directional impact on predictions, leading to suboptimal identification of significant points. Our analysis shows that conventional Integrated Gradients (IG) effectively capture critical points with both positive and negative impacts on predictions. However, current evaluation metrics fail to assess this capability, as they inadvertently cancel out opposing feature contributions. To address this limitation, we propose novel evaluation metrics-Cumulative Prediction Difference (CPD) and Cumulative Prediction Preservation (CPP)-to systematically assess whether attribution methods accurately identify significant positive and negative points in time series XAI. Under these metrics, conventional IG outperforms recent counterparts. However, directly applying IG to time series data may lead to suboptimal outcomes, as generated paths ignore temporal relationships and introduce out-of-distribution samples. To overcome these challenges, we introduce TIMING, which enhances IG by incorporating temporal awareness while maintaining its theoretical properties. Extensive experiments on synthetic and real-world time series benchmarks demonstrate that TIMING outperforms existing time series XAI baselines. Our code is available at https://github.com/drumpt/TIMING.

Recently, there has been a surge of Transformer-based solutions for the long-term time series forecasting (LTSF) task. Despite the growing performance over the past few years, we question the validity of this line of research in this work. Specifically, Transformers is arguably the most successful solution to extract the semantic correlations among the elements in a long sequence. However, in time series modeling, we are to extract the temporal relations in an ordered set of continuous points. While employing positional encoding and using tokens to embed sub-series in Transformers facilitate preserving some ordering information, the nature of the permutation-invariant self-attention mechanism inevitably results in temporal information loss. To validate our claim, we introduce a set of embarrassingly simple one-layer linear models named LTSF-Linear for comparison. Experimental results on nine real-life datasets show that LTSF-Linear surprisingly outperforms existing sophisticated Transformer-based LTSF models in all cases, and often by a large margin. Moreover, we conduct comprehensive empirical studies to explore the impacts of various design elements of LTSF models on their temporal relation extraction capability. We hope this surprising finding opens up new research directions for the LTSF task. We also advocate revisiting the validity of Transformer-based solutions for other time series analysis tasks (e.g., anomaly detection) in the future. Code is available at: https://github.com/cure-lab/LTSF-Linear.

Fast and scalable alignment of time series is a fundamental challenge in many domains. The standard solution, Dynamic Time Warping (DTW), struggles with poor scalability and sensitivity to noise. We introduce TimePoint, a self-supervised method that dramatically accelerates DTW-based alignment while typically improving alignment accuracy by learning keypoints and descriptors from synthetic data. Inspired by 2D keypoint detection but carefully adapted to the unique challenges of 1D signals, TimePoint leverages efficient 1D diffeomorphisms, which effectively model nonlinear time warping, to generate realistic training data. This approach, along with fully convolutional and wavelet convolutional architectures, enables the extraction of informative keypoints and descriptors. Applying DTW to these sparse representations yield major speedups and typically higher alignment accuracy than standard DTW applied to the full signals. TimePoint demonstrates strong generalization to real-world time series when trained solely on synthetic data, and further improves with fine-tuning on real data. Extensive experiments demonstrate that TimePoint consistently achieves faster and more accurate alignments than standard DTW, making it a scalable solution for time-series analysis. Our code is available at https://github.com/BGU-CS-VIL/TimePoint

In many real-world applications, modeling both the internal structure of sets and their temporal relationships is essential for capturing complex underlying patterns. Sequential multiple-instance learning aims to address this challenge by learning permutation-invariant representations of sets distributed across discrete timesteps. However, existing methods either focus on learning set representations at a static level, ignoring temporal dynamics, or treat sequences as ordered lists of individual elements, lacking explicit mechanisms for representing sets. Crucially, effective modeling of such sequences of sets often requires encoding both the positional ordering across timesteps and their absolute temporal values to jointly capture relative progression and temporal context. In this work, we propose Set2Seq Transformer, a novel architecture that jointly models permutation-invariant set structure and temporal dependencies by learning temporal and position-aware representations of sets within a sequence in an end-to-end multimodal manner. We evaluate our Set2Seq Transformer on two tasks that require modeling set structure alongside temporal and positional patterns, but differ significantly in domain, modality, and objective. First, we consider a fine art analysis task, modeling artists' oeuvres for predicting artistic success using a novel dataset, WikiArt-Seq2Rank. Second, we utilize our Set2Seq Transformer for short-term wildfire danger forecasting. Through extensive experimentation, we show that our Set2Seq Transformer consistently improves over traditional static multiple-instance learning methods by effectively learning permutation-invariant set, temporal, and position-aware representations across diverse domains, modalities, and tasks. We release all code and datasets at https://github.com/thefth/set2seq-transformer.

Diffusion-based generative models have emerged as powerful tools in the realm of generative modeling. Despite extensive research on denoising across various timesteps and noise levels, a conflict persists regarding the relative difficulties of the denoising tasks. While various studies argue that lower timesteps present more challenging tasks, others contend that higher timesteps are more difficult. To address this conflict, our study undertakes a comprehensive examination of task difficulties, focusing on convergence behavior and changes in relative entropy between consecutive probability distributions across timesteps. Our observational study reveals that denoising at earlier timesteps poses challenges characterized by slower convergence and higher relative entropy, indicating increased task difficulty at these lower timesteps. Building on these observations, we introduce an easy-to-hard learning scheme, drawing from curriculum learning, to enhance the training process of diffusion models. By organizing timesteps or noise levels into clusters and training models with ascending orders of difficulty, we facilitate an order-aware training regime, progressing from easier to harder denoising tasks, thereby deviating from the conventional approach of training diffusion models simultaneously across all timesteps. Our approach leads to improved performance and faster convergence by leveraging benefits of curriculum learning, while maintaining orthogonality with existing improvements in diffusion training techniques. We validate these advantages through comprehensive experiments in image generation tasks, including unconditional, class-conditional, and text-to-image generation.

Sequence learning reduces to similarity-based retrieval over a temporally indexed representation space, a constraint on any sequence model, not a property of a specific architecture. We show that a spiking Sparse Distributed Memory sequence machine (2007) and the transformer (2017) independently instantiate the same five functional operations (encoding, context maintenance, associative retrieval, storage, and decoding), with cosine similarity as the shared retrieval primitive in both. We formalise a Phase-Latency Isomorphism showing that sinusoidal positional phase and spike timing are linearly related, and prove that dot product attention is invariant to this mapping up to a global scale factor on the positional component (Lemma 1). Empirically, frequency-compressed positional encoding fails to converge on a positionally demanding copy task, while a learned rank-based embedding matches or exceeds sinusoidal encoding, indicating that the critical property for positional representation is distance discriminability under dot-product similarity, not sinusoidal form. Time, phase, and rank are three instantiations of the same computational primitive, an ordered index whose structure survives similarity-based retrieval.

We examine the problem of learning sequential tasks from a single visual demonstration. A key challenge arises when demonstrations are temporally misaligned due to variations in timing, differences in embodiment, or inconsistencies in execution. Existing approaches treat imitation as a distribution-matching problem, aligning individual frames between the agent and the demonstration. However, we show that such frame-level matching fails to enforce temporal ordering or ensure consistent progress. Our key insight is that matching should instead be defined at the level of sequences. We propose that perfect matching occurs when one sequence successfully covers all the subgoals in the same order as the other sequence. We present ORCA (ORdered Coverage Alignment), a dense per-timestep reward function that measures the probability of the agent covering demonstration frames in the correct order. On temporally misaligned demonstrations, we show that agents trained with the ORCA reward achieve 4.5x improvement (0.11 rightarrow 0.50 average normalized returns) for Meta-world tasks and 6.6x improvement (6.55 rightarrow 43.3 average returns) for Humanoid-v4 tasks compared to the best frame-level matching algorithms. We also provide empirical analysis showing that ORCA is robust to varying levels of temporal misalignment. Our code is available at https://github.com/portal-cornell/orca/

Evaluating retrieval-augmented generation (RAG) pipelines requires corpora where ground truth is knowable, temporally structured, and cross-artifact properties that real-world datasets rarely provide cleanly. Existing resources such as the Enron corpus carry legal ambiguity, demographic skew, and no structured ground truth. Purely LLM-generated synthetic data solves the legal problem but introduces a subtler one: the generating model cannot be prevented from hallucinating facts that contradict themselves across documents.We present OrgForge, an open-source multi-agent simulation framework that enforces a strict physics-cognition boundary: a deterministic Python engine maintains a SimEvent ground truth bus; large language models generate only surface prose, constrained by validated proposals. An actor-local clock enforces causal timestamp correctness across all artifact types, eliminating the class of timeline inconsistencies that arise when timestamps are sampled independently per document. We formalize three graph-dynamic subsystems stress propagation via betweenness centrality, temporal edge-weight decay, and Dijkstra escalation routing that govern organizational behavior independently of any LLM. Running a configurable N-day simulation, OrgForge produces interleaved Slack threads, JIRA tickets, Confluence pages, Git pull requests, and emails, all traceable to a shared, immutable event log. We additionally describe a causal chain tracking subsystem that accumulates cross-artifact evidence graphs per incident, a hybrid reciprocal-rank-fusion recurrence detector for identifying repeated failure classes, and an inbound/outbound email engine that routes vendor alerts, customer complaints, and HR correspondence through gated causal chains with probabilistic drop simulation. OrgForge is available under the MIT license.

Timestep sampling p(t) is a central design choice in Flow Matching models, yet common practice increasingly favors static middle-biased distributions (e.g., Logit-Normal). We show that this choice induces a speed--quality trade-off: middle-biased sampling accelerates early convergence but yields worse asymptotic fidelity than Uniform sampling. By analyzing per-timestep training losses, we identify a U-shaped difficulty profile with persistent errors near the boundary regimes, implying that under-sampling the endpoints leaves fine details unresolved. Guided by this insight, we propose Curriculum Sampling, a two-phase schedule that begins with middle-biased sampling for rapid structure learning and then switches to Uniform sampling for boundary refinement. On CIFAR-10, Curriculum Sampling improves the best FID from 3.85 (Uniform) to 3.22 while reaching peak performance at 100k rather than 150k training steps. Our results highlight that timestep sampling should be treated as an evolving curriculum rather than a fixed hyperparameter.

