Daily Papers

We introduce MoS (Mixture of States), a novel fusion paradigm for multimodal diffusion models that merges modalities using flexible, state-based interactions. The core of MoS is a learnable, token-wise router that creates denoising timestep- and input-dependent interactions between modalities' hidden states, precisely aligning token-level features with the diffusion trajectory. This router sparsely selects the top-k hidden states and is trained with an ε-greedy strategy, efficiently selecting contextual features with minimal learnable parameters and negligible computational overhead. We validate our design with text-to-image generation (MoS-Image) and editing (MoS-Editing), which achieve state-of-the-art results. With only 3B to 5B parameters, our models match or surpass counterparts up to 4times larger. These findings establish MoS as a flexible and compute-efficient paradigm for scaling multimodal diffusion models.

We discover that large language models exhibit spectral phase transitions in their hidden activation spaces when engaging in reasoning versus factual recall. Through systematic spectral analysis across 11 models spanning 5 architecture families (Qwen, Pythia, Phi, Llama, DeepSeek-R1), we identify seven core phenomena: (1)~Reasoning Spectral Compression -- 9/11 models show significantly lower α for reasoning (p < 0.05), with larger effects in stronger models; (2)~Instruction Tuning Spectral Reversal -- base models show reasoning α< factual α, while instruction-tuned models reverse this relationship; (3)~Architecture-Dependent Generation Taxonomy -- prompt-to-response shifts partition into expansion, compression, and equilibrium regimes; (4)~Spectral Scaling Law -- α_reasoning propto -0.074 ln N across 4 Qwen base models (R^2 = 0.46); (5)~Token-Level Spectral Cascade -- per-token alpha tracking reveals local synchronization that decays exponentially with layer distance, and is weaker for reasoning than factual tasks; (6)~Reasoning Step Spectral Punctuation -- phase-transition signatures align with reasoning step boundaries; and (7)~Spectral Correctness Prediction -- spectral α alone achieves AUC = 1.000 (Qwen2.5-7B, late layers) and mean AUC = 0.893 across 6 models in predicting correctness before the final answer is generated. Together, these findings establish a comprehensive spectral theory of reasoning in transformers, revealing that the geometry of thought is universal in direction, architecture-specific in dynamics, and predictive of outcome.

Multimodal large language models (MLLMs) generate responses autoregressively, integrating visual and linguistic information in an evolving context. Prior work on interpretability has focused on individual layers and circuits (where), leaving the token-level dynamics of multimodal computation during generation (when) underexplored. We address this gap and study attention shifts as per semantic role; tracking model attention to image, text, instruction, and previously generated tokens, One Token at a Time (OTaT). We introduce multimodal tasks that require explicit switching between visual and textual context within a single response. Across two mainstream model families and four open-weight MLLMs of varying sizes, we establish consistent patterns: attention to image peaks at tokens requiring image-derived information, instruction tokens are revisited during task transitions, and attention to previously generated tokens increases as the generation progresses. Causal attention blocking interventions validate the functional role of these trends. We profile model behavior under disrupted attention and observe responses falling back to language priors, or exhibiting cross-modal leakage, denial, or recovery. Finally, informed of the attention dynamics through our novel analysis, we propose a simple test-time intervention to boost attention to the relevant modality at the right time, significantly improving multimodal task performance.

Large Language Models (LLMs) are widely deployed in real-world applications, yet little is known about their training dynamics at the token level. Evaluation typically relies on aggregated training loss, measured at the batch level, which overlooks subtle per-token biases arising from (i) varying token-level dynamics and (ii) structural biases introduced by hyperparameters. While weight decay is commonly used to stabilize training, we reveal that it silently introduces performance biases detectable only at the token level. In fact, we empirically show across different dataset sizes, model architectures and sizes ranging from 270M to 3B parameters that as weight decay increases, low-frequency tokens are disproportionately depreciated. This is particularly concerning, as these neglected low-frequency tokens represent the vast majority of the token distribution in most languages, calling for novel regularization techniques that ensure fairness across all available tokens.

Reinforcement Learning with Verifiable Rewards algorithms like GRPO have emerged as the dominant post-training paradigm for complex reasoning in LLMs, yet commonly suffer from policy entropy collapse during training. We conduct a first-order gradient analysis of token-level entropy dynamics under GRPO and identify a token-level credit assignment mismatch: the per-token entropy variation decomposes into the product of the trajectory-level advantage and an entropy sensitivity function over the next-token distribution, yielding an advantage-surprisal four-quadrant structure and a near-criticality property. Motivated by it, we propose STARE (Surprisal-guided Token-level Advantage Reweighting for policy Entropy stability), which identifies entropy-critical token subsets via batch-internal surprisal quantiles, selectively reweights their effective advantages, and incorporates a target-entropy closed-loop gate for stable entropy regulation. Across model scales from 1.5B to 32B and three task families (Short CoT, Long CoT, and Multi-Turn Tool Use), STARE sustains stable RL training over thousands of steps while maintaining policy entropy within the target band. On AIME24 and AIME25, STARE outperforms DAPO and other competitive baselines by 4%-8% in average accuracy, with reflection tokens and response length growing in tandem, indicating sustained exploration-exploitation balance that further unlocks RL training potential.Code is available at https://github.com/hp-luo/STARE.

Previous language model pre-training methods have uniformly applied a next-token prediction loss to all training tokens. Challenging this norm, we posit that "Not all tokens in a corpus are equally important for language model training". Our initial analysis delves into token-level training dynamics of language model, revealing distinct loss patterns for different tokens. Leveraging these insights, we introduce a new language model called Rho-1. Unlike traditional LMs that learn to predict every next token in a corpus, Rho-1 employs Selective Language Modeling (SLM), which selectively trains on useful tokens that aligned with the desired distribution. This approach involves scoring pretraining tokens using a reference model, and then training the language model with a focused loss on tokens with higher excess loss. When continual pretraining on 15B OpenWebMath corpus, Rho-1 yields an absolute improvement in few-shot accuracy of up to 30% in 9 math tasks. After fine-tuning, Rho-1-1B and 7B achieved state-of-the-art results of 40.6% and 51.8% on MATH dataset, respectively - matching DeepSeekMath with only 3% of the pretraining tokens. Furthermore, when pretraining on 80B general tokens, Rho-1 achieves 6.8% average enhancement across 15 diverse tasks, increasing both efficiency and performance of the language model pre-training.

Reinforcement learning with verifiable rewards (RLVR) improves language-model reasoning, but GRPO-style optimization remains prone to collapse. We analyse this instability through token-level gradient dynamics, deriving a taxonomy that predicts how updates affect next-token probabilities and entropy. The taxonomy shows that stability depends jointly on the advantage sign and token distribution under the current policy. Motivated by this finding, we propose Winner Advantage Policy Optimization (WAPO), a simple online clipped policy-gradient objective that updates only on positive-advantage completions. Across mathematical reasoning and multi-hop QA benchmarks, WAPO improves training stability and matches or outperforms baselines across multiple model families. Full code can be found at https://github.com/layer6ai-labs/wapo.

While Reinforcement Learning with Verifiable Rewards (RLVR) can enhance LLM reasoning, its training process poses a critical risk: entropy collapse. This phenomenon is a rapid loss of policy diversity, stemming from the exploration-exploitation imbalance and leading to a lack of generalization. Recent entropy-intervention methods aim to prevent entropy collapse, yet their underlying mechanisms remain unclear. In this paper, we conduct a quantitative analysis to reveal token-level entropy changes and how existing entropy intervention methods help avoid entropy collapse. Our findings point out a fundamental limitation of existing methods: they attempt to control entropy dynamics indirectly. By only affecting related factors, such as the advantage signal and generation probability, their effectiveness is inherently limited and could potentially fail. To address this limitation, we introduce an entropy-change-aware reweighting scheme, namely Stabilizing Token-level Entropy-changE via Reweighting (STEER), that adaptively stabilizes entropy dynamics through fine-grained token-level adjustments. Our approach mitigates over-exploitation while fostering robust exploration. Extensive experiments demonstrate that STEER significantly mitigates entropy collapse, stabilizes entropy dynamics, and achieves stronger downstream performance across various mathematical reasoning benchmarks \footnote{Our code is available at https://github.com/zz-haooo/STEER.

