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Optimization · Bayesian & Black-box Optimization

Daniel Steinberg, Asiri Wijesinghe, Rafael Oliveira, Piotr Koniusz, Cheng Soon Ong, Edwin Bonilla

We introduce active generation of Pareto sets (A-GPS), a new framework for online discrete black-box multi-objective optimization (MOO). A-GPS learns a generative model of the Pareto set that supports a-posteriori conditioning on user preferences. The method employs a class probability estimator (CPE) to predict non-dominance relations and to condition the generative model toward high-performing regions of the search space. We also show that this non-dominance CPE implicitly estimates the probability of hypervolume improvement (PHVI). To incorporate subjective trade-offs, A-GPS introduces _preference direction vectors_ that encode user-specified preferences in objective space. At each iteration, the model is updated using both Pareto membership and alignment with these preference directions, producing an amortized generative model capable of sampling across the Pareto front without retraining. The result is a simple yet powerful approach that achieves high-quality Pareto set approximations, avoids explicit hypervolume computation, and flexibly captures user preferences. Empirical results on synthetic benchmarks and protein design tasks demonstrate strong sample efficiency and effective preference incorporation.

Theory · Learning Theory

WEI-KAI CHANG, Rajiv Khanna

Understanding the dynamics of optimization algorithms in deep learning has become increasingly critical, especially as models grow in scale and complexity. Despite the empirical success of stochastic gradient descent (SGD) and its variants in finding solutions that generalize well, the precise mechanisms underlying this generalization remain poorly understood. A particularly intriguing aspect of this phenomenon is the bias of optimization algorithms towards certain types of minima—often flatter or simpler—especially in overparameterized regimes. While prior works have associated flatness of the loss landscape with better generalization, tools to mechanistically connect data, optimization algorithms, and the nature of the resulting minima are still limited. For instance, methods like Sharpness-Aware Minimization (SAM) have shown practical gains by explicitly promoting flatness, but lack a unified theoretical framework explaining their influence across different data structures and model architectures. In this work, we introduce a comprehensive linear stability analysis framework to dissect the behavior of optimization algorithms—SGD, random perturbations, and SAM—in neural networks, focusing particularly on two-layer ReLU models. Our approach is built upon a novel coherence measure that captures the interaction between data geometry and gradient similarity, providing new insights into why and how certain solutions are favored.

Computer Vision · Vision Models & Multimodal

Lai Wei, Yuting Li, Chen Wang, Yue Wang, Linghe Kong, Weiran Huang, Lichao Sun

Improving Multi-modal Large Language Models (MLLMs) in the post-training stage typically relies on supervised fine-tuning (SFT) or reinforcement learning (RL), which require expensive and manually annotated multi-modal data--an ultimately unsustainable resource. This limitation has motivated a growing interest in unsupervised paradigms as a third stage of post-training after SFT and RL. While recent efforts have explored this direction, their methods are complex and difficult to iterate. To address this, we propose MM-UPT, a simple yet effective framework for unsupervised post-training of MLLMs, enabling continual self-improvement without any external supervision. The training method of MM-UPT builds upon GRPO, replacing traditional reward signals with a self-rewarding mechanism based on majority voting over multiple sampled responses. Our experiments demonstrate that such training method effectively improves the reasoning ability of Qwen2.5-VL-7B (e.g., 66.3\%$\rightarrow$72.9\% on MathVista, 62.9\%$\rightarrow$68.7\% on We-Math), using standard dataset without ground truth labels. To further explore scalability, we extend our framework to a data self-generation setting, designing two strategies that prompt the MLLM to synthesize new training samples on its own. Additional experiments show that combining these synthetic data with the unsupervised training method can also boost performance, highlighting a promising approach for scalable self-improvement. Overall, MM-UPT offers a new paradigm for autonomous enhancement of MLLMs, serving as a critical third step after initial SFT and RL in the absence of external supervision. Our code is available at \url{https://github.com/waltonfuture/MM-UPT}.