Time series is a collection of data instances that are ordered according to a time stamp. Stock prices, temperature, etc are examples of time series data in real life. Time series data are used for forecasting sales, predicting trends. Visualization is the process of visually representing data or the relationship between features of a data either in a two-dimensional plot or a three-dimensional plot. Visualizing the time series data constitutes an important part of the process for working with a time series dataset. Visualizing the data not only helps in the modelling process but it can also be used to identify trends and features that cause those trends. In this work, we take a real-life time series dataset and analyse how the target feature relates to other features of the dataset through visualization. From the work that has been carried out, we present an effective method of visualization for time series data which will be much useful for machine learning modelling with such datasets.

Timestep distillation is an effective approach for improving the generation efficiency of diffusion models. The Consistency Model (CM), as a trajectory-based framework, demonstrates significant potential due to its strong theoretical foundation and high-quality few-step generation. Nevertheless, current continuous-time consistency distillation methods still rely heavily on training data and computational resources, hindering their deployment in resource-constrained scenarios and limiting their scalability to diverse domains. To address this issue, we propose Trajectory-Backward Consistency Model (TBCM), which eliminates the dependence on external training data by extracting latent representations directly from the teacher model's generation trajectory. Unlike conventional methods that require VAE encoding and large-scale datasets, our self-contained distillation paradigm significantly improves both efficiency and simplicity. Moreover, the trajectory-extracted samples naturally bridge the distribution gap between training and inference, thereby enabling more effective knowledge transfer. Empirically, TBCM achieves 6.52 FID and 28.08 CLIP scores on MJHQ-30k under one-step generation, while reducing training time by approximately 40% compared to Sana-Sprint and saving a substantial amount of GPU memory, demonstrating superior efficiency without sacrificing quality. We further reveal the diffusion-generation space discrepancy in continuous-time consistency distillation and analyze how sampling strategies affect distillation performance, offering insights for future distillation research. GitHub Link: https://github.com/hustvl/TBCM.

Time is an important feature in many applications involving events that occur synchronously and/or asynchronously. To effectively consume time information, recent studies have focused on designing new architectures. In this paper, we take an orthogonal but complementary approach by providing a model-agnostic vector representation for time, called Time2Vec, that can be easily imported into many existing and future architectures and improve their performances. We show on a range of models and problems that replacing the notion of time with its Time2Vec representation improves the performance of the final model.

Extending discrete-time causal Prior-data Fitted Networks for time series to continuous time invites writing the mechanism as a stochastic differential equation (SDE) -- but if the SDE is integrated once per observation gap, the trajectory law depends on when it is observed, and the prior remains a discrete-time Markov model in SDE clothing. We propose a precise continuity criterion -- trajectory-law invariance to the observation schedule -- together with a three-tier taxonomy (discrete; naive observation-grid integration; fine-grid integration with decoupled observation) and a construction realising the top tier on a random DAG with OU or small-MLP nonlinear drifts, irregular observation schedules, and hard / soft / time-varying interventions. A 2 times 2 encoder times integrator ablation, run independently on a linear and a nonlinear prior, finds fine-grid integration beats naive on 8/8 cells (sign-consistency p < 1/256) with the gap growing as the eval grid refines; the encoder axis is null with fine integration but time-aware-leading with naive. We release the prior and a preliminary zero-shot protocol on pharmacokinetic and physical-system data.

Delayed outcomes are ubiquitous in online experimentation: treatment can affect whether an outcome occurs, when it occurs, and its realized value. To accommodate staggered entry while remaining robust to environmental nonstationarity and unit-level heterogeneity, we adopt a design-based perspective and target the sample cumulative reward in each arm as a function of calendar time. Our confidence sequences allow practitioners to continuously monitor the counterfactual incremental reward, such as revenue, that would have been realized by calendar time t had all entered units been assigned to treatment rather than control. The main technical challenge is the choice of design-based filtration, complicated by the presence of asynchronous potential outcome times. We show that the IPW treatment-effect estimation error is not a martingale with respect to any filtration, while each arm-specific IPW estimation error is a martingale with respect to a carefully chosen arm-specific event-time filtration. We therefore construct a confidence sequence for the treatment effect by combining two arm-level confidence sequences with a union bound, and further demonstrate that this can outperform the traditional design-based variance upper bound. Finally, we characterize the class of augmentations for which the per-arm AIPW estimation error remains a martingale.

In-context learning for tabular data sets strong predictive standards in observational settings; it however primarily relies on correlational structure, which becomes unreliable under distribution shift or intervention. While established methods to discover causal structure exist, they are often focused on structure identifiability and decoupled from the predictive architectures that could benefit from them. To bridge these perspectives, we study how to simultaneously infer and enforce causal structure in the form of topological variable orderings into tabular prediction. Unlike standard architectures, our model TabOrder uses causal order-constrained attention, basing predictions only on features that precede a target under a learned causal order. Similar to causal discovery methods, TabOrder learns the optimal variable ordering in an unsupervised manner through a likelihood-based objective. We justify this choice under standard functional model classes and also study how sample missingness, a common challenge in tabular data, interacts with causal direction identification. Empirically, we confirm that TabOrder recovers accurate variable orderings while addressing prediction and imputation tasks, as well as gives insight into real-world biological data under intervention.

Time series have numerous applications in finance, healthcare, IoT, and smart city. In many of these applications, time series typically contain personal data, so privacy infringement may occur if they are released directly to the public. Recently, local differential privacy (LDP) has emerged as the state-of-the-art approach to protecting data privacy. However, existing works on LDP-based collections cannot preserve the shape of time series. A recent work, PatternLDP, attempts to address this problem, but it can only protect a finite group of elements in a time series due to {\omega}-event level privacy guarantee. In this paper, we propose PrivShape, a trie-based mechanism under user-level LDP to protect all elements. PrivShape first transforms a time series to reduce its length, and then adopts trie-expansion and two-level refinement to improve utility. By extensive experiments on real-world datasets, we demonstrate that PrivShape outperforms PatternLDP when adapted for offline use, and can effectively extract frequent shapes.

Time-series analysis is critical for a wide range of fields such as healthcare, finance, transportation, and energy, among many others. The practical applications often involve analyzing time-series data alongside contextual information in the form of natural language to support informed decisions. However, current time-series models are limited in their ability to perform reasoning that involves both time-series and their textual content. In this work, we address this gap by introducing Chat-TS, a large language model (LLM) based framework, designed to support reasoning over time series and textual data. Unlike traditional models, Chat-TS integrates time-series tokens into LLMs' vocabulary, enhancing its reasoning ability over both modalities without compromising the core natural language capabilities, enabling practical analysis and reasoning across modalities. To support learning and evaluation in this setup, we contribute new datasets: the TS Instruct Training Dataset which pairs diverse time-series data with relevant text instructions and responses for instruction tuning, the TS Instruct Question and Answer (QA) Gold Dataset which provides multiple-choice questions designed to evaluate multimodal reasoning, and a TS Instruct Quantitative Probing Set which contains a small subset of the TS Instruct QA tasks alongside math and decision-making questions for LLM evaluation. We designed a training strategy to preserve the inherent reasoning capabilities of LLMs while augmenting them for time-series reasoning. Experiments show that Chat-TS achieves state-of-the-art performance in multi-modal reasoning tasks by maintaining strong natural language proficiency while improving time-series reasoning. ~To ensure replicability and facilitate future research, all models, datasets, and code will be available at [\texttt{Github-URL].}

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 https://github.com/blacksnail789521/Time-IMM, and the benchmark library can be accessed at https://github.com/blacksnail789521/IMM-TSF. Project page: https://blacksnail789521.github.io/time-imm-project-page/

Time Series Language Models (TSLMs) are emerging as unified models for reasoning over continuous signals in natural language. However, long-context retrieval remains a major limitation: existing models are typically trained and evaluated on short sequences, while real-world time-series sensor streams can span millions of datapoints. This mismatch requires precise temporal localization under strict computational constraints, a regime that is not captured by current benchmarks. We introduce TS-Haystack, a long-context temporal retrieval benchmark comprising ten task types across four categories: direct retrieval, temporal reasoning, multi-step reasoning and contextual anomaly. The benchmark uses controlled needle insertion by embedding short activity bouts into longer longitudinal accelerometer recordings, enabling systematic evaluation across context lengths ranging from seconds to 2 hours per sample. We hypothesize that existing TSLM time series encoders overlook temporal granularity as context length increases, creating a task-dependent effect: compression aids classification but impairs retrieval of localized events. Across multiple model and encoding strategies, we observe a consistent divergence between classification and retrieval behavior. Learned latent compression preserves or improves classification accuracy at compression ratios up to 176times, but retrieval performance degrades with context length, incurring in the loss of temporally localized information. These results highlight the importance of architectural designs that decouple sequence length from computational complexity while preserving temporal fidelity.

Online resources such as WikiHow compile a wide range of scripts for performing everyday tasks, which can assist models in learning to reason about procedures. However, the scripts are always presented in a linear manner, which does not reflect the flexibility displayed by people executing tasks in real life. For example, in the CrossTask Dataset, 64.5% of consecutive step pairs are also observed in the reverse order, suggesting their ordering is not fixed. In addition, each step has an average of 2.56 frequent next steps, demonstrating "branching". In this paper, we propose the new challenging task of non-sequential graph script induction, aiming to capture optional and interchangeable steps in procedural planning. To automate the induction of such graph scripts for given tasks, we propose to take advantage of loosely aligned videos of people performing the tasks. In particular, we design a multimodal framework to ground procedural videos to WikiHow textual steps and thus transform each video into an observed step path on the latent ground truth graph script. This key transformation enables us to train a script knowledge model capable of both generating explicit graph scripts for learnt tasks and predicting future steps given a partial step sequence. Our best model outperforms the strongest pure text/vision baselines by 17.52% absolute gains on F1@3 for next step prediction and 13.8% absolute gains on Acc@1 for partial sequence completion. Human evaluation shows our model outperforming the WikiHow linear baseline by 48.76% absolute gains in capturing sequential and non-sequential step relationships.

