Temporal Dynamics

Large language models remain fragile against malicious fine-tuning, motivating training-time defenses against harmful persona drift. Preventative Steering injects undesirable-trait persona vectors during fine-tuning and removes them at evaluation time, yet the mechanism behind its lasting protection remains unclear. Analyzing its temporal optimization dynamics, we find that the defense emerges from an early compensatory adaptation phase followed by a steady-state phase where the corrective signal decays; in parameter space, attention output projections emerge as the dominant residual-write route for defensive updates. Through Intervention Delta Preservation (IDP) and IDP Continuation experiments, we further show that preserving or reinjecting the weight offset fails to maintain protection, indicating that preventative steering relies on active adaptation rather than a static defense. Motivated by this finding, we propose Progressive Intensity Scheduling (PIS), which starts with a moderate injection strength and increases it after static-strength alignment begins to decay. Across the evaluated Qwen2.5 and Gemma-3 models, PIS improves safety robustness over static-strength steering while reducing harmful trait expression.

Urban region embeddings have shown promising results in diverse urban sensing tasks such as crime, income, and service-call prediction. Recent methods improve representation quality by integrating mobility data with auxiliary modalities, using cross-view attention or contrastive objectives to align heterogeneous features into a unified region representation. However, leveraging the temporal dynamics of human mobility remains under-explored. Regional inflow and outflow fluctuate throughout the day, and inter-region connections emerge, persist, and dissolve over time. Moreover, prevailing fusion strategies combine views additively and miss the joint signal that emerges only when views co-occur. To address these gaps, we propose Mobility Stream-Structure Synergy (MoSS), which derives complementary views from mobility data: a Sequence view that preserves each region's hourly inflow/outflow profile, and a Structure view based on zigzag persistence diagrams that capture how regional connectivity emerges, persists, and dissolves over time. A synergy module then extracts emergent representations from the co-occurrence of these views through multi-degree interactions, explicitly capturing higher-order signal across views. Extensive experiments on New York City and Chicago show that MoSS achieves state-of-the-art performance across three downstream tasks using mobility data alone, outperforming baselines that rely on auxiliary modalities.

Conventional neural networks learn predominantly through affine transformations followed by nonlinear activations, while elapsed time is often treated as an auxiliary feature or assumed to be uniformly sampled. This paper introduces Wave Function Backpropagation (WFB), a wave-parameterized learning formulation in which neural responses are represented by learnable amplitude, wavenumber, angular frequency, and phase. The formulation associates an observed state with its temporal interval Delta t through the phase of a differentiable spatiotemporal wave. We derive standard WFB gradients and a spatial-curvature correction based on the Laplacian of the wave response. WFB is instantiated in a deliberately feed-forward trajectory predictor to provide a controlled proof of concept; sequence learning is outside the scope of the present evaluation. With motion features, STD-WFB using real intervals reduces average displacement error (ADE) by 20.4% relative to the original FFN baseline. In a new position-only evaluation that removes temporal leakage through precomputed velocity and acceleration, real-interval WFB reduces ADE by 10.4% relative to the original FFN and remains competitive with parameter-matched ReLU controls, obtaining 2.1% lower mean ADE than the matched FFN with explicit Delta t. Shuffled-interval WFB attains the lowest mean ADE, indicating that the present evidence supports the effectiveness of the wave representation but does not attribute the gain to interval alignment. These results establish WFB as a viable structured feed-forward learning formulation and define a clear basis for subsequent architectural studies.

Recent vision-language-action (VLA) methods improve manipulation performance by aligning their representations with 3D scene geometry. However, these methods often struggle with long-horizon manipulation and observation aliasing between visually similar states due to a lack of temporal information: the 3D scene geometry captures only the current state, rather than how it has evolved over time. To resolve this, we present Temporal Forcing, a 4D representation alignment method for VLA models. Specifically, we first introduce a history pathway that enables a vanilla VLA model to summarize observation history into temporally aware latent representations. Then, the latent representations are aligned with the geometric features extracted by a pretrained 4D foundation model, which captures the evolving 3D world through temporally consistent geometric representations, enabling a deeper understanding of dynamic environments. Temporal Forcing reaches 98.8% on LIBERO, outperforming its base model by 2.2 points. On a physical hidden-placement task, it raises full-task success from 20.0% to 43.3%. Code will be publicly available.

Video-to-audio (V2A) generation faces significant challenges in achieving precise temporal synchronization and high perceptual quality due to the complex, ambiguous relationship between visual and auditory cues. Existing methods typically compress video inputs into single feature representations, leading to significant loss of temporal dynamics and fine-grained visual information. These approaches also rely on reconstruction-based training objectives that poorly correlate with human perceptual judgments of audio quality and appropriateness. We propose HarmoniDPO, a novel framework that integrates preference-based optimization into diffusion-based V2A generation to address these limitations. (1) Our approach leverages a dual video representation: combining global context with frame-wise features to preserve temporal dynamics and semantic detail. (2) Inspired by reinforcement learning from human feedback (RLHF), HarmoniDPO employs online Direct Preference Optimization (online-DPO) to fine-tune a diffusion-based V2A model from preference judgments, enhancing perceptual quality and alignment. (3) Additionally, we introduce Dual-scale Diffusion Search (DDS), a test time scaling algorithm that adaptively optimizes output fidelity during inference. Experiments demonstrate that HarmoniDPO outperforms state-of-the-art methods in audio-video synchronization and subjective audio quality, offering a robust solution for generating realistic, human-preferred audio from video.

Reinforcement learning (RL) post-training of Vision-Language-Action (VLA) models has shown strong promise for robotic manipulation. Among RL methods, critic-based approaches rely on a value estimator that predominantly operates on single-frame observations or single-frame VLM backbone latents, which is a fundamental mismatch with the partially observable nature of robot control. A naive approach to incorporate observation history into the critic incurs exponential complexity with high-dimensional visual space, and still fails because pure scalar-return regression provides insufficient supervision for learning cross-temporal dynamics. We identify the root cause as a state approximation problem: without an explicit world modeling objective, the critic's representation cannot capture the temporal structure needed for accurate value estimation. To address this, we propose the World Critic Model (WCM), built on a lightweight LeJEPA architecture; WCM jointly predicts future latent state and estimates values, such that the critic's representation is explicitly trained to capture temporal dynamics rather than merely regress scalar returns. WCM integrates seamlessly into both on-policy and off-policy training pipelines and is compatible with state-of-the-art VLA backbones including Pi0, Pi0.5, and OpenVLA-OFT. Extensive experiments on 149 tasks across four benchmarks demonstrate that WCM consistently achieves state-of-the-art performance in both in-distribution and out-of-distribution settings, with particularly strong generalization gains. We further validate WCM on seven real-world manipulation tasks using OpenVLA-OFT and Pi0.5 with off-policy RL, confirming stable deployment across diverse settings.

