MoRe: Modular Representations for Principled Continual Representation Learning on Squantial Data

Continual learning requires models to adapt to new data while preserving previously acquired knowledge. At its core, this challenge can be viewed as principled one-step adaptation: incorporating new information with minimal interference to existing representations. Most existing approaches address this challenge by modifying model parameters or architectures in a supervised, task-specific manner. However, the underlying issue is representational: tasks require distinct yet structured representations that can be selectively updated without disrupting representations, while structure should reflect intrinsic organization in the data rather than task boundaries. In sequential data, time-delayed dependencies provide a natural signal for uncovering this organization, revealing how fundamental representations give rise to more specific ones. Inspired by the modular organization of the human brain, we propose MoRe, a framework that identifies modularity in the representation itself rather than allocating it at the architectural level. MoRe decomposes knowledge into a hierarchy of fundamental and specific modules with identifiability guarantees, enabling principled module reuse, alignment, and expansion during adaptation while preserving old modules by construction. Experiments on synthetic benchmarks and real-world LLM activations demonstrate interpretable hierarchical structure, improved plasticity-stability trade-offs, suggesting MoRe as a principled foundation for continual adaptation

Rethinking Efficient Graph Coarsening via a Non-Selfishness Principle

Graph coarsening is a graph dimensionality reduction technique that aims to construct a smaller and more tractable graph while preserving the essential structural and semantic properties of the original graph. However, most existing methods rely on pair-wise similarity matching, where each node independently searches for its best partner based on global information. This selfishness matching paradigm incurs substantial computational and memory overhead. To address this problem, we shift to a non-selfishness principle that prioritizes the collective interference of neighborhood in coarsening, and propose an efficient method named NOPE, which achieves linear memory consumption and near-linear computational complexity in the number of nodes. Furthermore, we derive a faster variant NOPE*, which reduces O(δ\dot d) interference evaluation to O(d) based on the local isotropy assumption, and consequently alleviates the computational bottleneck for high-degree nodes. Experimental results show that NOPE* achieves 1.8-10\times speedup over NOPE and surpass almost all baselines with 1-3 orders of magnitude acceleration. Meanwhile, learning on coarsened graphs yields comparable performance to original graphs, and can even show superior performance over LLM-based graph reasoning owing to compact graph information. The code can be available at https://github.com/dazonglian/NOPE-main.

From Generalist to Specialist Representation

Given a generalist model, learning a task-relevant specialist representation is fundamental for downstream applications. Identifiability, the asymptotic guarantee of recovering the ground-truth representation, is critical because it sets the ultimate limit of any model, even with infinite data and computation. We study this problem in a completely nonparametric setting, without relying on interventions, parametric forms, or structural constraints. We first prove that the structure between time steps and tasks is identifiable in a fully unsupervised manner, even when sequences lack strict temporal dependence and may exhibit disconnections, and task assignments can follow arbitrarily complex and interleaving structures. We then prove that, within each time step, the task-relevant latent representation can be disentangled from the irrelevant part under a simple sparsity regularization, without any additional information or parametric constraints. Together, these results establish a hierarchical foundation: task structure is identifiable across time steps, and task-relevant latent representations are identifiable within each step. To our knowledge, each result provides a first general nonparametric identifiability guarantee, and together they mark a step toward provably moving from generalist to specialist models.

A General Representation-Based Approach to Multi-Source Domain Adaptation

A central problem in unsupervised domain adaptation is determining what to transfer from labeled source domains to an unlabeled target domain. To handle high-dimensional observations (e.g., images), a line of approaches use deep learning to learn latent representations of the observations, which facilitate knowledge transfer in the latent space. However, existing approaches often rely on restrictive assumptions to establish identifiability of the joint distribution in the target domain, such as independent latent variables or invariant label distributions, limiting their real-world applicability. In this work, we propose a general domain adaptation framework that learns compact latent representations to capture distribution shifts relative to the prediction task and address the fundamental question of what representations should be learned and transferred. Notably, we first demonstrate that learning representations based on all the predictive information, i.e., the label's Markov blanket in terms of the learned representations, is often underspecified in general settings. Instead, we show that, interestingly, general domain adaptation can be achieved by partitioning the representations of Markov blanket into those of the label's parents, children, and spouses. Moreover, its identifiability guarantee can be established. Building on these theoretical insights, we develop a practical, nonparametric approach for domain adaptation in a general setting, which can handle different types of distribution shifts.

Causal Representation Learning from General Environments under Nonparametric Mixing

Causal representation learning aims to recover the latent causal variables and their causal relations, typically represented by directed acyclic graphs (DAGs), from low-level observations such as image pixels. A prevailing line of research exploits multiple environments, which assume how data distributions change, including single-node interventions, coupled interventions, or hard interventions, or parametric constraints on the mixing function or the latent causal model, such as linearity. Despite the novelty and elegance of the results, they are often violated in real problems. Accordingly, we formalize a set of desiderata for causal representation learning that applies to a broader class of environments, referred to as general environments. Interestingly, we show that one can fully recover the latent DAG and identify the latent variables up to minor indeterminacies under a nonparametric mixing function and nonlinear latent causal models, such as additive (Gaussian) noise models or heteroscedastic noise models, by properly leveraging sufficient change conditions on the causal mechanisms up to third-order derivatives. These represent, to our knowledge, the first results to fully recover the latent DAG from general environments under nonparametric mixing. Notably, our results match or improve upon many existing works, but require less restrictive assumptions about changing environments.