The success of large pretrained models in natural language processing (NLP) and computer vision (CV) has opened new avenues for constructing foundation models for time series forecasting (TSF). Traditional TSF foundation models rely heavily on numerical data fitting. In contrast, the human brain is inherently skilled at processing visual information, prefer predicting future trends by observing visualized sequences. From a biomimetic perspective, utilizing models to directly process numerical sequences might not be the most effective route to achieving Artificial General Intelligence (AGI). This paper proposes ViTime, a novel Visual Intelligence-based foundation model for TSF. ViTime overcomes the limitations of numerical time series data fitting by utilizing visual data processing paradigms and employs a innovative data synthesis method during training, called Real Time Series (RealTS). Experiments on a diverse set of previously unseen forecasting datasets demonstrate that ViTime achieves state-of-the-art zero-shot performance, even surpassing the best individually trained supervised models in some situations. These findings suggest that visual intelligence can significantly enhance time series analysis and forecasting, paving the way for more advanced and versatile models in the field. The code for our framework is accessible at https://github.com/IkeYang/ViTime.

We introduce MOMENT, a family of open-source foundation models for general-purpose time-series analysis. Pre-training large models on time-series data is challenging due to (1) the absence of a large and cohesive public time-series repository, and (2) diverse time-series characteristics which make multi-dataset training onerous. Additionally, (3) experimental benchmarks to evaluate these models, especially in scenarios with limited resources, time, and supervision, are still in their nascent stages. To address these challenges, we compile a large and diverse collection of public time-series, called the Time-series Pile, and systematically tackle time-series-specific challenges to unlock large-scale multi-dataset pre-training. Finally, we build on recent work to design a benchmark to evaluate time-series foundation models on diverse tasks and datasets in limited supervision settings. Experiments on this benchmark demonstrate the effectiveness of our pre-trained models with minimal data and task-specific fine-tuning. Finally, we present several interesting empirical observations about large pre-trained time-series models. Our code is available anonymously at anonymous.4open.science/r/BETT-773F/.

LLMs have emerged as powerful tools for interpreting multimodal data. In medicine, they hold particular promise for synthesizing large volumes of clinical information into actionable insights and digital health applications. Yet, a major limitation remains their inability to handle time series. To overcome this gap, we present OpenTSLM, a family of Time Series Language Models (TSLMs) created by integrating time series as a native modality to pretrained LLMs, enabling reasoning over multiple time series of any length. We investigate two architectures for OpenTSLM. The first, OpenTSLM-SoftPrompt, models time series implicitly by concatenating learnable time series tokens with text tokens via soft prompting. Although parameter-efficient, we hypothesize that explicit time series modeling scales better and outperforms implicit approaches. We thus introduce OpenTSLM-Flamingo, which integrates time series with text via cross-attention. We benchmark both variants against baselines that treat time series as text tokens or plots, across a suite of text-time-series Chain-of-Thought (CoT) reasoning tasks. We introduce three datasets: HAR-CoT, Sleep-CoT, and ECG-QA-CoT. Across all, OpenTSLM models outperform baselines, reaching 69.9 F1 in sleep staging and 65.4 in HAR, compared to 9.05 and 52.2 for finetuned text-only models. Notably, even 1B-parameter OpenTSLM models surpass GPT-4o (15.47 and 2.95). OpenTSLM-Flamingo matches OpenTSLM-SoftPrompt in performance and outperforms on longer sequences, while maintaining stable memory requirements. By contrast, SoftPrompt grows exponentially in memory with sequence length, requiring around 110 GB compared to 40 GB VRAM when training on ECG-QA with LLaMA-3B. Expert reviews by clinicians find strong reasoning capabilities exhibited by OpenTSLMs on ECG-QA. To facilitate further research, we provide all code, datasets, and models open-source.

Linear time-invariant state space models (SSM) are a classical model from engineering and statistics, that have recently been shown to be very promising in machine learning through the Structured State Space sequence model (S4). A core component of S4 involves initializing the SSM state matrix to a particular matrix called a HiPPO matrix, which was empirically important for S4's ability to handle long sequences. However, the specific matrix that S4 uses was actually derived in previous work for a particular time-varying dynamical system, and the use of this matrix as a time-invariant SSM had no known mathematical interpretation. Consequently, the theoretical mechanism by which S4 models long-range dependencies actually remains unexplained. We derive a more general and intuitive formulation of the HiPPO framework, which provides a simple mathematical interpretation of S4 as a decomposition onto exponentially-warped Legendre polynomials, explaining its ability to capture long dependencies. Our generalization introduces a theoretically rich class of SSMs that also lets us derive more intuitive S4 variants for other bases such as the Fourier basis, and explains other aspects of training S4, such as how to initialize the important timescale parameter. These insights improve S4's performance to 86% on the Long Range Arena benchmark, with 96% on the most difficult Path-X task.

We develop a discipline-agnostic emergence calculus that treats theories as fixed points of idempotent operators acting on descriptions. We show that, once processes are composable but access to the underlying system is mediated by a bounded observational interface, a canonical toolkit of six closure-changing primitives (P1--P6) is unavoidable. The framework unifies order-theoretic closure operators with dynamics-induced endomaps E_{τ,f} built from a Markov kernel, a coarse-graining lens, and a time scale τ. We introduce a computable total-variation idempotence defect for E_{τ,f}; small retention error implies approximate idempotence and yields stable "objects" packaged at the chosen τ within a fixed lens. For directionality, we define an arrow-of-time functional as the path-space KL divergence between forward and time-reversed trajectories and prove it is monotone under coarse-graining (data processing); we also formalize a protocol-trap audit showing that protocol holonomy alone cannot sustain asymmetry without a genuine affinity in the lifted dynamics. Finally, we prove a finite forcing-style counting lemma: relative to a partition-based theory, definable predicate extensions are exponentially rare, giving a clean anti-saturation mechanism for strict ladder climbing.

Inferring music time structures has a broad range of applications in music production, processing and analysis. Scholars have proposed various methods to analyze different aspects of time structures, such as beat, downbeat, tempo and meter. Many state-of-the-art (SOFA) methods, however, are computationally expensive. This makes them inapplicable in real-world industrial settings where the scale of the music collections can be millions. This paper proposes a new state space and a semi-Markov model for music time structure analysis. The proposed approach turns the commonly used 2D state spaces into a 1D model through a jump-back reward strategy. It reduces the state spaces size drastically. We then utilize the proposed method for causal, joint beat, downbeat, tempo, and meter tracking, and compare it against several previous methods. The proposed method delivers similar performance with the SOFA joint causal models with a much smaller state space and a more than 30 times speedup.

Foundation models of time series have not been fully developed due to the limited availability of time series corpora and the underexploration of scalable pre-training. Based on the similar sequential formulation of time series and natural language, increasing research demonstrates the feasibility of leveraging large language models (LLM) for time series. Nevertheless, the inherent autoregressive property and decoder-only architecture of LLMs have not been fully considered, resulting in insufficient utilization of LLM abilities. To fully revitalize the general-purpose token transition and multi-step generation capability of large language models, we propose AutoTimes to repurpose LLMs as autoregressive time series forecasters, which projects time series into the embedding space of language tokens and autoregressively generates future predictions with arbitrary lengths. Compatible with any decoder-only LLMs, the consequent forecaster exhibits the flexibility of the lookback length and scalability with larger LLMs. Further, we formulate time series as prompts, extending the context for prediction beyond the lookback window, termed in-context forecasting. By introducing LLM-embedded textual timestamps, AutoTimes can utilize chronological information to align multivariate time series. Empirically, AutoTimes achieves state-of-the-art with 0.1% trainable parameters and over 5times training/inference speedup compared to advanced LLM-based forecasters. Code is available at this repository: https://github.com/thuml/AutoTimes.

Complex numerical time series analysis often demands multi-step reasoning capabilities beyond current models' reach. Tasks like medical diagnosis and weather forecasting require sequential reasoning processes - including counterfactual analysis, logical deduction, knowledge application, and multi-modal contextual integration - that existing time series models cannot explicitly perform. While recent research has shown large language models (LLMs) can achieve sophisticated Chain-of-Thought (CoT) reasoning through reinforcement learning (RL), these advances have primarily focused on mathematical and coding domains, with LLMs still demonstrating poor performance on time series tasks. We introduce Chain Of thought for Understanding Numerical Time Series (COUNTS), the first framework that trains LLMs to perform CoT reasoning across diverse time series tasks using RL with verifiable rewards. Our approach employs a Residual Vector-Quantized VAE to create high-fidelity discrete tokens that seamlessly integrate into a pre-trained LLM's vocabulary. COUNTS undergoes a two-stage training process: first, supervised fine-tuning on time series analysis tasks to master our novel representations, followed by Group Relative Policy Optimization training on verifiable problems using prompting strategies that encourage explicit reasoning steps before producing final answers. Our experiments demonstrate that this RL-driven approach with intermediate CoT reasoning significantly enhances LLM performance across various time series analysis tasks, opening new possibilities for complex temporal data reasoning.

We introduce Timer-S1, a strong Mixture-of-Experts (MoE) time series foundation model with 8.3B total parameters, 0.75B activated parameters for each token, and a context length of 11.5K. To overcome the scalability bottleneck in existing pre-trained time series foundation models, we perform Serial Scaling in three dimensions: model architecture, dataset, and training pipeline. Timer-S1 integrates sparse TimeMoE blocks and generic TimeSTP blocks for Serial-Token Prediction (STP), a generic training objective that adheres to the serial nature of forecasting. The proposed paradigm introduces serial computations to improve long-term predictions while avoiding costly rolling-style inference and pronounced error accumulation in the standard next-token prediction. Pursuing a high-quality and unbiased training dataset, we curate TimeBench, a corpus with one trillion time points, and apply meticulous data augmentation to mitigate predictive bias. We further pioneer a post-training stage, including continued pre-training and long-context extension, to enhance short-term and long-context performance. Evaluated on the large-scale GIFT-Eval leaderboard, Timer-S1 achieves state-of-the-art forecasting performance, attaining the best MASE and CRPS scores as a pre-trained model. Timer-S1 will be released to facilitate further research.

