Scaling laws have emerged as a unifying lens for understanding and guiding the training of large language models (LLMs). However, existing studies predominantly focus on the final-step loss, leaving open whether the entire $\textit{loss dynamics}$ obey similar laws and, crucially, how the $\textit{learning rate schedule}$ (LRS) shapes them. We address these gaps in a controlled theoretical setting by analyzing stochastic gradient descent (SGD) on a power-law kernel regression model. The key insight is a novel $\textbf{intrinsic-time}$ viewpoint, which captures the training progress more faithfully than iteration count. We then establish a $\textbf{Functional Scaling Law (FSL)}$ that captures the full loss trajectory under arbitrary LRSs, with the schedule’s influence entering through a simple convolutional functional. We further instantiate the theory for three representative LRSs---constant, exponential decay, and warmup–stable–decay (WSD)---and derive explicit scaling relations in both data- and compute-limited regimes. These comparisons explain key empirical phenomena: (i) higher-capacity models are more data- and compute-efficient; (ii) learning-rate decay improves training efficiency; and (iii) WSD-type schedules outperform pure decay. Finally, experiments on LLMs ranging from 0.1B to 1B parameters demonstrate the practical relevance of FSL as a surrogate model for fitting and predicting loss trajectories in large-scale pre-training.
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As the economic and environmental costs of training and deploying large vision or language models increase dramatically, analog in-memory computing (AIMC) emerges as a promising energy-efficient solution. However, the training perspective, especially its training dynamic, is underexplored. In AIMC hardware, the trainable weights are represented by the conductance of resistive elements and updated using consecutive electrical pulses. While the conductance changes by a constant in response to each pulse, in reality, the change is scaled by asymmetric and non-linear response functions, leading to a non-ideal training dynamic. This paper provides a theoretical foundation for gradient-based training on AIMC hardware with non-ideal response functions. We demonstrate that asymmetric response functions negatively impact Analog SGD by imposing an implicit penalty on the objective. To overcome the issue, we propose residual learning algorithm, which provably converges exactly to a critical point by solving a bilevel optimization problem. We show that the proposed method can be extended to deal with other hardware imperfections like limited response granularity. As far as we know, it is the first paper to investigate the impact of a class of generic non-ideal response functions. The conclusion is supported by simulations validating our theoretical insights.
Vehicle GPS trajectories provide valuable movement information that supports various downstream tasks and applications. A desirable trajectory learning model should be able to transfer across regions and tasks without retraining, avoiding the need to maintain multiple specialized models and subpar performance with limited training data. However, each region has its unique spatial features and contexts, which are reflected in vehicle movement patterns and are difficult to generalize. Additionally, transferring across different tasks faces technical challenges due to the varying input-output structures required for each task. Existing efforts towards transferability primarily involve learning embedding vectors for trajectories, which perform poorly in region transfer and require retraining of prediction modules for task transfer. To address these challenges, we propose $\textit{TransferTraj}$, a vehicle GPS trajectory learning model that excels in both region and task transferability. For region transferability, we introduce RTTE as the main learnable module within TransferTraj. It integrates spatial, temporal, POI, and road network modalities of trajectories to effectively manage variations in spatial context distribution across regions. It also introduces a TRIE module for incorporating relative information of spatial features and a spatial context MoE module for handling movement patterns in diverse contexts. For task transferability, we propose a task-transferable input-output scheme that unifies the input-output structure of different tasks into the masking and recovery of modalities and trajectory points. This approach allows TransferTraj to be pre-trained once and transferred to different tasks without retraining. We conduct extensive experiments on three real-world vehicle trajectory datasets under various transfer settings, including task transfer, zero-shot region transfer, and few-shot region transfer. Experimental results demonstrate that TransferTraj significantly outperforms state-of-the-art baselines in different scenarios, validating its effectiveness in region and task transfer. Code is available at https://github.com/wtl52656/TransferTraj.