Recent advances in video generation have shown remarkable potential for constructing world simulators. However, current models still struggle to produce physically consistent results, particularly when handling large-scale or complex dynamics. This limitation arises primarily because existing approaches respond isotropically to physical prompts and neglect the fine-grained alignment between generated content and localized physical cues. To address these challenges, we propose ProPhy, a Progressive Physical Alignment Framework that enables explicit physics-aware conditioning and anisotropic generation. ProPhy employs a two-stage Mixture-of-Physics-Experts (MoPE) mechanism for discriminative physical prior extraction, where Semantic Experts infer semantic-level physical principles from textual descriptions, and Refinement Experts capture token-level physical dynamics. This mechanism allows the model to learn fine-grained, physics-aware video representations that better reflect underlying physical laws. Furthermore, we introduce a physical alignment strategy that transfers the physical reasoning capabilities of vision-language models (VLMs) into the Refinement Experts, facilitating a more accurate representation of dynamic physical phenomena. Extensive experiments on physics-aware video generation benchmarks demonstrate that ProPhy produces more realistic, dynamic, and physically coherent results than existing state-of-the-art methods.

When a language model generates text, the selection of individual tokens might lead it down very different reasoning paths, making uncertainty difficult to quantify. In this work, we consider whether reasoning language models represent the alternate paths that they could take during generation. To test this hypothesis, we use hidden activations to control and predict a language model's uncertainty during chain-of-thought reasoning. In our experiments, we find a clear correlation between how uncertain a model is at different tokens, and how easily the model can be steered by controlling its activations. This suggests that activation interventions are most effective when there are alternate paths available to the model -- in other words, when it has not yet committed to a particular final answer. We also find that hidden activations can predict a model's future outcome distribution, demonstrating that models implicitly represent the space of possible paths.

Reinforcement learning from verifiable rewards has significantly advanced the reasoning capabilities of large language models. However, Group Relative Policy Optimization (GRPO) typically assigns a uniform, sequence-level advantage to all tokens, thereby overlooking the intrinsic information heterogeneity along reasoning chains. We show that this coarse-grained credit assignment leads to premature entropy collapse and encourages the model to generate redundant, low-quality reasoning paths. Through systematic empirical analysis, we identify Critical Decision Pivots (CDPs): transient high-entropy states where the policy's trajectory is most sensitive to perturbations. These pivots represent the "forks in the road" where effective multi-path exploration is most crucial yet often suppressed by uniform advantage signals. Building on these insights, we propose Entropy-Regulated Policy Optimization (ERPO), which transitions the optimization focus from coarse sequences to fine-grained token dynamics. ERPO introduces three synergistic components: (i) Entropy-aware Gating, which adaptively amplifies exploration at CDPs to facilitate diverse path discovery; (ii) Bucket-based Implicit Normalization, which mitigates difficulty bias by aligning token progress windows; and (iii) Result-anchored Advantage Synthesis, which re-weights token-level signals via outcome-driven anchors. Extensive experiments on competitive mathematical benchmarks demonstrate that ERPO significantly outperforms GRPO. Notably, ERPO not only boosts reasoning accuracy but also yields significantly more concise and robust derivation paths, while achieving performance comparable to large models with orders of magnitude more parameters.

Multimodal Chain-of-Thought (CoT) reasoning requires large vision-language models to construct reasoning trajectories that interleave perceptual grounding with multi-step inference. However, existing Reinforcement Learning with Verifiable Rewards (RLVR) methods typically optimize reasoning at a coarse granularity, treating CoT uniformly without distinguishing their varying degrees of visual grounding. In this work, we conduct a token-level analysis of multimodal reasoning trajectories and show that successful reasoning is characterized by structured token dynamics reflecting both perceptual grounding and exploratory inference. Building upon this analysis, we propose Perception-Exploration Policy Optimization (PEPO), which derives a perception prior from hidden state similarity and integrates it with token entropy through a smooth gating mechanism to produce token-level advantages. PEPO integrates seamlessly with existing RLVR frameworks such as GRPO and DAPO, requiring neither additional supervision nor auxiliary branches. Extensive experiments across diverse multimodal benchmarks demonstrate consistent and robust improvements over strong RL baselines, spanning geometry reasoning, visual grounding, visual puzzle solving, and few-shot classification, while maintaining stable training dynamics. Code: https://github.com/xzxxntxdy/PEPO

Token serves as the fundamental unit of computation in modern autoregressive models, and generation length directly influences both inference cost and reasoning performance. Despite its importance, existing approaches lack fine-grained length modeling, operating primarily at the coarse-grained sequence level. We introduce the Length Value Model (LenVM), a token-level framework that models the remaining generation length. By formulating length modeling as a value estimation problem and assigning a constant negative reward to each generated token, LenVM predicts a bounded, discounted return that serves as a monotone proxy for the remaining generation horizon. This formulation yields supervision that is annotation-free, dense, unbiased, and scalable. Experiments on LLMs and VLMs demonstrate LenVM provides a highly effective signal at inference time. On the LIFEBench exact length matching task, applying LenVM to a 7B model improves the length score from 30.9 to 64.8, significantly outperforming frontier closed-source models. Furthermore, LenVM enables continuous control over the trade off between performance and efficiency. On GSM8K at a budget of 200 tokens, LenVM maintains 63% accuracy compared to 6 percent for token budget baseline. It also accurately predicts total generation length from the prompt boundary. Finally, LenVM's token-level values offer an interpretable view of generation dynamics, revealing how specific tokens shift reasoning toward shorter or longer regimes. Results demonstrate that LenVM supports a broad range of applications and token length can be effectively modeled as a token-level value signal, highlighting the potential of LenVM as a general framework for length modeling and as a length-specific value signal that could support future RL training. Code is available at https://github.com/eric-ai-lab/Length-Value-Model.

Mixture-of-Experts (MoE) models are widely used to scale language models, yet their expert routing behavior and adaptation in a multilingual setting remain underexplored. In this work, we study multilingual routing dynamics during continual pre-training of an English-centric MoE model on a multilingual corpus, analyzing how expert usage varies across languages. We find that continual multilingual pre-training leads to diffused, language-agnostic routing in early and middle layers, with language specialization primarily emerging in the final layers. We also show that token-level vocabulary overlap between languages plays an important role in how languages are routed. Motivated by these findings, we propose a parameter-efficient adaptation strategy that updates language-specific and shared experts in the final MoE layers. Experiments on MultiBLiMP and Belebele show that our method achieves a strong performance-efficiency trade-off, attaining competitive performance relative to fine-tuning complete final layers, while updating less than 2% of the parameters. Overall, our findings provide insights into where and how language specialization emerges in MoEs during continual pre-training and provide practical insights for low-resource multilingual adaptation. Our code is available at https://github.com/aditi184/moe-routing-adaptation.

Jailbreak attacks reveal a persistent weakness in aligned Large Language Models: carefully crafted prompts can elicit policy-violating responses despite safety training. While most defenses operate at the prompt or output level, it remains unclear how harmful intent is encoded within the model's internal representations. We investigate this question by analyzing token-level predictive entropy trajectories across layers of a frozen LLM using the logit lens. We find that static aggregate statistics of prompt-level entropy (e.g., mean, variance) carry little discriminative signal, whereas features capturing how entropy evolves across token positions, such as monotonic rank-based trend scores, are substantially more informative. Importantly, this signal is not uniform across model depth: it is concentrated in intermediate layers and degrades at the final layer, indicating that jailbreak-relevant structure is most pronounced in mid-network representations rather than at the output head. Across multiple models (Llama, Qwen, Gemma) and adversarial benchmarks, these entropy dynamics provide architecture-consistent separation without additional training. Together, our findings show that jailbreak behavior is reflected in structured intermediate uncertainty dynamics, clarifying both which entropy-derived features encode harmful intent and where in the network that signal is most pronounced.

Reinforcement Learning has emerged as the fundamental technique for enhancing reasoning in LLMs. However, existing algorithms apply uniform optimization to all tokens, ignoring their different roles in reasoning process. To address this limitation, we introduce Heterogeneous Adaptive Policy Optimization (HAPO), a comprehensive token-aware algorithm that dynamically adapts optimization based on token entropy. For rollout sampling, we propose Adaptive Temperature Sampling, which adjusts sampling temperature in real time, promoting exploration at high-entropy tokens while preserving coherence at low-entropy ones. For advantage calculation, we introduce Token Level Group Average that normalizes advantages at token level, jointly accounting for sequence-length as in token-mean loss while preserving non-biased treatment. We then develop Differential Advantage Redistribution that leverages entropy and importance ratios to modulate rewards-adjusting updates for tokens with clear signals. For clipping loss, we design Asymmetric Adaptive Clipping, allowing aggressive probability reduction for noisy low-entropy tokens while enabling exploration for high-entropy tokens. Through systematic investigation between entropy and training dynamics, we embedded token-level treatment into every stages to achieve fine-grained control. Extensive experiments demonstrate that HAPO consistently outperforms DAPO across multiple model scales. Our code can be found in https://github.com/starriver030515/HAPO.