Deep Learning · Generative Models and Autoencoders

Xinxin You, Qixin Sun, Chenwei Yan, Xiao Zhang, Chen Ning, Xiangling Fu, Si Liu, Guoping Hu, Shijin Wang, Ji Wu 等

Inconsistent hallucinations remain a major challenge for large language models (LLMs), undermining the accuracy and reliability of fact-based reasoning in real-world applications. Existing approaches often rely on task-specific training or adaptation, such as hand-crafted synthetic datasets for domain tasks or solutions mainly focused on numerical reasoning, thereby limiting generalizability to broader, unseen NLP tasks. Inspired by the structural rigor and logical consistency of programming languages, we observe that fact-based texts can be mapped to programming structures due to their inherent patterns. We further propose FACT, a novel Fact-driven Alternating Code-text Training framework that alternates between text-to-code and code-to-text prediction. FACT is the first task-agnostic paradigm that embeds code and natural language in a shared semantic space, thereby transferring the logical consistency of code to LLM outputs in NLP tasks. Experiments show that with only a small subset of Wiki-40B-en for training, FACT reduces inconsistent hallucinations by 2.7%–8.0% and improves overall performance by 2.5%–6.1% in three leading LLMs and four diverse datasets covering QA and summarization tasks. This framework offers a new perspective on addressing challenging hallucinations in LLMs, contributing to more reliable AI.

Reinforcement Learning · Deep RL

Jiashun Liu, Zihao Wu, Johan Obando Ceron, Pablo Samuel Castro, Aaron Courville, Ling Pan

Deep reinforcement learning (RL) agents frequently suffer from neuronal activity loss, which impairs their ability to adapt to new data and learn continually. A common method to quantify and address this issue is the $\tau$-dormant neuron ratio, which uses activation statistics to measure the expressive ability of neurons. While effective for simple MLP-based agents, this approach loses statistical power in more complex architectures. To address this, we argue that in advanced RL agents, maintaining a neuron's **learning capacity**, its ability to adapt via gradient updates, is more critical than preserving its expressive ability. Based on this insight, we shift the statistical objective from activations to gradients, and introduce **GraMa** (**Gra**dient **Ma**gnitude Neural Activity Metric), a lightweight, architecture-agnostic metric for quantifying neuron-level learning capacity. We show that **GraMa** effectively reveals persistent neuron inactivity across diverse architectures, including residual networks, diffusion models, and agents with varied activation functions. Moreover, **re**setting neurons guided by **GraMa** (**ReGraMa**) consistently improves learning performance across multiple deep RL algorithms and benchmarks, such as MuJoCo and the DeepMind Control Suite. **We make our code available.**

Applications · Health

Yuxuan Zhou, Xien Liu, Xiao Zhang, Chen Ning, Shijin Wang, Guoping Hu, Ji Wu

Large Language Models (LLMs) are expected to possess comprehensive medical knowledge to support real-world clinical applications. While domain-specific fine-tuning effectively injects medical knowledge into LLMs, it often causes catastrophic forgetting of previously acquired knowledge and instruction-following capabilities. In this paper, we investigate this issue and reveal a pattern of proximity-dependent forgetting: knowledge that is semantically or topically close to the injected content is more likely to be forgotten, while unrelated knowledge shows minimal degradation. Moreover, we observe that existing mitigation techniques fail to address this type of forgetting effectively. Motivated by this observation and inspired by human learning mechanisms, we proposeInternAL (\Internal Knowledge Augmentation Learning), a novel approach that leverages LLMs' own internal knowledge to mitigate forgetting. InternAL first probes internal knowledge closely related to the injection by prompting the model with questions derived from the injected knowledge. This knowledge is then used to augment the original injection dataset, guiding the model to retain related prior knowledge during training. Experimental results on multiple LLMs (LLaMA, Qwen) demonstrate that InternAL significantly mitigates proximity-related forgetting while maintaining strong knowledge injection performance. Our findings provide new insights into the nature of catastrophic forgetting in medical knowledge injection and highlight a promising direction for robust domain adaptation in LLMs. Code and datasets are available at https://github.com/THUMLP/InternAL.

