Daily Papers

Accurate spatiotemporal pattern analysis is critical in fields such as urban traffic, meteorology, and public health monitoring. However, existing methods face performance bottlenecks, typically yielding only incremental gains and often exhibiting limited cross-domain transferability. We analyze this bottleneck through spatial and temporal entropy measures, which are used as diagnostic indicators of spatiotemporal complexity mismatch rather than as guarantees that entropy alignment alone yields better forecasting. Empirically, larger mismatch is often accompanied by higher prediction uncertainty, especially under a fixed model-capacity budget. Guided by this diagnostic, we propose a scalable, adaptive framework that harmonizes spatial and temporal feature representations. Spatial dimensionality is compressed via low-rank matrix embedding to preserve essential structure, while an extended temporal horizon captures long-range dependencies and mitigates cumulative errors arising from temporal heterogeneity. Extensive experiments on urban traffic, meteorological, and epidemic datasets demonstrate substantial accuracy gains and broad applicability across the evaluated domains, suggesting that the framework is promising for a wide range of spatiotemporal tasks beyond the current study. The code is available on GitHub at https://github.com/ST-Balance/ST-Balance.

Deep video compression has made remarkable process in recent years, with the majority of advancements concentrated on P-frame coding. Although efforts to enhance B-frame coding are ongoing, their compression performance is still far behind that of traditional bi-directional video codecs. In this paper, we introduce a bi-directional deep contextual video compression scheme tailored for B-frames, termed DCVC-B, to improve the compression performance of deep B-frame coding. Our scheme mainly has three key innovations. First, we develop a bi-directional motion difference context propagation method for effective motion difference coding, which significantly reduces the bit cost of bi-directional motions. Second, we propose a bi-directional contextual compression model and a corresponding bi-directional temporal entropy model, to make better use of the multi-scale temporal contexts. Third, we propose a hierarchical quality structure-based training strategy, leading to an effective bit allocation across large groups of pictures (GOP). Experimental results show that our DCVC-B achieves an average reduction of 26.6% in BD-Rate compared to the reference software for H.265/HEVC under random access conditions. Remarkably, it surpasses the performance of the H.266/VVC reference software on certain test datasets under the same configuration.

Diffusion large language models (dLLMs) generate text through iterative denoising, yet current decoding strategies discard rich intermediate predictions in favor of the final output. Our work here reveals a critical phenomenon, temporal oscillation, where correct answers often emerge in the middle process, but are overwritten in later denoising steps. To address this issue, we introduce two complementary methods that exploit temporal consistency: 1) Temporal Self-Consistency Voting, a training-free, test-time decoding strategy that aggregates predictions across denoising steps to select the most consistent output; and 2) a post-training method termed Temporal Consistency Reinforcement, which uses Temporal Semantic Entropy (TSE), a measure of semantic stability across intermediate predictions, as a reward signal to encourage stable generations. Empirical results across multiple benchmarks demonstrate the effectiveness of our approach. Using the negative TSE reward alone, we observe a remarkable average improvement of 24.7% on the Countdown dataset over an existing dLLM. Combined with the accuracy reward, we achieve absolute gains of 2.0% on GSM8K, 4.3% on MATH500, 6.6% on SVAMP, and 25.3% on Countdown, respectively. Our findings underscore the untapped potential of temporal dynamics in dLLMs and offer two simple yet effective tools to harness them.

Transformer-based models have significantly advanced time series forecasting, with patch-based input strategies offering efficiency and improved long-horizon modeling. Yet, existing approaches rely on temporally-agnostic patch construction, where arbitrary starting positions and fixed lengths fracture temporal coherence by splitting natural transitions across boundaries. This naive segmentation often disrupts short-term dependencies and weakens representation learning. In response, we propose EntroPE (Entropy-Guided Dynamic Patch Encoder), a novel, temporally informed framework that dynamically detects transition points via conditional entropy and dynamically places patch boundaries. This preserves temporal structure while retaining the computational benefits of patching. EntroPE consists of two key modules, namely an Entropy-based Dynamic Patcher (EDP) that applies information-theoretic criteria to locate natural temporal shifts and determine patch boundaries, and an Adaptive Patch Encoder (APE) that employs pooling and cross-attention to capture intra-patch dependencies and produce fixed-size latent representations. These embeddings are then processed by a global transformer to model inter-patch dynamics. Experiments across long-term forecasting benchmarks demonstrate that EntroPE improves both accuracy and efficiency, establishing entropy-guided dynamic patching as a promising new paradigm for time series modeling. Code is available at: https://github.com/Sachithx/EntroPE.

Last-mile logistics (LML) is characterized by high fragmentation, yet existing research treats this as an exogenous constraint rather than a quantifiable and optimizable system property. This paper introduces a framework for measuring LML complexity using structural entropy, derived from Boltzmann's statistical mechanics. Unlike traditional KPIs such as distance or cost, structural entropy quantifies the cardinality of the configuration space, providing a diagnostic of inherent system disorder. We establish a formal duality with Shannon entropy, linking absolute complexity burden to distributional balance. We apply our entropy framework to 6,112 Amazon last-mile routes across five U.S. cities. Current operations exhibit persistently high normalized entropy, indicating near-maximal fragmentation. A stable non-linear scaling relationship between entropy and route distance validates the metric as a predictive indicator of operational difficulty. To evaluate spatial consolidation, we develop a system-wide entropy measure accounting for all movements by both carriers and customers. We establish a theoretical conservation principle: under idealized conditions, spatial consolidation merely redistributes entropy from carrier to customer. Both idealizing conditions are violated in practice, thereby increasing total system entropy. Our system-wide measure reveals that spatial consolidation reduces carrier entropy by up to 40% under aggressive adoption but increases total system entropy by activating customer collection trips, though trip chaining can diminish this effect. Temporal consolidation, by contrast, genuinely reduces entropy by decreasing delivery events without creating new movements. By formalizing fragmentation as a measurable structural property, this research provides a new lens for network design, consolidation policy, and evaluation last-mile system performance.

Extracting informative representations from videos is fundamental for effectively learning various downstream tasks. We present a novel approach for unsupervised learning of meaningful representations from videos, leveraging the concept of image spatial entropy (ISE) that quantifies the per-pixel information in an image. We argue that local entropy of pixel neighborhoods and their temporal evolution create valuable intrinsic supervisory signals for learning prominent features. Building on this idea, we abstract visual features into a concise representation of keypoints that act as dynamic information transmitters, and design a deep learning model that learns, purely unsupervised, spatially and temporally consistent representations directly from video frames. Two original information-theoretic losses, computed from local entropy, guide our model to discover consistent keypoint representations; a loss that maximizes the spatial information covered by the keypoints and a loss that optimizes the keypoints' information transportation over time. We compare our keypoint representation to strong baselines for various downstream tasks, \eg, learning object dynamics. Our empirical results show superior performance for our information-driven keypoints that resolve challenges like attendance to static and dynamic objects or objects abruptly entering and leaving the scene.

The development of video diffusion models unveils a significant challenge: the substantial computational demands. To mitigate this challenge, we note that the reverse process of diffusion exhibits an inherent entropy-reducing nature. Given the inter-frame redundancy in video modality, maintaining full frame rates in high-entropy stages is unnecessary. Based on this insight, we propose TPDiff, a unified framework to enhance training and inference efficiency. By dividing diffusion into several stages, our framework progressively increases frame rate along the diffusion process with only the last stage operating on full frame rate, thereby optimizing computational efficiency. To train the multi-stage diffusion model, we introduce a dedicated training framework: stage-wise diffusion. By solving the partitioned probability flow ordinary differential equations (ODE) of diffusion under aligned data and noise, our training strategy is applicable to various diffusion forms and further enhances training efficiency. Comprehensive experimental evaluations validate the generality of our method, demonstrating 50% reduction in training cost and 1.5x improvement in inference efficiency.

Diffusion large language models (dLLMs) offer a promising paradigm for parallel text generation, but in practice they face an accuracy-parallelism trade-off, where increasing tokens per forward (TPF) often degrades generation quality. Existing acceleration methods often gain speed at the cost of accuracy. To address this limitation, we propose TAD, a Temporal-Aware trajectory self-Distillation framework. During data construction, we condition a teacher model on both the prompt and the ground-truth response to generate decoding trajectories, recording the intermediate masked states throughout the process. Based on how many decoding steps remain before each masked token is revealed, we partition masked positions into near and distant subsets. For near tokens, we train the student with a hard cross-entropy loss using the teacher trajectory tokens as labels, encouraging confident predictions for tokens that are about to be decoded. For distant tokens, we apply a soft KL divergence loss between the teacher and student token distributions, providing softer supervision and preserving future planning knowledge. This temporal-aware partition naturally gives rise to two deployment configurations: a Quality model that prioritizes accuracy and a Speed model that favors more aggressive acceleration. Experiments show that TAD consistently improves the accuracy-parallelism trade-off. On LLaDA, it raises average accuracy from 46.2\% to 51.6\% with the Quality model and average AUP from 46.2 to 257.1 with the Speed model. Our code is available at: https://github.com/BHmingyang/TAD

Remote sensing change detection is vital for monitoring environmental and urban transformations but faces challenges like manual feature extraction and sensitivity to noise. Traditional methods and early deep learning models, such as convolutional neural networks (CNNs), struggle to capture long-range dependencies and global context essential for accurate change detection in complex scenes. While Transformer-based models mitigate these issues, their computational complexity limits their applicability in high-resolution remote sensing. Building upon ChangeMamba architecture, which leverages state space models for efficient global context modeling, this paper proposes precision fusion blocks to capture channel-wise temporal variations and per-pixel differences for fine-grained change detection. An enhanced decoder pipeline, incorporating lightweight channel reduction mechanisms, preserves local details with minimal computational cost. Additionally, an optimized loss function combining Cross Entropy, Dice and Lovasz objectives addresses class imbalance and boosts Intersection-over-Union (IoU). Evaluations on SYSU-CD, LEVIR-CD+, and WHU-CD datasets demonstrate superior precision, recall, F1 score, IoU, and overall accuracy compared to state-of-the-art methods, highlighting the approach's robustness for remote sensing change detection. For complete transparency, the codes and pretrained models are accessible at https://github.com/Buddhi19/MambaCD.git

Machine unlearning aims to forget sensitive knowledge from Large Language Models (LLMs) while maintaining general utility. However, existing approaches typically treat all tokens in a response indiscriminately and enforce uncertainty over the entire vocabulary. This global treatment results in unnecessary utility degradation and extends optimization to content-agnostic regions. To address these limitations, we propose PALU (Prefix-Aware Localized Unlearning), a framework driven by a local entropy maximization objective across both temporal and vocabulary dimensions. PALU reveals that (i) suppressing the sensitive prefix alone is sufficient to sever the causal generation link, and (ii) flattening only the top-k logits is adequate to maximize uncertainty in the critical subspace. These findings allow PALU to avoid redundant optimization across the full vocabulary and parameter space while minimizing collateral damage to general model performance. Extensive experiments validate that PALU achieves superior forgetting efficacy and utility preservation compared to state-of-the-art baselines.

Reinforcement learning with verifiable rewards (RLVR) has become a core technique for post-training of Large Language Models (LLMs). While policy optimization is driven by all sampled tokens under a globally broadcast scalar reward, the heterogeneous policy behaviors exhibited along trajectories are largely overlooked without differentiation. Existing works address this by credit allocation, including token-level advantage reweighting, and selective token optimization, however, the allocation criterion are principally stagnant throughout training, limiting resilient policy evolution. In this work, we argue that when learning signals are scheduled can be as important as where they are allocated across tokens, and introduce the temporal dimension that scheduling the credit allocation criteria over the course of RLVR optimization. We find that prioritizing targeted tokens emphasized with specific policy behaviors, and gradually attenuating toward general optimization leads to more stable and efficient learning dynamics. Furthermore, we show that simple trajectory percentiles provide a natural perspective for distinguishing policy behaviors, and works effectively with temporal scheduling. Our analysis reveals that standard optimization substantially sacrifices policy entropy when simultaneously accommodating heterogeneous behaviors, whereas temporal scheduling yields healthier policy evolution dynamics. Experiments across mathematical and general reasoning benchmarks demonstrate consistent improvements, suggesting that temporal scheduling constitutes a promising optimization dimension.

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.

We investigate the time evolution of the Boltzmann entropy of a dilute gas of N particles, N>>1, as it undergoes a free expansion doubling its volume. The microstate of the system, a point in the 4N dimensional phase space, changes in time via Hamiltonian dynamics. Its entropy, at any time t, is given by the logarithm of the phase space volume of all the microstates giving rise to its macrostate at time t. The macrostates that we consider are defined by coarse graining the one-particle phase space into cells Δ_α. The initial and final macrostates of the system are equilibrium states in volumes V and 2V, with the same energy E and particle number N. Their entropy per particle is given, for sufficiently large systems, by the thermodynamic entropy as a function of the particle and energy density, whose leading term is independent of the size of the Δ_α. The intermediate (non-equilibrium) entropy does however depend on the size of the cells Δ_α. Its change with time is due to (i) dispersal in physical space from free motion and to (ii) the collisions between particles which change their velocities. The former depends strongly on the size of the velocity coarse graining Δv: it produces entropy at a rate proportional to Δv. This dependence is investigated numerically and analytically for a dilute two-dimensional gas of hard discs. It becomes significant when the mean free path between collisions is of the same order or larger than the length scale of the initial spatial inhomogeneity. In the opposite limit, the rate of entropy production is essentially independent of Δv and is given by the Boltzmann equation for the limit Δvrightarrow 0. We show that when both processes are active the time dependence of the entropy has a scaling form involving the ratio of the rates of its production by the two processes.