Applications · Neuroscience, Cognitive Science
Intracortical Brain-Computer Interfaces (iBCI) decode behavior from neural population activity to restore motor functions and communication abilities in individuals with motor impairments. A central challenge for long-term iBCI deployment is the nonstationarity of neural recordings, where the composition and tuning profiles of the recorded populations are unstable across recording sessions. Existing approaches attempt to address this issue by explicit alignment techniques; however, they rely on fixed neural identities and require test-time labels or parameter updates, limiting their generalization across sessions and imposing additional computational burden during deployment. In this work, we address the problem of cross-session nonstationarity in long-term iBCI systems and introduce SPINT - a Spatial Permutation-Invariant Neural Transformer framework for behavioral decoding that operates directly on unordered sets of neural units. Central to our approach is a novel context-dependent positional embedding scheme that dynamically infers unit-specific identities, enabling flexible generalization across recording sessions. SPINT supports inference on variable-size populations and allows few-shot, gradient-free adaptation using a small amount of unlabeled data from the test session. We evaluate SPINT on three multi-session datasets from the FALCON Benchmark, covering continuous motor decoding tasks in human and non-human primates. SPINT demonstrates robust cross-session generalization, outperforming existing zero-shot and few-shot unsupervised baselines while eliminating the need for test-time alignment and fine-tuning. Our work contributes an initial step toward a robust and scalable neural decoding framework for long-term iBCI applications.
Clinical decision‑making routinely demands reasoning over heterogeneous data, yet existing multimodal language models (MLLMs) remain largely vision‑centric and fail to generalize across clinical specialties. To bridge this gap, we introduce QoQ-Med-7B/32B, the first open generalist clinical foundation model that jointly reasons across medical images, time‑series signals, and text reports. QoQ-Med is trained with Domain‑aware Relative Policy Optimization (DRPO), a novel reinforcement‑learning objective that hierarchically scales normalized rewards according to domain rarity and modality difficulty, mitigating performance imbalance caused by skewed clinical data distributions. Trained on 2.61 million instruction tuning pairs spanning 9 clinical domains, we show that DRPO training boosts diagnostic performance by 43% in macro‑F1 on average across all visual domains as compared to other critic-free training methods like GRPO. Furthermore, with QoQ-Med trained on intensive segmentation data, it is able to highlight salient regions related to the diagnosis, with an IoU 10x higher than open models while reaching the performance of OpenAI o4-mini. To foster reproducibility and downstream research, we release (i) the full model weights, (ii) the modular training pipeline, and (iii) all intermediate reasoning traces.
Computer Vision · Vision Models & Multimodal
Current image fusion methods struggle with real-world composite degradations and lack the flexibility to accommodate user-specific needs. To address this, we propose ControlFusion, a controllable fusion network guided by language-vision prompts that adaptively mitigates composite degradations. On the one hand, we construct a degraded imaging model based on physical mechanisms, such as the Retinex theory and atmospheric scattering principle, to simulate composite degradations and provide a data foundation for addressing realistic degradations. On the other hand, we devise a prompt-modulated restoration and fusion network that dynamically enhances features according to degradation prompts, enabling adaptability to varying degradation levels. To support user-specific preferences in visual quality, a text encoder is incorporated to embed user-defined degradation types and levels as degradation prompts. Moreover, a spatial-frequency collaborative visual adapter is designed to autonomously perceive degradations from source images, thereby reducing complete reliance on user instructions. Extensive experiments demonstrate that ControlFusion outperforms SOTA fusion methods in fusion quality and degradation handling, particularly under real-world and compound degradations.
Deep Learning · Robustness
Poisoning attacks compromise the training phase of federated learning (FL) such that the learned global model misclassifies attacker-chosen inputs called target inputs. Existing defenses mainly focus on protecting the training phase of FL such that the learnt global model is poison free. However, these defenses often achieve limited effectiveness when the clients' local training data is highly non-iid or the number of malicious clients is large, as confirmed in our experiments. In this work, we propose FLForensics, the first poison-forensics method for FL. FLForensics complements existing training-phase defenses. In particular, when training-phase defenses fail and a poisoned global model is deployed, FLForensics aims to trace back the malicious clients that performed the poisoning attack after a misclassified target input is identified. We theoretically show that FLForensics can accurately distinguish between benign and malicious clients under a formal definition of poisoning attack. Moreover, we empirically show the effectiveness of FLForensics at tracing back both existing and adaptive poisoning attacks on five benchmark datasets.
Deep Learning · Graph Neural Networks
Graph Neural Networks (GNNs) are widely used for node classification, yet their opaque decision-making limits trust and adoption. While local explanations offer insights into individual predictions, global explanation methods—those that characterize an entire class—remain underdeveloped. Existing global explainers rely on motif discovery in small graphs, an approach that breaks down in large, real-world settings where subgraph repetition is rare, node attributes are high-dimensional, and predictions arise from complex structure-attribute interactions. We propose GnnXemplar, a novel global explainer inspired from Exemplar Theory from cognitive science. GnnXemplar identifies representative nodes in the GNN embedding space—exemplars—and explains predictions using natural language rules derived from their neighborhoods. Exemplar selection is framed as a coverage maximization problem over reverse $k$-nearest neighbors, for which we provide an efficient greedy approximation. To derive interpretable rules, we employ a self-refining prompt strategy using large language models (LLMs). Experiments across diverse benchmarks show that GnnXemplar significantly outperforms existing methods in fidelity, scalability, and human interpretability, as validated by a user study with 60 participants.