Reinforcement Learning · Deep RL

Wujiang Xu, Zujie Liang, Kai Mei, Hang Gao, Juntao Tan, Yongfeng Zhang

While large language model (LLM) agents can effectively use external tools for complex real-world tasks, they require memory systems to leverage historical experiences. Current memory systems enable basic storage and retrieval but lack sophisticated memory organization, despite recent attempts to incorporate graph databases. Moreover, these systems' fixed operations and structures limit their adaptability across diverse tasks. To address this limitation, this paper proposes a novel agentic memory system for LLM agents that can dynamically organize memories in an agentic way. Following the basic principles of the Zettelkasten method, we designed our memory system to create interconnected knowledge networks through dynamic indexing and linking. When a new memory is added, we generate a comprehensive note containing multiple structured attributes, including contextual descriptions, keywords, and tags. The system then analyzes historical memories to identify relevant connections, establishing links where meaningful similarities exist. Additionally, this process enables memory evolution -- as new memories are integrated, they can trigger updates to the contextual representations and attributes of existing historical memories, allowing the memory network to continuously refine its understanding. Our approach combines the structured organization principles of Zettelkasten with the flexibility of agent-driven decision making, allowing for more adaptive and context-aware memory management. Empirical experiments on six foundation models show superior improvement against existing SOTA baselines. The code is available at \url{https://anonymous.4open.science/r/AgenticMemory-76B4}.

Social Aspects · Accountability, Transparency and Interpretability

Murtaza Nazir, Matthew Finlayson, John Morris, Xiang Ren, Swabha Swayamdipta

Language model inversion seeks to recover hidden prompts using only language model outputs. This capability has implications for security and accountability in language model deployments, such as leaking private information from an API-protected language model’s system message. We propose a new method – prompt inversion from logprob sequences (PILS) – that recovers hidden prompts by gleaning clues from the model’s next-token probabilities over the course of multiple generation steps. Our method is enabled by a key insight: The vector-valued outputs of a language model occupy a low-dimensional subspace. This enables us to losslessly compress the full next-token probability distribution over multiple generation steps using a linear map, allowing more output information to be used for inversion. Our approach yields massive gains over previous state-of-the-art methods for recovering hidden prompts, achieving 2–3.5 times higher exact recovery rates across test sets, in one case increasing the recovery rate from 17% to 60%. Our method also exhibits surprisingly good generalization behavior; for instance, an inverter trained on 16 generations steps gets 5–27% higher prompt recovery when we increase the number of steps to 32 at test time. Furthermore, we demonstrate strong performance of our method on the more challenging task of recovering hidden system messages. We also analyze the role of verbatim repetition in prompt recovery and propose a new method for cross-family model transfer for logit-based inverters. Our findings suggest that next-token probabilities are a considerably more vulnerable attack surface for inversion attacks than previously known.

Deep Learning · Everything Else

Tianle Zhang, Wanlong Fang, Jonathan Woo, Paridhi Latawa, Deepak Subramanian, Alvin Chan

The remarkable performance of Large Language Models (LLMs) can be enhanced with test-time computation, which relies on external tools and even other deep learning models. However, existing approaches for integrating non-text modality representations into LLMs typically require additional costly supervised training, restricting on-the-fly adaptation to new domains and modalities. In this work, we explore the feasibility of integrating representations from non-text foundational models (FMs) into text-based LLMs in a training-free manner. We propose In-Context Representation Learning (ICRL) as a proof-of-concept to allow LLMs to adaptively utilize non-text modality representations with few-shot learning. Unlike traditional in-context learning, which incorporates text-label pairs, ICRL replaces text inputs with FM representations, enabling the LLM to perform multi-modal inference without fine-tuning. We evaluate ICRL on a suite of tasks in the molecular domain, investigating three core research questions: (i) how to map FM representations into LLMs in a training-free manner, (ii) what factors influence ICRL performance, and (iii) what mechanisms underlie the effectiveness of ICRL. To the best of our knowledge, ICRL is the first training-free framework for integrating non-text modality representations into text-based LLMs, presenting a promising direction for adaptable, multi-modal generalization.

Computer Vision · Vision Models & Multimodal

Ruiqi Wang, Hao Zhang

We present an open-vocabulary and zero-shot method for arbitrary referring expression segmentation (RES), targeting input expressions that are more general than what prior works were designed to handle. Specifically, our inputs encompass both object- and part-level labels as well as implicit references pointing to properties or qualities of object/part function, design, style, material, etc. Our model, coined RESAnything, leverages Chain-of-Thoughts (CoT) reasoning, where the key idea is attribute prompting. We generate detailed descriptions of object/part attributes including shape, color, and location for potential segment proposals through systematic prompting of a large language model (LLM), where the proposals are produced by a foundational image segmentation model. Our approach encourages deep reasoning about object or part attributes related to function, style, design, etc., enabling the system to handle implicit queries without any part annotations for training or fine-tuning. As the first zero-shot and LLM-based RES method, RESAnything achieves clearly superior performance among zero-shot methods on traditional RES benchmarks and significantly outperforms existing methods on challenging scenarios involving implicit queries and complex part-level relations. Finally, we contribute a new benchmark dataset to offer ~3K carefully curated RES instances to assess part-level, arbitrary RES solutions.