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

Transfer entropy (TE) is an information theoretic measure that reveals the directional flow of information between processes, providing valuable insights for a wide range of real-world applications. This work proposes Transfer Entropy Estimation via Transformers (TREET), a novel attention-based approach for estimating TE for stationary processes. The proposed approach employs Donsker-Varadhan representation to TE and leverages the attention mechanism for the task of neural estimation. We propose a detailed theoretical and empirical study of the TREET, comparing it to existing methods on a dedicated estimation benchmark. To increase its applicability, we design an estimated TE optimization scheme that is motivated by the functional representation lemma, and use it to estimate the capacity of communication channels with memory, which is a canonical optimization problem in information theory. We further demonstrate how an optimized TREET can be used to estimate underlying densities, providing experimental results. Finally, we apply TREET to feature analysis of patients with Apnea, demonstrating its applicability to real-world physiological data. Our work, applied with state-of-the-art deep learning methods, opens a new door for communication problems which are yet to be solved.

Temporal graphs are widely used to model dynamic systems with time-varying interactions. In real-world scenarios, the underlying mechanisms of generating future interactions in dynamic systems are typically governed by a set of recurring substructures within the graph, known as temporal motifs. Despite the success and prevalence of current temporal graph neural networks (TGNN), it remains uncertain which temporal motifs are recognized as the significant indications that trigger a certain prediction from the model, which is a critical challenge for advancing the explainability and trustworthiness of current TGNNs. To address this challenge, we propose a novel approach, called Temporal Motifs Explainer (TempME), which uncovers the most pivotal temporal motifs guiding the prediction of TGNNs. Derived from the information bottleneck principle, TempME extracts the most interaction-related motifs while minimizing the amount of contained information to preserve the sparsity and succinctness of the explanation. Events in the explanations generated by TempME are verified to be more spatiotemporally correlated than those of existing approaches, providing more understandable insights. Extensive experiments validate the superiority of TempME, with up to 8.21% increase in terms of explanation accuracy across six real-world datasets and up to 22.96% increase in boosting the prediction Average Precision of current TGNNs.

Time plays a critical role in how information is generated, retrieved, and interpreted. In this survey, we provide a comprehensive overview of Temporal Information Retrieval and Temporal Question Answering, two research areas aimed at handling and understanding time-sensitive information. As the amount of time-stamped content from sources like news articles, web archives, and knowledge bases increases, systems must address challenges such as detecting temporal intent, normalizing time expressions, ordering events, and reasoning over evolving or ambiguous facts. These challenges are critical across many dynamic and time-sensitive domains, from news and encyclopedias to science, history, and social media. We review both traditional approaches and modern neural methods, including those that use transformer models and Large Language Models (LLMs). We also review recent advances in temporal language modeling, multi-hop reasoning, and retrieval-augmented generation (RAG), alongside benchmark datasets and evaluation strategies that test temporal robustness, recency awareness, and generalization.

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.

We explore the relations between the zeta distribution and algorithmic information theory via a new model of the transfer learning problem. The program distribution is approximated by a zeta distribution with parameter near 1. We model the training sequence as a stochastic process. We analyze the upper temporal bound for learning a training sequence and its entropy rates, assuming an oracle for the transfer learning problem. We argue from empirical evidence that power-law models are suitable for natural processes. Four sequence models are proposed. Random typing model is like no-free lunch where transfer learning does not work. Zeta process independently samples programs from the zeta distribution. A model of common sub-programs inspired by genetics uses a database of sub-programs. An evolutionary zeta process samples mutations from Zeta distribution. The analysis of stochastic processes inspired by evolution suggest that AI may be feasible in nature, countering no-free lunch sort of arguments.

In this paper, we propose a simple yet effective approach for self-supervised video object segmentation (VOS). Our key insight is that the inherent structural dependencies present in DINO-pretrained Transformers can be leveraged to establish robust spatio-temporal correspondences in videos. Furthermore, simple clustering on this correspondence cue is sufficient to yield competitive segmentation results. Previous self-supervised VOS techniques majorly resort to auxiliary modalities or utilize iterative slot attention to assist in object discovery, which restricts their general applicability and imposes higher computational requirements. To deal with these challenges, we develop a simplified architecture that capitalizes on the emerging objectness from DINO-pretrained Transformers, bypassing the need for additional modalities or slot attention. Specifically, we first introduce a single spatio-temporal Transformer block to process the frame-wise DINO features and establish spatio-temporal dependencies in the form of self-attention. Subsequently, utilizing these attention maps, we implement hierarchical clustering to generate object segmentation masks. To train the spatio-temporal block in a fully self-supervised manner, we employ semantic and dynamic motion consistency coupled with entropy normalization. Our method demonstrates state-of-the-art performance across multiple unsupervised VOS benchmarks and particularly excels in complex real-world multi-object video segmentation tasks such as DAVIS-17-Unsupervised and YouTube-VIS-19. The code and model checkpoints will be released at https://github.com/shvdiwnkozbw/SSL-UVOS.

The goal of this work is to train strong models for visual speech recognition without requiring human annotated ground truth data. We achieve this by distilling from an Automatic Speech Recognition (ASR) model that has been trained on a large-scale audio-only corpus. We use a cross-modal distillation method that combines Connectionist Temporal Classification (CTC) with a frame-wise cross-entropy loss. Our contributions are fourfold: (i) we show that ground truth transcriptions are not necessary to train a lip reading system; (ii) we show how arbitrary amounts of unlabelled video data can be leveraged to improve performance; (iii) we demonstrate that distillation significantly speeds up training; and, (iv) we obtain state-of-the-art results on the challenging LRS2 and LRS3 datasets for training only on publicly available data.

This thesis addresses two persistent and closely related challenges in modern deep learning, reliability and efficiency, through a unified framework grounded in Spectral Geometry and Random Matrix Theory (RMT). As deep networks and large language models continue to scale, their internal behavior becomes increasingly opaque, leading to hallucinations, fragile generalization under distribution shift, and growing computational and energy demands. By analyzing the eigenvalue dynamics of hidden activations across layers and inputs, this work shows that spectral statistics provide a compact, stable, and interpretable lens on model behavior, capable of separating structured, causal representations from noise-dominated variability. Within this framework, the first contribution, EigenTrack, introduces a real-time method for detecting hallucinations and out-of-distribution behavior in large language and vision-language models. EigenTrack transforms streaming activations into spectral descriptors such as entropy, variance, and deviations from the Marchenko-Pastur baseline, and models their temporal evolution using lightweight recurrent classifiers, enabling early detection of reliability failures before they appear in model outputs while offering interpretable insight into representation dynamics. The second contribution, RMT-KD, presents a principled approach to compressing deep networks via random matrix theoretic knowledge distillation. By interpreting outlier eigenvalues in activation spectra as carriers of task-relevant information, RMT-KD progressively projects networks onto lower-dimensional subspaces through iterative self-distillation, yielding significantly more compact and energy-efficient models while preserving accuracy and dense, hardware-friendly structure.

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.

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.

Purpose. Handwriting is one of the most frequently occurring patterns in everyday life and with it come challenging applications such as handwriting recognition (HWR), writer identification, and signature verification. In contrast to offline HWR that only uses spatial information (i.e., images), online HWR (OnHWR) uses richer spatio-temporal information (i.e., trajectory data or inertial data). While there exist many offline HWR datasets, there is only little data available for the development of OnHWR methods on paper as it requires hardware-integrated pens. Methods. This paper presents data and benchmark models for real-time sequence-to-sequence (seq2seq) learning and single character-based recognition. Our data is recorded by a sensor-enhanced ballpoint pen, yielding sensor data streams from triaxial accelerometers, a gyroscope, a magnetometer and a force sensor at 100 Hz. We propose a variety of datasets including equations and words for both the writer-dependent and writer-independent tasks. Our datasets allow a comparison between classical OnHWR on tablets and on paper with sensor-enhanced pens. We provide an evaluation benchmark for seq2seq and single character-based HWR using recurrent and temporal convolutional networks and Transformers combined with a connectionist temporal classification (CTC) loss and cross-entropy (CE) losses. Results. Our convolutional network combined with BiLSTMs outperforms Transformer-based architectures, is on par with InceptionTime for sequence-based classification tasks, and yields better results compared to 28 state-of-the-art techniques. Time-series augmentation methods improve the sequence-based task, and we show that CE variants can improve the single classification task.

Key challenges for the deployment of reinforcement learning (RL) agents in the real world are the discovery, representation and reuse of skills in the absence of a reward function. To this end, we propose a novel approach to learn a task-agnostic skill embedding space from unlabeled multi-view videos. Our method learns a general skill embedding independently from the task context by using an adversarial loss. We combine a metric learning loss, which utilizes temporal video coherence to learn a state representation, with an entropy regularized adversarial skill-transfer loss. The metric learning loss learns a disentangled representation by attracting simultaneous viewpoints of the same observations and repelling visually similar frames from temporal neighbors. The adversarial skill-transfer loss enhances re-usability of learned skill embeddings over multiple task domains. We show that the learned embedding enables training of continuous control policies to solve novel tasks that require the interpolation of previously seen skills. Our extensive evaluation with both simulation and real world data demonstrates the effectiveness of our method in learning transferable skills from unlabeled interaction videos and composing them for new tasks. Code, pretrained models and dataset are available at http://robotskills.cs.uni-freiburg.de

Video-based pretraining offers immense potential for learning strong visual representations on an unprecedented scale. Recently, masked video modeling methods have shown promising scalability, yet fall short in capturing higher-level semantics due to reconstructing predefined low-level targets such as pixels. To tackle this, we present Sinkhorn-guided Masked Video Modelling (SIGMA), a novel video pretraining method that jointly learns the video model in addition to a target feature space using a projection network. However, this simple modification means that the regular L2 reconstruction loss will lead to trivial solutions as both networks are jointly optimized. As a solution, we distribute features of space-time tubes evenly across a limited number of learnable clusters. By posing this as an optimal transport problem, we enforce high entropy in the generated features across the batch, infusing semantic and temporal meaning into the feature space. The resulting cluster assignments are used as targets for a symmetric prediction task where the video model predicts cluster assignment of the projection network and vice versa. Experimental results on ten datasets across three benchmarks validate the effectiveness of SIGMA in learning more performant, temporally-aware, and robust video representations improving upon state-of-the-art methods. Our project website with code is available at: https://quva-lab.github.io/SIGMA.

Deep neural networks have achieved great success in many data processing applications. However, the high computational complexity and storage cost makes deep learning hard to be used on resource-constrained devices, and it is not environmental-friendly with much power cost. In this paper, we focus on low-rank optimization for efficient deep learning techniques. In the space domain, deep neural networks are compressed by low rank approximation of the network parameters, which directly reduces the storage requirement with a smaller number of network parameters. In the time domain, the network parameters can be trained in a few subspaces, which enables efficient training for fast convergence. The model compression in the spatial domain is summarized into three categories as pre-train, pre-set, and compression-aware methods, respectively. With a series of integrable techniques discussed, such as sparse pruning, quantization, and entropy coding, we can ensemble them in an integration framework with lower computational complexity and storage. Besides of summary of recent technical advances, we have two findings for motivating future works: one is that the effective rank outperforms other sparse measures for network compression. The other is a spatial and temporal balance for tensorized neural networks.

Reinforcement learning (RL) has shown strong potential for enhancing reasoning in multimodal large language models, yet existing video reasoning methods often rely on coarse sequence-level rewards or single-factor token selection, neglecting fine-grained links among visual inputs, temporal dynamics, and linguistic outputs, limiting both accuracy and interpretability. We propose Video-KTR, a modality-aware policy shaping framework that performs selective, token-level RL by combining three attribution signals: (1) visual-aware tokens identified via counterfactual masking to reveal perceptual dependence; (2) temporal-aware tokens detected through frame shuffling to expose temporal sensitivity; and (3) high-entropy tokens signaling predictive uncertainty. By reinforcing only these key tokens, Video-KTR focuses learning on semantically informative, modality-sensitive content while filtering out low-value tokens. Across five challenging benchmarks, Video-KTR achieves state-of-the-art or highly competitive results, achieving 42.7\% on Video-Holmes (surpassing GPT-4o) with consistent gains on both reasoning and general video understanding tasks. Ablation studies verify the complementary roles of the attribution signals and the robustness of targeted token-level updates. Overall, Video-KTR improves accuracy and interpretability, offering a simple, drop-in extension to RL for complex video reasoning. Our code and models are available at https://github.com/zywang0104/Video-KTR.

3D Gaussian Splatting (3DGS) has emerged as an efficient and high-fidelity paradigm for novel view synthesis. To adapt 3DGS for dynamic content, deformable 3DGS incorporates temporally deformable primitives with learnable latent embeddings to capture complex motions. Despite its impressive performance, the high-dimensional embeddings and vast number of primitives lead to substantial storage requirements. In this paper, we introduce a Lightweight 4DGS framework, called Light4GS, that employs significance pruning with a deep context model to provide a lightweight storage-efficient dynamic 3DGS representation. The proposed Light4GS is based on 4DGS that is a typical representation of deformable 3DGS. Specifically, our framework is built upon two core components: (1) a spatio-temporal significance pruning strategy that eliminates over 64\% of the deformable primitives, followed by an entropy-constrained spherical harmonics compression applied to the remainder; and (2) a deep context model that integrates intra- and inter-prediction with hyperprior into a coarse-to-fine context structure to enable efficient multiscale latent embedding compression. Our approach achieves over 120x compression and increases rendering FPS up to 20\% compared to the baseline 4DGS, and also superior to frame-wise state-of-the-art 3DGS compression methods, revealing the effectiveness of our Light4GS in terms of both intra- and inter-prediction methods without sacrificing rendering quality.