Large language models (LLMs) excel at natural language understanding and generation but remain vulnerable to factual errors, limiting their reliability in knowledge-intensive tasks. While decoding-time strategies provide a promising efficient solution without training, existing methods typically treat token-level and layer-level signals in isolation, overlooking the joint dynamics between them. In this work, we introduce a token-aware, layer-localized contrastive decoding method that aligns specific token types with their most influential transformer layers to improve factual generation. Through empirical attention analysis, we identify two key patterns: punctuation tokens receive dominant attention in early layers, while conceptual tokens govern semantic reasoning in intermediate layers. By selectively suppressing attention to these token types at their respective depths, we achieve the induction of controlled factual degradation and derive contrastive signals to guide the final factual decoding. Our method requires no additional training or model modification, and experiments demonstrate that our method consistently improves factuality across multiple LLMs and various benchmarks.

While Late Interaction models exhibit strong retrieval performance, many of their underlying dynamics remain understudied, potentially hiding performance bottlenecks. In this work, we focus on two topics in Late Interaction retrieval: a length bias that arises when using multi-vector scoring, and the similarity distribution beyond the best scores pooled by the MaxSim operator. We analyze these behaviors for state-of-the-art models on the NanoBEIR benchmark. Results show that while the theoretical length bias of causal Late Interaction models holds in practice, bi-directional models can also suffer from it in extreme cases. We also note that no significant similarity trend lies beyond the top-1 document token, validating that the MaxSim operator efficiently exploits the token-level similarity scores.

As context windows in LLMs scale to 100K+ tokens, the key-value (KV) cache becomes the dominant memory bottleneck, with recent methods claiming 80-90% savings and minimal benchmark degradation. We argue these evaluations miss a structural issue: attention is not just storage but routing, and retaining KV pairs does not guarantee semantic accessibility. We propose a physics-inspired view of KV compression as a controlled perturbation of token-level routing, distinguishing retention, accessibility, and utilization. Using synthetic tasks probing multi-entity tracking, disambiguation, coreference, and multi-hop reasoning, we find that moderate compression degrades internal representations with little accuracy loss, revealing redundancy; all models exhibit a sharp hallucination safety cliff near 90% compression, correlated with spikes in Global Eviction Ratio (GER), suggesting a phase transition in semantic reachability; and architectures differ in routing dynamics, with LLaMA showing early consensus and late diversification, and Qwen showing funnel-like late convergence, leading to distinct resilience profiles. Beyond erasure, we identify representational rigidity, where excessive head-level consensus collapses routing flexibility despite token survival. These results suggest sparse token-route structures govern compression tolerance, reframing KV compression as a structural probe of attention geometry and linking long-context scalability to sparsity and the lottery ticket hypothesis in self-attention.

Synthesizing coherent soundtracks for long-form videos remains a formidable challenge, currently stalled by three critical impediments: computational scalability, temporal coherence, and, most critically, a pervasive semantic blindness to evolving narrative logic. To bridge these gaps, we propose NarraScore, a hierarchical framework predicated on the core insight that emotion serves as a high-density compression of narrative logic. Uniquely, we repurpose frozen Vision-Language Models (VLMs) as continuous affective sensors, distilling high-dimensional visual streams into dense, narrative-aware Valence-Arousal trajectories. Mechanistically, NarraScore employs a Dual-Branch Injection strategy to reconcile global structure with local dynamism: a Global Semantic Anchor ensures stylistic stability, while a surgical Token-Level Affective Adapter modulates local tension via direct element-wise residual injection. This minimalist design bypasses the bottlenecks of dense attention and architectural cloning, effectively mitigating the overfitting risks associated with data scarcity. Experiments demonstrate that NarraScore achieves state-of-the-art consistency and narrative alignment with negligible computational overhead, establishing a fully autonomous paradigm for long-video soundtrack generation.

Large reasoning models (LRMs) extend large language models by generating explicit chain-of-thought (CoT) reasoning, significantly improving mathematical and logical problem solving. However, this explicit reasoning process also introduces new safety risks, as unsafe behaviors often emerge within intermediate reasoning trajectories, even when final answers appear harmless. Existing safety alignment approaches primarily rely on supervised fine-tuning (SFT) over safety-oriented long CoT datasets. While intuitive, we find that SFT produces inconsistent safety improvements, degrades reasoning ability, and generalizes poorly across model families. These limitations suggest that purely supervised approaches are insufficient for robust safety alignment in LRMs. To address this, we investigate reinforcement learning (RL) as a complementary optimization framework for LRM safety training. Unlike SFT, RL directly optimizes model policies with reward feedback, enabling more adaptive and stable alignment. Extensive experiments across multiple model families and benchmarks show that RL achieves stronger and more consistent safety gains while maintaining reasoning competence. Further analysis of reflection dynamics and token-level entropy reveals that RL suppresses unsafe exploratory reasoning while preserving reflective depth, leading to safer and more reliable reasoning processes.

Recent progress in multi-turn reinforcement learning (RL) has significantly improved reasoning LLMs' performances on complex interactive tasks. Despite advances in stabilization techniques such as fine-grained credit assignment and trajectory filtering, instability remains pervasive and often leads to training collapse. We argue that this instability stems from inefficient exploration in multi-turn settings, where policies continue to generate low-information actions that neither reduce uncertainty nor advance task progress. To address this issue, we propose Token- and Turn-level Policy Optimization (T^2PO), an uncertainty-aware framework that explicitly controls exploration at fine-grained levels. At the token level, T^2PO monitors uncertainty dynamics and triggers a thinking intervention once the marginal uncertainty change falls below a threshold. At the turn level, T^2PO identifies interactions with negligible exploration progress and dynamically resamples such turns to avoid wasted rollouts. We evaluate T^2PO in diverse environments, including WebShop, ALFWorld, and Search QA, demonstrating substantial gains in training stability and performance improvements with better exploration efficiency. Code is available at: https://github.com/WillDreamer/T2PO.

Reinforcement Learning with Verifiable Rewards (RLVR) has recently demonstrated remarkable potential in enhancing the reasoning capability of Large Reasoning Models (LRMs). However, RLVR often leads to entropy collapse, resulting in premature policy convergence and performance saturation. While manipulating token-level entropy has proven effective for promoting policy exploration, we argue that the latent dynamics underlying token generation encode a far richer computational structure for steering policy optimization toward a more effective exploration-exploitation tradeoff. To enable tractable analysis and intervention of the latent dynamics of LRMs, we leverage Koopman operator theory to obtain a linearized representation of their hidden-state dynamics. This enables us to introduce Dynamic Spectral Dispersion (DSD), a new metric to quantify the heterogeneity of the model's latent dynamics, serving as a direct indicator of policy exploration. Building upon these foundations, we propose Reasoning with Latent eXploration (ReLaX), a paradigm that explicitly incorporates latent dynamics to regulate exploration and exploitation during policy optimization. Comprehensive experiments across a wide range of multimodal and text-only reasoning benchmarks show that ReLaX significantly mitigates premature convergence and consistently achieves state-of-the-art performance.

Reinforcement learning (RL) post-training has increasingly demonstrated strong ability to elicit reasoning behaviors in large language models (LLMs). For training efficiency, rollouts are typically generated in an off-policy manner using an older sampling policy and then used to update the current target policy. To correct the resulting discrepancy between the sampling and target policies, most existing RL objectives rely on a token-level importance sampling ratio, primarily due to its computational simplicity and numerical stability. However, we observe that token-level correction often leads to unstable training dynamics when the degree of off-policyness is large. In this paper, we revisit LLM policy optimization under off-policy conditions and show that the theoretically rigorous correction term is the prefix importance ratio, and that relaxing it to a token-level approximation can induce instability in RL post-training. To stabilize LLM optimization under large off-policy drift, we propose a simple yet effective objective, Minimum Prefix Ratio (MinPRO). MinPRO replaces the unstable cumulative prefix ratio with a non-cumulative surrogate based on the minimum token-level ratio observed in the preceding prefix. Extensive experiments on both dense and mixture-of-experts LLMs, across multiple mathematical reasoning benchmarks, demonstrate that MinPRO substantially improves training stability and peak performance in off-policy regimes.

