ICLR 2026 Papers

The orienteering problem with time windows and variable profits (OPTWVP) is common in many real-world applications and involves continuous time variables. Current approaches fail to develop an efficient solver for this orienteering problem variant with discrete and continuous variables. In this paper, we propose a learning-based two-stage DEcoupled discrete-Continuous optimization with Service-time-guided Trajectory (DeCoST), which aims to effectively decouple the discrete and continuous decision variables in the OPTWVP problem, while enabling efficient and learnable coordination between them. In the first stage, a parallel decoding structure is employed to predict the path and the initial service time allocation. The second stage optimizes the service times through a linear programming (LP) formulation and provides a long-horizon learning of structure estimation. We rigorously prove the global optimality of the second-stage solution. Experiments on OPTWVP instances demonstrate that DeCoST outperforms both state-of-the-art constructive solvers and the latest meta-heuristic algorithms in terms of solution quality and computational efficiency, achieving up to 6.6x inference speedup on instances with fewer than 500 nodes. Moreover, the proposed framework is compatible with various constructive solvers and consistently enhances the solution quality for OPTWVP.

Learning instantaneous and time-lagged causal relationships from time-series data is essential for uncovering fine-grained, temporally-aware interactions. Although this problem has been formulated as a continuous optimization task amenable to modern machine learning methods, existing approaches largely neglect the use of coarse-grained, lag-agnostic causal priors, an important form of prior knowledge that is often available in practice. To address this gap, we propose a novel framework for structure learning from time series to integrate lag-agnostic priors, enabling the discovery of lag-specific causal links without requiring precise temporal annotations. We introduce formulations to precisely characterize the lag-agnostic prior, and demonstrate their consequential and process-equivalence to priors, maintaining consistency with the intended semantics of the priors throughout optimization. We further analyze the challenge for optimization due to the increased non-convexity by lag-agnostic prior constraints, and introduce a data-driven initialization to mitigate this issue. Experiments on both synthetic and real-world datasets show that our method effectively incorporates lag-agnostic prior knowledge to enhance the recovery of fine-grained, lag-aware structures.

Neural network models with latent recurrent processing, where identical layers are recursively applied to the latent state, have gained attention as promising models for performing reasoning tasks. A strength of such models is that they enable test-time scaling, where the models can enhance their performance in the test phase without additional training. Models such as the Hierarchical Reasoning Model (HRM) and Artificial Kuramoto Oscillatory Neurons (AKOrN) can facilitate deeper reasoning by increasing the number of recurrent steps, thereby enabling the completion of challenging tasks, including Sudoku, Maze solving, and AGI benchmarks. In this work, we introduce confidence-based voting (C-voting), a test-time scaling strategy designed for recurrent models with multiple latent candidate trajectories. Initializing the latent state with multiple candidates using random variables, C-voting selects the one maximizing the average of top-1 probabilities of the predictions, reflecting the model’s confidence. Additionally, it yields $4.9\\%$ higher accuracy on Sudoku-hard than the energy-based voting strategy, which is specific to models with explicit energy functions. An essential advantage of C‑voting is its applicability: it can be applied to recurrent models without requiring an explicit energy function. Finally, we introduce a simple attention-based recurrent model with randomized initial values named ItrSA++, and demonstrate that when combined with C-voting, it outperforms HRM on Sudoku-extreme ($95.2\\%$ vs. $55.0\\%$) and Maze ($78.6\\%$ vs. $74.5\\%$) tasks.

Score-based generative modeling through differential equations has driven breakthroughs in high-fidelity image synthesis, offering modular model design and efficient sampling. However, this success has not been widely translated to timeseries forecasting yet. This gap stems from the sequential nature of time series, in contrast to the unordered structure of images. Here, we extend the theoretical formulation used for images to explicitly address sequential structures. We propose a diffusion-based forecasting framework (TEDM) that adapts score estimation to temporal settings and elucidates its design space. Such a design allows empirical computation of noise and signal scaling directly from data, avoiding external schedules. Notably, this reduces sampling complexity to linear in the forecast horizon. Without elaborate preprocessing, TEDM sets new state-of-the-art results on multiple forecasting benchmarks. These results illustrate the growing potential of diffusion models beyond vision. TEDM generates low-latency forecasts using a lightweight architecture, making it ideal for real-time deployment.