What happens when a storyteller forgets its own story? Large Language Models (LLMs) can now generate narratives spanning tens of thousands of words, but they often fail to maintain consistency throughout. When generating long-form narratives, these models can contradict their own established facts, character traits, and world rules. Existing story generation benchmarks focus mainly on plot quality and fluency, leaving consistency errors largely unexplored. To address this gap, we present ConStory-Bench, a benchmark designed to evaluate narrative consistency in long-form story generation. It contains 2,000 prompts across four task scenarios and defines a taxonomy of five error categories with 19 fine-grained subtypes. We also develop ConStory-Checker, an automated pipeline that detects contradictions and grounds each judgment in explicit textual evidence. Evaluating a range of LLMs through five research questions, we find that consistency errors show clear tendencies: they are most common in factual and temporal dimensions, tend to appear around the middle of narratives, occur in text segments with higher token-level entropy, and certain error types tend to co-occur. These findings can inform future efforts to improve consistency in long-form narrative generation. Our project page is available at https://picrew.github.io/constory-bench.github.io/.

Experiencing high-fidelity volumetric video as seamlessly as 2D videos is a long-held dream. However, current dynamic 3DGS methods, despite their high rendering quality, face challenges in streaming on mobile devices due to computational and bandwidth constraints. In this paper, we introduce V3(Viewing Volumetric Videos), a novel approach that enables high-quality mobile rendering through the streaming of dynamic Gaussians. Our key innovation is to view dynamic 3DGS as 2D videos, facilitating the use of hardware video codecs. Additionally, we propose a two-stage training strategy to reduce storage requirements with rapid training speed. The first stage employs hash encoding and shallow MLP to learn motion, then reduces the number of Gaussians through pruning to meet the streaming requirements, while the second stage fine tunes other Gaussian attributes using residual entropy loss and temporal loss to improve temporal continuity. This strategy, which disentangles motion and appearance, maintains high rendering quality with compact storage requirements. Meanwhile, we designed a multi-platform player to decode and render 2D Gaussian videos. Extensive experiments demonstrate the effectiveness of V3, outperforming other methods by enabling high-quality rendering and streaming on common devices, which is unseen before. As the first to stream dynamic Gaussians on mobile devices, our companion player offers users an unprecedented volumetric video experience, including smooth scrolling and instant sharing. Our project page with source code is available at https://authoritywang.github.io/v3/.

Half a billion citation edges extracted from 100.7 million Ukrainian court decisions reveal that judicial citation structure encodes legal domain boundaries without supervision and predicts future legislative importance with near-perfect accuracy. We construct the first large-scale citation graph from the complete EDRSR registry (99.5 million full texts, 1.1 TB), extracting 502 million citation links across six types via regex on commodity hardware in approximately 5 hours, with precision of 1.00 on a 200-decision validation sample (95% Wilson CI: [0.982, 1.000]). Three principal findings emerge. (1) The degree distribution follows a power law (alpha = 1.57 +/- 0.008), placing the Ukrainian court network near the EU Court of Justice and below the US Supreme Court, with hub articles cited by millions of decisions. (2) Louvain community detection on the co-citation projection recovers legal domain boundaries (civil, criminal, administrative, commercial) with modularity Q = 0.44-0.55 and temporal stability (NMI = 0.83-0.86 across periods), constituting an automatically constructed legal ontology grounded in judicial practice. (3) Citation features predict top-1000 articles with AUC = 0.9984, substantially outperforming a naive frequency baseline (P@1000 = 0.655); temporal dynamics detect legislative regime changes as phase transitions and the 2022 invasion as a citation entropy spike (H: 11.02 -> 13.49) with emergent wartime legislation nodes. The citation-derived ontology is operationalized as the domain layer of a workflow memory system for LLM-assisted legal analysis, connecting to the ontology-controlled paradigm. The extraction pipeline, analysis code, and aggregated statistics are released as open data.

We present OpenDCVCs, an open-source PyTorch implementation designed to advance reproducible research in learned video compression. OpenDCVCs provides unified and training-ready implementations of four representative Deep Contextual Video Compression (DCVC) models--DCVC, DCVC with Temporal Context Modeling (DCVC-TCM), DCVC with Hybrid Entropy Modeling (DCVC-HEM), and DCVC with Diverse Contexts (DCVC-DC). While the DCVC series achieves substantial bitrate reductions over both classical codecs and advanced learned models, previous public code releases have been limited to evaluation codes, presenting significant barriers to reproducibility, benchmarking, and further development. OpenDCVCs bridges this gap by offering a comprehensive, self-contained framework that supports both end-to-end training and evaluation for all included algorithms. The implementation includes detailed documentation, evaluation protocols, and extensive benchmarking results across diverse datasets, providing a transparent and consistent foundation for comparison and extension. All code and experimental tools are publicly available at https://gitlab.com/viper-purdue/opendcvcs, empowering the community to accelerate research and foster collaboration.

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

We present a speaker-aware approach for simulating multi-speaker conversations that captures temporal consistency and realistic turn-taking dynamics. Prior work typically models aggregate conversational statistics under an independence assumption across speakers and turns. In contrast, our method uses speaker-specific deviation distributions enforcing intra-speaker temporal consistency, while a Markov chain governs turn-taking and a fixed room impulse response preserves spatial realism. We also unify pauses and overlaps into a single gap distribution, modeled with kernel density estimation for smooth continuity. Evaluation on Switchboard using intrinsic metrics - global gap statistics, correlations between consecutive gaps, copula-based higher-order dependencies, turn-taking entropy, and gap survival functions - shows that speaker-aware simulation better aligns with real conversational patterns than the baseline method, capturing fine-grained temporal dependencies and realistic speaker alternation, while revealing open challenges in modeling long-range conversational structure.

Knowledge is inherently time-sensitive and continuously evolves over time. Although current Retrieval-Augmented Generation (RAG) systems enrich LLMs with external knowledge, they largely ignore this temporal nature. This raises two challenges for RAG. First, current RAG methods lack effective time-aware representations. Same facts of different time are difficult to distinguish with vector embeddings or conventional knowledge graphs. Second, most RAG evaluations assume a static corpus, leaving a blind spot regarding update costs and retrieval stability as knowledge evolves. To make RAG time-aware, we propose Temporal GraphRAG (TG-RAG), which models external corpora as a bi-level temporal graph consisting of a temporal knowledge graph with timestamped relations and a hierarchical time graph. Multi-granularity temporal summaries are generated for each time node to capture both key events and broader trends at that time. The design supports incremental updates by extracting new temporal facts from the incoming corpus and merging them into the existing graph. The temporal graph explicitly represents identical facts at different times as distinct edges to avoid ambiguity, and the time hierarchy graph allows only generating reports for new leaf time nodes and their ancestors, ensuring effective and efficient updates. During inference, TG-RAG dynamically retrieves a subgraph within the temporal and semantic scope of the query, enabling precise evidence gathering. Moreover, we introduce ECT-QA, a time-sensitive question-answering dataset featuring both specific and abstract queries, along with a comprehensive evaluation protocol designed to assess incremental update capabilities of RAG systems. Extensive experiments show that TG-RAG significantly outperforms existing baselines, demonstrating the effectiveness of our method in handling temporal knowledge and incremental updates.

In nonstationary bandit learning problems, the decision-maker must continually gather information and adapt their action selection as the latent state of the environment evolves. In each time period, some latent optimal action maximizes expected reward under the environment state. We view the optimal action sequence as a stochastic process, and take an information-theoretic approach to analyze attainable performance. We bound limiting per-period regret in terms of the entropy rate of the optimal action process. The bound applies to a wide array of problems studied in the literature and reflects the problem's information structure through its information-ratio.

Temporal knowledge graphs represent temporal facts (s,p,o,tau) relating a subject s and an object o via a relation label p at time tau, where tau could be a time point or time interval. Temporal knowledge graphs may exhibit static temporal patterns at distinct points in time and dynamic temporal patterns between different timestamps. In order to learn a rich set of static and dynamic temporal patterns and apply them for inference, several embedding approaches have been suggested in the literature. However, as most of them resort to single underlying embedding spaces, their capability to model all kinds of temporal patterns was severely limited by having to adhere to the geometric property of their one embedding space. We lift this limitation by an embedding approach that maps temporal facts into a product space of several heterogeneous geometric subspaces with distinct geometric properties, i.e.\ Complex, Dual, and Split-complex spaces. In addition, we propose a temporal-geometric attention mechanism to integrate information from different geometric subspaces conveniently according to the captured relational and temporal information. Experimental results on standard temporal benchmark datasets favorably evaluate our approach against state-of-the-art models.

Structured memory representations such as knowledge graphs are central to autonomous agents and other long-lived systems. However, most existing approaches model time as discrete metadata, either sorting by recency (burying old-yet-permanent knowledge), simply overwriting outdated facts, or requiring an expensive LLM call at every ingestion step, leaving them unable to distinguish persistent facts from evolving ones. To address this, we introduce RoMem, a drop-in temporal knowledge graph module for structured memory systems, applicable to agentic memory and beyond. A pretrained Semantic Speed Gate maps each relation's text embedding to a volatility score, learning from data that evolving relations (e.g., "president of") should rotate fast while persistent ones (e.g., "born in") should remain stable. Combined with continuous phase rotation, this enables geometric shadowing: obsolete facts are rotated out of phase in complex vector space, so temporally correct facts naturally outrank contradictions without deletion. On temporal knowledge graph completion, RoMem achieves state-of-the-art results on ICEWS05-15 (72.6 MRR). Applied to agentic memory, it delivers 2-3x MRR and answer accuracy on temporal reasoning (MultiTQ), dominates hybrid benchmark (LoCoMo), preserves static memory with zero degradation (DMR-MSC), and generalises zero-shot to unseen financial domains (FinTMMBench).

Graph Neural Networks (GNNs) have recently become increasingly popular due to their ability to learn complex systems of relations or interactions arising in a broad spectrum of problems ranging from biology and particle physics to social networks and recommendation systems. Despite the plethora of different models for deep learning on graphs, few approaches have been proposed thus far for dealing with graphs that present some sort of dynamic nature (e.g. evolving features or connectivity over time). In this paper, we present Temporal Graph Networks (TGNs), a generic, efficient framework for deep learning on dynamic graphs represented as sequences of timed events. Thanks to a novel combination of memory modules and graph-based operators, TGNs are able to significantly outperform previous approaches being at the same time more computationally efficient. We furthermore show that several previous models for learning on dynamic graphs can be cast as specific instances of our framework. We perform a detailed ablation study of different components of our framework and devise the best configuration that achieves state-of-the-art performance on several transductive and inductive prediction tasks for dynamic graphs.

We present a concise dynamical picture of infant-driven household chaos. The framework has three postulations: recurrent daily chaos, overall entropy growth in household organization, and transient local ordering episodes with switching rules (a volatile Maxwell-demon effect). We illustrate entropy growth with a two-region toy model (organizer vs. play area), where entropy production is nonnegative and long-time behavior is typically play-area dominated. We also model toy diffusion and curiosity-driven behavior, where novelty matters more than punishment in the short term, while gradual learning still occurs.

Multi-horizon forecasting problems often contain a complex mix of inputs -- including static (i.e. time-invariant) covariates, known future inputs, and other exogenous time series that are only observed historically -- without any prior information on how they interact with the target. While several deep learning models have been proposed for multi-step prediction, they typically comprise black-box models which do not account for the full range of inputs present in common scenarios. In this paper, we introduce the Temporal Fusion Transformer (TFT) -- a novel attention-based architecture which combines high-performance multi-horizon forecasting with interpretable insights into temporal dynamics. To learn temporal relationships at different scales, the TFT utilizes recurrent layers for local processing and interpretable self-attention layers for learning long-term dependencies. The TFT also uses specialized components for the judicious selection of relevant features and a series of gating layers to suppress unnecessary components, enabling high performance in a wide range of regimes. On a variety of real-world datasets, we demonstrate significant performance improvements over existing benchmarks, and showcase three practical interpretability use-cases of TFT.

In the evolving field of Natural Language Processing, understanding the temporal context of text is increasingly crucial. This study investigates methods to incorporate temporal information during pre-training, aiming to achieve effective time-aware language representation for improved performance on time-related tasks. In contrast to common pre-trained models like BERT, which rely on synchronic document collections such as BookCorpus and Wikipedia, our research introduces BiTimeBERT 2.0, a novel language model pre-trained on a temporal news article collection. BiTimeBERT 2.0 utilizes this temporal news collection, focusing on three innovative pre-training objectives: Time-Aware Masked Language Modeling (TAMLM), Document Dating (DD), and Time-Sensitive Entity Replacement (TSER). Each objective targets a unique aspect of temporal information. TAMLM is designed to enhance the understanding of temporal contexts and relations, DD integrates document timestamps as chronological markers, and TSER focuses on the temporal dynamics of "Person" entities, recognizing their inherent temporal significance. The experimental results consistently demonstrate that BiTimeBERT 2.0 outperforms models like BERT and other existing pre-trained models, achieving substantial gains across a variety of downstream NLP tasks and applications where time plays a pivotal role.

Reinforcement learning (RL) has enabled complex reasoning abilities in large language models (LLMs). However, most RL algorithms suffer from performance saturation, preventing continued gains as RL training scales. This problem can be characterized by the collapse of entropy, a key diagnostic for exploration in RL. Existing attempts focus on preventing entropy collapse through regularization or clipping. However, their resulting entropy curves often exhibit instability in the long term, which hinders performance gains. In this paper, we introduce Entrocraft, a simple rejection-sampling approach that realizes user-customized entropy schedule by biasing the advantage distributions. Entrocraft requires no objective regularization and is advantage-estimator-agnostic. Theoretically, we relate per-step entropy change to the advantage distribution under minimal assumptions. This explains the behavior of existing RL and entropy-preserving methods. Entrocraft also enables a systematic study of entropy schedules, which reveals that linear annealing, which starts high and decays to a slightly lower target, performs best. Empirically, Entrocraft addresses performance saturation, significantly improving generalization, output diversity, and long-term training. It enables a 4B model to outperform an 8B baseline, sustains improvement for up to 4x longer before plateauing, and raises pass@K by 50% over the baseline.