Optimization · Discrete Optimization

Nikolaos Karalias, Akbar Rafiey, Yifei Xu, Zhishang Luo, Behrooz Tahmasebi, Connie Jiang, Stefanie Jegelka

Self-Supervised Learning (SSL) for Combinatorial Optimization (CO) is an emerging paradigm for solving combinatorial problems using neural networks. In this paper, we address a central challenge of SSL for CO: solving problems with discrete constraints. We design an end-to-end differentiable framework that enables us to solve discrete constrained optimization problems with neural networks. Concretely, we leverage algorithmic techniques from the literature on convex geometry and Carathéodory's theorem to decompose neural network outputs into convex combinations of polytope corners that correspond to feasible sets. This decomposition-based approach enables self-supervised training but also ensures efficient quality-preserving rounding of the neural net output into feasible solutions. Extensive experiments in cardinality-constrained optimization show that our approach can consistently outperform neural baselines. We further provide worked-out examples of how our method can be applied beyond cardinality-constrained problems to a diverse set of combinatorial optimization tasks, including finding independent sets in graphs, and solving matroid-constrained problems.

Computer Vision · Vision Models & Multimodal

Weihao Bo, Yanpeng Sun, Yu Wang, Xinyu Zhang, Zechao Li

In this paper, we introduce FedMGP, a new paradigm for personalized federated prompt learning in vision-language models (VLMs). Existing federated prompt learning (FPL) methods often rely on a single, text-only prompt representation, which leads to client-specific overfitting and unstable aggregation under heterogeneous data distributions. Toward this end, FedMGP equips each client with multiple groups of paired textual and visual prompts, enabling the model to capture diverse, fine-grained semantic and instance-level cues. A diversity loss is introduced to drive each prompt group to specialize in distinct and complementary semantic aspects, ensuring that the groups collectively cover a broader range of local characteristics.During communication, FedMGP employs a dynamic prompt aggregation strategy based on similarity-guided probabilistic sampling: each client computes the cosine similarity between its prompt groups and the global prompts from the previous round, then samples s groups via a softmax-weighted distribution. This soft selection mechanism preferentially aggregates semantically aligned knowledge while still enabling exploration of underrepresented patterns—effectively balancing the preservation of common knowledge with client-specific features. Notably, FedMGP maintains parameter efficiency by redistributing a fixed prompt capacity across multiple groups, achieving state-of-the-art performance with the lowest communication parameters (5.1k) among all federated prompt learning methods. Theoretical analysis shows that our dynamic aggregation strategy promotes robust global representation learning by reinforcing shared semantics while suppressing client-specific noise. Extensive experiments demonstrate that FedMGP consistently outperforms prior approaches in both personalization and domain generalization across diverse federated vision-language benchmarks.The code will be released on https://github.com/weihao-bo/FedMGP.git.

General Machine Learning · Transfer, Multitask and Meta-learning

Matthew Macfarlane, Clem Bonnet

General intelligence requires systems that acquire new skills efficiently and generalize beyond their training distributions. Although program synthesis approaches have strong generalization power, they face scaling issues due to large combinatorial spaces that quickly make them impractical and require human-generated DSLs or pre-trained priors to narrow this search space. On the other hand, deep learning methods have had high successes, but they lack structured test-time adaptation and rely on heavy stochastic sampling or expensive gradient updates for fine-tuning. In this work, we propose the Latent Program Network (LPN), a new architecture that builds in test-time search directly into neural models. LPN learns a latent space of implicit programs---neurally mapping inputs to outputs---through which it can search using gradients at test time. LPN combines the adaptability of symbolic approaches and the scalability of neural methods. It searches through a compact latent space at test time and bypasses the need for pre-defined domain-specific languages. On a range of programming-by-examples tasks, LPN either outperforms or matches performance compared to in-context learning and test-time training methods. Tested on the ARC-AGI benchmark, we demonstrate that LPN can both learn a compact program space and search through it at test time to adapt to novel tasks. LPN doubles its performance on out-of-distribution tasks when test-time search is switched on.