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.

We introduce a training-efficient framework for time-series learning that combines random features with controlled differential equations (CDEs). In this approach, large randomly parameterized CDEs act as continuous-time reservoirs, mapping input paths to rich representations. Only a linear readout layer is trained, resulting in fast, scalable models with strong inductive bias. Building on this foundation, we propose two variants: (i) Random Fourier CDEs (RF-CDEs): these lift the input signal using random Fourier features prior to the dynamics, providing a kernel-free approximation of RBF-enhanced sequence models; (ii) Random Rough DEs (R-RDEs): these operate directly on rough-path inputs via a log-ODE discretisation, using log-signatures to capture higher-order temporal interactions while remaining stable and efficient. We prove that in the infinite-width limit, these model induces the RBF-lifted signature kernel and the rough signature kernel, respectively, offering a unified perspective on random-feature reservoirs, continuous-time deep architectures, and path-signature theory. We evaluate both models across a range of time-series benchmarks, demonstrating competitive or state-of-the-art performance. These methods provide a practical alternative to explicit signature computations, retaining their inductive bias while benefiting from the efficiency of random features. Code is publicly available at: \url{https://anonymous.4open.science/r/RandomSigJax-C768/}

Aligning large language models with human preferences is critical for creating reliable and controllable AI systems. A human preference can be visualized as a high-dimensional vector where different directions represent trade-offs between desired attributes (e.g., helpfulness vs. verbosity). Yet, because the training data often reflects dominant, average preferences, LLMs tend to perform well on com- mon requests but falls short in specific, individual needs. This mismatch creates a preference coverage gap. Existing methods often address this through costly retraining, which may not be generalized to the full spectrum of diverse preferences. This brittleness means that when a user’s request reflects a nuanced preference deviating from the training data’s central tendency, model performance can degrade unpredictably. To address this challenge, we introduce Robust Preference Selection (RPS), a post-hoc, training-free method by leveraging directional neighborhood consensus. Instead of forcing a model to generate a response from a single, highly specific preference, RPS samples multiple responses from a local neighborhood of related preferences to create a superior candidate pool. It then selects the re- sponse that best aligns with the user’s original intent. We provide a theoretical framework showing that, under mild conditions where (i) nearby preference direc- tions correspond to better-trained regions of the model and (ii) the reward-model scores change smoothly with small angular changes in the preference vector, our neighborhood generation strategy yields a higher expected best score than a strong baseline that also samples multiple candidates. Comprehensive experiments across three distinct alignment paradigms (DPA, DPO, and SFT) demonstrate that RPS consistently improves robustness against this baseline, achieving win rates of up to 69% on challenging preferences from under-represented regions of the space without any model retraining. Our work presents a practical, theoretically-grounded solution for enhancing the reliability of preference-aligned models.

With the accelerated popularization of electric vehicles (EV), battery safety issues have become an important research focus. Data-driven battery fault diagnosis algorithms, built on real-world operational data, are critical methods for reducing safety risks. However, existing battery datasets have limitations such as insufficient scale, coarse-grained labels, and lack of coverage of real-world operating conditions, which seriously restrict the development of data-driven fault diagnosis algorithms. To address these issues, this paper introduces a large-scale benchmark dataset named CH-BatteryGen, which is, to the best of our knowledge, the first EV battery system fault diagnosis dataset based on real-world operating conditions. This dataset integrates real on-board operation data with mechanism-constrained generative modeling technology, balancing authenticity and scalability. It covers two mainstream battery chemistries, namely nickel-cobalt-manganese (NCM) lithium batteries and lithium iron phosphate (LFP) batteries, and involves charging, discharging, and operation data of 1000 electric vehicles. It provides four fault labels (normal, self-discharge, high-resistance, low-capacity) and three severity level annotations, supporting two benchmark tasks: fault classification and fault grading. Through systematic validation using traditional machine learning methods (random forest (RF), support vector machine (SVM)) and deep learning models (long short-term memory (LSTM), convolutional neural network (CNN)), the results show that the CNN model performs best in the fault classification task, achieving an F1-score of 0.9280 in the LFP discharging scenario; in the fault grading task, the F1-score reaches 0.8813. The CH-BatteryGen dataset has been open-sourced, aiming to provide a standardized evaluation platform for battery fault diagnosis algorithms, promote research development in this field, and contribute to the transformation of sustainable transportation systems.