Entropy serves as a critical metric for measuring the diversity of outputs generated by large language models (LLMs), providing valuable insights into their exploration capabilities. While recent studies increasingly focus on monitoring and adjusting entropy to better balance exploration and exploitation in reinforcement fine-tuning (RFT), a principled understanding of entropy dynamics during this process is yet to be thoroughly investigated. In this paper, we establish a theoretical framework for analyzing the entropy dynamics during the RFT process, which begins with a discriminant expression that quantifies entropy change under a single logit update. This foundation enables the derivation of a first-order expression for entropy change, which can be further extended to the update formula of Group Relative Policy Optimization (GRPO). The corollaries and insights drawn from the theoretical analysis inspire the design of entropy control methods, and also offer a unified lens for interpreting various entropy-based methods in existing studies. We provide empirical evidence to support the main conclusions of our analysis and demonstrate the effectiveness of the derived entropy-discriminator clipping methods. This study yields novel insights into RFT training dynamics, providing theoretical support and practical strategies for optimizing the exploration-exploitation balance during LLM fine-tuning.

Long-horizon conversational agents have to manage ever-growing interaction histories that quickly exceed the finite context windows of large language models (LLMs). Existing memory frameworks provide limited support for temporally structured information across hierarchical levels, often leading to fragmented memories and unstable long-horizon personalization. We present TiMem, a temporal--hierarchical memory framework that organizes conversations through a Temporal Memory Tree (TMT), enabling systematic memory consolidation from raw conversational observations to progressively abstracted persona representations. TiMem is characterized by three core properties: (1) temporal--hierarchical organization through TMT; (2) semantic-guided consolidation that enables memory integration across hierarchical levels without fine-tuning; and (3) complexity-aware memory recall that balances precision and efficiency across queries of varying complexity. Under a consistent evaluation setup, TiMem achieves state-of-the-art accuracy on both benchmarks, reaching 75.30% on LoCoMo and 76.88% on LongMemEval-S. It outperforms all evaluated baselines while reducing the recalled memory length by 52.20% on LoCoMo. Manifold analysis indicates clear persona separation on LoCoMo and reduced dispersion on LongMemEval-S. Overall, TiMem treats temporal continuity as a first-class organizing principle for long-horizon memory in conversational agents.

Understanding temporal relations and answering time-sensitive questions is crucial yet a challenging task for question-answering systems powered by large language models (LLMs). Existing approaches either update the parametric knowledge of LLMs with new facts, which is resource-intensive and often impractical, or integrate LLMs with external knowledge retrieval (i.e., retrieval-augmented generation). However, off-the-shelf retrievers often struggle to identify relevant documents that require intensive temporal reasoning. To systematically study time-sensitive question answering, we introduce the TempRAGEval benchmark, which repurposes existing datasets by incorporating temporal perturbations and gold evidence labels. As anticipated, all existing retrieval methods struggle with these temporal reasoning-intensive questions. We further propose Modular Retrieval (MRAG), a trainless framework that includes three modules: (1) Question Processing that decomposes question into a main content and a temporal constraint; (2) Retrieval and Summarization that retrieves evidence and uses LLMs to summarize according to the main content; (3) Semantic-Temporal Hybrid Ranking that scores each evidence summarization based on both semantic and temporal relevance. On TempRAGEval, MRAG significantly outperforms baseline retrievers in retrieval performance, leading to further improvements in final answer accuracy.

This paper aims to extend the Structured Knowledge Accumulation (SKA) framework recently proposed by mahi2025ska. We introduce two core concepts: the Tensor Net function and the characteristic time property of neural learning. First, we reinterpret the learning rate as a time step in a continuous system. This transforms neural learning from discrete optimization into continuous-time evolution. We show that learning dynamics remain consistent when the product of learning rate and iteration steps stays constant. This reveals a time-invariant behavior and identifies an intrinsic timescale of the network. Second, we define the Tensor Net function as a measure that captures the relationship between decision probabilities, entropy gradients, and knowledge change. Additionally, we define its zero-crossing as the equilibrium state between decision probabilities and entropy gradients. We show that the convergence of entropy and knowledge flow provides a natural stopping condition, replacing arbitrary thresholds with an information-theoretic criterion. We also establish that SKA dynamics satisfy a variational principle based on the Euler-Lagrange equation. These findings extend SKA into a continuous and self-organizing learning model. The framework links computational learning with physical systems that evolve by natural laws. By understanding learning as a time-based process, we open new directions for building efficient, robust, and biologically-inspired AI systems.

Markov processes are widely used mathematical models for describing dynamic systems in various fields. However, accurately simulating large-scale systems at long time scales is computationally expensive due to the short time steps required for accurate integration. In this paper, we introduce an inference process that maps complex systems into a simplified representational space and models large jumps in time. To achieve this, we propose Time-lagged Information Bottleneck (T-IB), a principled objective rooted in information theory, which aims to capture relevant temporal features while discarding high-frequency information to simplify the simulation task and minimize the inference error. Our experiments demonstrate that T-IB learns information-optimal representations for accurately modeling the statistical properties and dynamics of the original process at a selected time lag, outperforming existing time-lagged dimensionality reduction methods.

The striking fractal geometry of strange attractors underscores the generative nature of chaos: like probability distributions, chaotic systems can be repeatedly measured to produce arbitrarily-detailed information about the underlying attractor. Chaotic systems thus pose a unique challenge to modern statistical learning techniques, while retaining quantifiable mathematical properties that make them controllable and interpretable as benchmarks. Here, we present a growing database currently comprising 131 known chaotic dynamical systems spanning fields such as astrophysics, climatology, and biochemistry. Each system is paired with precomputed multivariate and univariate time series. Our dataset has comparable scale to existing static time series databases; however, our systems can be re-integrated to produce additional datasets of arbitrary length and granularity. Our dataset is annotated with known mathematical properties of each system, and we perform feature analysis to broadly categorize the diverse dynamics present across the collection. Chaotic systems inherently challenge forecasting models, and across extensive benchmarks we correlate forecasting performance with the degree of chaos present. We also exploit the unique generative properties of our dataset in several proof-of-concept experiments: surrogate transfer learning to improve time series classification, importance sampling to accelerate model training, and benchmarking symbolic regression algorithms.

The rapid expansion of digital information and knowledge across structured and unstructured sources has heightened the importance of Information Retrieval (IR). While dense retrieval methods have substantially improved semantic matching for general queries, they consistently underperform on queries with explicit temporal constraints--often those containing numerical expressions and time specifiers such as ``in 2015.'' Existing approaches to Temporal Information Retrieval (TIR) improve temporal reasoning but often suffer from catastrophic forgetting, leading to reduced performance on non-temporal queries. To address this, we propose Time-Specifier Model Merging (TSM), a novel method that enhances temporal retrieval while preserving accuracy on non-temporal queries. TSM trains specialized retrievers for individual time specifiers and merges them in to a unified model, enabling precise handling of temporal constraints without compromising non-temporal retrieval. Extensive experiments on both temporal and non-temporal datasets demonstrate that TSM significantly improves performance on temporally constrained queries while maintaining strong results on non-temporal queries, consistently outperforming other baseline methods. Our code is available at https://github.com/seungyoonee/TSM .

Collective motion in fish schools exemplifies emergent self-organization in active matter systems, yet computational tools for simulating and analyzing these dynamics remain fragmented across research groups. We present dewi-kadita, an open-source Python library implementing the three-dimensional Couzin zone-based model with comprehensive entropy diagnostics tailored for marine collective behavior research. The library introduces seven information-theoretic metrics -- school cohesion entropy, polarization entropy, depth stratification entropy, angular momentum entropy, nearest-neighbor entropy, velocity correlation entropy, and school shape entropy -- that characterize distinct organizational features inaccessible to classical order parameters. These metrics combine into an Oceanic Schooling Index (OSI) providing a single scalar measure of collective disorder. Validation across four canonical configurations (swarm, torus, dynamic parallel, highly parallel) confirms correct reproduction of known phase behaviors: the swarm maintains disorder with polarization P < 0.1 and OSI approx 0.71, while the highly parallel state achieves P = 0.998 with OSI = 0.24 and velocity correlation entropy vanishing to zero. The entropy framework successfully discriminates the torus and dynamic parallel configurations that exhibit comparable order parameter magnitudes through different organizational mechanisms. Numba just-in-time (JIT) compilation accelerates pairwise interaction calculations by 10--100times, enabling simulations of 150--250 agents over 1000--2000 time steps within five minutes on standard workstation hardware. NetCDF4 output ensures interoperability with oceanographic analysis tools. The library addresses the need for standardized, reproducible infrastructure in collective behavior modeling analogous to established molecular dynamics codes.

Test-time adaptation (TTA) fine-tunes pre-trained deep neural networks for unseen test data. The primary challenge of TTA is limited access to the entire test dataset during online updates, causing error accumulation. To mitigate it, TTA methods have utilized the model output's entropy as a confidence metric that aims to determine which samples have a lower likelihood of causing error. Through experimental studies, however, we observed the unreliability of entropy as a confidence metric for TTA under biased scenarios and theoretically revealed that it stems from the neglect of the influence of latent disentangled factors of data on predictions. Building upon these findings, we introduce a novel TTA method named Destroy Your Object (DeYO), which leverages a newly proposed confidence metric named Pseudo-Label Probability Difference (PLPD). PLPD quantifies the influence of the shape of an object on prediction by measuring the difference between predictions before and after applying an object-destructive transformation. DeYO consists of sample selection and sample weighting, which employ entropy and PLPD concurrently. For robust adaptation, DeYO prioritizes samples that dominantly incorporate shape information when making predictions. Our extensive experiments demonstrate the consistent superiority of DeYO over baseline methods across various scenarios, including biased and wild. Project page is publicly available at https://whitesnowdrop.github.io/DeYO/.

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

Time series analysis is of immense importance in extensive applications, such as weather forecasting, anomaly detection, and action recognition. This paper focuses on temporal variation modeling, which is the common key problem of extensive analysis tasks. Previous methods attempt to accomplish this directly from the 1D time series, which is extremely challenging due to the intricate temporal patterns. Based on the observation of multi-periodicity in time series, we ravel out the complex temporal variations into the multiple intraperiod- and interperiod-variations. To tackle the limitations of 1D time series in representation capability, we extend the analysis of temporal variations into the 2D space by transforming the 1D time series into a set of 2D tensors based on multiple periods. This transformation can embed the intraperiod- and interperiod-variations into the columns and rows of the 2D tensors respectively, making the 2D-variations to be easily modeled by 2D kernels. Technically, we propose the TimesNet with TimesBlock as a task-general backbone for time series analysis. TimesBlock can discover the multi-periodicity adaptively and extract the complex temporal variations from transformed 2D tensors by a parameter-efficient inception block. Our proposed TimesNet achieves consistent state-of-the-art in five mainstream time series analysis tasks, including short- and long-term forecasting, imputation, classification, and anomaly detection. Code is available at this repository: https://github.com/thuml/TimesNet.

Neural Temporal Point Processes (TPPs) are the prevalent paradigm for modeling continuous-time event sequences, such as user activities on the web and financial transactions. In real-world applications, event data is typically received in a streaming manner, where the distribution of patterns may shift over time. Additionally, privacy and memory constraints are commonly observed in practical scenarios, further compounding the challenges. Therefore, the continuous monitoring of a TPP to learn the streaming event sequence is an important yet under-explored problem. Our work paper addresses this challenge by adopting Continual Learning (CL), which makes the model capable of continuously learning a sequence of tasks without catastrophic forgetting under realistic constraints. Correspondingly, we propose a simple yet effective framework, PromptTPPOur code is available at {\small \url{ https://github.com/yanyanSann/PromptTPP}}, by integrating the base TPP with a continuous-time retrieval prompt pool. The prompts, small learnable parameters, are stored in a memory space and jointly optimized with the base TPP, ensuring that the model learns event streams sequentially without buffering past examples or task-specific attributes. We present a novel and realistic experimental setup for modeling event streams, where PromptTPP consistently achieves state-of-the-art performance across three real user behavior datasets.

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.

Temporal progression is an integral part of knowledge accumulation and update. Web search is frequently adopted as grounding for agent knowledge, yet an improper configuration affects the quality of the agent's responses. Here, we assess the agent behavior using distinct date-controlled tools (DCTs) as stress test to measure the knowledge variability of large language model (LLM) agents. We demonstrate the temporal effects of an LLM agent as a writing assistant, which uses web search to complete scientific publication abstracts. We show that the temporality of search engine translates into tool-dependent agent performance but can be alleviated with base model choice and explicit reasoning instructions such as chain-of-thought prompting. Our results indicate that agent design and evaluations should take a dynamical view and implement measures to account for the temporal influence of external resources to ensure reliability.

Mainstream Test-Time Adaptation (TTA) methods for adapting vision-language models, e.g., CLIP, typically rely on Shannon Entropy (SE) at test time to measure prediction uncertainty and inconsistency. However, since CLIP has a built-in bias from pretraining on highly imbalanced web-crawled data, SE inevitably results in producing biased estimates of uncertainty entropy. To address this issue, we notably find and demonstrate that Tsallis Entropy (TE), a generalized form of SE, is naturally suited for characterizing biased distributions by introducing a non-extensive parameter q, with the performance of SE serving as a lower bound for TE. Building upon this, we generalize TE into Adaptive Debiasing Tsallis Entropy (ADTE) for TTA, customizing a class-specific parameter q^l derived by normalizing the estimated label bias from continuously incoming test instances, for each category. This adaptive approach allows ADTE to accurately select high-confidence views and seamlessly integrate with a label adjustment strategy to enhance adaptation, without introducing distribution-specific hyperparameter tuning. Besides, our investigation reveals that both TE and ADTE can serve as direct, advanced alternatives to SE in TTA, without any other modifications. Experimental results show that ADTE outperforms state-of-the-art methods on ImageNet and its five variants, and achieves the highest average performance on 10 cross-domain benchmarks, regardless of the model architecture or text prompts used. Our code is available at https://github.com/Jinx630/ADTE.