Reinforcement learning with verifiable rewards (RLVR) has advanced the reasoning capabilities of large language models (LLMs). However, prevailing RLVR methods exhibit a systematic bias toward exploitation over exploration, as evidenced by improved pass@1 but reduced pass@K (K>1) performance. To understand this issue, we analyze training dynamics of RLVR methods by tracking the token-level probability distributions over vocabulary candidates. Our analysis reveals a consistent probability concentration effect where the top-1 candidate increasingly accumulates probability mass and suppresses that of other candidates. More importantly, stronger over-concentration correlates with worse pass@K performance. Inspired by this finding, we propose Simple Pass@K Optimization (SimKO), a method designed to mitigate the over-concentration issue, thereby encouraging exploration. SimKO operates in an asymmetrical manner. For verified-correct responses, it boosts the probabilities of the top-K candidates. For verified-incorrect responses, it applies stronger penalties to the top-1 candidate. We observe that this asymmetric design is particularly effective at mitigating over-concentration when applied at tokens with high entropy. Across various math and logical-reasoning benchmarks, SimKO consistently yields higher pass@K for a wide range of K, providing a simple way to improve RLVR's exploration.

Omni-modal large language models (OLLMs) aim to unify multimodal understanding and generation, yet incorporating speech with 3D facial animation remains largely unexplored despite its importance for natural interaction. A key challenge arises from the representation mismatch between discrete, token-level semantic reasoning in LLMs and the dense, fine-grained temporal dynamics required for 3D facial motion, which makes direct modeling difficult to optimize under limited data. We propose Expressive Omni (Ex-Omni), an open-source omni-modal framework that augments OLLMs with speech-accompanied 3D facial animation. Ex-Omni reduces learning difficulty by decoupling semantic reasoning from temporal generation, leveraging speech units as temporal scaffolding and a unified token-as-query gated fusion (TQGF) mechanism for controlled semantic injection. We further introduce InstructEx, a dataset aims to facilitate augment OLLMs with speech-accompanied 3D facial animation. Extensive experiments demonstrate that Ex-Omni performs competitively against existing open-source OLLMs while enabling stable aligned speech and facial animation generation.

Large language models increasingly expose reasoning traces, yet their underlying cognitive structure and steps remain difficult to identify and analyze beyond surface-level statistics. We adopt Schoenfeld's Episode Theory as an inductive, intermediate-scale lens and introduce ThinkARM (Anatomy of Reasoning in Models), a scalable framework that explicitly abstracts reasoning traces into functional reasoning steps such as Analysis, Explore, Implement, Verify, etc. When applied to mathematical problem solving by diverse models, this abstraction reveals reproducible thinking dynamics and structural differences between reasoning and non-reasoning models, which are not apparent from token-level views. We further present two diagnostic case studies showing that exploration functions as a critical branching step associated with correctness, and that efficiency-oriented methods selectively suppress evaluative feedback steps rather than uniformly shortening responses. Together, our results demonstrate that episode-level representations make reasoning steps explicit, enabling systematic analysis of how reasoning is structured, stabilized, and altered in modern language models.

Reinforcement learning (RL) has substantially improved the ability of large language model (LLM) agents to interact with environments and solve multi-turn tasks. However, effective agentic RL remains challenging: sparse outcome-only rewards provide limited guidance for assigning credit to individual steps within long interaction trajectories. Existing approaches often introduce dense intermediate supervision, such as process reward models or auxiliary self-supervised signals, which increases supervision and tuning complexity and may limit generalization across tasks and domains. We present AEM, a supervision-free credit assignment method that adaptively modulates entropy dynamics during RL training to improve the exploration-exploitation trade-off. Since in agentic RL the environment is typically affected by a complete response, rather than an individual token, our analysis lifts entropy dynamics from the token level to the response level, aligning uncertainty estimation with the effective action granularity of LLM agents and reducing sensitivity to token-level sampling noise. We further show that entropy drift under natural-gradient updates is governed by the interaction between the sampled-response advantage and its relative surprisal. Motivated by this result, AEM derives a practical response-level uncertainty proxy and uses it to rescale advantages, leveraging the evolving balance between positive and negative samples to naturally transition from exploration to exploitation. Extensive experiments on ALFWorld, WebShop, and SWE-bench-Verified with models ranging from 1.5B to 32B demonstrate that AEM consistently improves strong RL baselines, including a +1.4\% gain when integrated into a state-of-the-art software-engineering RL training framework.

Large Language Models (LLMs) are increasingly deployed in scenarios demanding ultra-long context reasoning, such as agentic workflows and deep research understanding. However, long-context inference is constrained by the KV cache, a transient memory structure that grows linearly with sequence length and batch size, quickly dominating GPU memory usage. Existing memory reduction techniques, including eviction and quantization, often rely on static heuristics and suffer from degraded quality under tight budgets. In this paper, we propose ARKV, a lightweight and adaptive framework that dynamically allocates precision levels to cached tokens based on per-layer attention dynamics and token-level importance. During a short prefill phase, ARKV estimates the original quantization (OQ) ratio of each layer by computing statistical scores such as attention entropy, variance and kurtosis. During decoding, tokens are assigned to one of three states, Original (full precision), Quantization (low precision), or Eviction, according to a fast heavy-hitter scoring strategy. Our experiments on LLaMA3 and Qwen3 models across diverse long- and short-context tasks demonstrate that ARKV preserves ~97% of baseline accuracy on long-context benchmarks while reducing KV memory usage by 4x, with minimal throughput loss. On short-context tasks, ARKV matches full-precision baselines; on GSM8K math reasoning, it significantly outperforms uniform quantization. These results highlight the practical viability of ARKV for scalable LLM deployment, offering fine-grained, data-driven memory control without retraining or architectural modifications. The source code and artifacts can be found in: https://github.com/Large-scale-Sustainable-Computing-LSC/ARKV

Recently, reinforcement learning with verifiable rewards (RLVR) has been widely used for enhancing the reasoning abilities of large language models (LLMs). A core challenge in RLVR involves managing the exchange between entropy and performance of policies. Despite the importance of this exchange, a fine-grained understanding of when and how this exchange operates most effectively remains limited. To bridge this gap, we conduct a systematic empirical analysis of the entropy-performance exchange mechanism of RLVR across different levels of granularity. Specifically, we first divide the training process into two distinct stages based on entropy dynamics, i.e., rising stage and plateau stage, and then systematically investigate how this mechanism varies across stage-level, instance-level, and token-level granularitiess. Our analysis reveals that, in the rising stage, entropy reduction in negative samples facilitates the learning of effective reasoning patterns, which in turn drives rapid performance gains. Moreover, in the plateau stage, learning efficiency strongly correlates with high-entropy tokens present in low-perplexity samples and those located at the end of sequences. Motivated by these findings, we propose two methods that dynamically adjust the reward signal using perplexity and positional information to focus RL updates on tokens that exhibit high learning potential, achieving improvements compared to the baseline methods on various LLMs.

Bidirectional masked Transformers have become the core theme in the current NLP landscape. Despite their impressive benchmarks, a recurring theme in recent research has been to question such models' capacity for syntactic generalization. In this work, we seek to address this question by adding a supervised, token-level supertagging objective to standard unsupervised pretraining, enabling the explicit incorporation of syntactic biases into the network's training dynamics. Our approach is straightforward to implement, induces a marginal computational overhead and is general enough to adapt to a variety of settings. We apply our methodology on Lassy Large, an automatically annotated corpus of written Dutch. Our experiments suggest that our syntax-aware model performs on par with established baselines, despite Lassy Large being one order of magnitude smaller than commonly used corpora.