Rotary Position Embedding (RoPE) has been widely adopted in transformer-based large language models. However, its log-linear frequency schedule, originally designed to produce long-term attention decay, limits its adoption in domains with more complex distance-correlation patterns, such as temporal periodicity in sequential recommendation. We investigate the expressiveness of general query/key rotations and find that any normalized continuous positive-definite attention modulation function can be approximated by random rotations induced by its own Fourier transform, which we term Random Fourier Rotations. Building on this theory, we propose ClockRoPE for routine modeling in sequential recommendation, where rotation frequencies are derived from periodic attention modulation functions. In online A/B tests, ClockRoPE demonstrates consistent improvements in valued engagement metrics, and has been successfully deployed in production-scale generative retrieval system at a major video-sharing platform.

Falls represent a critical public health challenge, and accurate detection of the impact moment when an individual hits the ground is crucial for timely intervention. Existing skeleton-based methods rely on graph neural networks modeling only pairwise joint connections, failing to capture multi-joint coordination characteristic of fall impacts, while transformer-based temporal models suffer from quadratic complexity limiting real-time deployment. We propose FLASH, a novel framework integrating single-matrix hypergraph representations with Mamba's selective state-space models through adaptive feedback mechanisms for efficient impact detection. Our approach constructs biomechanically-grounded hyperedges to model functional joint coordination while leveraging Mamba's linear-time complexity to capture temporal dynamics. Experiments on UP-Fall and UMAFall datasets demonstrate that FLASH achieves state-of-the-art accuracy with real-time inference capability and strong zero-shot cross-dataset generalization, while significantly reducing computational cost compared to dual-representation and transformer-based methods. The model provides interpretable feedback through learned attention patterns aligned with biomechanical principles. Code is available at https://github.com/Tresor-Koffi/FLASH-Impact-Fall-Detection.

Digitized musical heritage collections offer new opportunities to examine how stylistic traditions change over historical time, but computational analyses often reduce musical works to static classifications or similarity scores. This article proposes a representation-to-dynamics framework for studying cross-cultural harmonic change in Western art music. Starting from symbolic chord sequences, we derive contextual chord embeddings, project work-level representations into a shared harmonic space, and reconstruct country-level trajectories through temporally causal Kalman filtering. These trajectories are then modeled with DeGroot and Friedkin--Johnsen dynamics, yielding interpretable influence-like networks and estimates of stylistic anchoring. We apply the framework to a curated corpus of 480 dated works from 1875 to 1940 across Russia, France, Germany, Austria, and a heterogeneous ''Others'' group. Models fitted on 1875--1925 are evaluated through recursive forecasts for 1930--1940, testing whether the estimated dependency structure remains informative across a potentially changing historical and stylistic regime. The estimated trajectories and influence patterns are broadly consistent with established music-historical accounts of late Romantic and early modernist exchange, including the close relationship between German and Austrian traditions and historically plausible cross-currents between Russian and French traditions. PCA-variance-weighted estimation provides modest improvements while preserving a single interpretable influence network. Rather than treating the estimated matrices as direct causal evidence, the framework offers a reproducible quantitative layer for cultural heritage research, complementing archival and musicological interpretation.

Modeling multi-entity temporal data requires capturing dependencies across entities, time, and their interactions. Transformer-based approaches perform well but often rely on deep stacks of layers to learn these heterogeneous dependencies implicitly, increasing computational cost. We revisit this problem from a structural perspective and decompose multi-entity temporal dynamics into three interaction types: spatial interactions among entities, temporal interactions across time, and cross interactions coupling the two domains. We propose a structured spatio-temporal transformer block that explicitly models all three within a single stage. It uses parallel spatial and temporal self-attention, followed by bidirectional cross-attention, and combines the outputs through learnable gated fusion. By directly encoding these complementary views, the model reduces the need for deep stacking. We evaluate the approach on video-based group activity recognition, skeleton-based human interaction analysis, and wearable sensor-based activity recognition. Despite its simplicity, the single structured Transformer block matches or outperforms deeper architectures with only 1.76M parameters. The results suggest that depth in prior models partly compensates for implicit and entangled interaction modeling, whereas explicit factorization offers a more efficient and transparent alternative. More broadly, this work supports a structure-first design principle: expressive multi-entity temporal reasoning can emerge by exposing interaction structure rather than relying on depth.

This paper develops temporal-causal unity (TCU), a framework connecting a process-philosophical thesis -- time is the ordered unfolding of causal change -- to an operational model of cognitive and social dynamics. The framework deliberately separates three claims: an interpretive thesis about becoming, a measurable causal-progress coordinate, and a stochastic network model. Causal progress is defined by $τ(t)=\int_0^tλ(s\mid\mathcal H_s)\,{\rm d}s$, where the nonnegative event intensity $λ$ must be specified independently of the outcome. Agents carry an orientation phase and an activation amplitude; weighted interaction, heterogeneous drift, external input, anchoring, and diffusion govern their evolution in $τ$. First- and second-harmonic order parameters separate consensus from bipolar polarization. For the all-to-all noisy Kuramoto special case with Lorentzian drift width $Δ$, synchronization begins at the conditional threshold $K_c = 2(Δ+ D)$, not at a universal constant. Reproducible numerical illustrations illustrate (not empirically demonstrate) this threshold, causal-clock curve collapse, and the consensus-polarization distinction. Six historical episodes are treated as scope probes rather than validation data. The paper derives falsifiable hypotheses and an out-of-sample protocol for comparing causal-progress and chronological-time models. TCU is therefore offered as a disciplined bridge between process ontology and complex-systems modeling, not as a replacement for spacetime physics or as an empirically established identity between time and causation.

World models are typically trained to predict discrete-time physical dynamics with a fixed step size baked into the model weights, preventing prediction at variable temporal resolutions. This matters for hierarchical planning, sim-to-real transfer, and scientific or game-engine applications that must query the same dynamics at multiple timescales. Hamiltonian Generative Networks (HGN) offer a principled path forward, grounding predictions in a continuous-time energy function that is, in principle, independent of the observation frame rate. In practice, however, their temporal generalization breaks down in non-conservative settings. We show that in externally forced, dissipative environments, HGN rollouts at step sizes beyond the training regime fail due to distinct failure modes, including latent magnitude growth driven by an unconstrained action-force map, and global truncation error accumulation from an under-resolved integrator. We identify a targeted fix for each mechanism and demonstrate stable dynamics prediction at temporal resolutions well outside the training distribution. In a detailed analysis, we recommend several strategies for enabling temporal generalization in continuous-time video generation.

Generating temporally continuous and socially coherent human motion from text remains a fundamental challenge, particularly in realistic streams where people act alone, enter interactions, and later disengage. Most existing methods generate fixed-length motion clips under static agent configurations, which makes them brittle to solo-social transitions and unsuitable for incremental generation over long horizons. We propose ARMS, an Anchor-Relational Motion Streaming framework that unifies solo motion and human-human interaction within a single causal generative process. ARMS introduces a dynamics-asymmetric representation that decouples per-person temporal evolution from inter-person alignment via a partner-referenced relative-translation term, enabling seamless switching of social coupling without sacrificing long-horizon stability or spatial consistency between agents. On top of a causal latent space, a causal relational diffusion model progressively refines motion segment by segment using only past context, capturing both intra-person temporal dependencies and inter-person relations. Mode-aware relational gating activates or masks cross-agent connections, allowing the same model to support both solo and interaction generation. Experiments show that ARMS improves transition smoothness and social coherence compared to interaction-centric baselines, while also achieving competitive results on human-human interaction benchmarks.