Computer Vision · Vision Models & Multimodal
Text-3D Scene Retrieval (T3SR) aims to retrieve relevant scenes using linguistic queries. Although traditional T3SR methods have made significant progress in capturing fine-grained associations, they implicitly assume that query descriptions are information-complete. In practical deployments, however, limited by the capabilities of users and models, it is difficult or even impossible to directly obtain a perfect textual query suiting the entire scene and model, thereby leading to performance degradation. To address this issue, we propose a novel Interactive Text-3D Scene Retrieval Method (IDeal), which promotes the enhancement of the alignment between texts and 3D scenes through continuous interaction. To achieve this, we present an Interactive Retrieval Refinement framework (IRR), which employs a questioner to pose contextually relevant questions to an answerer in successive rounds that either promote detailed probing or encourage exploratory divergence within scenes. Upon the iterative responses received from the answerer, IRR adopts a retriever to perform both feature-level and semantic-level information fusion, facilitating scene-level interaction and understanding for more precise re-rankings. To bridge the domain gap between queries and interactive texts, we propose an Interaction Adaptation Tuning strategy (IAT). IAT mitigates the discriminability and diversity risks among augmented text features that approximate the interaction text domain, achieving contrastive domain adaptation for our retriever. Extensive experimental results on three datasets demonstrate the superiority of IDeal.
Recent works of Mei et al. (2023, 2024) have deepened the theoretical understanding of the *Stochastic Gradient Bandit* (SGB) policy, showing that using a constant learning rate guarantees asymptotic convergence to the optimal policy, and that sufficiently *small* learning rates can yield logarithmic regret. However, whether logarithmic regret holds beyond small learning rates remains unclear. In this work, we take a step towards characterizing the regret *regimes* of SGB as a function of its learning rate. For two--armed bandits, we identify a sharp threshold, scaling with the sub-optimality gap $\Delta$, below which SGB achieves *logarithmic* regret on all instances, and above which it can incur *polynomial* regret on some instances. This result highlights the necessity of knowing (or estimating) $\Delta$ to ensure logarithmic regret with a constant learning rate. For general $K$-armed bandits, we further show the learning rate must scale inversely with $K$ to avoid polynomial regret. We introduce novel techniques to derive regret upper bounds for SGB, laying the groundwork for future advances in the theory of gradient-based bandit algorithms.
Theory · Domain Adaptation and Transfer Learning
Empirical risk minimization often performs poorly when the distribution of the target domain differs from those of the source domains. To address such potential distributional shifts, we develop an unsupervised domain adaptation approach that leverages labeled data from multiple source domains and unlabeled data from the target domain. We introduce a distributionally robust model that optimizes an adversarial reward based on explained variance across a class of target distributions, ensuring generalization to the target domain. We show that the proposed robust model is a weighted average of conditional outcome models from the source domains. This formulation allows us to compute the robust model through the aggregation of source models, which can be estimated using various machine learning algorithms of the user’s choice such as random forests, boosting, and neural networks. Additionally, we introduce a bias-correction step to obtain a more accurate aggregation weight, which is effective for various machine learning algorithms. Our framework can be interpreted as a distributionally robust federated learning approach that satisfies privacy constraints while providing insights into the importance of each source for prediction on the target domain. The performance of our method is evaluated on both simulated and real data.
General Machine Learning · Everything Else
Machine learning (ML) is transforming modeling and control in the physical, engineering, and biological sciences. However, rapid development has outpaced the creation of standardized, objective benchmarks—leading to weak baselines, reporting bias, and inconsistent evaluations across methods. This undermines reproducibility, misguides resource allocation, and obscures scientific progress. To address this, we propose a Common Task Framework (CTF) for scientific machine learning. The CTF features a curated set of datasets and task-specific metrics spanning forecasting, state reconstruction, and generalization under realistic constraints, including noise and limited data. Inspired by the success of CTFs in fields like natural language processing and computer vision, our framework provides a structured, rigorous foundation for head-to-head evaluation of diverse algorithms. As a first step, we benchmark methods on two canonical nonlinear systems: Kuramoto-Sivashinsky and Lorenz. These results illustrate the utility of the CTF in revealing method strengths, limitations, and suitability for specific classes of problems and diverse objectives. Next, we are launching a competition around a global real world sea surface temperature dataset with a true holdout dataset to foster community engagement. Our long-term vision is to replace ad hoc comparisons with standardized evaluations on hidden test sets that raise the bar for rigor and reproducibility in scientific ML.