Time series foundation models (TSFMs) are increasingly being adopted as highly-capable general-purpose time series representation learners. Although their training corpora are vast, they exclude astronomical time series data. Observations of stars produce peta-scale time series with unique challenges including irregular sampling and heteroskedasticity. We introduce StarEmbed, the first public benchmark for rigorous and standardized evaluation of state-of-the-art TSFMs on stellar time series observations (``light curves''). We benchmark on three scientifically-motivated downstream tasks: unsupervised clustering, supervised classification, and out-of-distribution source detection. StarEmbed integrates a catalog of expert-vetted labels with multi-variate light curves from the Zwicky Transient Facility, yielding ~40k hand-labeled light curves spread across seven astrophysical classes. We evaluate the zero-shot representation capabilities of three TSFMs (MOIRAI, Chronos, Chronos-Bolt) and a domain-specific transformer (Astromer) against handcrafted feature extraction, the long-standing baseline in the astrophysics literature. Our results demonstrate that these TSFMs, especially the Chronos models, which are trained on data completely unlike the astronomical observations, can outperform established astrophysics-specific baselines in some tasks and effectively generalize to entirely new data. In particular, TSFMs deliver state-of-the-art performance on our out-of-distribution source detection benchmark. With the first benchmark of TSFMs on astronomical time series data, we test the limits of their generalization and motivate a paradigm shift in time-domain astronomy from using task-specific, fully supervised pipelines toward adopting generic foundation model representations for the analysis of peta-scale datasets from forthcoming observatories.

We introduce TimeZero, a reasoning-guided LVLM designed for the temporal video grounding (TVG) task. This task requires precisely localizing relevant video segments within long videos based on a given language query. TimeZero tackles this challenge by extending the inference process, enabling the model to reason about video-language relationships solely through reinforcement learning. To evaluate the effectiveness of TimeZero, we conduct experiments on two benchmarks, where TimeZero achieves state-of-the-art performance on Charades-STA. Code is available at https://github.com/www-Ye/TimeZero.

Grasping the concept of time is a fundamental facet of human cognition, indispensable for truly comprehending the intricacies of the world. Previous studies typically focus on specific aspects of time, lacking a comprehensive temporal reasoning benchmark. To address this, we propose TimeBench, a comprehensive hierarchical temporal reasoning benchmark that covers a broad spectrum of temporal reasoning phenomena. TimeBench provides a thorough evaluation for investigating the temporal reasoning capabilities of large language models. We conduct extensive experiments on GPT-4, LLaMA2, and other popular LLMs under various settings. Our experimental results indicate a significant performance gap between the state-of-the-art LLMs and humans, highlighting that there is still a considerable distance to cover in temporal reasoning. Besides, LLMs exhibit capability discrepancies across different reasoning categories. Furthermore, we thoroughly analyze the impact of multiple aspects on temporal reasoning and emphasize the associated challenges. We aspire for TimeBench to serve as a comprehensive benchmark, fostering research in temporal reasoning. Resources are available at: https://github.com/zchuz/TimeBench

Time series has been left behind in the era of pre-training and transfer learning. While research in the fields of natural language processing and computer vision are enjoying progressively larger datasets to train massive models, the most popular time series datasets consist of only tens of thousands of time steps, limiting our ability to study the effectiveness of pre-training and scaling. Recent studies have also cast doubt on the need for expressive models and scale. To alleviate these issues, we introduce three large-scale time series forecasting datasets from the cloud operations (CloudOps) domain, the largest having billions of observations, enabling further study into pre-training and scaling of time series models. We build the empirical groundwork for studying pre-training and scaling of time series models and pave the way for future research by identifying a promising candidate architecture. We show that it is a strong zero-shot baseline and benefits from further scaling, both in model and dataset size. Accompanying these datasets and results is a suite of comprehensive benchmark results comparing classical and deep learning baselines to our pre-trained method - achieving a 27% reduction in error on the largest dataset. Code and datasets will be released.

Forecasting multiple future events within a given time horizon is essential for applications in finance, retail, social networks, and healthcare. Marked Temporal Point Processes (MTPP) provide a principled framework to model both the timing and labels of events. However, most existing research focuses on predicting only the next event, leaving long-horizon forecasting largely underexplored. To address this gap, we introduce HoTPP, the first benchmark specifically designed to rigorously evaluate long-horizon predictions. We identify shortcomings in widely used evaluation metrics, propose a theoretically grounded T-mAP metric, present strong statistical baselines, and offer efficient implementations of popular models. Our empirical results demonstrate that modern MTPP approaches often underperform simple statistical baselines. Furthermore, we analyze the diversity of predicted sequences and find that most methods exhibit mode collapse. Finally, we analyze the impact of autoregression and intensity-based losses on prediction quality, and outline promising directions for future research. The HoTPP source code, hyperparameters, and full evaluation results are available at GitHub.

LLM-for-time series (TS) methods typically treat time shallowly, injecting positional or prompt-based cues once at the input of a largely frozen decoder, which limits temporal reasoning as this information degrades through the layers. We introduce Temporal-Prior Conditioning (TPC), which elevates time to a first-class modality that conditions the model at multiple depths. TPC attaches a small set of learnable time series tokens to the patch stream; at selected layers these tokens cross-attend to temporal embeddings derived from compact, human-readable temporal descriptors encoded by the same frozen LLM, then feed temporal context back via self-attention. This disentangles time series signal and temporal information while maintaining a low parameter budget. We show that by training only the cross-attention modules and explicitly disentangling time series signal and temporal information, TPC consistently outperforms both full fine-tuning and shallow conditioning strategies, achieving state-of-the-art performance in long-term forecasting across diverse datasets. Code available at: https://github.com/fil-mp/Deep_tpc

Time series analysis has witnessed the inspiring development from traditional autoregressive models, deep learning models, to recent Transformers and Large Language Models (LLMs). Efforts in leveraging vision models for time series analysis have also been made along the way but are less visible to the community due to the predominant research on sequence modeling in this domain. However, the discrepancy between continuous time series and the discrete token space of LLMs, and the challenges in explicitly modeling the correlations of variates in multivariate time series have shifted some research attentions to the equally successful Large Vision Models (LVMs) and Vision Language Models (VLMs). To fill the blank in the existing literature, this survey discusses the advantages of vision models over LLMs in time series analysis. It provides a comprehensive and in-depth overview of the existing methods, with dual views of detailed taxonomy that answer the key research questions including how to encode time series as images and how to model the imaged time series for various tasks. Additionally, we address the challenges in the pre- and post-processing steps involved in this framework and outline future directions to further advance time series analysis with vision models.

Changepoints are abrupt variations in the generative parameters of a data sequence. Online detection of changepoints is useful in modelling and prediction of time series in application areas such as finance, biometrics, and robotics. While frequentist methods have yielded online filtering and prediction techniques, most Bayesian papers have focused on the retrospective segmentation problem. Here we examine the case where the model parameters before and after the changepoint are independent and we derive an online algorithm for exact inference of the most recent changepoint. We compute the probability distribution of the length of the current ``run,'' or time since the last changepoint, using a simple message-passing algorithm. Our implementation is highly modular so that the algorithm may be applied to a variety of types of data. We illustrate this modularity by demonstrating the algorithm on three different real-world data sets.

Time series research has gathered lots of interests in the last decade, especially for Time Series Classification (TSC) and Time Series Forecasting (TSF). Research in TSC has greatly benefited from the University of California Riverside and University of East Anglia (UCR/UEA) Time Series Archives. On the other hand, the advancement in Time Series Forecasting relies on time series forecasting competitions such as the Makridakis competitions, NN3 and NN5 Neural Network competitions, and a few Kaggle competitions. Each year, thousands of papers proposing new algorithms for TSC and TSF have utilized these benchmarking archives. These algorithms are designed for these specific problems, but may not be useful for tasks such as predicting the heart rate of a person using photoplethysmogram (PPG) and accelerometer data. We refer to this problem as Time Series Extrinsic Regression (TSER), where we are interested in a more general methodology of predicting a single continuous value, from univariate or multivariate time series. This prediction can be from the same time series or not directly related to the predictor time series and does not necessarily need to be a future value or depend heavily on recent values. To the best of our knowledge, research into TSER has received much less attention in the time series research community and there are no models developed for general time series extrinsic regression problems. Most models are developed for a specific problem. Therefore, we aim to motivate and support the research into TSER by introducing the first TSER benchmarking archive. This archive contains 19 datasets from different domains, with varying number of dimensions, unequal length dimensions, and missing values. In this paper, we introduce the datasets in this archive and did an initial benchmark on existing models.

AI agents need to plan to achieve complex goals that involve orchestrating perception, sub-goal decomposition, and execution. These plans consist of ordered steps structured according to a Temporal Execution Order (TEO, a directed acyclic graph that ensures each step executes only after its preconditions are satisfied. Existing research on foundational models' understanding of temporal execution is limited to automatically derived annotations, approximations of the TEO as a linear chain, or text-only inputs. To address this gap, we introduce MATEO (MultimodAl Temporal Execution Order), a benchmark designed to assess and improve the temporal reasoning abilities of Large Vision Language Models (LVLMs) required for real-world planning. We acquire a high-quality professional multimodal recipe corpus, authored through a standardized editorial process that decomposes instructions into discrete steps, each paired with corresponding images. We collect TEO annotations as graphs by designing and using a scalable crowdsourcing pipeline. Using MATEO, we evaluate six state-of-the-art LVLMs across model scales, varying language context, multimodal input structure, and fine-tuning strategies.