Decentralised federated learning, based on peer-to-peer communication, is increasingly proposed for on-device training of machine learning models, promising a privacy-preserving, communication-efficient training process with no risk of single-point failure. However, the role of structural and temporal inhomogeneities in such fully decentralised settings remains poorly understood. Here, we investigate their effects when model parameters are locally averaged during aggregation. We show that the decentralised federated learning process is governed, both in the early phase and the late, stationary limit, by the same dynamics as a lazy random-walk diffusion process on temporal networks. Based on this mapping, we demonstrate that the typical experimental scenario used in decentralised federated learning leads to unrealistically rapid convergence because of ignoring the temporal and structural inhomogeneities inherent in the communication network. We analyse real-world temporal networks and find that inhomogeneities most often dramatically slow down diffusion, hence the convergence process.

Most Vision-Language-Action (VLA) models build on a Vision-Language Model (VLM) backbone by attaching an action module and optimizing the full policy jointly. This design inherits strong visual and linguistic priors from the VLM, but leaves the action module to learn physical motion almost from scratch. As a result, the policy lacks an explicit motion prior, forcing early optimization to simultaneously discover temporal action dynamics and cross-modal alignment, a challenge further amplified in cross-embodiment settings. In this work, we propose to pretrain the action module with motion priors before cross-modal VLA alignment. Specifically, we introduce a two-stage training framework that equips the action module with cross-embodiment temporal motion structure before VLA training begins. In Stage1, a lightweight flow-matching-based encoder-decoder action module efficiently learns temporal motion structure solely from unconditioned action trajectories, without processing visual or language tokens. In Stage2, this learned prior is transferred to VLA training through decoder reuse and early-stage latent distillation, aligning visual-language features with the action embedding space while still allowing end-to-end policy refinement. In addition, the trained encoder serves as a compact history compressor, summarizing state-action histories into a single temporal context token for history-aware modeling at negligible cost. Extensive experiments across 13 diverse cross-embodiment tasks on both simulated and real-world platforms validate the effectiveness of our approach. Compared with VLA training without action priors, our model achieves faster convergence, higher success rates, and substantially stronger performance on data-scarce real-world tasks. Moreover, scaling up the action data in Stage~1 yields a more generalizable action prior that directly improves downstream VLA performance.

Pedestrian trajectory prediction requires modeling temporal dynamics, multimodal cues, and social interactions in crowded environments. Existing methods often address these factors separately or entangle them in costly attention blocks, limiting scalability, flexibility, and interpretability. We propose a three-step hierarchical Transformer that explicitly separates temporal encoding, multimodal fusion, and scene-level interaction reasoning. Lightweight GRU summaries enable efficient cross-modal attention, while social attention over time--agent tokens captures inter-pedestrian influences at manageable cost. Experiments on JTA, JRDB, and the Pedestrians and Cyclists in Road Traffic dataset show state-of-the-art performance on real-world datasets (JRDB, Urban) and competitive results on JTA. Ablation and qualitative analyses confirm the contribution of each stage and the model's ability to anticipate complex behaviors such as early turning.

Activities in numerous evolving systems can be represented as dynamic graphs in snapshot form at different time intervals, i.e., discrete-time dynamic graphs (DTDGs). Existing methods show impressive advances in capturing historical temporal evolution patterns in DTDGs, but they focus on addressing an offline learning setting, where models are trained using historical snapshots once and then evaluated to all subsequent graph snapshots without further updating. This fails to capture 1) the nature of evolving complexities across graph snapshots and 2) the distribution shift in the testing graph snapshots. To address these problems, we propose PromptDyG, a novel framework that leverages unsupervised test-time Prompt adaptation for Dynamic Graph learning under a live-update online setting. The key insight is that an expressive dynamic graph prompt can be learned on a frozen backbone via minimization of feature-wise, label-free entropy to efficiently and continuously model the evolving patterns. We show theoretically that this unsupervised prompt adaptation can guarantee a larger similarity margin between positive and negative pairs, facilitating more accurate dynamic predictions. It is further confirmed by our extensive empirical results on six benchmark datasets that show consistent and significant improvements of PromptDyG over state-of-the-art baselines.

Choreographic motion generation poses unique challenges for AI, demanding precise semantic control over complex, temporally structured, and expressive full-body dynamics. While existing models can synthesize motion from music, they remain largely black boxes. Conversely, attempting to condition generation on both text and music frequently leads to modality collapse, where dense acoustic rhythms overwhelm sparse semantic text prompts, destroying user controllability. To resolve this spatial-temporal conflict, we propose STREAM (Structural-Temporal Rhythmic Energy-based Attention for Motion), a modality-decoupled diffusion transformer. STREAM strictly separates conditioning pathways: global text semantics dictate the kinematic structure via Adaptive Layer Normalization (AdaLN), while a novel Bimodal Energy-Based Attention Module (BEAM) routes these features to the musical beat without overwriting the semantics. We further introduce Motorica++, a newly curated dataset enriched with domain-specific dance vocabulary and frame-level semantic annotations from existing Motorica dataset. Additionally, to rigorously quantify zero-shot editability, we propose the Exchange Evaluation Protocol and Editable Dance Score (EDS). Through extensive experiments, STREAM achieves state-of-the-art alignment between motion and music while perfectly preserving choreographic semantics, positioning AI not merely as a reactive synthesizer, but as a controllable, collaborative partner for artistic direction. The source code and datasets are available at https://github.com/SeongJong-Yoo/STREAM.

Standard continuous-depth models, such as Neural Ordinary Differential Equations (NODEs), offer significant advantages in modeling physical systems by learning continuous vector fields rather than discrete temporal steps. However, when applied to complex dynamical systems, standard NODEs frequently struggle with highly nonlinear dynamics. This paper investigates the Frequency-domain Neural ODE (FNODE), an architecture that projects continuous temporal dynamics into the frequency domain using the Fast Fourier Transform (FFT). By operating in the frequency domain, the model provides better generalization to the dynamical system. The architecture is empirically evaluated against discrete models, specifically Gated Recurrent Units (GRUs) and Long Short-Term Memory (LSTMs), and other continuous-depth variants, including Augmented Neural ODE (ANODE), across four distinct dynamical systems: the Lotka-Volterra model, the forced Duffing oscillator, the Van der Pol oscillator, and the Lorenz system. To rigorously assess generalization and robustness, curriculum and ensemble learning are used to evaluate the model's convergence by estimating confidence intervals across different ensemble models. The empirical results demonstrate that the FNODE architecture achieves better generalization while exhibiting remarkable convergence stability.