Large Vision Language Models (LVLMs) have achieved remarkable success in a range of downstream tasks that require multimodal interaction, but their capabilities come with substantial computational and memory overhead, which hinders practical deployment. Among numerous acceleration techniques, post-training quantization is a popular and effective strategy for reducing memory cost and accelerating inference. However, existing LVLM quantization methods typically measure token sensitivity at the modality level, which fails to capture the complex cross-token interactions and falls short in quantitatively measuring the quantization error at the token level. As tokens interact within the model, the distinction between modalities gradually diminishes, suggesting the need for fine-grained calibration. Inspired by axiomatic attribution in mechanistic interpretability, we introduce a fine-grained quantization strategy on Quantization-aware Integrated Gradients (QIG), which leverages integrated gradients to quantitatively evaluate token sensitivity and push the granularity from modality level to token level, reflecting both inter-modality and intra-modality dynamics. Extensive experiments on multiple LVLMs under both W4A8 and W3A16 settings show that our method improves accuracy across models and benchmarks with negligible latency overhead. For example, under 3-bit weight-only quantization, our method improves the average accuracy of LLaVA-onevision-7B by 1.60%, reducing the gap to its full-precision counterpart to only 1.33%. The code is available at https://github.com/ucas-xiang/QIG.

For robotic agents operating in dynamic environments, learning visual state representations from streaming video observations is essential for sequential decision making. Recent self-supervised learning methods have shown strong transferability across vision tasks, but they do not explicitly address what a good visual state should encode. We argue that effective visual states must capture what-is-where by jointly encoding the semantic identities of scene elements and their spatial locations, enabling reliable detection of subtle dynamics across observations. To this end, we propose CroBo, a visual state representation learning framework based on a global-to-local reconstruction objective. Given a reference observation compressed into a compact bottleneck token, CroBo learns to reconstruct heavily masked patches in a local target crop from sparse visible cues, using the global bottleneck token as context. This learning objective encourages the bottleneck token to encode a fine-grained representation of scene-wide semantic entities, including their identities, spatial locations, and configurations. As a result, the learned visual states reveal how scene elements move and interact over time, supporting sequential decision making. We evaluate CroBo on diverse vision-based robot policy learning benchmarks, where it achieves state-of-the-art performance. Reconstruction analyses and perceptual straightness experiments further show that the learned representations preserve pixel-level scene composition and encode what-moves-where across observations. Project page available at: https://seokminlee-chris.github.io/CroBo-ProjectPage.

Reinforcement learning (RL) has shown strong potential for enhancing reasoning in multimodal large language models, yet existing video reasoning methods often rely on coarse sequence-level rewards or single-factor token selection, neglecting fine-grained links among visual inputs, temporal dynamics, and linguistic outputs, limiting both accuracy and interpretability. We propose Video-KTR, a modality-aware policy shaping framework that performs selective, token-level RL by combining three attribution signals: (1) visual-aware tokens identified via counterfactual masking to reveal perceptual dependence; (2) temporal-aware tokens detected through frame shuffling to expose temporal sensitivity; and (3) high-entropy tokens signaling predictive uncertainty. By reinforcing only these key tokens, Video-KTR focuses learning on semantically informative, modality-sensitive content while filtering out low-value tokens. Across five challenging benchmarks, Video-KTR achieves state-of-the-art or highly competitive results, achieving 42.7\% on Video-Holmes (surpassing GPT-4o) with consistent gains on both reasoning and general video understanding tasks. Ablation studies verify the complementary roles of the attribution signals and the robustness of targeted token-level updates. Overall, Video-KTR improves accuracy and interpretability, offering a simple, drop-in extension to RL for complex video reasoning. Our code and models are available at https://github.com/zywang0104/Video-KTR.

Multi-agent systems (MAS) have emerged as a prominent paradigm for leveraging large language models (LLMs) to tackle complex tasks. However, the mechanisms governing the effectiveness of MAS built upon publicly available LLMs, specifically the underlying rationales for their success or failure, remain largely unexplored. In this paper, we revisit MAS through the perspective of entropy, considering both intra- and inter-agent dynamics by investigating entropy transitions during problem-solving across various topologies, six reasoning benchmarks, and two agentic tasks. By analyzing 245 features spanning token-, agent-, and round-level entropy, we counterintuitively find that a single agent outperforms MAS in approximately 43.3\% of cases, and that entropy dynamics are largely determined during the first round of interaction. Furthermore, we provide three key observations: 1) Certainty Preference: peak entropy directly harms and stable entropy directly benefits MAS correctness; 2) Base Entropy: base models with lower entropy during problem-solving causally drive MAS performance; and 3) Task Awareness: entropy dynamics of MAS play varying roles across different tasks. Building on these insights, we introduce a simple yet effective algorithm, the Entropy Judger, to select solutions from MAS's pass@k results, leading to consistent accuracy improvements across all MAS configurations and tasks. Our source code is available at https://github.com/AgenticFinLab/multiagent-entropy{this https URL}.

The Transformer architecture has significantly advanced natural language processing (NLP) and has been foundational in developing large language models (LLMs) such as LLaMA and OPT, which have come to dominate a broad range of NLP tasks. Despite their superior accuracy, LLMs present unique challenges in practical inference, concerning the compute and memory-intensive nature. Thanks to the autoregressive characteristic of LLM inference, KV caching for the attention layers in Transformers can effectively accelerate LLM inference by substituting quadratic-complexity computation with linear-complexity memory accesses. Yet, this approach requires increasing memory as demand grows for processing longer sequences. The overhead leads to reduced throughput due to I/O bottlenecks and even out-of-memory errors, particularly on resource-constrained systems like a single commodity GPU. In this paper, we propose ALISA, a novel algorithm-system co-design solution to address the challenges imposed by KV caching. On the algorithm level, ALISA prioritizes tokens that are most important in generating a new token via a Sparse Window Attention (SWA) algorithm. SWA introduces high sparsity in attention layers and reduces the memory footprint of KV caching at negligible accuracy loss. On the system level, ALISA employs three-phase token-level dynamical scheduling and optimizes the trade-off between caching and recomputation, thus maximizing the overall performance in resource-constrained systems. In a single GPU-CPU system, we demonstrate that under varying workloads, ALISA improves the throughput of baseline systems such as FlexGen and vLLM by up to 3X and 1.9X, respectively.

Large Language Models (LLMs) for complex reasoning is often hindered by high computational costs and latency, while resource-efficient Small Language Models (SLMs) typically lack the necessary reasoning capacity. Existing collaborative approaches, such as cascading or routing, operate at a coarse granularity by offloading entire queries to LLMs, resulting in significant computational waste when the SLM is capable of handling the majority of reasoning steps. To address this, we propose RelayLLM, a novel framework for efficient reasoning via token-level collaborative decoding. Unlike routers, RelayLLM empowers the SLM to act as an active controller that dynamically invokes the LLM only for critical tokens via a special command, effectively "relaying" the generation process. We introduce a two-stage training framework, including warm-up and Group Relative Policy Optimization (GRPO) to teach the model to balance independence with strategic help-seeking. Empirical results across six benchmarks demonstrate that RelayLLM achieves an average accuracy of 49.52%, effectively bridging the performance gap between the two models. Notably, this is achieved by invoking the LLM for only 1.07% of the total generated tokens, offering a 98.2% cost reduction compared to performance-matched random routers.

Vision Transformers (ViTs) have achieved remarkable success in image recognition, yet standard ViT architectures are hampered by substantial parameter redundancy and high computational cost, limiting their practical deployment. While recent efforts on efficient ViTs primarily focus on static model compression or token-level sparsification, they remain constrained by fixed computational depth for all tokens. In this work, we present MoR-ViT, a novel vision transformer framework that, for the first time, incorporates a token-level dynamic recursion mechanism inspired by the Mixture-of-Recursions (MoR) paradigm. This approach enables each token to adaptively determine its processing depth, yielding a flexible and input-dependent allocation of computational resources. Extensive experiments on ImageNet-1K and transfer benchmarks demonstrate that MoR-ViT not only achieves state-of-the-art accuracy with up to 70% parameter reduction and 2.5x inference acceleration, but also outperforms leading efficient ViT baselines such as DynamicViT and TinyViT under comparable conditions. These results establish dynamic recursion as an effective strategy for efficient vision transformers and open new avenues for scalable and deployable deep learning models in real-world scenarios.

