An expressivity analysis of hierarchical modelling in deep transformers via bounded-depth grammars

Deep neural networks are widely believed to derive their expressive power from their ability to form \textbf{hierarchical representations}, capturing progressively more abstract and compositional features across layers. In language modeling, \textbf{transformers} have emerged as the dominant architecture, with early layers capturing local syntactic patterns and later layers encoding more complex clause-level dependencies. While this intuition has shaped model design, there remains a lack of rigorous theoretical work demonstrating \textbf{how} deep transformers represent such hierarchical structures. In this work, we analyze the expressiveness of deep transformer models through the formal lens of bounded-depth, non-recursive context-free grammars. For this class of grammars, we explicitly construct transformers with positional attention whose depth grows linearly with grammar depth, while the neuron count scales with the number of derivation-tree shapes and quadratically with the number of production rules. Our theoretical results support the linear representation hypothesis by demonstrating that these architectures possess the structural capacity to encode abstract grammatical states into low-dimensional, linearly separable subspaces within the residual stream.

Understanding Diversity Collapse in RLVR via the Lens of Overtraining

Reinforcement learning with verifiable rewards (RLVR) has become a key approach for enhancing the reasoning abilities of large language models. However, RLVR often suffers from \emph{diversity collapse}: Pass@$1$ improves while high-$k$ Pass@$k$ degrades, which is viewed as a narrowing of the model's reasoning boundary. We formalize this diversity collapse through the lens of \emph{overtraining}: once a problem's contribution to the reference metric has effectively saturated, further updates no longer expand what the model can solve but still concentrate probability mass on the trajectories favored by on-policy sampling. Under a standard setup with few rollouts per problem, even a single observed success places a problem in a nearly saturated regime for high-$k$ Pass@$k$, so most updates in standard RLVR are overtraining from the boundary perspective. This perspective also suggests a reading of whether RLVR can expand the model's reasoning abilities beyond the base model: since RLVR is structurally biased against high-$k$ Pass@$k$, its aggregate decline does not by itself mean that no new reasoning gains occurred. Interventionally, restricting updates to problems with zero observed success lifts Pass@$256$ above the base model on difficult benchmarks; observationally, a non-trivial fraction of initially unsolvable problems become solvable during standard RLVR training. Building on these findings, we propose \emph{Bayesian Boundary Gating} (BBG), which redirects optimization away from overtraining by estimating each problem's marginal contribution to the reasoning boundary. Across multiple reasoning benchmarks, BBG improves average Pass@$k$ across a wide range of $k$.

A theoretical model for task routing in mixture-of-expert transformers

Mixture-of-experts (MoE) layers enable the scaling of transformer models while keeping the inference compute fixed. While task-expert specialization has been observed in empirical studies of frontier MoE transformer models, existing theoretical work analyzes this using continuous mixture models that cannot be used to model natural language effectively. An important open question is to \textit{theoretically explain task-expert specialization in transformer MoE models using discrete models of language}. To address this, we represent structured knowledge via syntactic templates and finite key-value dictionaries, and prove formally that a single-layer MoE transformer can encode knowledge by using experts that specialize in the corresponding tasks. Our construction shows how queries are routed to unique, task-specific experts whose size depends solely on the intrinsic complexity of the given task (i.e. the combined size of its syntactic templates and factual dictionary). Our construction provides a theoretical support for empirical results on localized knowledge circuits in MoE models. We support our theoretical findings with experiments evaluating model performance under varying MoE loss functions.