Recent advances in generative modeling have led to promising progress on synthesizing 3D human motion from text, with methods that can generate character animations from short prompts and specified durations. However, using a single text prompt as input lacks the fine-grained control needed by animators, such as composing multiple actions and defining precise durations for parts of the motion. To address this, we introduce the new problem of timeline control for text-driven motion synthesis, which provides an intuitive, yet fine-grained, input interface for users. Instead of a single prompt, users can specify a multi-track timeline of multiple prompts organized in temporal intervals that may overlap. This enables specifying the exact timings of each action and composing multiple actions in sequence or at overlapping intervals. To generate composite animations from a multi-track timeline, we propose a new test-time denoising method. This method can be integrated with any pre-trained motion diffusion model to synthesize realistic motions that accurately reflect the timeline. At every step of denoising, our method processes each timeline interval (text prompt) individually, subsequently aggregating the predictions with consideration for the specific body parts engaged in each action. Experimental comparisons and ablations validate that our method produces realistic motions that respect the semantics and timing of given text prompts. Our code and models are publicly available at https://mathis.petrovich.fr/stmc.

Time series foundation models (TSFMs) have emerged as a powerful paradigm for time series analysis, driven by large-scale pretraining on diverse data corpora. However, time series inherently exhibit heterogeneous information density over time, influenced by system states and signal complexity, presenting significant modeling challenges especially in a zero-shot scenario. Current TSFMs rely on non-adaptive processing pipelines that fail to capture this dynamic nature. For example, common tokenization strategies such as fixed-size patching enforce rigid observational granularity, limiting their ability to adapt to varying information densities. Similarly, conventional positional encodings impose a uniform temporal scale, making it difficult to model diverse periodicities and trends across series. To overcome these limitations, we propose Kairos, a flexible TSFM framework that integrates a dynamic patching tokenizer and an instance-adaptive positional embedding. Kairos adaptively selects tokenization granularity and tailors positional encodings to the unique characteristics of each time series instance. Trained on a large-scale Predictability-Stratified Time Series (PreSTS) corpus comprising over 300 billion time points and adopting a multi-patch prediction strategy in the inference stage, Kairos achieves superior performance with much fewer parameters on two common zero-shot benchmarks, GIFT-Eval and the Time-Series-Library benchmark, consistently outperforming established methods across diverse tasks. The project page is at https://foundation-model-research.github.io/Kairos .

A temporal point process is a mathematical model for a time series of discrete events, which covers various applications. Recently, recurrent neural network (RNN) based models have been developed for point processes and have been found effective. RNN based models usually assume a specific functional form for the time course of the intensity function of a point process (e.g., exponentially decreasing or increasing with the time since the most recent event). However, such an assumption can restrict the expressive power of the model. We herein propose a novel RNN based model in which the time course of the intensity function is represented in a general manner. In our approach, we first model the integral of the intensity function using a feedforward neural network and then obtain the intensity function as its derivative. This approach enables us to both obtain a flexible model of the intensity function and exactly evaluate the log-likelihood function, which contains the integral of the intensity function, without any numerical approximations. Our model achieves competitive or superior performances compared to the previous state-of-the-art methods for both synthetic and real datasets.

Recent research on time-series foundation models (TSFMs) has underscored the scarcity of real-world data, often supplemented with synthetic sources in existing datasets, whose generalizability remains however debated. As such, in this work, we propose a novel benchmarking approach: in particular, we aim at building a curated dataset reflecting real world physical temporal dynamics, extracting temporal signals from real-world videos using optical flow. As such, we introduce REAL-V-TSFM, a novel dataset designed to capture rich and diverse time series derived from real-world videos. Experimental results on state-of-the-art TSFMs under zero-shot forecasting show that, despite strong performance on conventional benchmarks, these models exhibit performance degradation on the proposed dataset, suggesting limited generalizability to novel datasets. These findings underscore the need for novel approaches to acquiring time series data and highlight the lack of universality in recent TSFMs, while further validating the effectiveness of our video-based time series data extraction pipeline.

Sequence models such as transformers require inputs to be represented as one-dimensional sequences. In vision, this typically involves flattening images using a fixed row-major (raster-scan) order. While full self-attention is permutation-equivariant, modern long-sequence transformers increasingly rely on architectural approximations that break this invariance and introduce sensitivity to patch ordering. We show that patch order significantly affects model performance in such settings, with simple alternatives like column-major or Hilbert curves yielding notable accuracy shifts. Motivated by this, we propose REOrder, a two-stage framework for discovering task-optimal patch orderings. First, we derive an information-theoretic prior by evaluating the compressibility of various patch sequences. Then, we learn a policy over permutations by optimizing a Plackett-Luce policy using REINFORCE. This approach enables efficient learning in a combinatorial permutation space. REOrder improves top-1 accuracy over row-major ordering on ImageNet-1K by up to 3.01% and Functional Map of the World by 13.35%.

In this work, we build a simple but strong baseline for sounding video generation. Given base diffusion models for audio and video, we integrate them with additional modules into a single model and train it to make the model jointly generate audio and video. To enhance alignment between audio-video pairs, we introduce two novel mechanisms in our model. The first one is timestep adjustment, which provides different timestep information to each base model. It is designed to align how samples are generated along with timesteps across modalities. The second one is a new design of the additional modules, termed Cross-Modal Conditioning as Positional Encoding (CMC-PE). In CMC-PE, cross-modal information is embedded as if it represents temporal position information, and the embeddings are fed into the model like positional encoding. Compared with the popular cross-attention mechanism, CMC-PE provides a better inductive bias for temporal alignment in the generated data. Experimental results validate the effectiveness of the two newly introduced mechanisms and also demonstrate that our method outperforms existing methods.

Temporal Point Processes (TPP) are probabilistic generative frameworks. They model discrete event sequences localized in continuous time. Generally, real-life events reveal descriptive information, known as marks. Marked TPPs model time and marks of the event together for practical relevance. Conditioned on past events, marked TPPs aim to learn the joint distribution of the time and the mark of the next event. For simplicity, conditionally independent TPP models assume time and marks are independent given event history. They factorize the conditional joint distribution of time and mark into the product of individual conditional distributions. This structural limitation in the design of TPP models hurt the predictive performance on entangled time and mark interactions. In this work, we model the conditional inter-dependence of time and mark to overcome the limitations of conditionally independent models. We construct a multivariate TPP conditioning the time distribution on the current event mark in addition to past events. Besides the conventional intensity-based models for conditional joint distribution, we also draw on flexible intensity-free TPP models from the literature. The proposed TPP models outperform conditionally independent and dependent models in standard prediction tasks. Our experimentation on various datasets with multiple evaluation metrics highlights the merit of the proposed approach.

Human cognition is deeply intertwined with a sense of time, known as Chronoception. This sense allows us to judge how long facts remain valid and when knowledge becomes outdated. Despite progress in vision, language, and motor control, AI still struggles to reason about temporal validity. We introduce Chronocept, the first benchmark to model temporal validity as a continuous probability distribution over time. Using skew-normal curves fitted along semantically decomposed temporal axes, Chronocept captures nuanced patterns of emergence, decay, and peak relevance. It includes two datasets: Benchmark I (atomic facts) and Benchmark II (multi-sentence passages). Annotations show strong inter-annotator agreement (84% and 89%). Our baselines predict curve parameters - location, scale, and skewness - enabling interpretable, generalizable learning and outperforming classification-based approaches. Chronocept fills a foundational gap in AI's temporal reasoning, supporting applications in knowledge grounding, fact-checking, retrieval-augmented generation (RAG), and proactive agents. Code and data are publicly available.

Many real-world systems exhibit temporal, dynamic behaviors, which are captured as time series of complex agent interactions. To perform temporal reasoning, current methods primarily encode temporal dynamics through simple sequence-based models. However, in general these models fail to efficiently capture the full spectrum of rich dynamics in the input, since the dynamics is not uniformly distributed. In particular, relevant information might be harder to extract and computing power is wasted for processing all individual timesteps, even if they contain no significant changes or no new information. Here we propose TimeGraphs, a novel approach that characterizes dynamic interactions as a hierarchical temporal graph, diverging from traditional sequential representations. Our approach models the interactions using a compact graph-based representation, enabling adaptive reasoning across diverse time scales. Adopting a self-supervised method, TimeGraphs constructs a multi-level event hierarchy from a temporal input, which is then used to efficiently reason about the unevenly distributed dynamics. This construction process is scalable and incremental to accommodate streaming data. We evaluate TimeGraphs on multiple datasets with complex, dynamic agent interactions, including a football simulator, the Resistance game, and the MOMA human activity dataset. The results demonstrate both robustness and efficiency of TimeGraphs on a range of temporal reasoning tasks. Our approach obtains state-of-the-art performance and leads to a performance increase of up to 12.2% on event prediction and recognition tasks over current approaches. Our experiments further demonstrate a wide array of capabilities including zero-shot generalization, robustness in case of data sparsity, and adaptability to streaming data flow.

Macro placement is a fundamental step in modern chip physical design, playing a crucial role in determining the solution quality of high-dimensional combinatorial optimization problems. Despite recent advancements in machine learning for spatial coordinate determination, the temporal dimension of placement sequencing remains largely governed by static heuristics. In this work, we demonstrate that the placement sequence is not merely a preprocessing step but a decisive factor in optimization, where suboptimal early decisions trigger irreversible domino effects that constrain the solution space. To harness this unexplored dimension, we propose OrderPlace, a proxy-guided LLM evolution framework for automatically discovering macro placement order strategies. Instead of relying on manually crafted heuristics such as area- or connectivity-based ordering, OrderPlace explores a broader space of code-level policies, ranging from static scoring metrics to dynamic physics-inspired mechanisms. To mitigate the prohibitive cost of evaluating sequences, we introduce a lightweight proxy evaluation mechanism that efficiently filters candidates using a deterministic greedy probe. Experimental results on the standard ISPD 2005 benchmarks demonstrate that OrderPlace discovers novel ordering strategies. Compared with WireMask-EA and the state-of-the-art method EGPlace, OrderPlace reduces wirelength by 34.04\% and 14.08\%, respectively.