The Mixture-of-Experts (MoE) architecture has demonstrated significant advantages in the era of Large Language Models (LLMs), offering enhanced capabilities with reduced inference costs. However, deploying MoE-based LLMs on memoryconstrained edge devices remains challenging due to their substantial memory requirements. While existing expertoffloading methods alleviate the memory requirements, they often incur significant expert-loading costs or compromise model accuracy. We present HOBBIT, a mixed precision expert offloading system to enable flexible and efficient MoE inference. Our key insight is that dynamically replacing less critical cache-miss experts with low precision versions can substantially reduce expert-loading latency while preserving model accuracy. HOBBIT introduces three innovative techniques that map the natural hierarchy of MoE computation: (1) a token-level dynamic expert loading mechanism, (2) a layer-level adaptive expert prefetching technique, and (3) a sequence-level multidimensional expert caching policy. These innovations fully leverage the benefits of mixedprecision expert inference. By implementing HOBBIT on top of the renowned LLM inference framework Llama.cpp, we evaluate its performance across different edge devices with representative MoE models. The results demonstrate that HOBBIT achieves up to a 9.93x speedup in decoding compared to state-of-the-art MoE offloading systems.

On-policy distillation is pivotal for transferring reasoning capabilities to capacity-constrained models, yet remains prone to instability and negative transfer. We show that on-policy distillation can be interpreted, both theoretically and empirically, as a form of policy optimization, where the teacher-student log-likelihood ratio acts as a token reward. From this insight, we introduce REOPOLD (Relaxed On-Policy Distillation) a framework that stabilizes optimization by relaxing the strict imitation constraints of standard on-policy distillation. Specifically, REOPOLD temperately and selectively leverages rewards from the teacher through mixture-based reward clipping, entropy-based token-level dynamic sampling, and a unified exploration-to-refinement training strategy. Empirically, REOPOLD surpasses its baselines with superior sample efficiency during training and enhanced test-time scaling at inference, across mathematical, visual, and agentic tool-use reasoning tasks. Specifically, REOPOLD outperforms recent RL approaches achieving 6.7~12x greater sample efficiency and enables a 7B student to match a 32B teacher in visual reasoning with a ~3.32x inference speedup.

Enabling large language models to achieve stable self-improvement without external expert supervision remains a central challenge in complex reasoning tasks. Existing self-distillation and reinforcement learning methods lack explicit mechanisms for tracking problem-level learning progress and adapting optimization strategies accordingly. Consequently, training may over-optimize easy problems, receive weak supervision from hard problems, and fail to sufficiently explore borderline cases. To resolve these issues, we propose DRIFT, an online self-evolution policy optimization framework for large language models. DRIFT regulates the model's self-improvement process through the joint use of Difficulty Routing and Rhythm Gating. The former identifies the model's learning state at the problem level and dynamically allocates self-distillation and reinforcement learning signals, while the latter refines policy updates at the token level, concentrating exploration on critical reasoning positions. By further incorporating a success buffer and a two-stage curriculum learning strategy, DRIFT preserves high-quality historical experience while progressively guiding the model from reliable behavior acquisition toward stable policy evolution. Evaluated across five benchmarks and three model scales, DRIFT surpasses the peak performance of both GRPO and SDPO across all evaluated metrics. On the average score over the five benchmarks, DRIFT achieves 79.5%, outperforming GRPO by 9.5% and SDPO by 7.5%, establishing a new state-of-the-art result. Notably, on ToolUse, DRIFT reaches an accuracy of 79.2%, improving over GRPO by 13.5% and SDPO by 10.7%, setting a new state-of-the-art and substantially outperforming all concurrent methods.

Vision Transformer and its variants have demonstrated great potential in various computer vision tasks. But conventional vision transformers often focus on global dependency at a coarse level, which suffer from a learning challenge on global relationships and fine-grained representation at a token level. In this paper, we introduce Multi-scale Attention Fusion into transformer (MAFormer), which explores local aggregation and global feature extraction in a dual-stream framework for visual recognition. We develop a simple but effective module to explore the full potential of transformers for visual representation by learning fine-grained and coarse-grained features at a token level and dynamically fusing them. Our Multi-scale Attention Fusion (MAF) block consists of: i) a local window attention branch that learns short-range interactions within windows, aggregating fine-grained local features; ii) global feature extraction through a novel Global Learning with Down-sampling (GLD) operation to efficiently capture long-range context information within the whole image; iii) a fusion module that self-explores the integration of both features via attention. Our MAFormer achieves state-of-the-art performance on common vision tasks. In particular, MAFormer-L achieves 85.9% Top-1 accuracy on ImageNet, surpassing CSWin-B and LV-ViT-L by 1.7% and 0.6% respectively. On MSCOCO, MAFormer outperforms the prior art CSWin by 1.7% mAPs on object detection and 1.4% on instance segmentation with similar-sized parameters, demonstrating the potential to be a general backbone network.

Mixture-of-Experts (MoE) architectures have emerged as a powerful paradigm for scaling neural networks while maintaining computational efficiency. However, standard MoE implementations rely on two rigid design assumptions: (1) fixed Top-K routing where exactly K experts are activated per token, and (2) uniform expert allocation across all layers. This paper introduces DynaMoE, a novel MoE framework that relaxes both constraints through dynamic token-level expert activation and layer-wise adaptive capacity allocation. DynaMoE introduces a principled routing mechanism where the number of active experts per token varies based on input complexity. Concurrently, the framework implements six distinct scheduling strategies for distributing expert capacity across network depth, including descending, ascending, pyramid, and wave patterns. We theoretically analyze the expressivity gains of dynamic routing and derive bounds on computational efficiency. Through extensive experiments on MNIST, Fashion-MNIST, CIFAR-10 (image classification), and Recycling-the-Web (language modeling) across multiple model scales, we demonstrate that DynaMoE achieves superior parameter efficiency compared to static baselines. Our key finding is that optimal expert schedules are task- and scale-dependent: descending schedules (concentrating capacity in early layers) outperform uniform baselines on image classification. For language modeling, optimal schedules vary by model size, descending for Tiny, ascending for Small, and uniform for Medium. Furthermore, dynamic routing reduces gradient variance during training, leading to improved convergence stability. DynaMoE establishes a new framework for adaptive computation in neural networks, providing principled guidance for MoE architecture design.

Scaling language models unlocks impressive capabilities, but the accompanying computational and memory demands make both training and deployment expensive. Existing efficiency efforts typically target either parameter sharing or adaptive computation, leaving open the question of how to attain both simultaneously. We introduce Mixture-of-Recursions (MoR), a unified framework that combines the two axes of efficiency inside a single Recursive Transformer. MoR reuses a shared stack of layers across recursion steps to achieve parameter efficiency, while lightweight routers enable adaptive token-level thinking by dynamically assigning different recursion depths to individual tokens. This allows MoR to focus quadratic attention computation only among tokens still active at a given recursion depth, further improving memory access efficiency by selectively caching only their key-value pairs. Beyond these core mechanisms, we also propose a KV sharing variant that reuses KV pairs from the first recursion, specifically designed to decrease prefill latency and memory footprint. Across model scales ranging from 135M to 1.7B parameters, MoR forms a new Pareto frontier: at equal training FLOPs and smaller model sizes, it significantly lowers validation perplexity and improves few-shot accuracy, while delivering higher throughput compared with vanilla and existing recursive baselines. These gains demonstrate that MoR is an effective path towards large-model quality without incurring large-model cost.

With the development of large language models (LLMs), the ability to handle longer contexts has become a key capability for Web applications such as cross-document understanding and LLM-powered search systems. However, this progress faces two major challenges: performance degradation due to sequence lengths out-of-distribution, and excessively long inference times caused by the quadratic computational complexity of attention. These issues hinder the application of LLMs in long-context scenarios. In this paper, we propose Dynamic Token-Level KV Cache Selection (TokenSelect), a model-agnostic, training-free method for efficient and accurate long-context inference. TokenSelect builds upon the observation of non-contiguous attention sparsity, using Query-Key dot products to measure per-head KV Cache criticality at token-level. By per-head soft voting mechanism, TokenSelect selectively involves a small number of critical KV cache tokens in the attention calculation without sacrificing accuracy. To further accelerate TokenSelect, we designed the Selection Cache based on observations of consecutive Query similarity and implemented efficient dot product kernel, significantly reducing the overhead of token selection. A comprehensive evaluation of TokenSelect demonstrates up to 23.84x speedup in attention computation and up to 2.28x acceleration in end-to-end latency, while providing superior performance compared to state-of-the-art long-context inference methods.