Applications · Physics
Conditional diffusion models provide a natural framework for probabilistic prediction of dynamical systems and have been successfully applied to fluid dynamics and weather prediction. However, in many settings, the available information at a given time represents only a small fraction of what is needed to predict future states, either due to measurement uncertainty or because only a small fraction of the state can be observed. This is true for example in solar physics, where we can observe the Sun’s surface and atmosphere, but its evolution is driven by internal processes for which we lack direct measurements. In this paper, we tackle the probabilistic prediction of partially observable, long-memory dynamical systems, with applications to solar dynamics and the evolution of active regions. We show that standard inference schemes, such as autoregressive rollouts, fail to capture long-range dependencies in the data, largely because they do not integrate past information effectively. To overcome this, we propose a multiscale inference scheme for diffusion models, tailored to physical processes. Our method generates trajectories that are temporally fine-grained near the present and coarser as we move farther away, which enables capturing long-range temporal dependencies without increasing computational cost. When integrated into a diffusion model, we show that our inference scheme significantly reduces the bias of the predicted distributions and improves rollout stability.
Social Aspects · Trustworthy Machine Learning
Estimators in statistics and machine learning must typically trade off between efficiency, having low variance for a fixed target, and distributional robustness, such as \textit{multiaccuracy}, or having low bias over a range of possible targets. In this paper, we consider a simple estimator, \emph{ridge boosting}: starting with any initial predictor, perform a single boosting step with (kernel) ridge regression. Surprisingly, we show that ridge boosting simultaneously achieves both efficiency and distributional robustness: for target distribution shifts that lie within an RKHS unit ball, this estimator maintains low bias across all such shifts and has variance at the semiparametric efficiency bound for each target. In addition to bridging otherwise distinct research areas, this result has immediate practical value. Since ridge boosting uses only data from the source distribution, researchers can train a single model to obtain both robust and efficient estimates for multiple target estimands at the same time, eliminating the need to fit separate semiparametric efficient estimators for each target. We assess this approach through simulations and an application estimating the age profile of retirement income.
Recognizing the physical states of objects and their transformations within videos is crucial for structured video understanding and enabling robust real-world applications, such as robotic manipulation. However, pretrained vision-language models often struggle to capture these nuanced dynamics and their temporal context, and specialized object state recognition frameworks may not generalize to unseen actions or objects. We introduce SAGE (State-Action Graph Embeddings), a novel framework that offers a unified model of physical state transitions by decomposing states into fine-grained, language-described visual concepts that are sharable across different objects and actions. SAGE initially leverages Large Language Models to construct a State-Action Graph, which is then multimodally refined using Vision-Language Models. Extensive experiments show that our method significantly outperforms baselines, generalizes effectively to unseen objects and actions in open-world settings. SAGE improves the prior state-of-the-art by as much as 14.6% on novel state recognition with less than 5% of its inference time.
Deep Learning · Everything Else
Transformer-based language models exhibit complex behavior, but their internal computations remain poorly understood. Most mechanistic interpretability approaches treat components, such as attention heads and MLPs, as atomic units, ignoring potential functional substructure. We propose a finer-grained perspective that models components as superpositions of orthogonal singular directions. This perspective allows multiple independent computations to coexist within a single head or MLP, enabling selective intervention, attribution, and interpretation at a level of granularity beyond previous methods. We demonstrate this approach on the Indirect Object Identification (IOI) task, showing that well-known functional heads, like the “name mover,” encode overlapping subfunctions aligned with distinct singular directions. Nodes previously identified as part of circuits exhibit strong engagement along specific directions, supporting the view that meaningful computations are embedded in low-rank subspaces. While some functional axes remain difficult to interpret, our results reveal that transformer components are more distributed, compact, and compositional than assumed. This opens a new direction for fine-grained mechanistic interpretability and the study of model behavior.