Deep Learning · Generative Models and Autoencoders

Keshigeyan Chandrasegaran, Michael Poli, Dan Fu, Dongjun Kim, Lea M. Hadzic, Manling Li, Agrim Gupta, Stefano Massaroli, Azalia Mirhoseini, Juan Carlos Niebles 等

Designing model architectures requires decisions such as selecting operators (e.g., attention, convolution) and configurations (e.g., depth, width). However, evaluating the impact of these decisions on model quality requires costly pretraining, limiting architectural investigation. Inspired by how new software is built on existing code, we ask: can new architecture designs be studied using pretrained models? To this end, we present *grafting*, a simple approach for editing pretrained diffusion transformers (DiTs) to materialize new architectures under small compute budgets. Informed by our analysis of activation behavior and attention locality, we construct a testbed based on the DiT-XL/2 design to study the impact of grafting on model quality. Using this testbed, we develop a family of hybrid designs via grafting: replacing softmax attention with gated convolution, local attention, and linear attention, and replacing MLPs with variable expansion ratio and convolutional variants. Notably, many hybrid designs achieve good quality (FID: 2.38–2.64 vs. 2.27 for DiT-XL/2) using $<2$% pretraining compute. We then graft a text-to-image model (PixArt-$\Sigma$), achieving a 1.43$\times$ speedup with less than a 2% drop in GenEval score. Finally, we present a case study that restructures DiT-XL/2 by converting every pair of sequential transformer blocks into parallel blocks via grafting. This reduces model depth by 2$\times$ and yields better quality (FID: 2.77) than other models of comparable depth. Together, we show that new diffusion model designs can be explored by grafting pretrained DiTs, with edits ranging from operator replacement to architecture restructuring. Code and grafted models: https://grafting.stanford.edu.

Panagiotis Theodoropoulos, Augustinos Saravanos, Evangelos Theodorou, Guan-Horng Liu

Understanding complex systems by inferring trajectories from sparse sample snapshots is a fundamental challenge in a wide range of domains, e.g., single-cell biology, meteorology, and economics. Despite advancements in Bridge and Flow matching frameworks, current methodologies rely on pairwise interpolation between adjacent snapshots. This hinders their ability to capture long-range temporal dependencies and potentially affects the coherence of the inferred trajectories. To address these issues, we introduce Momentum Multi-Marginal Schrödinger Bridge Matching (3MSBM), a novel matching framework that learns smooth measure-valued splines for stochastic systems that satisfy multiple positional constraints. This is achieved by lifting the dynamics to phase space and generalizing stochastic bridges to be conditioned on several points, forming a multi-marginal conditional stochastic optimal control problem. The underlying dynamics are then learned by minimizing a variational objective, having fixed the path induced by the multi-marginal conditional bridge. As a matching approach, 3MSBM learns transport maps that preserve intermediate marginals throughout training, significantly improving convergence and scalability. Extensive experimentation in a series of real-world applications validates the superior performance of 3MSBM compared to existing methods in capturing complex dynamics with temporal dependencies, opening new avenues for training matching frameworks in multi-marginal settings.

Deep Learning · Algorithms

Stephen Zhao, Aidan Li, Rob Brekelmans, Roger Grosse

Reinforcement learning (RL) has become a predominant technique to align language models (LMs) with human preferences or promote outputs which are deemed to be desirable by a given reward function. Standard RL approaches optimize average reward, while methods explicitly focused on reducing the probability of undesired outputs typically come at a cost to average-case performance. To improve this tradeoff, we introduce RePULSe, a new training method that augments the standard RL loss with an additional loss that uses learned proposals to guide sampling low-reward outputs, and then reduces those outputs’ probability. We run experiments demonstrating that RePULSe produces a better tradeoff of expected reward versus the probability of undesired outputs and is more adversarially robust, compared to standard RL alignment approaches and alternatives.