Memory enables Large Language Model (LLM) agents to perceive, store, and use information from past dialogues, which is essential for personalization. However, existing methods fail to properly model the temporal dimension of memory in two aspects: 1) Temporal inaccuracy: memories are organized by dialogue time rather than their actual occurrence time; 2) Temporal fragmentation: existing methods focus on point-wise memory, losing durative information that captures persistent states and evolving patterns. To address these limitations, we propose Temporal Semantic Memory (TSM), a memory framework that models semantic time for point-wise memory and supports the construction and utilization of durative memory. During memory construction, it first builds a semantic timeline rather than a dialogue one. Then, it consolidates temporally continuous and semantically related information into a durative memory. During memory utilization, it incorporates the query's temporal intent on the semantic timeline, enabling the retrieval of temporally appropriate durative memories and providing time-valid, duration-consistent context to support response generation. Experiments on LongMemEval and LoCoMo show that TSM consistently outperforms existing methods and achieves up to 12.2% absolute improvement in accuracy, demonstrating the effectiveness of the proposed method.

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.

Large language models (LLMs) have significantly impacted many aspects of our lives. However, assessing and ensuring their chronological knowledge remains challenging. Existing approaches fall short in addressing the accumulative nature of knowledge, often relying on a single time stamp. To overcome this, we introduce ChroKnowBench, a benchmark dataset designed to evaluate chronologically accumulated knowledge across three key aspects: multiple domains, time dependency, temporal state. Our benchmark distinguishes between knowledge that evolves (e.g., scientific discoveries, amended laws) and knowledge that remain constant (e.g., mathematical truths, commonsense facts). Building on this benchmark, we present ChroKnowledge (Chronological Categorization of Knowledge), a novel sampling-based framework for evaluating and updating LLMs' non-parametric chronological knowledge. Our evaluation shows: (1) The ability of eliciting temporal knowledge varies depending on the data format that model was trained on. (2) LLMs partially recall knowledge or show a cut-off at temporal boundaries rather than recalling all aspects of knowledge correctly. Thus, we apply our ChroKnowPrompt, an in-depth prompting to elicit chronological knowledge by traversing step-by-step through the surrounding time spans. We observe that our framework successfully updates the overall knowledge across the entire timeline in both the biomedical domain (+11.9%) and the general domain (+2.8%), demonstrating its effectiveness in refining temporal knowledge. This non-parametric approach also enables knowledge updates not only in open-source models but also in proprietary LLMs, ensuring comprehensive applicability across model types. We perform a comprehensive analysis based on temporal characteristics of ChroKnowPrompt and validate the potential of various models to elicit intrinsic temporal knowledge through our method.

Large Language Models (LLMs) are increasingly becoming ubiquitous, yet their ability to reason about and retain temporal information remains limited. This hinders their application in real-world scenarios where understanding the sequential nature of events is crucial. This paper experiments with state-of-the-art models on a novel, large-scale temporal dataset, TempUN, to reveal significant limitations in temporal retention and reasoning abilities. Interestingly, closed-source models indicate knowledge gaps more frequently, potentially suggesting a trade-off between uncertainty awareness and incorrect responses. Further, exploring various fine-tuning approaches yielded no major performance improvements. The associated dataset and code are available at the following URL (https://github.com/lingoiitgn/TempUN).

Temporal reasoning is a crucial NLP task, providing a nuanced understanding of time-sensitive contexts within textual data. Although recent advancements in LLMs have demonstrated their potential in temporal reasoning, the predominant focus has been on tasks such as temporal expression and temporal relation extraction. These tasks are primarily designed for the extraction of direct and past temporal cues and to engage in simple reasoning processes. A significant gap remains when considering complex reasoning tasks such as event forecasting, which requires multi-step temporal reasoning on events and prediction on the future timestamp. Another notable limitation of existing methods is their incapability to provide an illustration of their reasoning process, hindering explainability. In this paper, we introduce the first task of explainable temporal reasoning, to predict an event's occurrence at a future timestamp based on context which requires multiple reasoning over multiple events, and subsequently provide a clear explanation for their prediction. Our task offers a comprehensive evaluation of both the LLMs' complex temporal reasoning ability, the future event prediction ability, and explainability-a critical attribute for AI applications. To support this task, we present the first multi-source instruction-tuning dataset of explainable temporal reasoning (ExpTime) with 26k derived from the temporal knowledge graph datasets and their temporal reasoning paths, using a novel knowledge-graph-instructed-generation strategy. Based on the dataset, we propose the first open-source LLM series TimeLlaMA based on the foundation LlaMA2, with the ability of instruction following for explainable temporal reasoning. We compare the performance of our method and a variety of LLMs, where our method achieves the state-of-the-art performance of temporal prediction and explanation.

We establish a fundamental connection between score-based diffusion models and non-equilibrium thermodynamics by deriving performance limits based on entropy rates. Our main theoretical contribution is a lower bound on the negative log-likelihood of the data that relates model performance to entropy rates of diffusion processes. We numerically validate this bound on a synthetic dataset and investigate its tightness. By building a bridge to entropy rates - system, intrinsic, and exchange entropy - we provide new insights into the thermodynamic operation of these models, drawing parallels to Maxwell's demon and implications for thermodynamic computing hardware. Our framework connects generative modeling performance to fundamental physical principles through stochastic thermodynamics.

We address the challenge of exploration in reinforcement learning (RL) when the agent operates in an unknown environment with sparse or no rewards. In this work, we study the maximum entropy exploration problem of two different types. The first type is visitation entropy maximization previously considered by Hazan et al.(2019) in the discounted setting. For this type of exploration, we propose a game-theoretic algorithm that has mathcal{O}(H^3S^2A/varepsilon^2) sample complexity thus improving the varepsilon-dependence upon existing results, where S is a number of states, A is a number of actions, H is an episode length, and varepsilon is a desired accuracy. The second type of entropy we study is the trajectory entropy. This objective function is closely related to the entropy-regularized MDPs, and we propose a simple algorithm that has a sample complexity of order mathcal{O}(poly(S,A,H)/varepsilon). Interestingly, it is the first theoretical result in RL literature that establishes the potential statistical advantage of regularized MDPs for exploration. Finally, we apply developed regularization techniques to reduce sample complexity of visitation entropy maximization to mathcal{O}(H^2SA/varepsilon^2), yielding a statistical separation between maximum entropy exploration and reward-free exploration.

Temporal Awareness, the ability to reason dynamically based on the timestamp when a question is raised, is the key distinction between offline and online video LLMs. Unlike offline models, which rely on complete videos for static, post hoc analysis, online models process video streams incrementally and dynamically adapt their responses based on the timestamp at which the question is posed. Despite its significance, temporal awareness has not been adequately evaluated in existing benchmarks. To fill this gap, we present OVO-Bench (Online-VideO-Benchmark), a novel video benchmark that emphasizes the importance of timestamps for advanced online video understanding capability benchmarking. OVO-Bench evaluates the ability of video LLMs to reason and respond to events occurring at specific timestamps under three distinct scenarios: (1) Backward tracing: trace back to past events to answer the question. (2) Real-time understanding: understand and respond to events as they unfold at the current timestamp. (3) Forward active responding: delay the response until sufficient future information becomes available to answer the question accurately. OVO-Bench comprises 12 tasks, featuring 644 unique videos and approximately human-curated 2,800 fine-grained meta-annotations with precise timestamps. We combine automated generation pipelines with human curation. With these high-quality samples, we further developed an evaluation pipeline to systematically query video LLMs along the video timeline. Evaluations of nine Video-LLMs reveal that, despite advancements on traditional benchmarks, current models struggle with online video understanding, showing a significant gap compared to human agents. We hope OVO-Bench will drive progress in video LLMs and inspire future research in online video reasoning. Our benchmark and code can be accessed at https://github.com/JoeLeelyf/OVO-Bench.

Causality testing, the act of determining cause and effect from measurements, is widely used in physics, climatology, neuroscience, econometrics and other disciplines. As a result, a large number of causality testing methods based on various principles have been developed. Causal relationships in complex systems are typically accompanied by entropic exchanges which are encoded in patterns of dynamical measurements. A data compression algorithm which can extract these encoded patterns could be used for inferring these relations. This motivates us to propose, for the first time, a generic causality testing framework based on data compression. The framework unifies existing causality testing methods and enables us to innovate a novel Compression-Complexity Causality measure. This measure is rigorously tested on simulated and real-world time series and is found to overcome the limitations of Granger Causality and Transfer Entropy, especially for noisy and non-synchronous measurements. Additionally, it gives insight on the `kind' of causal influence between input time series by the notions of positive and negative causality.

Temporal reasoning over long, multi-session dialogues is a critical capability for conversational agents. However, existing works and our pilot study have shown that as dialogue histories grow in length and accumulate noise, current long-context models struggle to accurately identify temporally pertinent information, significantly impairing reasoning performance. To address this, we introduce Memory-T1, a framework that learns a time-aware memory selection policy using reinforcement learning (RL). It employs a coarse-to-fine strategy, first pruning the dialogue history into a candidate set using temporal and relevance filters, followed by an RL agent that selects the precise evidence sessions. The RL training is guided by a multi-level reward function optimizing (i) answer accuracy, (ii) evidence grounding, and (iii) temporal consistency. In particular, the temporal consistency reward provides a dense signal by evaluating alignment with the query time scope at both the session-level (chronological proximity) and the utterance-level (chronological fidelity), enabling the agent to resolve subtle chronological ambiguities. On the Time-Dialog benchmark, Memory-T1 boosts a 7B model to an overall score of 67.0\%, establishing a new state-of-the-art performance for open-source models and outperforming a 14B baseline by 10.2\%. Ablation studies show temporal consistency and evidence grounding rewards jointly contribute to a 15.0\% performance gain. Moreover, Memory-T1 maintains robustness up to 128k tokens, where baseline models collapse, proving effectiveness against noise in extensive dialogue histories. The code and datasets are publicly available at https://github.com/Elvin-Yiming-Du/Memory-T1/

The varying significance of distinct primitive behaviors during the policy learning process has been overlooked by prior model-free RL algorithms. Leveraging this insight, we explore the causal relationship between different action dimensions and rewards to evaluate the significance of various primitive behaviors during training. We introduce a causality-aware entropy term that effectively identifies and prioritizes actions with high potential impacts for efficient exploration. Furthermore, to prevent excessive focus on specific primitive behaviors, we analyze the gradient dormancy phenomenon and introduce a dormancy-guided reset mechanism to further enhance the efficacy of our method. Our proposed algorithm, ACE: Off-policy Actor-critic with Causality-aware Entropy regularization, demonstrates a substantial performance advantage across 29 diverse continuous control tasks spanning 7 domains compared to model-free RL baselines, which underscores the effectiveness, versatility, and efficient sample efficiency of our approach. Benchmark results and videos are available at https://ace-rl.github.io/.

Can we learn more from data than existed in the generating process itself? Can new and useful information be constructed from merely applying deterministic transformations to existing data? Can the learnable content in data be evaluated without considering a downstream task? On these questions, Shannon information and Kolmogorov complexity come up nearly empty-handed, in part because they assume observers with unlimited computational capacity and fail to target the useful information content. In this work, we identify and exemplify three seeming paradoxes in information theory: (1) information cannot be increased by deterministic transformations; (2) information is independent of the order of data; (3) likelihood modeling is merely distribution matching. To shed light on the tension between these results and modern practice, and to quantify the value of data, we introduce epiplexity, a formalization of information capturing what computationally bounded observers can learn from data. Epiplexity captures the structural content in data while excluding time-bounded entropy, the random unpredictable content exemplified by pseudorandom number generators and chaotic dynamical systems. With these concepts, we demonstrate how information can be created with computation, how it depends on the ordering of the data, and how likelihood modeling can produce more complex programs than present in the data generating process itself. We also present practical procedures to estimate epiplexity which we show capture differences across data sources, track with downstream performance, and highlight dataset interventions that improve out-of-distribution generalization. In contrast to principles of model selection, epiplexity provides a theoretical foundation for data selection, guiding how to select, generate, or transform data for learning systems.

The measurement of time is central to intelligent behavior. We know that both animals and artificial agents can successfully use temporal dependencies to select actions. In artificial agents, little work has directly addressed (1) which architectural components are necessary for successful development of this ability, (2) how this timing ability comes to be represented in the units and actions of the agent, and (3) whether the resulting behavior of the system converges on solutions similar to those of biology. Here we studied interval timing abilities in deep reinforcement learning agents trained end-to-end on an interval reproduction paradigm inspired by experimental literature on mechanisms of timing. We characterize the strategies developed by recurrent and feedforward agents, which both succeed at temporal reproduction using distinct mechanisms, some of which bear specific and intriguing similarities to biological systems. These findings advance our understanding of how agents come to represent time, and they highlight the value of experimentally inspired approaches to characterizing agent abilities.

Dynamic graph learning methods have recently emerged as powerful tools for modelling relational data evolving through time. However, despite extensive benchmarking efforts, it remains unclear whether current Temporal Graph Neural Networks (TGNNs) effectively capture core temporal patterns such as periodicity, cause-and-effect, and long-range dependencies. In this work, we introduce the Temporal Graph Reasoning Benchmark (T-GRAB), a comprehensive set of synthetic tasks designed to systematically probe the capabilities of TGNNs to reason across time. T-GRAB provides controlled, interpretable tasks that isolate key temporal skills: counting/memorizing periodic repetitions, inferring delayed causal effects, and capturing long-range dependencies over both spatial and temporal dimensions. We evaluate 11 temporal graph learning methods on these tasks, revealing fundamental shortcomings in their ability to generalize temporal patterns. Our findings offer actionable insights into the limitations of current models, highlight challenges hidden by traditional real-world benchmarks, and motivate the development of architectures with stronger temporal reasoning abilities. The code for T-GRAB can be found at: https://github.com/alirezadizaji/T-GRAB.