Using a nearly-frozen pretrained model, the continual representation learning paradigm reframes parameter updates as a similarity-matching problem to mitigate catastrophic forgetting. However, directly leveraging pretrained features for downstream tasks often suffers from multicollinearity in the similarity-matching stage, and more advanced methods can be computationally prohibitive for real-time, low-latency applications. Inspired by the fly olfactory circuit, we propose Fly-CL, a bio-inspired framework compatible with a wide range of pretrained backbones. Fly-CL substantially reduces training time while achieving performance comparable to or exceeding that of current state-of-the-art methods. We theoretically show how Fly-CL progressively resolves multicollinearity, enabling more effective similarity matching with low time complexity. Extensive simulation experiments across diverse network architectures and data regimes validate Fly-CL’s effectiveness in addressing this challenge through a biologically inspired design.

Learning nonlinear dynamical models from data is central to control. Two fundamental challenges exist: (1) how to learn accurate models from limited data, and (2) how to ensure the learned models are suitable for control design of the nominal system. We address both by enforcing a critical \emph{a priori} property of the nominal system during learning: \emph{controllability}. Controllability guarantees the existence of control policies that can drive the learned model from any initial state to any desired state. From a modeling perspective, it captures key structural features of the nominal system, thereby improving data efficiency. For downstream control, it enables the use of modern techniques such as model predictive control (MPC). Our approach is based on controllability-preserving Koopman representation learning. Rather than learning dynamics directly in the nominal state space, we learn in a latent space where the system admits a linear representation. We prove that controllability of the learned latent model implies controllability in the nominal state space. To enforce this property, we introduce a novel canonical parameterization of the latent dynamics matrices. We further incorporate Gramian-based regularization to shape the degree of controllability, yielding well-conditioned models for control. Implemented as an end-to-end Neural ODE framework, our method learns models that are both predictive and controllable from limited data. Experiments on nonlinear benchmarks demonstrate accurate long-horizon prediction, reliable MPC performance, and substantially improved data efficiency.

Modeling the relationships among variables has become increasingly important, particularly in high-dimensional multivariate time series forecasting tasks. However, most existing methods primarily focus on capturing coarse-grained correlations between variables, overlooking a finer and more dynamic aspect: the variable interactions often manifest differently as time progresses. To address this limitation, we propose FACT, an Fine-grained Across-variable Convolution architecture for multivariate Time series forecasting that explicitly models fine-grained variable interactions from both the time and frequency domains. Technically, we introduce a depth-wise convolution block DConvBlock, which leverages a depth-wise convolution architecture with channel-specific kernels to model dynamic variable interactions at each granularity. To further enhance efficiency, we reconfigure the original one-dimensional variables into a two-dimensional space, reducing the variable distance and the required model layers. Then DConvBlock incorporates multi-dilated 2D convolutions with progressively increasing dilation rates, enabling the model to capture fine-grained and dynamic variable interactions while efficiently attaining a global reception field. Extensive experiments on twelve benchmark datasets demonstrate that FACT not only achieves state-of-the-art forecasting accuracy but also delivers substantial efficiency gains, significantly reducing both training time and memory consumption compared to attention mechanism. The code is available at https://anonymous.4open.science/r/FACT-MTSF.