MLUBench: A Benchmark for Lifelong Unlearning Evaluation in MLLMs

Multimodal large language models (MLLMs) are trained on massive multimodal data, making data unlearning increasingly important as data owners may request the removal of specific content. In practice, these requests often arrive sequentially over time, giving rise to the challenging problem of MLLM Lifelong Unlearning. However, most existing benchmarks are limited in scale and scope, failing to capture the complexities of MLLM lifelong unlearning. To fill this gap, we introduce the MLUBench, a large-scale and comprehensive benchmark featuring 127 entities across 9 classes under lifelong unlearning requests. We perform extensive experiments using MLUBench and reveal that existing unlearning methods suffer from severe, cumulative degradation. More critically, we further identify the unique challenge of this problem: unlike in unimodal models, MLLM lifelong unlearning is constrained by the need to preserve multimodal alignment. Continually unlearning from one modality could degrade the entire model. To alleviate this challenge, we propose LUMoE, an effective method. Experiments demonstrate that LUMoE significantly mitigates the degradation problem faced by baselines. The source code and the MLUBench dataset are open-sourced in https://github.com/lihe-maxsize/Lifelong_Unlearning_main.

Causal Ensemble Agent: Hierarchical Causal Discovery with LLM-guided Expert Reweighting

Causal discovery aims to uncover causal structures from observational data, which is crucial for real-world decision-making. However, different causal discovery algorithms can produce divergent results that conflict with each other, complicating the identification of accurate causal graphs. Traditional approaches rely on numerical values and statistical assumptions, often ignoring rich domain-specific information, such as feature descriptions, which could also help structure learning. While recent works explore using Large Language Models (LLMs) to infer causal relations via direct queries, such methods can be unreliable due to a lack of alignment with the actual data. To address these limitations, we propose Causal Ensemble Agent (CEA), a novel framework that aggregates structural insights from statistical discovery experts across different graph levels via linear opinion pooling, and uses an LLM as a meta-referee to dynamically reweight experts when the aggregated confidence is close to the decision boundary, thereby composing an improved and more complete causal graph. Extensive experiments on both synthetic and real-world datasets demonstrate that CEA achieves the strongest overall performance across a wide range of causal discovery methods, highlighting the effectiveness of using LLMs for meta-analysis in causal discovery.

Exploring the Design Space of Reward Backpropagation for Flow Matching

Aligning text-to-image flow matching models with human preferences via direct reward backpropagation is sample-efficient but hampered by two well-known pathologies: activations cannot be stored across the full sampling trajectory at modern model scale, and chained Jacobian products across steps inflate the reward gradient as it travels back to early indices. Connector-based methods, such as LeapAlign, address these issues by replacing the full backward trajectory with a short pinned path, highlighting a useful decoupling between sampling and optimization. However, the quality of the resulting gradient depends on how accurately this short path approximates the full rollout, especially over long intervals. We propose FlowBP, a unified surrogate-trajectory framework that treats the backward trajectory itself as the design object. FlowBP keeps a no-gradient cached rollout for sampling, then builds a lightweight backward surrogate from cached and selectively re-forwarded velocities. This view separates four choices: the reward-model input, active set, integration weights, and bridge coupling, and recovers prior direct-gradient methods as particular settings. Within this framework, we instantiate three variants: FlowBP-Sparse uses sparse Euler reconstruction, FlowBP-Bridge adds controlled bridge coupling, and FlowBP-Lagrange raises the order of leap quadrature. All three bound memory by the active-set size and limit gradient chaining to at most one Jacobian factor. Across SD3.5-M, FLUX.1-dev, and FLUX.2-Klein-base on preference, quality, and compositional metrics, the three variants improve over direct-gradient baselines on most metrics.

The Easy, the Hard, and the Learnable: Confidence and Difficulty-Adaptive Policy Optimization for LLM Reasoning

RL with verifiable rewards can substantially improve LLM reasoning, yet standard GRPO-style training often treats easy, hard, and learnable questions alike through uniform sampling and weighting, leading to inefficient compute allocation. We study GRPO by tracking token log-probabilities, group-normalized advantages, and the induced token-level update weights. This reveals three recurring dynamics as training proceeds: (1) confidence inflation, (2) advantage contraction, and (3) hierarchical convergence. These findings suggest that the utility of each update depends strongly on both question difficulty and the model's current competence. Motivated by this, we propose Confidence and Difficulty-adaptive Policy Optimization (CoDaPO), which assigns each question a bounded value from rollout confidence and empirical difficulty. CoDaPO then uses this value to reweight policy updates and resample high-value learnable questions within mini-batches, thereby increasing discovery within the learnable band under a fixed compute budget. Across twelve benchmarks, CoDaPO consistently improves accuracy over existing RL methods. Our code is publicly available at https://github.com/tmlr-group/CoDaPO.