Recent advancements in Large Language Models have yielded significant improvements in complex reasoning tasks such as mathematics and programming. However, these models remain heavily dependent on annotated data and exhibit limited adaptability in unsupervised scenarios. To address these limitations, test-time reinforcement learning (TTRL) has been proposed, which enables self-optimization by leveraging model-generated pseudo-labels. Despite its promise, TTRL faces several key challenges, including high inference costs due to parallel rollouts and early-stage estimation bias that fosters overconfidence, reducing output diversity and causing performance plateaus. To address these challenges, we introduce an entropy-based mechanism to enhance the exploration-exploitation balance in test-time reinforcement learning through two strategies: Entropy-fork Tree Majority Rollout (ETMR) and Entropy-based Advantage Reshaping (EAR). Compared with the baseline, our approach enables Llama3.1-8B to achieve a 68 percent relative improvement in Pass at 1 metric on the AIME 2024 benchmark, while consuming only 60 percent of the rollout tokens budget. This highlights our method's ability to effectively optimize the trade-off between inference efficiency, diversity, and estimation robustness, thereby advancing unsupervised reinforcement learning for open-domain reasoning tasks.

Seeking high-quality representations with latent variable models (LVMs) to reveal the intrinsic correlation between neural activity and behavior or sensory stimuli has attracted much interest. In the study of the biological visual system, naturalistic visual stimuli are inherently high-dimensional and time-dependent, leading to intricate dynamics within visual neural activity. However, most work on LVMs has not explicitly considered neural temporal relationships. To cope with such conditions, we propose Time-Evolving Visual Dynamical System (TE-ViDS), a sequential LVM that decomposes neural activity into low-dimensional latent representations that evolve over time. To better align the model with the characteristics of visual neural activity, we split latent representations into two parts and apply contrastive learning to shape them. Extensive experiments on synthetic datasets and real neural datasets from the mouse visual cortex demonstrate that TE-ViDS achieves the best decoding performance on naturalistic scenes/movies, extracts interpretable latent trajectories that uncover clear underlying neural dynamics, and provides new insights into differences in visual information processing between subjects and between cortical regions. In summary, TE-ViDS is markedly competent in extracting stimulus-relevant embeddings from visual neural activity and contributes to the understanding of visual processing mechanisms. Our codes are available at https://github.com/Grasshlw/Time-Evolving-Visual-Dynamical-System.

Reasoning about time is of fundamental importance. Many facts are time-dependent. For example, athletes change teams from time to time, and different government officials are elected periodically. Previous time-dependent question answering (QA) datasets tend to be biased in either their coverage of time spans or question types. In this paper, we introduce a comprehensive probing dataset \tempreason to evaluate the temporal reasoning capability of large language models. Our dataset includes questions of three temporal reasoning levels. In addition, we also propose a novel learning framework to improve the temporal reasoning capability of large language models, based on temporal span extraction and time-sensitive reinforcement learning. We conducted experiments in closed book QA, open book QA, and reasoning QA settings and demonstrated the effectiveness of our approach. Our code and data are released on https://github.com/DAMO-NLP-SG/TempReason.

We introduce the Structured Knowledge Accumulation (SKA) framework, which reinterprets entropy as a dynamic, layer-wise measure of knowledge alignment in neural networks. Instead of relying on traditional gradient-based optimization, SKA defines entropy in terms of knowledge vectors and their influence on decision probabilities across multiple layers. This formulation naturally leads to the emergence of activation functions such as the sigmoid as a consequence of entropy minimization. Unlike conventional backpropagation, SKA allows each layer to optimize independently by aligning its knowledge representation with changes in decision probabilities. As a result, total network entropy decreases in a hierarchical manner, allowing knowledge structures to evolve progressively. This approach provides a scalable, biologically plausible alternative to gradient-based learning, bridging information theory and artificial intelligence while offering promising applications in resource-constrained and parallel computing environments.

Speech emotion recognition (SER) plays a vital role in improving the interactions between humans and machines by inferring human emotion and affective states from speech signals. Whereas recent works primarily focus on mining spatiotemporal information from hand-crafted features, we explore how to model the temporal patterns of speech emotions from dynamic temporal scales. Towards that goal, we introduce a novel temporal emotional modeling approach for SER, termed Temporal-aware bI-direction Multi-scale Network (TIM-Net), which learns multi-scale contextual affective representations from various time scales. Specifically, TIM-Net first employs temporal-aware blocks to learn temporal affective representation, then integrates complementary information from the past and the future to enrich contextual representations, and finally, fuses multiple time scale features for better adaptation to the emotional variation. Extensive experimental results on six benchmark SER datasets demonstrate the superior performance of TIM-Net, gaining 2.34% and 2.61% improvements of the average UAR and WAR over the second-best on each corpus. The source code is available at https://github.com/Jiaxin-Ye/TIM-Net_SER.

Hallucination in large language models (LLMs) can be detected by assessing the uncertainty of model outputs, typically measured using entropy. Semantic entropy (SE) enhances traditional entropy estimation by quantifying uncertainty at the semantic cluster level. However, as modern LLMs generate longer one-sentence responses, SE becomes less effective because it overlooks two crucial factors: intra-cluster similarity (the spread within a cluster) and inter-cluster similarity (the distance between clusters). To address these limitations, we propose a simple black-box uncertainty quantification method inspired by nearest neighbor estimates of entropy. Our approach can also be easily extended to white-box settings by incorporating token probabilities. Additionally, we provide theoretical results showing that our method generalizes semantic entropy. Extensive empirical results demonstrate its effectiveness compared to semantic entropy across two recent LLMs (Phi3 and Llama3) and three common text generation tasks: question answering, text summarization, and machine translation. Our code is available at https://github.com/BigML-CS-UCLA/SNNE.

Combining attention with recurrence has shown to be valuable in sequence modeling, including hydrological predictions. Here, we explore the strength of Temporal Fusion Transformers (TFTs) over Long Short-Term Memory (LSTM) networks in rainfall-runoff modeling. We train ten randomly initialized models, TFT and LSTM, for 531 CAMELS catchments in the US. We repeat the experiment with five subsets of the Caravan dataset, each representing catchments in the US, Australia, Brazil, Great Britain, and Chile. Then, the performance of the models, their variability regarding the catchment attributes, and the difference according to the datasets are assessed. Our findings show that TFT slightly outperforms LSTM, especially in simulating the midsection and peak of hydrographs. Furthermore, we show the ability of TFT to handle longer sequences and why it can be a better candidate for higher or larger catchments. Being an explainable AI technique, TFT identifies the key dynamic and static variables, providing valuable scientific insights. However, both TFT and LSTM exhibit a considerable drop in performance with the Caravan dataset, indicating possible data quality issues. Overall, the study highlights the potential of TFT in improving hydrological modeling and understanding.

The Diffusion model, a prevalent framework for image generation, encounters significant challenges in terms of broad applicability due to its extended inference times and substantial memory requirements. Efficient Post-training Quantization (PTQ) is pivotal for addressing these issues in traditional models. Different from traditional models, diffusion models heavily depend on the time-step t to achieve satisfactory multi-round denoising. Usually, t from the finite set {1, ldots, T} is encoded to a temporal feature by a few modules totally irrespective of the sampling data. However, existing PTQ methods do not optimize these modules separately. They adopt inappropriate reconstruction targets and complex calibration methods, resulting in a severe disturbance of the temporal feature and denoising trajectory, as well as a low compression efficiency. To solve these, we propose a Temporal Feature Maintenance Quantization (TFMQ) framework building upon a Temporal Information Block which is just related to the time-step t and unrelated to the sampling data. Powered by the pioneering block design, we devise temporal information aware reconstruction (TIAR) and finite set calibration (FSC) to align the full-precision temporal features in a limited time. Equipped with the framework, we can maintain the most temporal information and ensure the end-to-end generation quality. Extensive experiments on various datasets and diffusion models prove our state-of-the-art results. Remarkably, our quantization approach, for the first time, achieves model performance nearly on par with the full-precision model under 4-bit weight quantization. Additionally, our method incurs almost no extra computational cost and accelerates quantization time by 2.0 times on LSUN-Bedrooms 256 times 256 compared to previous works.

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

State-of-the-art language generation models can degenerate when applied to open-ended generation problems such as text completion, story generation, or dialog modeling. This degeneration usually shows up in the form of incoherence, lack of vocabulary diversity, and self-repetition or copying from the context. In this paper, we postulate that ``human-like'' generations usually lie in a narrow and nearly flat entropy band, and violation of these entropy bounds correlates with degenerate behavior. Our experiments show that this stable narrow entropy zone exists across models, tasks, and domains and confirm the hypothesis that violations of this zone correlate with degeneration. We then use this insight to propose an entropy-aware decoding algorithm that respects these entropy bounds resulting in less degenerate, more contextual, and "human-like" language generation in open-ended text generation settings.

Recently, unsupervised representation learning (URL) has improved the sample efficiency of Reinforcement Learning (RL) by pretraining a model from a large unlabeled dataset. The underlying principle of these methods is to learn temporally predictive representations by predicting future states in the latent space. However, an important challenge of this approach is the representational collapse, where the subspace of the latent representations collapses into a low-dimensional manifold. To address this issue, we propose a novel URL framework that causally predicts future states while increasing the dimension of the latent manifold by decorrelating the features in the latent space. Through extensive empirical studies, we demonstrate that our framework effectively learns predictive representations without collapse, which significantly improves the sample efficiency of state-of-the-art URL methods on the Atari 100k benchmark. The code is available at https://github.com/dojeon-ai/SimTPR.

Large language models (LLMs) and multimodal LLMs (MLLMs) excel at chain-of-thought reasoning but face distribution shift at test-time and a lack of verifiable supervision. Recent test-time reinforcement learning (TTRL) methods derive label-free pseudo-rewards from self-consistency voting over sampled trajectories, yet they often collapse: the majority-vote reward prevails, responses shorten, and Pass@1 declines. We trace this to uniform sequence updates in which most tokens are low-entropy followers, while a small high-entropy subset determines the reasoning branches. Thus we propose SPINE, a token-selective test-time reinforcement learning framework that (i) updates only forking tokens, the high-entropy branch points identified from forward-pass statistics, and (ii) applies an entropy-band regularizer at those tokens to sustain exploration when entropy is too low and to suppress noisy supervision when it is too high. SPINE plugs into GRPO-style objectives, optionally with a KL anchor, and requires no labels or reward models. Across ten benchmarks spanning multimodal VQA, general and expert QA, mathematical reasoning, and medical QA, SPINE consistently improves Pass@1 over TTRL while avoiding response-length collapse and yielding more stable training dynamics on both LLM and MLLM backbones. These results indicate that aligning updates with chain-of-thought branch points is a simple and label-free mechanism for stable and effective test-time adaptation in reasoning models. Code is available at https://github.com/JianghaoWu/SPINE.

As Large Language Models (LLMs) continue to advance, they exhibit certain cognitive patterns similar to those of humans that are not directly specified in training data. This study investigates this phenomenon by focusing on temporal cognition in LLMs. Leveraging the similarity judgment task, we find that larger models spontaneously establish a subjective temporal reference point and adhere to the Weber-Fechner law, whereby the perceived distance logarithmically compresses as years recede from this reference point. To uncover the mechanisms behind this behavior, we conducted multiple analyses across neuronal, representational, and informational levels. We first identify a set of temporal-preferential neurons and find that this group exhibits minimal activation at the subjective reference point and implements a logarithmic coding scheme convergently found in biological systems. Probing representations of years reveals a hierarchical construction process, where years evolve from basic numerical values in shallow layers to abstract temporal orientation in deep layers. Finally, using pre-trained embedding models, we found that the training corpus itself possesses an inherent, non-linear temporal structure, which provides the raw material for the model's internal construction. In discussion, we propose an experientialist perspective for understanding these findings, where the LLMs' cognition is viewed as a subjective construction of the external world by its internal representational system. This nuanced perspective implies the potential emergence of alien cognitive frameworks that humans cannot intuitively predict, pointing toward a direction for AI alignment that focuses on guiding internal constructions. Our code is available at https://TheOtherMind.github.io.

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.

While the ability of language models to elicit facts has been widely investigated, how they handle temporally changing facts remains underexplored. We discover Temporal Heads, specific attention heads primarily responsible for processing temporal knowledge through circuit analysis. We confirm that these heads are present across multiple models, though their specific locations may vary, and their responses differ depending on the type of knowledge and its corresponding years. Disabling these heads degrades the model's ability to recall time-specific knowledge while maintaining its general capabilities without compromising time-invariant and question-answering performances. Moreover, the heads are activated not only numeric conditions ("In 2004") but also textual aliases ("In the year ..."), indicating that they encode a temporal dimension beyond simple numerical representation. Furthermore, we expand the potential of our findings by demonstrating how temporal knowledge can be edited by adjusting the values of these heads.

We show how to extract from a sufficiently long time series of stationary fluctuations of chemical reactions an estimate of the entropy production. This method, which is based on recent work on fluctuation theorems, is direct, non-invasive, does not require any knowledge about the underlying dynamics, and is applicable even when only partial information is available. We apply it to simple stochastic models of chemical reactions involving a finite number of states, and for this case, we study how the estimate of dissipation is affected by the degree of coarse-graining present in the input data.