Is bigger always better for time series foundation models? With the question in mind, we explore an alternative to training a single, large monolithic model: building a portfolio of smaller, pretrained forecasting models. By applying ensembling or model selection over these portfolios, we achieve competitive performance on large-scale benchmarks using much fewer parameters. We explore strategies for designing such portfolios and find that collections of specialist models consistently outperform portfolios of independently trained generalists. Remarkably, we demonstrate that post-training a base model is a compute-effective approach for creating sufficiently diverse specialists, and provide evidences that ensembling and model selection are more compute-efficient than test-time fine-tuning.

Wearable sensors provide abundant physiological time series observations, yet the resolution at which we should extract features for downstream tasks remain unclear. We hypothesize that temporal resolution is a fundamental axis of representation learning, with different clinical and behavioral outcomes relying on features at distinct scales. To test this resolution hypothesis, we introduce HiMAE (Hierarchical Masked Autoencoder), a self-supervised framework that combines masked autoencoding with a hierarchical convolutional encoder–decoder. HiMAE produces multi-resolution embeddings across its intermediate layers that enable systematic evaluation of which temporal scales carry predictive signal, transforming resolution from a hyperparameter into a probe for interpretability. Across classification and generative benchmarks, HiMAE consistently outperforms state-of-the-art foundation models that collapse scale, while being orders of magnitude smaller. Due to the convolution based design choices behind HiMAE, the model is also compact enough to run entirely on-device, achieving sub-millisecond inference on smartwatch-class CPUs for true edge inference. Together, these contributions position HiMAE as both an efficient self supervised learning method and a discovery tool for understanding how time resolution contributes to downstream task alignment.

We give a comprehensive theoretical analysis of transformers as time series pre- diction models, with a focus on MOIRAI (Woo et al., 2024). We study its ap- proximation and generalization capabilities. First, we demonstrate that there exist transformers that fit an autoregressive model on input univariate time series via gradient descent. We then analyze MOIRAI, one of the state-of-the-art multivariate time series prediction models capable of modeling arbitrary number of covariates. We prove that MOIRAI is capable of automatically fitting autoregressive models with an arbitrary number of covariates, offering insights into its design and em- pirical success. For generalization, we establish learning bounds for pretraining when the data satisfies Dobrushin’s condition. Experiments support our theoretical findings, highlighting the efficacy of using transformers for time series forecasting.

Test-time compute can be scaled both sequentially and in parallel. Sequential scaling involves lengthening the generation process, while parallel scaling involves verifying and selecting among multiple candidate outputs. Combining these two strategies has led to the most powerful AI systems, such as Grok 4 Heavy, GPT-5 Pro, and Gemini-2.5 Pro Deep Think. A key observation is that, in certain contexts (e.g., solving Sudoku puzzles), verifying responses can be substantially easier than generating them. This property, referred to as \emph{asymmetric verification}, highlights the strong potential of test-time scaling. In this work, we study both sequential and parallel test-time scaling of deep search agents, motivated by the intuition that verification in this setting is often much easier than generation. In experiments, we first show that sequential scaling methods, such as budget forcing, can be effective initially but eventually degrade performance when over-applied in agentic search. Due to asymmetric verification, however, we are able to achieve substantial improvements by allocating only a modest amount of compute to the verifier. We conduct experiments with flagship open-source models, including GLM-4.5, K2, Qwen3-2507 and Tongyi-DeepResearch, and extend them to their ``Heavy'' variants through test-time scaling. These deep research agents achieve improvements of up to 20 absolute points on benchmarks such as BrowseComp. Remarkably, as an open-source alternative, GLM-4.5 Heavy reaches accuracy of {\bf 54.0\%} on BrowseComp, {\bf 66.0\%} on GAIA, and {\bf 68.0\%} on xbench-DeepSearch, placing it on par with the best proprietary choices such as OpenAI Deep Research and o3. Tongyi-DeepResearch Heavy pushes performance even further, attaining {\bf 69.0\%} accuracy on BrowseComp.