Large Language Models (LLMs) have achieved remarkable success in various NLP tasks, yet they still face significant challenges in reasoning and arithmetic. Temporal reasoning, a critical component of natural language understanding, has raised increasing research attention. However, comprehensive testing of Allen's interval relations (e.g., before, after, during) -- a fundamental framework for temporal relationships -- remains underexplored. To fill this gap, we present ChronoSense, a new benchmark for evaluating LLMs' temporal understanding. It includes 16 tasks, focusing on identifying the Allen relation between two temporal events and temporal arithmetic, using both abstract events and real-world data from Wikidata. We assess the performance of seven recent LLMs using this benchmark and the results indicate that models handle Allen relations, even symmetrical ones, quite differently. Moreover, the findings suggest that the models may rely on memorization to answer time-related questions. Overall, the models' low performance highlights the need for improved temporal understanding in LLMs and ChronoSense offers a robust framework for future research in this area. Our dataset and the source code are available at https://github.com/duyguislakoglu/chronosense.

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.

Geo-temporal understanding, the ability to infer location, time, and contextual properties from visual input alone, underpins applications such as disaster management, traffic planning, embodied navigation, world modeling, and geography education. Although recent vision-language models (VLMs) have advanced image geo-localization using cues like landmarks and road signs, their ability to reason about temporal signals and physically grounded spatial cues remains limited. To address this gap, we introduce TimeSpot, a benchmark for evaluating real-world geo-temporal reasoning in VLMs. TimeSpot comprises 1,455 ground-level images from 80 countries and requires structured prediction of temporal attributes (season, month, time of day, daylight phase) and geographic attributes (continent, country, climate zone, environment type, latitude-longitude) directly from visual evidence. It also includes spatial-temporal reasoning tasks that test physical plausibility under real-world uncertainty. Evaluations of state-of-the-art open- and closed-source VLMs show low performance, particularly for temporal inference. While supervised fine-tuning yields improvements, results remain insufficient, highlighting the need for new methods to achieve robust, physically grounded geo-temporal understanding. TimeSpot is available at: https://TimeSpot-GT.github.io.

Procedural activities follow well-defined structures: whether we consider a cooking recipe or a mechanic repairing a car, these activities naturally decompose in a hierarchy of steps and sub-steps. Traditional approaches for step grounding require extensive annotations and scale poorly. Instead, we argue that such hierarchical structure can emerge naturally from uncurated videos of human activities through recurring patterns of co-occurring actions and activities. Our approach builds on HiERO, a weakly-supervised representation learning approach that maps close in the feature space actions that are functionally related to each other, leveraging only fine-grained action-level narrations. In this feature space, procedure steps can be detected by a simple clustering, with no additional task-specific fine-tuning. For the Ego4D Step Grounding challenge, we augment this approach by ensuring fine and coarse level agreement in step assignments, enforcing strict temporal monotonicity of the grounded steps and post-processing the detected steps to reduce the impact of noisy predictions. We call this approach HiERO-StepG and it achieves 56.27 % on the R@1 (IoU = 0.3) metric on the global leaderboard at submission time, ranking second while being completely zero-shot and not requiring procedure-specific annotations. Project page: https://github.com/andreazenotto/HiERO-StepG.

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

Sequence and channel mixers, the core mechanism in sequence models, have become the de facto standard in time series analysis (TSA). However, recent studies have questioned the necessity of complex sequence mixers, such as attention mechanisms, demonstrating that simpler architectures can achieve comparable or even superior performance. This suggests that the benefits attributed to complex sequencemixers might instead emerge from other architectural or optimization factors. Based on this observation, we pose a central question: Are common sequence mixers necessary for time-series analysis? Therefore, we propose JustDense, an empirical study that systematically replaces sequence mixers in various well-established TSA models with dense layers. Grounded in the MatrixMixer framework, JustDense treats any sequence mixer as a mixing matrix and replaces it with a dense layer. This substitution isolates the mixing operation, enabling a clear theoretical foundation for understanding its role. Therefore, we conducted extensive experiments on 29 benchmarks covering five representative TSA tasks using seven state-of-the-art TSA models to address our research question. The results show that replacing sequence mixers with dense layers yields comparable or even superior performance. In the cases where dedicated sequence mixers still offer benefits, JustDense challenges the assumption that "deeper and more complex architectures are inherently better" in TSA.

Many problems in astrophysics cover multiple orders of magnitude in spatial and temporal scales. While simulating systems that experience rapid changes in these conditions, it is essential to adapt the (time-) step size to capture the behavior of the system during those rapid changes and use a less accurate time step at other, less demanding, moments. We encounter three problems with traditional methods. Firstly, making such changes requires expert knowledge of the astrophysics as well as of the details of the numerical implementation. Secondly, some parameters that determine the time-step size are fixed throughout the simulation, which means that they do not adapt to the rapidly changing conditions of the problem. Lastly, we would like the choice of time-step size to balance accuracy and computation effort. We address these challenges with Reinforcement Learning by training it to select the time-step size dynamically. We use the integration of a system of three equal-mass bodies that move due to their mutual gravity as an example of its application. With our method, the selected integration parameter adapts to the specific requirements of the problem, both in terms of computation time and accuracy while eliminating the expert knowledge needed to set up these simulations. Our method produces results competitive to existing methods and improve the results found with the most commonly-used values of time-step parameter. This method can be applied to other integrators without further retraining. We show that this extrapolation works for variable time-step integrators but does not perform to the desired accuracy for fixed time-step integrators.

Multivariate time series data, collected across various fields such as manufacturing and wearable technology, exhibit states at multiple levels of granularity, from coarse-grained system behaviors to fine-grained, detailed events. Effectively segmenting and integrating states across these different granularities is crucial for tasks like predictive maintenance and performance optimization. However, existing time series segmentation methods face two key challenges: (1) the inability to handle multiple levels of granularity within a unified model, and (2) limited adaptability to new, evolving patterns in dynamic environments. To address these challenges, we propose PromptTSS, a novel framework for time series segmentation with multi-granularity states. PromptTSS uses a unified model with a prompting mechanism that leverages label and boundary information to guide segmentation, capturing both coarse- and fine-grained patterns while adapting dynamically to unseen patterns. Experiments show PromptTSS improves accuracy by 24.49% in multi-granularity segmentation, 17.88% in single-granularity segmentation, and up to 599.24% in transfer learning, demonstrating its adaptability to hierarchical states and evolving time series dynamics. Our code is available at https://github.com/blacksnail789521/PromptTSS.

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

We present a novel prompt design for Large Language Models (LLMs) tailored to Asynchronous Time Series. Unlike regular time series, which assume values at evenly spaced time points, asynchronous time series consist of timestamped events occurring at irregular intervals, each described in natural language. Our approach effectively utilizes the rich natural language of event descriptions, allowing LLMs to benefit from their broad world knowledge for reasoning across different domains and tasks. This allows us to extend the scope of asynchronous time series analysis beyond forecasting to include tasks like anomaly detection and data imputation. We further introduce Stochastic Soft Prompting, a novel prompt-tuning mechanism that significantly improves model performance, outperforming existing fine-tuning methods such as QLoRA. Through extensive experiments on real world datasets, we demonstrate that our approach achieves state-of-the-art performance across different tasks and datasets.

Time awareness is a fundamental ability of omni large language models, especially for understanding long videos and answering complex questions. Previous approaches mainly target vision-language scenarios and focus on the explicit temporal grounding questions, such as identifying when a visual event occurs or determining what event happens at aspecific time. However, they often make insufficient use of the audio modality, and overlook implicit temporal grounding across modalities--for example, identifying what is visually present when a character speaks, or determining what is said when a visual event occurs--despite such cross-modal temporal relations being prevalent in real-world scenarios. In this paper, we propose ChronusOmni, an omni large language model designed to enhance temporal awareness for both explicit and implicit audiovisual temporal grounding. First, we interleave text-based timestamp tokens with visual and audio representations at each time unit, enabling unified temporal modeling across modalities. Second, to enforce correct temporal ordering and strengthen fine-grained temporal reasoning, we incorporate reinforcement learning with specially designed reward functions. Moreover, we construct ChronusAV, a temporally-accurate, modality-complete, and cross-modal-aligned dataset to support the training and evaluation on audiovisual temporal grounding task. Experimental results demonstrate that ChronusOmni achieves state-of-the-art performance on ChronusAV with more than 30% improvement and top results on most metrics upon other temporal grounding benchmarks. This highlights the strong temporal awareness of our model across modalities, while preserving general video and audio understanding capabilities.

State-of-the-art approaches in time series generation (TSG), such as TimeVQVAE, utilize vector quantization-based tokenization to effectively model complex distributions of time series. These approaches first learn to transform time series into a sequence of discrete latent vectors, and then a prior model is learned to model the sequence. The discrete latent vectors, however, only capture low-level semantics (e.g., shapes). We hypothesize that higher-fidelity time series can be generated by training a prior model on more informative discrete latent vectors that contain both low and high-level semantics (e.g., characteristic dynamics). In this paper, we introduce a novel framework, termed NC-VQVAE, to integrate self-supervised learning into those TSG methods to derive a discrete latent space where low and high-level semantics are captured. Our experimental results demonstrate that NC-VQVAE results in a considerable improvement in the quality of synthetic samples.

We show that for all functions t(n) geq n, every multitape Turing machine running in time t can be simulated in space only O(t log t). This is a substantial improvement over Hopcroft, Paul, and Valiant's simulation of time t in O(t/log t) space from 50 years ago [FOCS 1975, JACM 1977]. Among other results, our simulation implies that bounded fan-in circuits of size s can be evaluated on any input in only s cdot poly(log s) space, and that there are explicit problems solvable in O(n) space which require n^{2-varepsilon} time on a multitape Turing machine for all varepsilon > 0, thereby making a little progress on the P versus PSPACE problem. Our simulation reduces the problem of simulating time-bounded multitape Turing machines to a series of implicitly-defined Tree Evaluation instances with nice parameters, leveraging the remarkable space-efficient algorithm for Tree Evaluation recently found by Cook and Mertz [STOC 2024].