Understanding how a nervous system wires itself from birth to adulthood is a fundamental challenge in developmental neuroscience. We present DevoTG, a temporal graph framework that applies Temporal Graph Neural Networks (TGNs) to two complementary representations of C. elegans neural development: a Continuous-Time Dynamic Graph (CTDG) of cell division events derived from cell lineage data, and a Discrete-Time Dynamic Graph (DTDG) of the developing synaptic connectome spanning eight reconstructed electron-microscopy datasets. On the lineage prediction task, our TGN achieves a mean test AUC of 0.839 +/- 0.007 (5 seeds; validation AUC 0.937 +/- 0.001), outperforming a static GNN with the identical architecture by 26 AUC points (0.577 +/- 0.080), demonstrating that temporal memory is the decisive factor. Applied to the connectome DTDG, DevoTG identifies three connection stability classes (stable, developmental, and variable) across 225 neurons and 858 to 2,496 connections over development (L1 birth to adult), providing a temporal-graph-theoretic complement to the individual-variability classification of Witvliet et al. Analysis of hub command interneurons AVA, AVB, and AVE reveals their persistent centrality and how their integration roles are progressively reinforced across larval stages. Accompanying interactive visualizations (3D animated networks, centrality heatmaps, and a spatiotemporal lineage graph) make developmental dynamics accessible for biological hypothesis generation. DevoTG is open-source and designed for extension to other developing nervous systems. Code is publicly available at https://github.com/DevoLearn/DevoGraph/tree/main/DevoTG.

Existing sequence models, including RNNs, LSTMs, continuous-time networks, and Transformers, share a common structural principle: layer-wise dynamics, where all neurons in the same layer co-evolve through a shared parameterized operator, leaving individual neurons no freedom to evolve independently. Yet in many complex dynamical systems, rich global behavior emerges precisely from locally evolving units interacting through structured connectivity. Inspired by this principle, we introduce Topological Neural Dynamics (TND), a sequence modeling framework that shifts computation from layer-wise to neuron-wise dynamics. TND represents a neural system as a directed neuron graph, an interaction operator, and a local dynamics function, where each neuron evolves independently and collective computation emerges from interactions through the explicit graph topology. We instantiate TND as a discrete-time graph-coupled dynamical system and evaluate it as a case study on a behavior cloning task in single-player Pong. Compared with Vanilla RNN, Sparse RNN, LSTM, Closed-form continuous-time neural network (CfC), and Transformer baselines, TND achieves the best catch rate and a mean of 17.47 consecutive catches per round, more than three times that of the strongest baseline. These results suggest that shifting from layer-wise to neuron-wise dynamics provides an effective inductive bias for sequence modeling.

Neural population activity models can recover rich temporal structure from binned spikes, but their read-in and readout layers often remain tied to a fixed set of recorded neurons. This coupling limits reuse in long-term brain-computer interfaces, where recorded neuron identities, counts, and response statistics can change across days. We introduce GRAFT, a Transformer-based neural population activity model that separates reusable temporal dynamics from a recalibratable neuron interface. The neuron interface controls how recorded neurons enter and leave the shared backbone, and auxiliary gain and positional mechanisms support neural activity modeling inside the Transformer. On MC Maze under the standard NLB'21 protocol, GRAFT reaches 0.3866 co-bps as an ensemble, setting a new state of the art on the primary co-bps metric among public and reported NLB'21 results. In a cross-day protocol constructed from the NLB'21 MC Maze dataset series, GRAFT recalibrates from MC Maze to the scaled MC Maze datasets (Large/Medium/Small) by updating only 9.21% of parameters, reaching 0.3749, 0.3112, and 0.3152 co-bps with restricted target-day support sets. These results show that the same interface-backbone separation supports both strong Transformer-based neural population activity modeling and data-efficient cross-day recalibration.

Modern Diffusion Transformers for video generation provide limited control over the progression of time and the editing of temporal dynamics. We propose a temporal-control methodology that extends a pretrained DiT with explicit time editing, allowing control over motion speed and temporal structure without redesigning the backbone. Its core implementation augments the pretrained model with a lightweight temporal module, preserving the original generative prior while expanding its controllable dynamic range.

Classical theories of cognition describe problem solving as exploratory search through structured problem spaces in which repeated interaction gradually compresses search into efficient representational structures. Predictive artificial intelligence systems introduce a distinct regime in which stabilization may occur before exploratory diversification unfolds, supplying solutions and decision trajectories prior to internally generated search. This paper develops a geometric dynamical framework in which attention evolves over a landscape of strategies shaped by stabilizing drift, endogenous exploratory perturbation, and responsiveness-gated learning. Predictive assistance is modeled as a process of exogenous exploratory compression that stabilizes trajectories before self-generated exploration broadens the accessible regions of strategy space. The framework yields three main results. First, sustained predictive stabilization reduces exploratory responsiveness by attenuating the effective influence of intrinsic perturbations even when exploratory variability remains present. Second, curvature accumulates and relaxes asymmetrically, producing hysteresis and delayed recovery of exploratory mobility after assistance withdrawal. Third, developmental outcomes depend critically on the timing of stabilization, with early intervention narrowing future exploratory traversal before broad representational diversification has occurred. The framework generates empirically testable predictions concerning exploratory entropy, premature convergence, and delayed recovery following predictive stabilization. More broadly, the results suggest that predictive systems may reshape the geometry of exploratory cognition itself.

Modeling interacting dynamical systems requires capturing spatial interactions alongside long-range temporal dependencies. Graph neural networks (GNNs) provide a natural representation but typically rely on autoregressive rollouts and treat spatial and temporal dynamics separately, leading to error accumulation over long horizons. Existing approaches also focus on local interactions and short temporal contexts, limiting their ability to capture multi-hop dependencies and global structure. We introduce the Graph Mamba Operator (GraMO), a latent-space simulator that integrates state-space models with graph-based interaction learning. In contrast to prior work that sequences nodes or applies spatial and temporal updates in separate stages, GraMO couples graph-based interactions and temporal state updates within a single recurrence. The update is linear in the latent state, with input-dependent coefficients that adapt across regimes. We evaluate GraMO on N-body systems, motion capture, and robotics datasets, achieving the lowest error across benchmarks and the largest gains in long-horizon prediction.

Glaucoma is a leading cause of irreversible blindness worldwide, and early detection from fundus images is critical for effective disease management. While deep learning has achieved promising performance in fundus image analysis, most existing methods rely on single time-point images and fail to capture longitudinal structural and vascular changes associated with disease progression. Sequential fundus images acquired during clinical follow-up provide valuable temporal information; however, current sequential models often struggle to detect subtle early progression signals and commonly depend on fixed-length inputs or diagnostic cues from already glaucomatous images, limiting their clinical utility for early prediction. To address these limitations, we propose DiffSight-Former, a framework for glaucoma progression prediction from sequential fundus images. It incorporates a time-variant feature extraction module based on a fundus-specific foundation model to obtain robust anatomical representations. A multi-structure difference modeling module is introduced to quantify progression-related changes in the optic disc/cup region and retinal vasculature. These representations are integrated with temporal interval embeddings and processed by a time-aware Transformer to model disease progression and estimate the probability of future glaucoma onset. Experiments were conducted on two longitudinal datasets, SIGF (405 sequences) and GRAPE (263 sequences). On SIGF, DiffSight-Former achieved an AUC of 91.54% and a sensitivity of 92.16% for progression prediction. On GRAPE, it achieved an average accuracy of 87.48% across three clinical visual-field progression criteria. Compared with existing approaches, DiffSight-Former demonstrates strong performance and robustness across different temporal settings, highlighting its potential for longitudinal glaucoma monitoring and early risk prediction.