Dynamic Time Warping (DTW) is a classical method for measuring similarity between time series, but its non-differentiability hinders integration into end-to-end learning frameworks. To address this, soft-DTW replaces the minimum operator with a smooth soft-min, enabling differentiability and efficient computation. Motivated by soft-DTW, we propose perturbed-DTW, a differentiable framework of DTW obtained by adding random perturbations to warping costs and taking the expected minimum. Under Gumbel noise, perturbed-DTW exactly recovers soft-DTW, providing a natural probabilistic interpretation of soft-DTW. We further generalize this framework by extending the Gumbel noise to the broader family of generalized extreme value (GEV) distributions, leading to a new class of soft-DTW variants. Building on this insight, we introduce nested-soft-DTW (ns-DTW), which integrates GEV perturbations into the dynamic programming formulation of perturbed-DTW. This extension induces alignments with tunable skewness, offering greater flexibility in modeling diverse alignment structures. We validate ns-DTW on barycenter computation, clustering, and classification, demonstrating its effectiveness over existing approaches.

Designing efficient and effective architectural backbones has been in the core of research efforts to enhance the capability of foundation models. Inspired by the human cognitive phenomenon of attentional bias—the natural tendency to prioritize certain events or stimuli—we reconceptualize neural architectures, including Transformers, Titans, and modern linear recurrent neural networks as associative memory modules with attentional bias. We define and formalize the concept of attentional bias as the internal memory objective deep learning architectures. We show that existing deep learning architectures leverage the same attentional bias based on $L_2$ loss function. Going beyond $L_2$ loss function, we present a set of alternative attentional bias configurations along with their effective approximations. We then reinterpret forgetting mechanisms in modern deep learning architectures as a form of retention regularization. Building upon these insights, we present Miras, a general framework to design deep learning architectures based on the choice of attentional bias objective, retention gate, associative memory architecture, and memory learning algorithm. Our experiments show different designs yield models with varying strengths. Furthermore, our special instances of Miras achieve exceptional performance in language modeling, commonsense reasoning, recall intensive, and time series tasks, outperforming Transformers and other modern linear recurrent models.

Traffic systems are inherently multi-scale: microscopic vehicle interactions and macroscopic flow co-evolve nonlinearly. Microscopic models capture local interactions but miss flow evolution; macroscopic models enforce aggregated consistency yet overlook stochastic vehicle-level dynamics. We propose Micro–Macro Coupled Koopman Modeling (MMCKM), which lifts the coupled dynamics to a high-dimensional linear observation space for a unified linear-operator representation. Unlike grid-based discretizations, MMCKM adopts a vehicle-centric dynamic graph that preserves microscopic perturbations while respecting macroscopic conservation laws by discretizing PDEs onto this graph. At the micro scale, scenario-adaptive Koopman evolvers selected by an Intent Discriminator are designed to model vehicle dynamics. A Koopman control module explicitly formulate how flow state influences individual vehicles, yielding bidirectional couplings. To our knowledge, this is the first work to jointly model vehicle trajectories and traffic flow density using a unified Koopman framework without requiring historical trajectories. The proposed MMCKM is validated for trajectory prediction on NGSIM and HighD. While MMCKM uses only real-time measurement, it achieves comparable or even higher accuracy than history-dependent baselines. We further analyze the effect of the operator interval and provide ablations to show the improvement by intent inference, macro-to-micro control, and diffusion. Code and implementation details are included to facilitate reproducibility.

Time series anomaly detection plays a critical role in many dynamic systems. However, previous approaches have primarily relied on unimodal numerical data, overlooking the importance of complementary information from other modalities. In this paper, we propose a novel multimodal time series anomaly detection model (MindTS) that focuses on addressing two key challenges: (1) how to achieve semantically consistent alignment across heterogeneous multimodal data, and (2) how to filter out redundant modality information to enhance cross-modal interaction effectively. To address the first challenge, we propose Fine-grained Time-text Semantic Alignment. It integrates exogenous and endogenous text information through cross-view text fusion and a multimodal alignment mechanism, achieving semantically consistent alignment between time and text modalities. For the second challenge, we introduce Content Condenser Reconstruction, which filters redundant information within the aligned text modality and performs cross-modal reconstruction to enable interaction. Extensive experiments on six real-world multimodal datasets demonstrate that the proposed MindTS achieves competitive or superior results compared to existing methods.