Time is an important dimension in our physical world. Lots of facts can evolve with respect to time. For example, the U.S. President might change every four years. Therefore, it is important to consider the time dimension and empower the existing QA models to reason over time. However, the existing QA datasets contain rather few time-sensitive questions, hence not suitable for diagnosing or benchmarking the model's temporal reasoning capability. In order to promote research in this direction, we propose to construct a time-sensitive QA dataset. The dataset is constructed by 1) mining time-evolving facts from WikiData and aligning them to their corresponding Wikipedia page, 2) employing crowd workers to verify and calibrate these noisy facts, 3) generating question-answer pairs based on the annotated time-sensitive facts. Our dataset poses challenges in the aspect of both temporal understanding and temporal reasoning. We evaluate different SoTA long-document QA systems like BigBird and FiD on our dataset. The best-performing model FiD can only achieve 46\% accuracy, still far behind the human performance of 87\%. We demonstrate that these models are still lacking the ability to perform consistent temporal reasoning. Therefore, we believe that our dataset could serve as a benchmark to develop NLP models more sensitive to temporal shifts. The dataset and code are released in~https://github.com/wenhuchen/Time-Sensitive-QA.

In our work we not explicitly hint that it is a misconception to think that humans learn fast. Learning process takes time. Babies start learning to move in the restricted liquid area called placenta. Children often are limited by underdeveloped body. Even adults are not allowed to participate in complex competitions right away. However, with robots, when learning from scratch, we often don't have the privilege of waiting for dozen millions of steps. "Swaddling" regularization is responsible for restraining an agent in rapid but unstable development penalizing action strength in a specific way not affecting actions directly. The Symphony, Transitional-policy Deterministic Actor and Critic algorithm, is a concise combination of different ideas for possibility of training humanoid robots from scratch with Sample Efficiency, Sample Proximity and Safety of Actions in mind. It is no secret that continuous increase in Gaussian noise without appropriate smoothing is harmful for motors and gearboxes. Compared to Stochastic algorithms, we set a limited parametric noise and promote a reduced strength of actions, safely increasing entropy, since the actions are kind of immersed in weaker noise. When actions require more extreme values, actions rise above the weak noise. Training becomes empirically much safer for both the environment around and the robot's mechanisms. We use Fading Replay Buffer: using a fixed formula containing the hyperbolic tangent, we adjust the batch sampling probability: the memory contains a recent memory and a long-term memory trail. Fading Replay Buffer allows us to use Temporal Advantage when we improve the current Critic Network prediction compared to the exponential moving average. Temporal Advantage allows us to update Actor and Critic in one pass, as well as combine Actor and Critic in one Object and implement their Losses in one line.

Explaining deep learning models operating on time series data is crucial in various applications of interest which require interpretable and transparent insights from time series signals. In this work, we investigate this problem from an information theoretic perspective and show that most existing measures of explainability may suffer from trivial solutions and distributional shift issues. To address these issues, we introduce a simple yet practical objective function for time series explainable learning. The design of the objective function builds upon the principle of information bottleneck (IB), and modifies the IB objective function to avoid trivial solutions and distributional shift issues. We further present TimeX++, a novel explanation framework that leverages a parametric network to produce explanation-embedded instances that are both in-distributed and label-preserving. We evaluate TimeX++ on both synthetic and real-world datasets comparing its performance against leading baselines, and validate its practical efficacy through case studies in a real-world environmental application. Quantitative and qualitative evaluations show that TimeX++ outperforms baselines across all datasets, demonstrating a substantial improvement in explanation quality for time series data. The source code is available at https://github.com/zichuan-liu/TimeXplusplus.

Temporal Point Processes (TPPs) have been widely used for event sequence modeling, but they often struggle to incorporate rich textual event descriptions effectively. Conversely, while Large Language Models (LLMs) have been shown remarkable capabilities in processing textual data, they lack mechanisms for handling temporal dynamics. To bridge this gap, we introduce Language-TPP, a unified framework that integrates TPPs with LLMs for enhanced event sequence modeling. Language-TPP introduces a novel temporal encoding mechanism that converts continuous time intervals into specialized byte-tokens, enabling seamless integration with standard LLM architectures. This approach allows Language-TPP to achieve state-of-the-art performance across multiple TPP tasks, including event time prediction, type prediction, and intensity estimation, on five datasets. Additionally, we demonstrate that incorporating temporal information significantly improves the quality of generated event descriptions.

The past decade has witnessed significant advances in time series modeling with deep learning. While achieving state-of-the-art results, the best-performing architectures vary highly across applications and domains. Meanwhile, for natural language processing, the Generative Pre-trained Transformer (GPT) has demonstrated impressive performance via training one general-purpose model across various textual datasets. It is intriguing to explore whether GPT-type architectures can be effective for time series, capturing the intrinsic dynamic attributes and leading to significant accuracy improvements. In this paper, we propose a novel framework, TEMPO, that can effectively learn time series representations. We focus on utilizing two essential inductive biases of the time series task for pre-trained models: (i) decomposition of the complex interaction between trend, seasonal and residual components; and (ii) introducing the selection-based prompts to facilitate distribution adaptation in non-stationary time series. TEMPO expands the capability for dynamically modeling real-world temporal phenomena from data within diverse domains. Our experiments demonstrate the superior performance of TEMPO over state-of-the-art methods on a number of time series benchmark datasets. This performance gain is observed not only in standard supervised learning settings but also in scenarios involving previously unseen datasets as well as in scenarios with multi-modal inputs. This compelling finding highlights TEMPO's potential to constitute a foundational model-building framework.

We introduce a new class of time-continuous recurrent neural network models. Instead of declaring a learning system's dynamics by implicit nonlinearities, we construct networks of linear first-order dynamical systems modulated via nonlinear interlinked gates. The resulting models represent dynamical systems with varying (i.e., liquid) time-constants coupled to their hidden state, with outputs being computed by numerical differential equation solvers. These neural networks exhibit stable and bounded behavior, yield superior expressivity within the family of neural ordinary differential equations, and give rise to improved performance on time-series prediction tasks. To demonstrate these properties, we first take a theoretical approach to find bounds over their dynamics and compute their expressive power by the trajectory length measure in latent trajectory space. We then conduct a series of time-series prediction experiments to manifest the approximation capability of Liquid Time-Constant Networks (LTCs) compared to classical and modern RNNs. Code and data are available at https://github.com/raminmh/liquid_time_constant_networks

Sequential recommendation models often struggle to capture latent periodic patterns in user interests, primarily due to the noise inherent in time-domain behavioral data. While frequency-domain analysis offers a global perspective to address this, existing approaches typically treat user sequences in isolation, overlooking the crucial context of the target item. In this work, we present a novel empirical observation: user attention scores exhibit distinct spectral entropy distributions when conditioned on positive versus negative target items. Specifically, true user interests manifest as highly concentrated spectral patterns with lower entropy in the frequency domain, whereas irrelevant behaviors appear as high-entropy noise. Leveraging this insight, we propose the Frequency-Enhanced Deep Interest Network (FEDIN). FEDIN introduces a frequency-domain branch that utilizes a target-aware spectrum filtering mechanism to isolate these periodic interest signals. Extensive experiments on three public datasets demonstrate that FEDIN consistently outperforms state-of-the-art sequential recommendation baselines, demonstrating superior robustness against noise. We have released our code at: https://github.com/otokoneko/FEDIN.

The ability to recognize and predict temporal sequences of sensory inputs is vital for survival in natural environments. Based on many known properties of cortical neurons, hierarchical temporal memory (HTM) sequence memory is recently proposed as a theoretical framework for sequence learning in the cortex. In this paper, we analyze properties of HTM sequence memory and apply it to sequence learning and prediction problems with streaming data. We show the model is able to continuously learn a large number of variable-order temporal sequences using an unsupervised Hebbian-like learning rule. The sparse temporal codes formed by the model can robustly handle branching temporal sequences by maintaining multiple predictions until there is sufficient disambiguating evidence. We compare the HTM sequence memory with other sequence learning algorithms, including statistical methods: autoregressive integrated moving average (ARIMA), feedforward neural networks: online sequential extreme learning machine (ELM), and recurrent neural networks: long short-term memory (LSTM) and echo-state networks (ESN), on sequence prediction problems with both artificial and real-world data. The HTM model achieves comparable accuracy to other state-of-the-art algorithms. The model also exhibits properties that are critical for sequence learning, including continuous online learning, the ability to handle multiple predictions and branching sequences with high order statistics, robustness to sensor noise and fault tolerance, and good performance without task-specific hyper- parameters tuning. Therefore the HTM sequence memory not only advances our understanding of how the brain may solve the sequence learning problem, but is also applicable to a wide range of real-world problems such as discrete and continuous sequence prediction, anomaly detection, and sequence classification.

Temporal distribution shift (TDS) erodes the long-term accuracy of recommender systems, yet industrial practice still relies on periodic incremental training, which struggles to capture both stable and transient patterns. Existing approaches such as invariant learning and self-supervised learning offer partial solutions but often suffer from unstable temporal generalization, representation collapse, or inefficient data utilization. To address these limitations, we propose ELBO_TDS, a probabilistic framework that integrates seamlessly into industry-scale incremental learning pipelines. First, we identify key shifting factors through statistical analysis of real-world production data and design a simple yet effective data augmentation strategy that resamples these time-varying factors to extend the training support. Second, to harness the benefits of this extended distribution while preventing representation collapse, we model the temporal recommendation scenario using a causal graph and derive a self-supervised variational objective, ELBO_TDS, grounded in the causal structure. Extensive experiments supported by both theoretical and empirical analysis demonstrate that our method achieves superior temporal generalization, yielding a 2.33\% uplift in GMV per user and has been successfully deployed in Shopee Product Search. Code is available at https://github.com/FuCongResearchSquad/ELBO4TDS.

Recent progress in using recurrent neural networks (RNNs) for image description has motivated the exploration of their application for video description. However, while images are static, working with videos requires modeling their dynamic temporal structure and then properly integrating that information into a natural language description. In this context, we propose an approach that successfully takes into account both the local and global temporal structure of videos to produce descriptions. First, our approach incorporates a spatial temporal 3-D convolutional neural network (3-D CNN) representation of the short temporal dynamics. The 3-D CNN representation is trained on video action recognition tasks, so as to produce a representation that is tuned to human motion and behavior. Second we propose a temporal attention mechanism that allows to go beyond local temporal modeling and learns to automatically select the most relevant temporal segments given the text-generating RNN. Our approach exceeds the current state-of-art for both BLEU and METEOR metrics on the Youtube2Text dataset. We also present results on a new, larger and more challenging dataset of paired video and natural language descriptions.

Generating high-quality videos from complex temporal descriptions that contain multiple sequential actions is a key unsolved problem. Existing methods are constrained by an inherent trade-off: using multiple short prompts fed sequentially into the model improves action fidelity but compromises temporal consistency, while a single complex prompt preserves consistency at the cost of prompt-following capability. We attribute this problem to two primary causes: 1) temporal misalignment between video content and the prompt, and 2) conflicting attention coupling between motion-related visual objects and their associated text conditions. To address these challenges, we propose a novel, training-free attention mechanism, Temporal-wise Separable Attention (TS-Attn), which dynamically rearranges attention distribution to ensure temporal awareness and global coherence in multi-event scenarios. TS-Attn can be seamlessly integrated into various pre-trained text-to-video models, boosting StoryEval-Bench scores by 33.5% and 16.4% on Wan2.1-T2V-14B and Wan2.2-T2V-A14B with only a 2% increase in inference time. It also supports plug-and-play usage across models for multi-event image-to-video generation. The source code and project page are available at https://github.com/Hong-yu-Zhang/TS-Attn.

Temporal point processes (TPP) are a natural tool for modeling event-based data. Among all TPP models, Hawkes processes have proven to be the most widely used, mainly due to their adequate modeling for various applications, particularly when considering exponential or non-parametric kernels. Although non-parametric kernels are an option, such models require large datasets. While exponential kernels are more data efficient and relevant for specific applications where events immediately trigger more events, they are ill-suited for applications where latencies need to be estimated, such as in neuroscience. This work aims to offer an efficient solution to TPP inference using general parametric kernels with finite support. The developed solution consists of a fast ell_2 gradient-based solver leveraging a discretized version of the events. After theoretically supporting the use of discretization, the statistical and computational efficiency of the novel approach is demonstrated through various numerical experiments. Finally, the method's effectiveness is evaluated by modeling the occurrence of stimuli-induced patterns from brain signals recorded with magnetoencephalography (MEG). Given the use of general parametric kernels, results show that the proposed approach leads to an improved estimation of pattern latency than the state-of-the-art.

Test-time adaptation (TTA) aims to address the distribution shift between the training and test data with only unlabeled data at test time. Existing TTA methods often focus on improving recognition performance specifically for test data associated with classes in the training set. However, during the open-world inference process, there are inevitably test data instances from unknown classes, commonly referred to as outliers. This paper pays attention to the problem that conducts both sample recognition and outlier rejection during inference while outliers exist. To address this problem, we propose a new approach called STAble Memory rePlay (STAMP), which performs optimization over a stable memory bank instead of the risky mini-batch. In particular, the memory bank is dynamically updated by selecting low-entropy and label-consistent samples in a class-balanced manner. In addition, we develop a self-weighted entropy minimization strategy that assigns higher weight to low-entropy samples. Extensive results demonstrate that STAMP outperforms existing TTA methods in terms of both recognition and outlier detection performance. The code is released at https://github.com/yuyongcan/STAMP.

Multivariate time series forecasting is an important machine learning problem across many domains, including predictions of solar plant energy output, electricity consumption, and traffic jam situation. Temporal data arise in these real-world applications often involves a mixture of long-term and short-term patterns, for which traditional approaches such as Autoregressive models and Gaussian Process may fail. In this paper, we proposed a novel deep learning framework, namely Long- and Short-term Time-series network (LSTNet), to address this open challenge. LSTNet uses the Convolution Neural Network (CNN) and the Recurrent Neural Network (RNN) to extract short-term local dependency patterns among variables and to discover long-term patterns for time series trends. Furthermore, we leverage traditional autoregressive model to tackle the scale insensitive problem of the neural network model. In our evaluation on real-world data with complex mixtures of repetitive patterns, LSTNet achieved significant performance improvements over that of several state-of-the-art baseline methods. All the data and experiment codes are available online.