Critic-free methods like GRPO reduce memory demands by estimating advantages from multiple rollouts but tend to converge slowly, as critical learning signals are diluted by an abundance of uninformative samples and tokens. To tackle this challenge, we propose the Dynamic Dual-Level Down-Sampling (D^3S) framework that prioritizes the most informative samples and tokens across groups to improve the efficient of policy optimization. D^3S operates along two levels: (1) the sample-level, which selects a subset of rollouts to maximize advantage variance (Var(A)). We theoretically proven that this selection is positively correlated with the upper bound of the policy gradient norms, yielding higher policy gradients. (2) the token-level, which prioritizes tokens with a high product of advantage magnitude and policy entropy (|A_{i,t}|times H_{i,t}), focusing updates on tokens where the policy is both uncertain and impactful. Moreover, to prevent overfitting to high-signal data, D^3S employs a dynamic down-sampling schedule inspired by curriculum learning. This schedule starts with aggressive down-sampling to accelerate early learning and gradually relaxes to promote robust generalization. Extensive experiments on Qwen2.5 and Llama3.1 demonstrate that integrating D^3S into advanced RL algorithms achieves state-of-the-art performance and generalization while requiring fewer samples and tokens across diverse reasoning benchmarks. Our code is added in the supplementary materials and will be made publicly available.

The deployment of large language models (LLMs) in real-world applications is increasingly limited by their high inference cost. While recent advances in dynamic token-level computation allocation attempt to improve efficiency by selectively activating model components per token, existing methods rely on greedy routing--a myopic execute-or-skip mechanism that often leads to irreversible information loss and suboptimal token selection. This paper introduces informed routing, a new paradigm that proactively addresses these issues. The key insight is to assess not only a token's immediate importance but also its recoverability, i.e., how well its transformation can be approximated. To this end, we propose the Lightweight Feature Forecaster (LFF), a small predictive module that estimates a unit's output before routing decisions are made. This enables a flexible execute-or-approximate policy that preserves model fidelity while drastically reducing computation. Extensive experiments on both language modeling and reasoning tasks show that informed routing achieves state-of-the-art efficiency-performance trade-offs across multiple sparsity levels. Notably, even without final LoRA fine-tuning, our method matches or surpasses strong baselines that require full fine-tuning, all while reducing training time by over 50%. The code is available at: https://github.com/EIT-NLP/informed-routing

The quadratic complexity of attention remains the central bottleneck in long-context inference for large language models. Prior acceleration methods either sparsify the attention map with structured patterns or permanently evict tokens at specific layers, which can retain irrelevant tokens or rely on irreversible early decisions despite the layer-/head-wise dynamics of token importance. In this paper, we propose Token Sparse Attention, a lightweight and dynamic token-level sparsification mechanism that compresses per-head Q, K, V to a reduced token set during attention and then decompresses the output back to the original sequence, enabling token information to be reconsidered in subsequent layers. Furthermore, Token Sparse Attention exposes a new design point at the intersection of token selection and sparse attention. Our approach is fully compatible with dense attention implementations, including Flash Attention, and can be seamlessly composed with existing sparse attention kernels. Experimental results show that Token Sparse Attention consistently improves accuracy-latency trade-off, achieving up to times3.23 attention speedup at 128K context with less than 1% accuracy degradation. These results demonstrate that dynamic and interleaved token-level sparsification is a complementary and effective strategy for scalable long-context inference.

In large language models (LLMs), each block operates on the residual stream to map input token sequences to output token distributions. However, most of the interpretability literature focuses on internal latent representations, leaving token-space dynamics underexplored. The high dimensionality and categoricity of token distributions hinder their analysis, as standard statistical descriptors are not suitable. We show that the entropy of logit-lens predictions overcomes these issues. In doing so, it provides a per-layer scalar, permutation-invariant metric. We introduce Entropy-Lens to distill the token-space dynamics of the residual stream into a low-dimensional signal. We call this signal the entropy profile. We apply our method to a variety of model sizes and families, showing that (i) entropy profiles uncover token prediction dynamics driven by expansion and pruning strategies; (ii) these dynamics are family-specific and invariant under depth rescaling; (iii) they are characteristic of task type and output format; (iv) these strategies have unequal impact on downstream performance, with the expansion strategy usually being more critical. Ultimately, our findings further enhance our understanding of the residual stream, enabling a granular assessment of how information is processed across model depth.

Direct preference optimization (DPO), a widely adopted offline preference optimization algorithm, aims to align large language models (LLMs) with human-desired behaviors using pairwise preference data. However, the winning response and the losing response within pairwise data are generated isolatedly, leading to weak correlations between them as well as suboptimal alignment performance. To address this issue, we propose an effective framework named BMC, for bridging and modeling correlations in pairwise data. Firstly, we increase the consistency and informativeness of the pairwise preference signals by targeted modifications, synthesizing a pseudo winning response through improving the losing response based on the winning response. Secondly, we identify that DPO alone is insufficient to model these correlations and capture nuanced variations. Therefore, we propose learning token-level correlations by dynamically leveraging the policy model's confidence during training. Comprehensive experiments on QA, math, and instruction-following tasks demonstrate the effectiveness of our approach, significantly surpassing competitive baselines, including DPO. Additionally, our in-depth quantitative analysis reveals the reasons behind our method's superior performance over DPO and showcases its versatility to other DPO variants.

Selective state space models (SSM), such as Mamba, have gained prominence for their effectiveness in modeling sequential data. Despite their outstanding empirical performance, a comprehensive theoretical understanding of deep selective SSM remains elusive, hindering their further development and adoption for applications that need high fidelity. In this paper, we investigate the dynamical properties of tokens in a pre-trained Mamba model. In particular, we derive the dynamical system governing the continuous-time limit of the Mamba model and characterize the asymptotic behavior of its solutions. In the one-dimensional case, we prove that only one of the following two scenarios happens: either all tokens converge to zero, or all tokens diverge to infinity. We provide criteria based on model parameters to determine when each scenario occurs. For the convergent scenario, we empirically verify that this scenario negatively impacts the model's performance. For the divergent scenario, we prove that different tokens will diverge to infinity at different rates, thereby contributing unequally to the updates during model training. Based on these investigations, we propose two refinements for the model: excluding the convergent scenario and reordering tokens based on their importance scores, both aimed at improving practical performance. Our experimental results validate these refinements, offering insights into enhancing Mamba's effectiveness in real-world applications.

Transformer architecture has shown impressive performance in multiple research domains and has become the backbone of many neural network models. However, there is limited understanding on how it works. In particular, with a simple predictive loss, how the representation emerges from the gradient training dynamics remains a mystery. In this paper, for 1-layer transformer with one self-attention layer plus one decoder layer, we analyze its SGD training dynamics for the task of next token prediction in a mathematically rigorous manner. We open the black box of the dynamic process of how the self-attention layer combines input tokens, and reveal the nature of underlying inductive bias. More specifically, with the assumption (a) no positional encoding, (b) long input sequence, and (c) the decoder layer learns faster than the self-attention layer, we prove that self-attention acts as a discriminative scanning algorithm: starting from uniform attention, it gradually attends more to distinct key tokens for a specific next token to be predicted, and pays less attention to common key tokens that occur across different next tokens. Among distinct tokens, it progressively drops attention weights, following the order of low to high co-occurrence between the key and the query token in the training set. Interestingly, this procedure does not lead to winner-takes-all, but decelerates due to a phase transition that is controllable by the learning rates of the two layers, leaving (almost) fixed token combination. We verify this \emph{scan and snap} dynamics on synthetic and real-world data (WikiText).

Recent advancements in large language models (LLMs) have significantly enhanced their reasoning capabilities. However, they continue to struggle with basic character-level tasks, such as counting letters in words, a problem rooted in their tokenization process. While existing benchmarks have highlighted this weakness through basic character operations, such failures are often dismissed due to lacking practical relevance. Yet, many real-world applications, such as navigating text-based maps or interpreting structured tables, rely heavily on precise sub-token understanding. In this regard, we introduce SubTokenTest, a comprehensive benchmark that assesses sub-token understanding through practical, utility-driven tasks. Our benchmark includes ten tasks across four domains and isolates tokenization-related failures by decoupling performance from complex reasoning. We provide a comprehensive evaluation of nine advanced LLMs. Additionally, we investigate the impact of test-time scaling on sub-token reasoning and explore how character-level information is encoded within the hidden states.