A diffusion model, which is formulated to produce an image using thousands of denoising steps, usually suffers from a slow inference speed. Existing acceleration algorithms simplify the sampling by skipping most steps yet exhibit considerable performance degradation. By viewing the generation of diffusion models as a discretized integrating process, we argue that the quality drop is partly caused by applying an inaccurate integral direction to a timestep interval. To rectify this issue, we propose a timestep aligner that helps find a more accurate integral direction for a particular interval at the minimum cost. Specifically, at each denoising step, we replace the original parameterization by conditioning the network on a new timestep, which is obtained by aligning the sampling distribution to the real distribution. Extensive experiments show that our plug-in design can be trained efficiently and boost the inference performance of various state-of-the-art acceleration methods, especially when there are few denoising steps. For example, when using 10 denoising steps on the popular LSUN Bedroom dataset, we improve the FID of DDIM from 9.65 to 6.07, simply by adopting our method for a more appropriate set of timesteps. Code will be made publicly available.

Time Series Foundation Models (TSFMs) advance generalization and data efficiency in time series forecasting by unified large-scale pretraining. But TSFMs remain lacking when adapting to specific downstream forecasting tasks for two reasons. First, the non-stationary and uncertain nature of time series data lead to inevitable temporal distribution shifts between historical training and future testing data, while current Supervised FineTuning (SFT)-based methods are prone to overfitting and may degrade generalization. Second, training data availability varies across forecasting tasks, requiring TSFMs to generalize well under diverse data regimes. To address these challenges, we introduce the Time series Reinforcement Finetuning (TimeRFT) paradigm for TSFM downstream adaptation, which consists of two task-specific training recipes: i) A forecasting quality-based temporal reward mechanism that conducts a multi-faceted evaluation of the contribution of each prediction step to overall forecasting accuracy. ii) A forecasting difficulty-based data selection strategy to identify time series samples with generalizable predictive patterns and informative training signals. Extensive experiments demonstrate TimeRFT can consistently outperform SFT-based adaptation methods across various real-world forecasting tasks and training data regimes, enhancing prediction accuracy and generalization against unforeseen distribution shifts.

Autoregressive (AR) video diffusion models enable low-latency streaming generation by synthesizing videos chunk by chunk with cached visual context, but this chunk-wise formulation makes temporal instruction following ambiguous. A single global prompt does not specify which sub-event should be realized in each chunk, while naively switching to step-wise prompts often leads to delayed reactions, blended step semantics, and error propagation across prompt transitions. These failures are difficult to address with supervised fine-tuning or distillation alone: SFT suffers from exposure bias, while rollout-based distillation still optimizes low-level denoising or teacher-distribution matching rather than directly enforcing action ordering and prompt-transition correctness. We address these challenges with TempAct, a planner--executor reinforcement learning framework that jointly optimizes temporal decomposition and step-conditioned execution for temporally plausible AR video generation. TempAct uses an LLM planner to explore span-aware step prompts that are executable by the video model, and trains an AR diffusion executor to follow these prompts under its own generated histories. Its key mechanism is hierarchical group exploration: candidate plans form planning groups, and each plan induces an execution group of multiple continuations from a shared visual context, enabling plan-level credit assignment for long-horizon temporal outcomes and executor-level credit assignment for prompt-switch behavior. We further design hierarchical rewards that combine plan-quality and full-video temporal feedback for the planner with local transition-level step-following rewards, aesthetic regularization, and KL constraints for the executor. Experiments on Self-Forcing and LongLive show that TempAct improves temporal consistency while preserving overall visual quality.

Watch time prediction (WTP) has emerged as a pivotal task in short video recommendation systems, designed to quantify user engagement through continuous interaction modeling. Predicting users' watch times on videos often encounters fundamental challenges, including wide value ranges and imbalanced data distributions, which can lead to significant estimation bias when directly applying regression techniques. Recent studies have attempted to address these issues by converting the continuous watch time estimation into an ordinal regression task. While these methods demonstrate partial effectiveness, they exhibit notable limitations: (1) the discretization process frequently relies on bucket partitioning, inherently reducing prediction flexibility and accuracy and (2) the interdependencies among different partition intervals remain underutilized, missing opportunities for effective error correction. Inspired by language modeling paradigms, we propose a novel Generative Regression (GR) framework that reformulates WTP as a sequence generation task. Our approach employs structural discretization to enable nearly lossless value reconstruction while maintaining prediction fidelity. Through carefully designed vocabulary construction and label encoding schemes, each watch time is bijectively mapped to a token sequence. To mitigate the training-inference discrepancy caused by teacher-forcing, we introduce a curriculum learning with embedding mixup strategy that gradually transitions from guided to free-generation modes. We evaluate our method against state-of-the-art approaches on two public datasets and one industrial dataset. We also perform online A/B testing on the Kuaishou App to confirm the real-world effectiveness. The results conclusively show that GR outperforms existing techniques significantly.

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

Sequences have become first class citizens in supervised learning thanks to the resurgence of recurrent neural networks. Many complex tasks that require mapping from or to a sequence of observations can now be formulated with the sequence-to-sequence (seq2seq) framework which employs the chain rule to efficiently represent the joint probability of sequences. In many cases, however, variable sized inputs and/or outputs might not be naturally expressed as sequences. For instance, it is not clear how to input a set of numbers into a model where the task is to sort them; similarly, we do not know how to organize outputs when they correspond to random variables and the task is to model their unknown joint probability. In this paper, we first show using various examples that the order in which we organize input and/or output data matters significantly when learning an underlying model. We then discuss an extension of the seq2seq framework that goes beyond sequences and handles input sets in a principled way. In addition, we propose a loss which, by searching over possible orders during training, deals with the lack of structure of output sets. We show empirical evidence of our claims regarding ordering, and on the modifications to the seq2seq framework on benchmark language modeling and parsing tasks, as well as two artificial tasks -- sorting numbers and estimating the joint probability of unknown graphical models.

State-space models (SSMs) offer a powerful framework for dynamical system analysis, wherein the temporal dynamics of the system are assumed to be captured through the evolution of the latent states, which govern the values of the observations. This paper provides a selective review of recent advancements in deep neural network-based approaches for SSMs, and presents a unified perspective for discrete time deep state space models and continuous time ones such as latent neural Ordinary Differential and Stochastic Differential Equations. It starts with an overview of the classical maximum likelihood based approach for learning SSMs, reviews variational autoencoder as a general learning pipeline for neural network-based approaches in the presence of latent variables, and discusses in detail representative deep learning models that fall under the SSM framework. Very recent developments, where SSMs are used as standalone architectural modules for improving efficiency in sequence modeling, are also examined. Finally, examples involving mixed frequency and irregularly-spaced time series data are presented to demonstrate the advantage of SSMs in these settings.

Bitcoin constructs temporal order internally rather than synchronizing to any external clock. Empirical evidence shows that its time evolution is non-continuous, probabilistic, and self-regulated. Block discovery follows a stochastic process in which uncertainty accumulates during the search phase and collapses abruptly when a valid proof-of-work solution appears. Difficulty adjustment maintains the system near the entropy-maximizing regime and allows the network to infer the underlying global hash rate. Building on these observations, we present a unified framework in which Bitcoin time emerges from four interacting mechanisms: proof of work as a distributed entropy source, difficulty adjustment as temporal feedback, entropy collapse as discrete temporal updates, and recursive sealing through hash pointers. Together these mechanisms form a self-regulating temporal architecture that transforms distributed randomness into a coherent and irreversible global timeline, offering a generalizable foundation for autonomous timekeeping in permissionless systems.

Foundation models have become increasingly popular for forecasting due to their ability to provide predictions without requiring a lot of training data. In this work, we demonstrate how TabPFN-v2, a general tabular foundation model, can be effectively applied to time series forecasting. We introduce TabPFN-TS, a simple method that combines TabPFN-v2 with lightweight feature engineering to enable both point and probabilistic forecasting. Despite its simplicity and compact size (11M parameters), TabPFN-TS achieves top rank on the public GIFT-Eval leaderboard in both forecasting tasks. Through ablation studies, we investigate factors contributing to this surprising effectiveness, especially considering TabPFN-v2 was pretrained solely on synthetic tabular data with no exposure to time series. Our results highlights the potential of tabular foundation models like TabPFN-v2 as a valuable new approach for time series forecasting. Our implementation is available at https://github.com/PriorLabs/tabpfn-time-series.

Time series are the primary data type used to record dynamic system measurements and generated in great volume by both physical sensors and online processes (virtual sensors). Time series analytics is therefore crucial to unlocking the wealth of information implicit in available data. With the recent advancements in graph neural networks (GNNs), there has been a surge in GNN-based approaches for time series analysis. These approaches can explicitly model inter-temporal and inter-variable relationships, which traditional and other deep neural network-based methods struggle to do. In this survey, we provide a comprehensive review of graph neural networks for time series analysis (GNN4TS), encompassing four fundamental dimensions: forecasting, classification, anomaly detection, and imputation. Our aim is to guide designers and practitioners to understand, build applications, and advance research of GNN4TS. At first, we provide a comprehensive task-oriented taxonomy of GNN4TS. Then, we present and discuss representative research works and introduce mainstream applications of GNN4TS. A comprehensive discussion of potential future research directions completes the survey. This survey, for the first time, brings together a vast array of knowledge on GNN-based time series research, highlighting foundations, practical applications, and opportunities of graph neural networks for time series analysis.

Large language models (LLMs) are typically trained on shuffled corpora, yielding models whose knowledge is frozen at train time and whose temporal grounding remains poorly understood. In this work, we study the impact of pre-training dynamics on the acquisition of time-sensitive factual knowledge, focusing specifically on data ordering. Our main contributions are twofold. First, we introduce a comprehensive benchmark of over 7,000 temporally grounded questions and an evaluation protocol that enables analysis of whether models correctly associate facts with their corresponding time periods. Second, we pretrain 6B-parameter models on temporally ordered Common Crawl snapshots and compare them against standard shuffled pre-training. Our results show that sequentially trained models match shuffled baselines on general language understanding and common knowledge while consistently exhibiting more up-to-date and temporally precise knowledge. Temporally ordered pre-training yields improved factual freshness, while shuffled pre-training peaks on older data, possibly due to increased factual repetition. These findings, along with the release of our code at https://github.com/kyutai-labs/kairos , checkpoints, and datasets at https://huggingface.co/collections/kyutai/kairos provide a foundation for future research on continual learning for LLMs.