AgentHijack: Benchmarking Computer Use Agent Robustness to Common Environment Corruptions

Autonomous computer use agents that powered by multimodal large language models (MLLMs) are emerging as capable assistants for completing complex digital workflows. However, real-world execution environments are far from ideal: pop-ups, resolution changes, and competing applications frequently interfere with agent perception and control. We introduce AgentHijack, a benchmark designed to evaluate the robustness of computer-use agents under common corruptions, where the uncertainties in dynamic environment disrupt the execution flow without direct adversarial intent. Specifically, AgentHijack introduces 9 configurable common corruptions to replicate realistic imperfect scenarios. We evaluate a variety of desktop tasks that utilize MLLM-based agents and discover that even minor instances of corruption can result in substantial performance degradation, which emphasizes the fragility of agents and underscores the necessity of robustness evaluation. Afterward, we propose AgentHijack-Agent, a framework that integrates an action generator with enhanced grounding capabilities and an onlooker responsible for behavior summarization and environment checking. Extensive experiments validate its effectiveness. Our code, environment, baseline models and data are publicly available at: https://AgentHijack.github.io.

Rethinking How to Remember: Beyond Atomic Facts in Lifelong LLM Agent Memory

To enable reliable long-term interaction, LLM agents require a memory system that can faithfully store, efficiently retrieve, and deeply reason over accumulated dialogue history. Most existing methods adopt an extracted fact based paradigm: handcrafted static prompts compress raw dialogues into atomic facts, which are then stored, matched, and injected into downstream reasoning. Nevertheless, such fact-centric designs inevitably discard fine-grained details in original dialogues and fail to support deep reasoning over scattered isolated facts. Moreover, static prompts cannot maintain consistent extraction granularity across diverse dialogue styles. To address these limitations, we propose TriMem, which maintains three coexisting representation granularities, including raw dialogue segments anchored by source identifiers for storage fidelity, extracted atomic facts for efficient memory retrieval, synthesized profiles that aggregate dispersed facts into holistic semantic understanding for deep reasoning. We further adopt TextGrad-based prompt optimization, which iteratively refines extraction and profiling prompts via response quality feedback, achieving lifelong evolution without any parameter updating. Extensive experiments on LoCoMo and PerLTQA across multiple LLM backbones demonstrate that TriMem consistently outperforms strong memory baselines. The code is available at https://TMLR-TriMem.github.io .

Beyond Individual Intelligence: Surveying Collaboration, Failure Attribution, and Self-Evolution in LLM-based Multi-Agent Systems

LLM-based autonomous agents have demonstrated strong capabilities in reasoning, planning, and tool use, yet remain limited when tasks require sustained coordination across roles, tools, and environments. Multi-agent systems address this through structured collaboration among specialized agents, but tighter coordination also amplifies a less explored risk: errors can propagate across agents and interaction rounds, producing failures that are difficult to diagnose and rarely translate into structural self-improvement. Existing surveys cover individual agent capabilities, multi-agent collaboration, or agent self-evolution separately, leaving the causal dependencies among them unexamined. This survey provides a unified review organized around four causally linked stages, which we term the LIFE progression: Lay the capability foundation, Integrate agents through collaboration, Find faults through attribution, and Evolve through autonomous self-improvement. For each stage, we provide systematic taxonomies and formally characterize the dependencies between adjacent stages, revealing how each stage both depends on and constrains the next. Beyond synthesizing existing work, we identify open challenges at stage boundaries and propose a cross-stage research agenda for closed-loop multi-agent systems capable of continuously diagnosing failures, reorganizing structures, and refining agent behaviors, extending current coordination frameworks toward more self-organizing forms of collective intelligence. By bridging these previously fragmented research threads, this survey aims to offer both a systematic reference and a conceptual roadmap toward autonomous, self-improving multi-agent intelligence.