Dynamic origin-destination (OD) flow generation seeks to synthesize realistic mobility dynamics from temporal context alone, without relying on historical OD observations. A key challenge is to translate semantic temporal signals into temporally coherent OD patterns while preserving the inherent spatial heterogeneity of urban regions. We propose DynaOD, a semantic-driven framework that models temporal dynamics through two complementary perspectives: discrete directional trends that characterize qualitative shifts in urban activity patterns, and continuous temporal evolution that captures how such shifts unfold over time. By jointly encoding these temporal semantics, the framework constructs time-varying region representations that condition pretrained static OD generators in a lightweight and plug-and-play fashion. This modular design further supports scalable deployment and cross-city transferability. Extensive experiments on large-scale real-world datasets show that our method consistently outperforms representative baselines in both predictive accuracy and distributional fidelity. Code is publicly available at https://github.com/csjiezhao/DynaOD.

Multi-Modality Spatio-Temporal Forecasting (MoSTF) extends traditional spatio-temporal forecasting by incorporating diverse traffic modalities. Despite significant recent strides in spatio-temporal modeling, existing approaches often fail to explicitly model the coupling relationships between different modality variables. Accurate MoSTF is challenging, as it requires modeling (1) temporal dynamic heterogeneity under exogenous influences and (2) heterogeneous spatial dependencies alongside complex cross-variable couplings. To address these challenges, we propose the Dual-Domain Spectral Filtering Network (DSFNet). Our framework employs dual-domain spectral filtering to capture heterogeneous spatial patterns and explicitly model the relationships between variables. Unlike graph-based message passing or dense attention over node-modality pairs, DSFNet factorizes space-modality interactions into feature-domain and spatial-domain spectral operators, enabling scalable modeling of nonlocal dependencies and cross-modality couplings. Furthermore, we introduce an external gating mechanism to adaptively regulate temporal dynamics under external influences. We validate our method through extensive experiments on five representative real-world traffic datasets. Compared with the second-best baselines, DSFNet reduces MAE by 3.21%-10.16% across these datasets. The results demonstrate that DSFNet significantly outperforms existing state-of-the-art baselines in accuracy while exhibiting efficiency and robustness.

Customer churn prediction is a central task in customer analytics, particularly in non-contractual, pay-per-use service environments where disengagement is not explicitly observed and must be inferred from behavioral inactivity. Existing churn prediction approaches often rely on simplified temporal assumptions or single-point representations of customer behavior, which limit their ability to support continuous risk assessment, interpretability, and realistic deployment over time. This study proposes a temporally explicit churn prediction framework that models customer behavior using rolling behavioral windows, enabling repeated and instance-level churn risk estimation as customer activity evolves. Customer behavior is summarized within a fixed 30-day observation window, followed by a 30-day future churn evaluation window, ensuring a clear temporal separation between behavioral evidence and churn outcomes. The framework integrates feature-based and sequence-based learning approaches within a unified temporal design. The proposed approach is evaluated on a large-scale, real-world dataset from a non-contractual service platform. Empirical results demonstrate strong and stable predictive performance, with accuracy reaching 87.6% and ROC-AUC of 0.94 for the feature-based model, while the sequence-based model achieves recall as high as 96.1% by capturing temporal disengagement patterns. Evaluation on future unseen data confirms meaningful robustness under temporal shift, with accuracy remaining above 83% and ROC-AUC exceeding 0.91 without model retraining. Overall, the findings highlight that carefully designed temporal framing, rather than model complexity alone, is critical for achieving robust, interpretable, and deployment-ready churn prediction. The study provides a practical foundation for churn-oriented decision support in dynamic service environments.

Long-term time series forecasting benefits from inductive biases that expose recurring temporal structure. Existing periodic forecasting methods typically model recurrence through predefined periods, global spectral components, or fixed learnable templates. However, real-world temporal dynamics are rarely rigidly periodic: around a nominal cycle, oscillatory behavior often exhibits \emph{non-rigid periodicity} (NRP), where cycle magnitude, cycle alignment, and local cycle duration vary over time. Under these conditions, fixed-template periodic modeling can become fundamentally mismatched to the underlying temporal states. We propose AOSNet, a Hilbert-guided forecasting framework that reformulates periodic forecasting from fixed template matching to adaptive oscillatory-state alignment. AOSNet extracts analytic-signal descriptors from both the observed sequence and a learnable global oscillatory prior, then adaptively aligns local states through a descriptor-conditioned gate that selectively preserves reliable observations while softly correcting mismatched regions. The learned prior serves not as a rigid repeated template but as a flexible oscillatory reference interpreted through local state dynamics. Experiments on eight public benchmarks and two cloud workload traces demonstrate leading or highly competitive accuracy with a compact model size and low inference latency, supporting repeated forecasting settings such as capacity planning and autoscaling. Controlled synthetic studies that isolate cycle-magnitude and cycle-alignment variation and combine them with cycle-duration changes show that the advantage of oscillatory-state alignment increases as NRP intensifies.

Time series are often embedded in rich contexts that are essential for holistic modeling. Moreover, real-world practitioners often require end-to-end workflows for analyzing temporal dynamics, where widely studied tasks such as forecasting are only one step in a broader solution loop. While generalist AI agents offer a promising interface for such workflows under complex contexts, they still operate primarily in textual spaces that are not fully aligned with structured temporal signals. In this work, we introduce TimeClaw, an agentic harness framework for time series that equips generalist LLM agents with the time series-native runtime support needed for contextualized temporal reasoning. TimeClaw integrates executable temporal tools for grounded and auditable analysis, experience-driven capability evolution for creating reusable analytical routines, and episodic multimodal memory for retrieving relevant reasoning traces. Together, these components unlock harnessed open-ended temporal reasoning with contextual information. Extensive evaluation on multiple benchmarks covering diverse tasks across energy, finance, weather, traffic, and other real-world domains demonstrates improved performance of TimeClaw. Code is available at https://github.com/iDEA-iSAIL-Lab-UIUC/TimeClaw.

Modeling temporal evolution is important to analyzing and reasoning about scientific phenomena, yet most machine learning methods provide deterministic forward predictions that overlook multiple plausible outcomes and rarely support backward reasoning, limiting their usefulness in practical scientific workflows. We present a framework that integrates diffusion-based generative modeling with interactive visual analytics for scientific exploration. We introduce DiffUNet^2, a conditional diffusion model that enables bidirectional, any-to-any generation across time and captures distributions of plausible system evolutions. Built upon the model, our interactive system supports branching timeline exploration, user-guided state editing, and probability-space navigation, enabling scientists to actively explore alternative hypotheses rather than passively observe predictions. We evaluate the model on 5 datasets across different scientific domains to validate its predictive accuracy and probability-space ensemble quality. In collaboration with domain experts, we demonstrate the effectiveness of our approach in supporting practical scientific temporal data analysis workflows. By integrating modeling and visual interaction, our approach enables scientists to interactively explore system dynamics, transforming generative models into tools for hypothesis-driven scientific analysis.