Multivariate time-series data in numerous real-world applications (e.g., healthcare and industry) are informative but challenging due to the lack of labels and high dimensionality. Recent studies in self-supervised learning have shown their potential in learning rich representations without relying on labels, yet they fall short in learning disentangled embeddings and addressing issues of inductive bias (e.g., transformation-invariance). To tackle these challenges, we propose TimeDRL, a generic multivariate time-series representation learning framework with disentangled dual-level embeddings. TimeDRL is characterized by three novel features: (i) disentangled derivation of timestamp-level and instance-level embeddings from patched time-series data using a [CLS] token strategy; (ii) utilization of timestamp-predictive and instance-contrastive tasks for disentangled representation learning, with the former optimizing timestamp-level embeddings with predictive loss, and the latter optimizing instance-level embeddings with contrastive loss; and (iii) avoidance of augmentation methods to eliminate inductive biases, such as transformation-invariance from cropping and masking. Comprehensive experiments on 6 time-series forecasting datasets and 5 time-series classification datasets have shown that TimeDRL consistently surpasses existing representation learning approaches, achieving an average improvement of forecasting by 58.02% in MSE and classification by 1.48% in accuracy. Furthermore, extensive ablation studies confirmed the relative contribution of each component in TimeDRL's architecture, and semi-supervised learning evaluations demonstrated its effectiveness in real-world scenarios, even with limited labeled data. The code is available at https://github.com/blacksnail789521/TimeDRL.

Multi-hop logical reasoning over knowledge graph (KG) plays a fundamental role in many artificial intelligence tasks. Recent complex query embedding (CQE) methods for reasoning focus on static KGs, while temporal knowledge graphs (TKGs) have not been fully explored. Reasoning over TKGs has two challenges: 1. The query should answer entities or timestamps; 2. The operators should consider both set logic on entity set and temporal logic on timestamp set. To bridge this gap, we define the multi-hop logical reasoning problem on TKGs. With generated three datasets, we propose the first temporal CQE named Temporal Feature-Logic Embedding framework (TFLEX) to answer the temporal complex queries. We utilize vector logic to compute the logic part of Temporal Feature-Logic embeddings, thus naturally modeling all First-Order Logic (FOL) operations on entity set. In addition, our framework extends vector logic on timestamp set to cope with three extra temporal operators (After, Before and Between). Experiments on numerous query patterns demonstrate the effectiveness of our method.

An orientation of a given static graph is called transitive if for any three vertices a,b,c, the presence of arcs (a,b) and (b,c) forces the presence of the arc (a,c). If only the presence of an arc between a and c is required, but its orientation is unconstrained, the orientation is called quasi-transitive. A fundamental result presented by Ghouila-Houri guarantees that any static graph admitting a quasi-transitive orientation also admits a transitive orientation. In a seminal work, Mertzios et al. introduced the notion of temporal transitivity in order to model information flows in simple temporal networks. We revisit the model introduced by Mertzios et al. and propose an analogous to Ghouila-Houri's characterization for the temporal scenario. We present a structure theorem that will allow us to express by a 2-SAT formula all the constraints imposed by temporal transitive orientations. The latter produces an efficient recognition algorithm for graphs admitting such orientations. Additionally, we extend the temporal transitivity model to temporal graphs having multiple time-labels associated to their edges and claim that the previous results hold in the multilabel setting. Finally, we propose a characterization of temporal comparability graphs via forbidden temporal ordered patterns.

Clinical time series are central to patient monitoring, risk assessment, and clinical decision support. However, they are often sparse, irregularly sampled, and asynchronous, making it difficult for models to identify the temporal evidence required for clinical Question Answering (QA). Existing benchmarks primarily focus on regularly sampled time-series QA or medical QA over static data, and therefore rarely assess whether models can faithfully ground their answers in irregular temporal observations. To fill this gap, we introduce CLIR-Bench, a benchmark for irregular clinical time series QA constructed from de-identified ICU records through a principled four-stage pipeline. CLIR-Bench contains 6,600 QA instances spanning 11 clinical variables, organized into four capability dimensions and 11 tasks. Each question is linked to explicit temporal evidence and task-specific answer derivation rules, enabling evaluation of both answer accuracy and evidence use. Experiments show that existing generalist models struggle to retrieve and reason over sparse clinical evidence, highlighting the need for stronger irregular time-series reasoning methods. Our code and data are available at https://huggingface.co/datasets/winall/CLIR-Bench.

Generating temporal data under conditions is crucial for forecasting, imputation, and generative tasks. Such data often has metadata and partially observed signals that jointly influence the generated values. However, existing methods face three key limitations: (1) they condition on either the metadata or observed values, but rarely both together; (2) they adopt either training-time approaches that fail to generalize to unseen scenarios, or inference-time approaches that ignore metadata; and (3) they suffer from trade-offs between generation speed and temporal coherence across time windows--choosing either slow but coherent autoregressive methods or fast but incoherent parallel ones. We propose WaveStitch, a novel diffusion-based method to overcome these hurdles through: (1) dual-sourced conditioning on both metadata and partially observed signals; (2) a hybrid training-inference architecture, incorporating metadata during training and observations at inference via gradient-based guidance; and (3) a novel pipeline-style paradigm that generates time windows in parallel while preserving coherence through an inference-time conditional loss and a stitching mechanism. Across diverse datasets, WaveStitch demonstrates adaptability to arbitrary patterns of observed signals, achieving 1.81x lower mean-squared-error compared to the state-of-the-art, and generates data up to 166.48x faster than autoregressive methods while maintaining coherence. Our code is available at: https://github.com/adis98/WaveStitch

Deep learning has been actively applied to time series forecasting, leading to a deluge of new methods, belonging to the class of historical-value models. Yet, despite the attractive properties of time-index models, such as being able to model the continuous nature of underlying time series dynamics, little attention has been given to them. Indeed, while naive deep time-index models are far more expressive than the manually predefined function representations of classical time-index models, they are inadequate for forecasting, being unable to generalize to unseen time steps due to the lack of inductive bias. In this paper, we propose DeepTime, a meta-optimization framework to learn deep time-index models which overcome these limitations, yielding an efficient and accurate forecasting model. Extensive experiments on real world datasets in the long sequence time-series forecasting setting demonstrate that our approach achieves competitive results with state-of-the-art methods, and is highly efficient. Code is available at https://github.com/salesforce/DeepTime.

We present a self-supervised, time-to-event (TTE) foundation model called MOTOR (Many Outcome Time Oriented Representations) which is pretrained on timestamped sequences of events in electronic health records (EHR) and health insurance claims. TTE models are used for estimating the probability distribution of the time until a specific event occurs, which is an important task in medical settings. TTE models provide many advantages over classification using fixed time horizons, including naturally handling censored observations, but are challenging to train with limited labeled data. MOTOR addresses this challenge by pretraining on up to 55M patient records (9B clinical events). We evaluate MOTOR's transfer learning performance on 19 tasks, across 3 patient databases (a private EHR system, MIMIC-IV, and Merative claims data). Task-specific models adapted from MOTOR improve time-dependent C statistics by 4.6% over state-of-the-art, improve label efficiency by up to 95% ,and are more robust to temporal distributional shifts. We further evaluate cross-site portability by adapting our MOTOR foundation model for six prediction tasks on the MIMIC-IV dataset, where it outperforms all baselines. MOTOR is the first foundation model for medical TTE predictions and we release a 143M parameter pretrained model for research use at [redacted URL].

Recognizing the flow of time in a story is a crucial aspect of understanding it. Prior work related to time has primarily focused on identifying temporal expressions or relative sequencing of events, but here we propose computationally annotating each line of a book with wall clock times, even in the absence of explicit time-descriptive phrases. To do so, we construct a data set of hourly time phrases from 52,183 fictional books. We then construct a time-of-day classification model that achieves an average error of 2.27 hours. Furthermore, we show that by analyzing a book in whole using dynamic programming of breakpoints, we can roughly partition a book into segments that each correspond to a particular time-of-day. This approach improves upon baselines by over two hours. Finally, we apply our model to a corpus of literature categorized by different periods in history, to show interesting trends of hourly activity throughout the past. Among several observations we find that the fraction of events taking place past 10 P.M jumps past 1880 - coincident with the advent of the electric light bulb and city lights.

In this paper we present an approach for localizing steps of procedural activities in narrated how-to videos. To deal with the scarcity of labeled data at scale, we source the step descriptions from a language knowledge base (wikiHow) containing instructional articles for a large variety of procedural tasks. Without any form of manual supervision, our model learns to temporally ground the steps of procedural articles in how-to videos by matching three modalities: frames, narrations, and step descriptions. Specifically, our method aligns steps to video by fusing information from two distinct pathways: i) {\em direct} alignment of step descriptions to frames, ii) {\em indirect} alignment obtained by composing steps-to-narrations with narrations-to-video correspondences. Notably, our approach performs global temporal grounding of all steps in an article at once by exploiting order information, and is trained with step pseudo-labels which are iteratively refined and aggressively filtered. In order to validate our model we introduce a new evaluation benchmark -- HT-Step -- obtained by manually annotating a 124-hour subset of HowTo100MA test server is accessible at \url{https://eval.ai/web/challenges/challenge-page/2082.} with steps sourced from wikiHow articles. Experiments on this benchmark as well as zero-shot evaluations on CrossTask demonstrate that our multi-modality alignment yields dramatic gains over several baselines and prior works. Finally, we show that our inner module for matching narration-to-video outperforms by a large margin the state of the art on the HTM-Align narration-video alignment benchmark.