Diverse Dictionary Learning

Given only observational data $X = g(Z)$, where both the latent variables $Z$ and the generating process $g$ are unknown, recovering $Z$ is ill-posed without additional assumptions. Existing methods often assume linearity or rely on auxiliary supervision and functional constraints. However, such assumptions are rarely verifiable in practice, and most theoretical guarantees break down under even mild violations, leaving uncertainty about how to reliably understand the hidden world. To make identifiability actionable in the real-world scenarios, we take a complementary view: in the general settings where full identifiability is unattainable, what can still be recovered with guarantees, and what biases could be universally adopted? We introduce the problem of diverse dictionary learning to formalize this view. Specifically, we show that intersections, complements, and symmetric differences of latent variables linked to arbitrary observations, along with the latent-to-observed dependency structure, are still identifiable up to appropriate indeterminacies even without strong assumptions. These set-theoretic results can be composed using set algebra to construct structured and essential views of the hidden world, such as genus-differentia definitions. When sufficient structural diversity is present, they further imply full identifiability of all latent variables. Notably, all identifiability benefits follow from a simple inductive bias during estimation that can be readily integrated into most models. We validate the theory and demonstrate the benefits of the bias on both synthetic and real-world data.

World Action Verifier: Self-Improving World Models via Forward-Inverse Asymmetry

General-purpose world models promise scalable policy evaluation, optimization, and planning, yet achieving the required level of robustness remains challenging. Unlike policy learning, which primarily focuses on optimal actions, a world model must be reliable over a much broader range of suboptimal actions, which are often insufficiently covered by action-labeled interaction data. To address this challenge, we propose World Action Verifier (WAV), a framework that enables world models to identify their own prediction errors and self-improve. The key idea is to decompose action-conditioned state prediction into two factors -- state plausibility and action reachability -- and verify each separately. We show that these verification problems can be substantially easier than predicting future states due to two underlying asymmetries: the broader availability of action-free data and the lower dimensionality of action-relevant features. Leveraging these asymmetries, we augment a world model with (i) a diverse subgoal generator obtained from video corpora and (ii) a sparse inverse model that infers actions from a subset of state features. By enforcing cycle consistency among generated subgoals, inferred actions, and forward rollouts, WAV provides an effective verification mechanism in under-explored regimes, where existing methods typically fail. Across nine tasks spanning MiniGrid, RoboMimic, and ManiSkill, our method achieves 2x higher sample efficiency while improving downstream policy performance by 18%.

SEDGE: Structural Extrapolated Data Generation

This paper proposes a framework for Structural Extrapolated Data GEneration (SEDGE) based on suitable assumptions on the underlying data generating process. We provide conditions under which data satisfying new specifications can be generated reliably, together with the approximate identifiability of the distribution of such data under certain ``conservative" assumptions. On the algorithmic side, we develop practical methods to achieve extrapolated data generation, based on the structure-informed optimization strategy or diffusion posterior sampling, respectively. We verify the extrapolation performance on synthetic data and also consider extrapolated image generation as a real-world scenario to illustrate the validity of the proposed framework.

Scaling the Long Video Understanding of Multimodal Large Language Models via Visual Memory Mechanism

Long video understanding is a key challenge that plagues the advancement of \emph{Multimodal Large language Models} (MLLMs). In this paper, we study this problem from the perspective of visual memory mechanism, and proposed a novel and training-free approach, termed \emph{Flexible Memory} (\textbf{FlexMem}). In principle, FlexMem aims to mimic human behavior of video watching, \emph{i.e.}, continually watching video content and recalling the most relevant memory fragments to answer the question. In this way, FlexMem can help MLLMs achieve video understanding of infinite lengths, unlike previous methods that process all video information at once and have input upper-limit. Concretely, FlexMem first consider the visual KV caches as the memory sources, and realize the effective memory transfer and writing via a dual-pathway compression design. Afterwards, FlexMem also explores different memory reading strategies for the diverse video understanding tasks, including the popular streaming one. To validate FlexMem, we apply it to two popular video-MLLMs, and conduct extensive experiments on five long video and one streaming video task. The experimental results show that on \textbf{a single 3090 GPU}, our FlexMem can achieve obvious improvements than existing efficient video understanding methods and process more than \textbf{1k frames}, which also helps the base MLLMs achieve comparable or even better performance than SOTA MLLMs on some benchmarks, \emph{e.g.} , GPT-4o and Gemini-1.5 Pro.

DiffVP: Differential Visual Semantic Prompting for LLM-Based CT Report Generation

While large language models (LLMs) have advanced CT report generation, existing methods typically encode 3D volumes holistically, failing to distinguish informative cues from redundant anatomical background. Inspired by radiological cognitive subtraction, we propose Differential Visual Prompting (DiffVP), which conditions report generation on explicit, high-level semantic scan-to-reference differences rather than solely on absolute visual features. DiffVP employs a hierarchical difference extractor to capture complementary global and local semantic discrepancies into a shared latent space, along with a difference-to-prompt generator that transforms these signals into learnable visual prefix tokens for LLM conditioning. These difference prompts serve as structured conditioning signals that implicitly suppress invariant anatomy while amplifying diagnostically relevant visual evidence, thereby facilitating accurate report generation without explicit lesion localization. On two large-scale benchmarks, DiffVP consistently outperforms prior methods, improving the average BLEU-1-4 by +10.98 and +4.36, respectively, and further boosts clinical efficacy on RadGenome-ChestCT (F1 score 0.421). All codes will be released at https://github.com/ArielTYH/DiffVP/.