Multivariate time series forecasting plays a critical role in real-world applications, including weather prediction, stock analysis, and health monitoring. Due to the diversity of data sources, time series exhibit diverse temporal dynamics, often accompanied by various irregularities such as missing values and non-uniform sampling frequencies. Such irregularities lead to complex and asynchronous temporal dependencies across channels. Thus, a single model with a fixed patching scheme often fails to adapt well to diverse multivariate time series, hindering accurate forecasting. In this paper, we propose TiWeaver, a unified framework designed to handle temporal dynamics and fine-grained inter-channel dependencies adaptively. Specifically, we introduce a Graph-Guided Adaptive Tokenizer (G$^2$AT) that divides time series into high contextually coherent patches by jointly considering temporal density and representation consistency. In addition, we propose a Fine-grained Asynchronous Dependency Extractor (FADE), which is designed to model fine-grained asynchronous inter-channel dependencies while incorporating long-term historical dependencies. We evaluate TiWeaver on 12 real-world time series datasets, where it achieves state-of-the-art performance, outperforming existing methods up to 25%. These results demonstrate its robustness and effectiveness across diverse domains and data characteristics.

Biological foundation models have shown strong performance in single-cell representation learning by applying transformer architectures directly to gene-expression matrices. However, these approaches predominantly operate in static settings and do not explicitly model the temporal evolution of developmental programs in the cell. Modeling such dynamics is important for understanding how cellular states progressively emerge, differentiate, and reorganize during development or disease progression. In this work-in-progress paper, we investigate an alternative temporal graph-based perspective in which cellular states are represented through pseudotime-resolved gene regulatory networks and modeled as evolving graph structures over persistent gene identities. Starting from single-cell transcriptomic data, we infer pseudotime trajectories, discretize cells into developmental snapshots, reconstruct one gene regulatory network per snapshot, and apply temporal graph neural networks to forecast biological states. We evaluate this framework on two publicly available mouse developmental datasets, erythroid gastrulation and pancreatic endocrinogenesis, considering three complementary tasks: gene-expression forecasting, link prediction, and out-degree centrality prediction. Our results show that graph-based models outperform well-known foundation-model such as scGPT and scFoundation, suggesting that explicitly modeling evolving regulatory structure provides useful information beyond static pretrained representations. For link prediction and centrality forecasting, temporal graph learning captures non-trivial regulatory dynamics and enables the identification of temporally important gene hubs. Overall, our findings support temporal graph learning as a promising direction for modeling dynamic biological systems and as a complementary paradigm to current foundation model approaches in single-cell biology.

Irregular Multivariate Time Series (IMTS) are common in practice, yet their irregular sampling complicates effective modeling. Existing approaches typically either (i) design specialized architectures that limit the reuse of proven Multivariate Time Series (MTS) models, or (ii) map IMTS onto regular temporal grids through interpolation, which may distort temporal dynamics by introducing artificial values. To address these limitations, we propose a new input-embedding-based approach. We identify that the key bottleneck lies not in the backbone architecture, but in conventional embedding layers that assume uniform sampling. In this work, we introduce QuITE (Query-Based Irregular Time Series Embedding), a simple yet effective plug-and-play embedding module for IMTS. QuITE employs learnable query tokens to aggregate irregular observations through a single self-attention layer, directly producing backbone-compatible latent representations without artificial value generation or architectural modification. Extensive experiments on real-world benchmarks show that QuITE consistently improves MTS models, yielding average relative gains of up to $54.7\%$ in forecasting and $15.8\%$ in classification across diverse datasets and backbone architectures. Code is available at: https://github.com/Meaningfull9502/QuITE.

Predicting how a cell will change its transcriptional state under a developmental signal or a genetic perturbation is the computational core of in-silico biology and the AI Virtual Cell program. Existing approaches either fit static control-to-treated maps that discard time, or solve multi-step ODE / Schrödinger-bridge problems on each dataset independently. We introduce Chreode, a one-step cell world model that predicts action-conditioned cell-state transitions through a structured residual transition operator. It shifts distributional evolution from inference time to training time, enabling single-pass generation while preserving a Waddington-inspired decomposition into downhill landscape flow, rotational in-tangent dynamics, and stochastic spread. The model is pretrained with a shared scVI encoder and a DiT-based dynamics backbone on a 2.4M-cell mouse embryonic atlas spanning 7 datasets. As a fine-tuning initialization, Chreode improves per-target Sinkhorn distance on Weinreb hematopoiesis and Veres islet differentiation over matched scratch models, PI-SDE, and PRESCIENT. As a transferable gene-state embedding for GEARS, the pretrained dynamics representation reduces shared-vocabulary DE20 mean squared error on Norman Perturb-seq from 0.2121 to 0.1858, a 12.4% relative improvement, without changing the GEARS training procedure. We interpret this transfer to perturbation prediction as evidence that pretrained developmental-trajectory dynamics encode differentiation primitives transferable to CRISPR-induced state shifts, since both involve cell-state transitions in a shared latent geometry. The pretrained backbone additionally produces zero-shot clonal fate scores on Weinreb that are competitive with strong dynamic-OT baselines.

Existing precipitation nowcasting methods typically adopt an autoregressive formulation, where future states are predicted from previous outputs. However, such an approach accumulates errors over long rollouts, causing forecasts to drift away from physically plausible evolution trajectories. Although various studies have attempted to alleviate this problem by improving step-wise prediction accuracy, they largely neglect the global temporal evolution of meteorological systems and lack mechanisms to actively correct drift during rollouts. To address this issue, we propose McCast, a memory-guided latent drift correction method for precipitation nowcasting. Rather than treating memory as an unordered dictionary of latent states for passive conditioning, McCast leverages temporally organized memory to actively correct autoregressive latent evolution. Specifically, McCast introduces a Drift-Corrective Memory Bank (DCBank) that explicitly estimates the temporally consistent drift corrections to calibrate the divergent trajectory. DCBank performs drift correction in two stages: a Corrective Latent Extractor first predicts an initial correction from the current prediction and a reference latent state, and a Correction-Aware Memory Retrieval module then refines the initial correction using temporally organized historical memory. By explicitly correcting latent evolution, instead of improving step-wise prediction accuracy only, McCast produces more temporally coherent and reliable long-horizon forecasts. Experiments on two widely used benchmarks, SEVIR and MeteoNet, show that McCast achieves state-of-the-art performance, particularly in challenging long-horizon forecasting scenarios.