The Diffusion models, widely used for image generation, face significant challenges related to their broad applicability due to prolonged inference times and high memory demands. Efficient Post-Training Quantization (PTQ) is crucial to address these issues. However, unlike traditional models, diffusion models critically rely on the time-step for the multi-round denoising. Typically, each time-step is encoded into a hypersensitive temporal feature by several modules. Despite this, existing PTQ methods do not optimize these modules individually. Instead, they employ unsuitable reconstruction objectives and complex calibration methods, leading to significant disturbances in the temporal feature and denoising trajectory, as well as reduced compression efficiency. To address these challenges, we introduce a novel quantization framework that includes three strategies: 1) TIB-based Maintenance: Based on our innovative Temporal Information Block (TIB) definition, Temporal Information-aware Reconstruction (TIAR) and Finite Set Calibration (FSC) are developed to efficiently align original temporal features. 2) Cache-based Maintenance: Instead of indirect and complex optimization for the related modules, pre-computing and caching quantized counterparts of temporal features are developed to minimize errors. 3) Disturbance-aware Selection: Employ temporal feature errors to guide a fine-grained selection between the two maintenance strategies for further disturbance reduction. This framework preserves most of the temporal information and ensures high-quality end-to-end generation. Extensive testing on various datasets, diffusion models and hardware confirms our superior performance and acceleration..

Large language models (LLMs) are typically trained on fixed snapshots of the web, which means that their knowledge becomes stale and their predictions risk temporal leakage: relying on information that lies in the future relative to a query. We tackle this problem by pre-training from scratch a set of GPT-style experts on disjoint two-year slices of a 2013-2024 corpus and combining them through TiMoE, a Time-aware Mixture of Language Experts. At inference time, TiMoE masks all experts whose training window ends after the query timestamp and merges the remaining log-probabilities in a shared space, guaranteeing strict causal validity while retaining the breadth of multi-period knowledge. We also release TSQA, a 10k-question benchmark whose alternatives are explicitly labelled as past, future or irrelevant, allowing fine-grained measurement of temporal hallucinations. Experiments on eight standard NLP tasks plus TSQA show that a co-adapted TiMoE variant matches or exceeds the best single-period expert and cuts future-knowledge errors by up to 15%. Our results demonstrate that modular, time-segmented pre-training paired with causal routing is a simple yet effective path toward LLMs that stay chronologically grounded without sacrificing general performance much. We open source our code at TiMoE (Github): https://github.com/epfml/TiMoE

Entropy and mutual information in neural networks provide rich information on the learning process, but they have proven difficult to compute reliably in high dimensions. Indeed, in noisy and high-dimensional data, traditional estimates in ambient dimensions approach a fixed entropy and are prohibitively hard to compute. To address these issues, we leverage data geometry to access the underlying manifold and reliably compute these information-theoretic measures. Specifically, we define diffusion spectral entropy (DSE) in neural representations of a dataset as well as diffusion spectral mutual information (DSMI) between different variables representing data. First, we show that they form noise-resistant measures of intrinsic dimensionality and relationship strength in high-dimensional simulated data that outperform classic Shannon entropy, nonparametric estimation, and mutual information neural estimation (MINE). We then study the evolution of representations in classification networks with supervised learning, self-supervision, or overfitting. We observe that (1) DSE of neural representations increases during training; (2) DSMI with the class label increases during generalizable learning but stays stagnant during overfitting; (3) DSMI with the input signal shows differing trends: on MNIST it increases, while on CIFAR-10 and STL-10 it decreases. Finally, we show that DSE can be used to guide better network initialization and that DSMI can be used to predict downstream classification accuracy across 962 models on ImageNet. The official implementation is available at https://github.com/ChenLiu-1996/DiffusionSpectralEntropy.

Recent years have witnessed Spiking Neural Networks (SNNs) gaining attention for their ultra-low energy consumption and high biological plausibility compared with traditional Artificial Neural Networks (ANNs). Despite their distinguished properties, the application of SNNs in the computationally intensive field of image generation is still under exploration. In this paper, we propose the Spiking Diffusion Models (SDMs), an innovative family of SNN-based generative models that excel in producing high-quality samples with significantly reduced energy consumption. In particular, we propose a Temporal-wise Spiking Mechanism (TSM) that allows SNNs to capture more temporal features from a bio-plasticity perspective. In addition, we propose a threshold-guided strategy that can further improve the performances by up to 16.7% without any additional training. We also make the first attempt to use the ANN-SNN approach for SNN-based generation tasks. Extensive experimental results reveal that our approach not only exhibits comparable performance to its ANN counterpart with few spiking time steps, but also outperforms previous SNN-based generative models by a large margin. Moreover, we also demonstrate the high-quality generation ability of SDM on large-scale datasets, e.g., LSUN bedroom. This development marks a pivotal advancement in the capabilities of SNN-based generation, paving the way for future research avenues to realize low-energy and low-latency generative applications. Our code is available at https://github.com/AndyCao1125/SDM.

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.

The statistical mechanics of Gibbs is a juxtaposition of subjective, probabilistic ideas on the one hand and objective, mechanical ideas on the other. In this paper, we follow the path set out by Jaynes, including elements added subsequently to that original work, to explore the consequences of the purely statistical point of view. We show how standard methods in the equilibrium theory could have been derived simply from a description of the available problem information. In addition, our presentation leads to novel insights into questions associated with symmetry and non-equilibrium statistical mechanics. Two surprising consequences to be explored in further work are that (in)distinguishability factors are automatically predicted from the problem formulation and that a quantity related to the thermodynamic entropy production is found by considering information loss in non-equilibrium processes. Using the problem of ion channel thermodynamics as an example, we illustrate the idea of building up complexity by successively adding information to create progressively more complex descriptions of a physical system. Our result is that such statistical mechanical descriptions can be used to create transparent, computable, experimentally-relevant models that may be informed by more detailed atomistic simulations. We also derive a theory for the kinetic behavior of this system, identifying the nonequilibrium `process' free energy functional. The Gibbs relation for this functional is a fluctuation-dissipation theorem applicable arbitrarily far from equilibrium, that captures the effect of non-local and time-dependent behavior from transient driving forces. Based on this work, it is clear that statistical mechanics is a general tool for constructing the relationships between constraints on system information.

The deep neural nets of modern artificial intelligence (AI) have not achieved defining features of biological intelligence, including abstraction, causal learning, and energy-efficiency. While scaling to larger models has delivered performance improvements for current applications, more brain-like capacities may demand new theories, models, and methods for designing artificial learning systems. Here, we argue that this opportunity to reassess insights from the brain should stimulate cooperation between AI research and theory-driven computational neuroscience (CN). To motivate a brain basis of neural computation, we present a dynamical view of intelligence from which we elaborate concepts of sparsity in network structure, temporal dynamics, and interactive learning. In particular, we suggest that temporal dynamics, as expressed through neural synchrony, nested oscillations, and flexible sequences, provide a rich computational layer for reading and updating hierarchical models distributed in long-term memory networks. Moreover, embracing agent-centered paradigms in AI and CN will accelerate our understanding of the complex dynamics and behaviors that build useful world models. A convergence of AI/CN theories and objectives will reveal dynamical principles of intelligence for brains and engineered learning systems. This article was inspired by our symposium on dynamical neuroscience and machine learning at the 6th Annual US/NIH BRAIN Initiative Investigators Meeting.

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

Recent advancements in audio generation have enabled the creation of high-fidelity audio clips from free-form textual descriptions. However, temporal relationships, a critical feature for audio content, are currently underrepresented in mainstream models, resulting in an imprecise temporal controllability. Specifically, users cannot accurately control the timestamps of sound events using free-form text. We acknowledge that a significant factor is the absence of high-quality, temporally-aligned audio-text datasets, which are essential for training models with temporal control. The more temporally-aligned the annotations, the better the models can understand the precise relationship between audio outputs and temporal textual prompts. Therefore, we present a strongly aligned audio-text dataset, AudioTime. It provides text annotations rich in temporal information such as timestamps, duration, frequency, and ordering, covering almost all aspects of temporal control. Additionally, we offer a comprehensive test set and evaluation metric to assess the temporal control performance of various models. Examples are available on the https://zeyuxie29.github.io/AudioTime/

Time series foundation models (TSFMs) offer strong zero-shot forecasting via large-scale pre-training, yet fine-tuning remains critical for boosting performance in domains with limited public data. With the growing number of TSFMs, efficiently identifying the best model for downstream fine-tuning becomes increasingly challenging. In this work, we introduce TimeTic, a transferability estimation framework that recasts model selection as an in-context-learning problem: given observations on known (source) datasets, it predicts how a TSFM will perform after fine-tuning on a downstream (target) dataset. TimeTic flexibly organizes the observed model-data relationships as contextual information, allowing it to adapt seamlessly to various test-time scenarios. Leveraging the natural tabular structure formed by dataset meta-features, model characteristics, and fine-tuned performance, we employ tabular foundation models to serve as in-context learners. We further introduce a novel model characterization based on entropy evolution across model layers, capturing embedding-space distinctions and enabling TimeTic to generalize across arbitrary model sets. We establish a comprehensive benchmark for transferability estimation including 10 datasets, 10 foundation models, and 3 forecasting tasks. On this benchmark, TimeTic's estimation demonstrates strong alignment with actual fine-tuned performance for previously unseen datasets, achieving a mean rank correlation of approximately 0.6 and a 30% improvement compared to using zero-shot performance as the transferability score.

Active matter systems, from self-propelled colloids to motile bacteria, are characterized by the conversion of free energy into useful work at the microscopic scale. These systems generically involve physics beyond the reach of equilibrium statistical mechanics, and a persistent challenge has been to understand the nature of their nonequilibrium states. The entropy production rate and the magnitude of the steady-state probability current provide quantitative ways to do so by measuring the breakdown of time-reversal symmetry and the strength of nonequilibrium transport of measure. Yet, their efficient computation has remained elusive, as they depend on the system's unknown and high-dimensional probability density. Here, building upon recent advances in generative modeling, we develop a deep learning framework that estimates the score of this density. We show that the score, together with the microscopic equations of motion, gives direct access to the entropy production rate, the probability current, and their decomposition into local contributions from individual particles, spatial regions, and degrees of freedom. To represent the score, we introduce a novel, spatially-local transformer-based network architecture that learns high-order interactions between particles while respecting their underlying permutation symmetry. We demonstrate the broad utility and scalability of the method by applying it to several high-dimensional systems of interacting active particles undergoing motility-induced phase separation (MIPS). We show that a single instance of our network trained on a system of 4096 particles at one packing fraction can generalize to other regions of the phase diagram, including systems with as many as 32768 particles. We use this observation to quantify the spatial structure of the departure from equilibrium in MIPS as a function of the number of particles and the packing fraction.

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.

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

In this work, we investigate how a model's tendency to broadly integrate its parametric knowledge evolves throughout pretraining, and how this behavior affects overall performance, particularly in terms of knowledge acquisition and forgetting. We introduce the concept of knowledge entropy, which quantifies the range of memory sources the model engages with; high knowledge entropy indicates that the model utilizes a wide range of memory sources, while low knowledge entropy suggests reliance on specific sources with greater certainty. Our analysis reveals a consistent decline in knowledge entropy as pretraining advances. We also find that the decline is closely associated with a reduction in the model's ability to acquire and retain knowledge, leading us to conclude that diminishing knowledge entropy (smaller number of active memory sources) impairs the model's knowledge acquisition and retention capabilities. We find further support for this by demonstrating that increasing the activity of inactive memory sources enhances the model's capacity for knowledge acquisition and retention.

Our work explores temporal self-supervision for GAN-based video generation tasks. While adversarial training successfully yields generative models for a variety of areas, temporal relationships in the generated data are much less explored. Natural temporal changes are crucial for sequential generation tasks, e.g. video super-resolution and unpaired video translation. For the former, state-of-the-art methods often favor simpler norm losses such as L^2 over adversarial training. However, their averaging nature easily leads to temporally smooth results with an undesirable lack of spatial detail. For unpaired video translation, existing approaches modify the generator networks to form spatio-temporal cycle consistencies. In contrast, we focus on improving learning objectives and propose a temporally self-supervised algorithm. For both tasks, we show that temporal adversarial learning is key to achieving temporally coherent solutions without sacrificing spatial detail. We also propose a novel Ping-Pong loss to improve the long-term temporal consistency. It effectively prevents recurrent networks from accumulating artifacts temporally without depressing detailed features. Additionally, we propose a first set of metrics to quantitatively evaluate the accuracy as well as the perceptual quality of the temporal evolution. A series of user studies confirm the rankings computed with these metrics. Code, data, models, and results are provided at https://github.com/thunil/TecoGAN. The project page https://ge.in.tum.de/publications/2019-tecogan-chu/ contains supplemental materials.

Entropy regularization is a standard technique in reinforcement learning (RL) to enhance exploration, yet it yields negligible effects or even degrades performance in Large Language Models (LLMs). We attribute this failure to the cumulative tail risk inherent to LLMs with massive vocabularies and long generation horizons. In such environments, standard global entropy maximization indiscriminately dilutes probability mass into the vast tail of invalid tokens rather than focusing on plausible candidates, thereby disrupting coherent reasoning. To address this, we propose Trust Region Entropy (TRE), a method that encourages exploration strictly within the model's trust region. Extensive experiments across mathematical reasoning (MATH), combinatorial search (Countdown), and preference alignment (HH) tasks demonstrate that TRE consistently outperforms vanilla PPO, standard entropy regularization, and other exploration baselines. Our code is available at https://github.com/WhyChaos/TRE-Encouraging-Exploration-in-the-Trust-Region.