Applications · Robotics
Neuromorphic computing systems are set to revolutionize energy-constrained robotics by achieving orders-of-magnitude efficiency gains, while enabling native temporal processing. Spiking Neural Networks (SNNs) represent a promising algorithmic approach for these systems, yet their application to complex control tasks faces two critical challenges: (1) the non-differentiable nature of spiking neurons necessitates surrogate gradients with unclear optimization properties, and (2) the stateful dynamics of SNNs require training on sequences, which in reinforcement learning (RL) is hindered by limited sequence lengths during early training, preventing the network from bridging its warm-up period. We address these challenges by systematically analyzing surrogate gradient slope settings, showing that shallower slopes increase gradient magnitude in deeper layers but reduce alignment with true gradients. In supervised learning, we find no clear preference for fixed or scheduled slopes. The effect is much more pronounced in RL settings, where shallower slopes or scheduled slopes lead to a $\times2.1$ improvement in both training and final deployed performance. Next, we propose a novel training approach that leverages a privileged guiding policy to bootstrap the learning process, while still exploiting online environment interactions with the spiking policy. Combining our method with an adaptive slope schedule for a real-world drone position control task, we achieve an average return of 400 points, substantially outperforming prior techniques, including Behavioral Cloning and TD3BC, which achieve at most –200 points under the same conditions. This work advances both the theoretical understanding of surrogate gradient learning in SNNs and practical training methodologies for neuromorphic controllers demonstrated in real-world robotic systems.
Deep Learning · Everything Else
Large Language Models (LLMs) show strong generalization across diverse tasks, yet the internal decision-making processes behind their predictions remain opaque. In this work, we study the geometry of hidden representations in LLMs through the lens of intrinsic dimension (ID), focusing specifically on decision-making dynamics in a multiple-choice question answering (MCQA) setting. We perform a large-scale study, with 28 open-weight transformer models and estimate ID across layers using multiple estimators, while also quantifying per-layer performance on MCQA tasks. Our findings reveal a consistent ID pattern across models: early layers operate on low-dimensional manifolds, middle layers expand this space, and later layers compress it again, converging to decision-relevant representations. Together, these results suggest LLMs implicitly learn to project linguistic inputs onto structured, low-dimensional manifolds aligned with task-specific decisions, providing new geometric insights into how generalization and reasoning emerge in language models.
Computer Vision · Vision Models & Multimodal
Vision-and-Language Navigation (VLN) is a core task where embodied agents leverage their spatial mobility to navigate in 3D environments toward designated destinations based on natural language instructions. Recently, video-language large models (Video-VLMs) with strong generalization capabilities and rich commonsense knowledge have shown remarkable performance when applied to VLN tasks. However, these models still encounter the following challenges when applied to real-world 3D navigation: 1) Insufficient understanding of 3D geometry and spatial semantics; 2) Limited capacity for large-scale exploration and long-term environmental memory; 3) Poor adaptability to dynamic and changing environments.To address these limitations, we propose Dynam3D, a dynamic layered 3D representation model that leverages language-aligned, generalizable, and hierarchical 3D representations as visual input to train 3D-VLM in navigation action prediction. Given posed RGB-D images, our Dynam3D projects 2D CLIP features into 3D space and constructs multi-level 3D patch-instance-zone representations for 3D geometric and semantic understanding with a dynamic and layer-wise update strategy. Our Dynam3D is capable of online encoding and localization of 3D instances, and dynamically updates them in changing environments to provide large-scale exploration and long-term memory capabilities for navigation. By leveraging large-scale 3D-language pretraining and task-specific adaptation, our Dynam3D sets new state-of-the-art performance on VLN benchmarks including R2R-CE, REVERIE-CE and NavRAG-CE under monocular settings. Furthermore, experiments for pre-exploration, lifelong memory, and real-world robot validate the effectiveness of practical deployment.
Graph Foundation Models (GFMs) have demonstrated remarkable potential across graph learning tasks but face significant challenges in knowledge updating and reasoning faithfulness. To address these issues, we introduce the Retrieval-Augmented Generation (RAG) paradigm for GFMs, which leverages graph knowledge retrieval. We propose RAG4GFM, an end-to-end framework that seamlessly integrates multi-level graph indexing, task-aware retrieval, and graph fusion enhancement. RAG4GFM implements a hierarchical graph indexing architecture, enabling multi-granular graph indexing while achieving efficient logarithmic-time retrieval. The task-aware retriever implements adaptive retrieval strategies for node, edge, and graph-level tasks to surface structurally and semantically relevant evidence. The graph fusion enhancement module fuses retrieved graph features with query features and augments the topology with sparse adjacency links that preserve structural and semantic proximity, yielding a fused graph for GFM inference. Extensive experiments conducted across diverse GFM applications demonstrate that RAG4GFM significantly enhances both the efficiency of knowledge updating and reasoning faithfulness\footnote{Code: \url{https://github.com/Matrixmax/RAG4GFM}.}.