Task completion in digital and physical environments increasingly involves complex temporal interaction, where actions and observations unfold over different time scales rather than align with fixed observation--action steps. To model such interactions, we propose \emph{Engagement Process} (EP), an interaction formalism that inherits the decision-theoretic structure of POMDPs while making time explicit in the action--observation interface. EP represents actions and observations as decoupled event streams along time, rather than updates paired at fixed decision steps. This interface captures single-agent timing issues such as deliberation latency, delayed feedback, and persistent actions, while supporting richer agent-side organization, multi-rate coordination, and compositional interaction among subsystems. Across toy, LLM-agent, and learning experiments, EP exposes temporal behaviors hidden by step-based interfaces and enables policies to adapt under explicit time costs.

Vision-Language-Action (VLA) models achieve remarkable flexibility and generalization beyond classical control paradigms. However, most prevailing VLAs are trained under a single-frame observation paradigm, which leaves them structurally blind to temporal dynamics. Consequently, these models degrade severely in non-stationary scenarios, even when trained or finetuned on dynamic datasets. Existing approaches either require expensive retraining or suffer from latency bottlenecks and poor temporal consistency across action chunks. We propose Pace-and-Path Correction, a training-free, closed-form inference-time operator that wraps any chunked-action VLA. From a single quadratic cost, joint minimization yields a unified solution that decomposes orthogonally into two distinct channels. The pace channel compresses execution along the planned direction, while the path channel applies an orthogonal spatial offset, jointly absorbing the perceived dynamics within the chunk window. We evaluate our approach on a comprehensive diagnostic benchmark MoveBench designed to isolate motion as the sole controlled variable. Empirical results demonstrate that our framework consistently outperforms state-of-the-art training-free wrappers and dynamic-adaptive methods and improves success rates by up to 28.8% and 25.9% in absolute terms over foundational VLA models in dynamic-only and static-dynamic mixed environments, respectively.

Adaptive behavior requires the brain to transition between distinct contexts while maintaining representations of prior experience. The ability to reconfigure neural representations without erasing previously acquired knowledge is central to learning in dynamic environments, yet the neural mechanisms that support this balance remain unclear. Understanding these mechanisms is also critical for addressing catastrophic forgetting in artificial systems designed for lifelong learning. Here, we identify joint sparse coding and temporal dynamics in both the mouse medial prefrontal cortex (mPFC) and computational networks as mechanisms that help preserve prior representations during context transitions. Specifically, sparsity in context-dependent representations reduces cross-context interference, whereas temporal dynamics within the network activity further enhance context separability across time. Strikingly, networks endowed with both properties, such as spiking neural networks, exhibit improved retention during lifelong learning without auxiliary heuristics. These findings establish joint sparse coding and temporal dynamics as a core mechanism supporting flexible context reconfiguration in lifelong learning and, through their activity constraining nature, as an energy-efficient architectural principle for stable adaptation. Together, they provide a mechanistic framework for understanding how the brain preserves prior knowledge while flexibly adapting to new contexts.

Biosignals acquired from different locations on the body often provide temporally ordered views of the same underlying physiological process. However, most existing self supervised learning methods treat these signals as interchangeable views, overlooking the directional temporal dynamics that link them. A canonical example is the relationship between electrocardiography (ECG), which captures the electrical activation initiating each heartbeat, and photoplethysmography (PPG), which records the resulting peripheral pulse delayed by vascular dynamics. To capture this structured relationship, we introduce xMAE, a biosignal pretraining framework that leverages masked cross modal reconstruction across temporally ordered biosignals as a training time constraint to encourage physiologically meaningful timing structure in the learned representations. We show that pretraining with xMAE yields representations that outperform both unimodal and multimodal baselines on 15 of 19 downstream tasks, including cardiovascular outcome prediction, abnormal laboratory test detection, sleep staging, and demographic inference, while generalizing across devices, body locations, and acquisition settings. Further analysis suggests that the ECG PPG timing structure is reflected in the learned PPG representations. More broadly, xMAE demonstrates the effectiveness of incorporating temporal structure into multimodal pretraining when signals observe different stages of a shared underlying process. Code is available at https://github.com/hzhou3/xMAE.

Time-series data augmentation plays a crucial role in regression-oriented forecasting tasks, where limited data restricts the performance of deep learning models. While Generative Adversarial Networks (GANs) have shown promise in synthetic time-series generation, existing approaches primarily focus on matching marginal data distributions and often overlook the temporal dynamics that naturally exist in the original multivariate time series. When generating multivariate time series, this mismatch leads to distribution shift and temporal drift, thereby degrading the fidelity of the synthetic sequences. In this work, we propose a model-agnostic Markov Chain Monte Carlo (MCMC)-based framework to mitigate distribution shift and preserve temporal dynamics in synthetic time series. We provide a theoretical analysis of how conditional generative models accumulate deviations under sequential generation and demonstrate that the MCMC algorithm can correct these discrepancies by enforcing consistency with empirical transition statistics between neighboring time points. Extensive experiments on the Lorenz, Licor, ETTh, and ILI datasets using RCGAN, GCWGAN, TimeGAN, SigCWGAN, and AECGAN demonstrate that the proposed MCMC framework consistently improves autocorrelation alignment, skewness error, kurtosis error, R$^2$, discriminative score, and predictive score. These results suggest that synthetic time series consistent with the original data require explicit preservation of transition laws rather than solely relying on adversarial distribution matching, thereby offering a principled direction for improving generative modeling of time-series data.

Sensor-based Human Activity Recognition (HAR) has attracted increasing attention in medical and healthcare monitoring, particularly with the growth of Internet of Medical Things (IoMT). However, in real-world wearable sensing scenarios, IoMT signals are often corrupted by missing measurements, sensor failures, and environmental noise, which significantly degrade the performance of conventional deep learning models that assume clean and complete inputs. To address this challenge, we propose a Manifold-Consistent Spatio-Temporal Network (MCSTN) for robust HAR under imperfect sensing conditions. The proposed framework introduces a dual-level corruption modeling mechanism that simulates realistic sensor imperfections through both physical-level corruption and diffusion-driven continuous corruption. By enforcing representation consistency across multiple corrupted views, the model learns stable and corruption-invariant semantic representations. Furthermore, we design a dual-stream spatio-temporal architecture that explicitly decouples temporal dynamics modeling and spatial correlation learning. The temporal stream captures long-term activity dynamics, while the spatial stream models inter-sensor relationships, enabling more effective spatio-temporal representation learning. Extensive experiments on three widely used HAR benchmark datasets, PAMAP2, Opportunity, and WISDM, demonstrate that the proposed MCSTN achieves competitive performance compared with existing state-of-the-art methods, particularly under imperfect sensing conditions. These results validate the effectiveness and robustness of the proposed framework for real-world wearable IoMT sensing applications.