Computer Vision · Vision Models & Multimodal

Qizhe Zhang, Mengzhen Liu, Lichen Li, Ming Lu, Yuan Zhang, Junwen Pan, Qi She, Shanghang Zhang

In multimodal large language models (MLLMs), the length of input visual tokens is often significantly greater than that of their textual counterparts, leading to a high inference cost. Many works aim to address this issue by removing redundant visual tokens. However, current approaches either rely on attention-based pruning, which retains numerous duplicate tokens, or use similarity-based pruning, overlooking the instruction relevance, consequently causing suboptimal performance. In this paper, we go beyond attention or similarity by proposing a novel visual token pruning method named **CDPruner**, which maximizes the conditional diversity of retained tokens. We first define the conditional similarity between visual tokens conditioned on the instruction, and then reformulate the token pruning problem with determinantal point process (DPP) to maximize the conditional diversity of the selected subset. The proposed CDPruner is training-free and model-agnostic, allowing easy application to various MLLMs. Extensive experiments across diverse MLLMs show that CDPruner establishes new state-of-the-art on various vision-language benchmarks. By maximizing conditional diversity through DPP, the selected subset better represents the input images while closely adhering to user instructions, thereby preserving strong performance even with high reduction ratios. When applied to LLaVA, CDPruner reduces FLOPs by **95\%** and CUDA latency by **78\%**, while maintaining **94\%** of the original accuracy. Our code is available at https://github.com/Theia-4869/CDPruner.

Computer Vision · Image and Video Generation

Zeyu Zhang, Yiran Wang, Danning Li, Dong Gong, Ian Reid, Richard Hartley

Diffusion models have recently advanced 3D human motion generation by producing smoother and more realistic sequences from natural language. However, existing approaches face two major challenges: high computational cost during training and inference, and limited scalability due to reliance on U-Net inductive bias. To address these challenges, we propose **FlashMo**, a frequency-aware sparse motion diffusion model that prunes low-frequency tokens to enhance efficiency without custom kernel design. We further introduce *MotionSiT*, a scalable diffusion transformer based on a joint-temporal factorized interpolant with Lie group geodesics over $\mathrm{SO}(3)$ manifolds, enabling principled generation of joint rotations. Extensive experiments on the large-scale MotionHub V2 dataset and standard benchmarks including HumanML3D and KIT-ML demonstrate that our method significantly outperforms previous approaches in motion quality, efficiency, and scalability. Compared to the state-of-the-art 1-step distillation baseline, FlashMo reduces **12.9%** inference time and FID by **34.1%**. Project website: https://steve-zeyu-zhang.github.io/FlashMo.

Deep Learning · Everything Else

Xiaoyang Yi, Yang Liu, Binhan Yang, Jian Zhang

Federated continual learning (FCL) aims to maintain the model's performance on old tasks (i.e., stability) while enhancing its ability to acquire knowledge from current tasks (i.e., plasticity). With the development of pre-trained models (PTMs), fine-tuning PTMs on clients has become a promising approach to leveraging their extensive knowledge in FCL. In this paper, we propose MultiFCL, a novel FCL framework that fine-tunes PTMs to adapt to FCL while preserving their strong generalization capabilities. Specifically, to ensure the stability, MultiFCL introduces lightweight adapters for task adaption, which are subsequently frozen to prevent catastrophic forgetting. Moreover, by utilizing the semantic features of old tasks, MultiFCL performs multi-modal initialization of new task class prototypes. To enhance the plasticity, MultiFCL employs a multi-expert training mechanism that integrates multi-scale feature learning with multi-teacher dynamic self-distillation. Through intra-client and inter-client expert communication, MultiFCL facilitates cross-task and cross-client knowledge fusion. Experimental results demonstrate that MultiFCL achieves state-of-the-art performance across multiple datasets and settings, showcasing its effectiveness in FCL scenarios.

Computer Vision · Classification and Understanding

Li-Jun Zhao, Zhen-Duo Chen, Yongxin Wang, Xin Luo, Xin-Shun Xu

Recently proposed Fine-Grained Few-Shot Class-Incremental Learning (FG-FSCIL) offers a practical and efficient solution for enabling models to incrementally learn new fine-grained categories under limited data conditions. However, existing methods still settle for the fine-grained feature extraction capabilities learned from the base classes. Unlike conventional datasets, fine-grained categories exhibit subtle inter-class variations, naturally fostering latent synergy among sub-categories. Meanwhile, the incremental learning framework offers an opportunity to progressively strengthen this synergy by incorporating new sub-category data over time. Motivated by this, we theoretically formulate the FSCIL problem and derive a generalization error bound within a shared fine-grained meta-category environment. Guided by our theoretical insights, we design a novel Meta-Environment Learner (MEL) for FG-FSCIL, which evolves fine-grained feature extraction to enhance meta-environment understanding and simultaneously regularizes hypothesis space complexity. Extensive experiments demonstrate that our method consistently and significantly outperforms existing approaches.