There is growing concern that AI chatbots might fuel delusional beliefs in users. Some have suggested that humans and chatbots mutually reinforce false beliefs over time, but quantitative evidence is lacking. Using a unique dataset of chat logs from individuals who exhibited delusional thinking, we developed a latent state model that captures accumulating and decaying influences between humans and chatbots. We find that a bidirectional influence model substantially outperforms a unidirectional alternative where humans are the primary driver of delusion. We find that humans exert strong but short-lived influence on chatbots, whereas chatbots exert longer-lasting influence on humans. Moreover, chatbots exert strong, stable self-influence over their own future outputs that tends to perpetuate delusions over long stretches of conversation. In fact, this chatbot self-influence constituted the dominant pathway when considering accumulated influence over time. Overall, these results indicate that humans tend to drive sharp, immediate increases in delusion, whereas chatbots sustain and propagate these effects over longer timescales. Together, these findings provide the first quantitative evidence that human-chatbot interactions can form feedback loops of delusion, decomposable into distinct pathways with dissociable temporal dynamics. By doing so, they can inform the development of safer AI systems.

Standard reinforcement learning (RL) optimizes policies for reward but imposes few constraints on how decisions evolve over time. As a result, policies may achieve high performance while exhibiting temporally incoherent behavior such as abrupt confidence shifts, oscillations, or degenerate inactivity. We introduce Dynamical Prior Reinforcement Learning (DP-RL), a training framework that augments policy gradient learning with an auxiliary loss derived from external state dynamics that implement evidence accumulation and hysteresis. Without modifying the reward, environment, or policy architecture, this prior shapes the temporal evolution of action probabilities during learning. Across three minimal environments, we show that dynamical priors systematically alter decision trajectories in task-dependent ways, promoting temporally structured behavior that cannot be explained by generic smoothing. These results demonstrate that training objectives alone can control the temporal geometry of decision-making in RL agents.

Experimental evidence indicates that intrinsic temporal dynamics operating across multiple time scales are closely associated with the emergence of periodic spatial activity of increasing complexity. However, how information encoded in grid-like firing patterns for path integration is processed across these intrinsic time scales remains unclear. To address this question, we introduce adaptive time scales through a leak term in recurrent neural networks (RNNs), forming leaky RNNs discretized from the continuous attractors of firing rate models. Our results demonstrate that leaky RNNs substantially enhance the emergence of well-defined and highly regular hexagonal firing patterns. Compared with vanilla RNNs lacking a leak term, the trained leaky RNNs produce more accurate position estimates while generating reliable grid-cell-like representations. Furthermore, under identical noise conditions, leaky RNNs consistently exhibit more stable dynamics and better-defined grid structures. The learned dynamics also give rise to stable torus attractors with a clear central hole, supporting robust and regular grid-like activity. Overall, the dynamic leak acts as a low-pass filtering mechanism that protects recurrent neural circuitry from noise, stabilizes network dynamics, and improves path-integration accuracy in recurrent neural networks.

Edge classification on directed dynamic graphs requires modeling interactions between source and destination nodes exhibiting asymmetrical behavioral patterns and temporal dynamics. However, existing dynamic graph architectures largely rely on shared parameters for processing source and destination nodes, with limited or no systematic role-aware modeling. We propose DyGnROLE (Dynamic Graph Node-Role-Oriented Latent Encoding), a Transformer-based architecture that disentangles source and destination representations. By using separate embedding tables and role-semantic positional encodings, the model captures the distinct structural and temporal contexts unique to each role. Critical in limited-label settings, which are common in edge classification, is a self-supervised pretraining objective we introduce: Directional Role Alignment (DRA). DRA learns distinct but aligned source and destination embedding spaces by training source representations to retrieve their corresponding destination representations while a historical positive masking strategy excludes previously observed interactions from future negative comparisons. The masks introduce a temporally directional training signal in which node pairs progress monotonically from unseen to observed, after which the relationship is eligible only for further alignment. A comprehensive evaluation on four edge classification tasks across eight datasets demonstrates that DyGnROLE consistently outperforms a wide range of state-of-the-art baselines, highlighting the importance of role-aware representation learning and asymmetric pretraining for modeling complex directed interactions when labeled data is limited.

Time series generation (TSG) is widely used across domains, yet most existing methods assume regular sampling and fixed output resolutions. These assumptions are often violated in practice, where observations are irregular and sparse, while downstream applications require continuous and high-resolution TS. Although Neural Controlled Differential Equation (NCDE) is promising for modeling irregular TS, it is constrained by a single dynamics function, tightly coupled optimization, and limited ability to adapt learned dynamics to newly generated samples from the generative model. We propose Diff-MN, a continuous TSG framework that enhances NCDE with a Mixture-of-Experts (MoE) dynamics function and a decoupled architectural design for dynamics-focused training. To further enable NCDE to generalize to newly generated samples, Diff-MN employs a diffusion model to parameterize the NCDE temporal dynamics parameters (MoE weights), i.e., jointly learn the distribution of TS data and MoE weights. This design allows sample-specific NCDE parameters to be generated for continuous TS generation. Experiments on ten public and synthetic datasets demonstrate that Diff-MN consistently outperforms strong baselines on both irregular-to-regular and irregular-to-continuous TSG tasks. The code is available at the link https://github.com/microsoft/TimeCraft/tree/main/Diff-MN.

Despite the rapid progress of video generation models, the role of data in influencing motion is poorly understood. We present Motive (MOTIon attribution for Video gEneration), a motion-centric, gradient-based data attribution framework that scales to modern, large, high-quality video datasets and models. We use this to study which fine-tuning clips improve or degrade temporal dynamics. Motive isolates temporal dynamics from static appearance via motion-weighted loss masks, yielding efficient and scalable motion-specific influence computation. On text-to-video models, Motive identifies clips that strongly affect motion and guides data curation that improves temporal consistency and physical plausibility. With Motive-selected high-influence data, our method improves both motion smoothness and dynamic degree on VBench, achieving a 74.1% human preference win rate compared with the pretrained base model. To our knowledge, this is the first framework to attribute motion rather than visual appearance in video generative models and to use it to curate fine-tuning data.

Time series extrinsic regression (TSER) refers to the task of predicting a continuous target variable from an input time series. It appears in many domains, including healthcare, finance, environmental monitoring, and engineering. In these settings, accurate predictions and trustworthy reasoning are both essential. Although state-of-the-art TSER models achieve strong predictive performance, they typically operate as black boxes, making it difficult to understand which temporal patterns drive their decisions. Post-hoc interpretability techniques, such as feature attribution, aim to to explain how the model arrives at its predictions, but often produce coarse, noisy, or unstable explanations. Recently, inherently interpretable approaches based on concepts, additive decompositions, or symbolic regression, have emerged as promising alternatives. However, these approaches remain limited: they require explicit supervision on the concepts themselves, often cannot capture interactions between time-series features, lack expressiveness for complex temporal patterns, and struggle to scale to high-dimensional multivariate data. To address these limitations, we propose MAGNETS (Mask-and-AGgregate NEtwork for Time Series), an inherently interpretable neural architecture for TSER. MAGNETS learns a compact set of human-understandable concepts without requiring any annotations. Each concept corresponds to a learned, mask-based aggregation over selected input features, explicitly revealing both which features drive predictions and when they matter in the sequence. Predictions are formed as combinations of these learned concepts through a transparent, additive structure, enabling clear insight into the model's decision process. The code implementation and datasets are publicly available at https://github.com/FlorentF9/MAGNETS.