Practitioners have consistently observed three puzzling phenomena in transformer-based large language models (LLMs): attention sinks, value-state drains, and residual-state peaks, collectively referred to as extreme-token phenomena. These phenomena are characterized by certain so-called "sink tokens" receiving disproportionately high attention weights, exhibiting significantly smaller value states, and having much larger residual-state norms than those of other tokens. These extreme tokens give rise to various challenges in LLM inference, quantization, and interpretability. We elucidate the mechanisms behind extreme-token phenomena. First, we show that these phenomena arise in very simple architectures -- transformers with one to three layers -- trained on a toy model, the Bigram-Backcopy (BB) task. In this setting, we identify an active-dormant mechanism, where attention heads become sinks for specific input domains while remaining non-sinks for others. Our theoretical analysis of the training dynamics reveals that these phenomena are driven by a mutual reinforcement mechanism. Building on these insights, we propose strategies to mitigate extreme-token phenomena during pretraining, including replacing softmax with ReLU and Adam with SGD. Next, we extend our analysis to pretrained LLMs, including Llama and OLMo, showing that many attention heads exhibit a similar active-dormant mechanism as in the BB task, and that the mutual reinforcement mechanism also governs the emergence of extreme-token phenomena during LLM pretraining. Our results reveal that many of the static and dynamic properties of extreme-token phenomena predicted by the BB task align with observations in pretrained LLMs.

This paper addresses the critical challenge of deriving interpretable confidence scores from generative language models (LLMs) when applied to multi-label content safety classification. While models like LLaMA Guard are effective for identifying unsafe content and its categories, their generative architecture inherently lacks direct class-level probabilities, which hinders model confidence assessment and performance interpretation. This limitation complicates the setting of dynamic thresholds for content moderation and impedes fine-grained error analysis. This research proposes and evaluates three novel token-level probability estimation approaches to bridge this gap. The aim is to enhance model interpretability and accuracy, and evaluate the generalizability of this framework across different instruction-tuned models. Through extensive experimentation on a synthetically generated, rigorously annotated dataset, it is demonstrated that leveraging token logits significantly improves the interpretability and reliability of generative classifiers, enabling more nuanced content safety moderation.

Model parallelism has become a necessity for training modern large-scale deep language models. In this work, we identify a new and orthogonal dimension from existing model parallel approaches: it is possible to perform pipeline parallelism within a single training sequence for Transformer-based language models thanks to its autoregressive property. This enables a more fine-grained pipeline compared with previous work. With this key idea, we design TeraPipe, a high-performance token-level pipeline parallel algorithm for synchronous model-parallel training of Transformer-based language models. We develop a novel dynamic programming-based algorithm to calculate the optimal pipelining execution scheme given a specific model and cluster configuration. We show that TeraPipe can speed up the training by 5.0x for the largest GPT-3 model with 175 billion parameters on an AWS cluster with 48 p3.16xlarge instances compared with state-of-the-art model-parallel methods. The code for reproduction can be found at https://github.com/zhuohan123/terapipe

Multimodal Continual Instruction Tuning aims to continually enhance Large Vision Language Models (LVLMs) by learning from new data without forgetting previously acquired knowledge. Mixture of Experts (MoE) architectures naturally facilitate this by incrementally adding new experts and expanding routers while keeping the existing ones frozen. However, despite expert isolation, MoE-based continual learners still suffer from forgetting due to routing-drift: old-task tokens become mistakenly attracted to newly added experts, degrading performance on prior tasks. We analyze the failure mode at the token level and reveal the token's dilemma: ambiguous and old tokens in new-task data offer minimal learning benefit yet induce forgetting when routed to new experts, due to their ambiguous routing assignment during training. Motivated by this, we propose LLaVA-DyMoE, a dynamic MoE framework that incrementally expands the MoE with drift-aware token assignment. We characterize token types via their routing score distributions and apply targeted regularization. Specifically, a token-level assignment guidance steers ambiguous and old tokens away from new experts to preserve established routing patterns and alleviate routing-drift, while complementary routing score regularizations enforce expert-group separation and promote new-expert specialization. Extensive experiments demonstrate that our LLaVA-DyMoE effectively mitigates routing-drift-induced forgetting, achieving over a 7% gain in mean final accuracy and a 12% reduction in forgetting compared to baselines. The project page is https://zhaoc5.github.io/DyMoE.

Sparse autoencoders (SAEs) decompose language model activations into interpretable features, but existing methods reveal only which features activate, not which change model outputs when amplified. We introduce Control Reinforcement Learning (CRL), which trains a policy to select SAE features for steering at each token, producing interpretable intervention logs: the learned policy identifies features that change model outputs when amplified. Adaptive Feature Masking encourages diverse feature discovery while preserving singlefeature interpretability. The framework yields new analysis capabilities: branch point tracking locates tokens where feature choice determines output correctness; critic trajectory analysis separates policy limitations from value estimation errors; layer-wise comparison reveals syntactic features in early layers and semantic features in later layers. On Gemma 2 2B across MMLU, BBQ, GSM8K, HarmBench, and XSTest, CRL achieves improvements while providing per-token intervention logs. These results establish learned feature steering as a mechanistic interpretability tool that complements static feature analysis with dynamic intervention probes

Scaling the size of a model enhances its capabilities but significantly increases computation complexity. Mixture-of-Experts models (MoE) address the issue by allowing model size to scale up without substantially increasing training or inference costs. Despite their promising results, MoE models encounter several challenges. Primarily, for dynamic routing methods, the dispersion of training tokens across multiple experts can lead to underfitting, particularly for infrequent tokens. Additionally, while fixed routing methods can mitigate that issue, they compromise on the diversity of representations. In this paper, we propose MaskMoE, a method designed to enhance token-level learning by employing a routing masking technique within the Mixture-of-Experts model. MaskMoE is capable of maintaining representation diversity while achieving more comprehensive training. Experimental results demonstrate that our method outperforms previous dominant Mixture-of-Experts models in terms of both perplexity (PPL) and downstream task performance.

The quadratic computational complexity of softmax transformers has become a bottleneck in long-context scenarios. In contrast, linear attention model families provide a promising direction towards a more efficient sequential model. These linear attention models compress past KV values into a single hidden state, thereby efficiently reducing complexity during both training and inference. However, their expressivity remains limited by the size of their hidden state. Previous work proposed interleaving softmax and linear attention layers to reduce computational complexity while preserving expressivity. Nevertheless, the efficiency of these models remains bottlenecked by their softmax attention layers. In this paper, we propose Neural Attention Search Linear (NAtS-L), a framework that applies both linear attention and softmax attention operations within the same layer on different tokens. NAtS-L automatically determines whether a token can be handled by a linear attention model, i.e., tokens that have only short-term impact and can be encoded into fixed-size hidden states, or require softmax attention, i.e., tokens that contain information related to long-term retrieval and need to be preserved for future queries. By searching for optimal Gated DeltaNet and softmax attention combinations across tokens, we show that NAtS-L provides a strong yet efficient token-level hybrid architecture.

Current language models (LMs) use a fixed, static subword tokenizer. This choice, often taken for granted, typically results in degraded efficiency and capabilities in languages other than English, and makes it challenging to apply LMs to new domains or languages. To address these issues, we propose retrofitting LMs with dynamic tokenization: a way to dynamically decide on token boundaries based on the input text. For encoder-style models, we introduce a subword-merging algorithm inspired by byte-pair encoding (BPE), but at a batch level. We merge frequent subword sequences in a batch, then apply a pretrained embedding-prediction hypernetwork to compute the token embeddings on-the-fly. When applied with word-level boundaries, this on average reduces token sequence lengths by >20% across 14 languages on XNLI with XLM-R while degrading its task performance by less than 2%. For decoder-style models, we apply dynamic tokenization in two ways: 1) for prefilling, maintaining performance of Mistral-7B almost completely with up to 40% sequence reduction - relative to the word-level; and 2) via an approximate nearest neighbor index, achieving fast generation with a one million token vocabulary, demonstrating scalability to even larger, dynamic vocabularies. Overall, our findings show that dynamic tokenization substantially improves inference speed and promotes fairness across languages, making a leap towards overcoming the limitations of static tokenization and enabling more equitable and adaptable LMs.

Medical image segmentation is vital for clinical diagnosis and quantitative analysis, yet remains challenging due to the heterogeneity of imaging modalities and the high cost of pixel-level annotations. Although general interactive segmentation models like SAM have achieved remarkable progress, their transfer to medical imaging still faces two key bottlenecks: (i) the lack of adaptive mechanisms for modality- and anatomy-specific tasks, which limits generalization in out-of-distribution medical scenarios; and (ii) current medical adaptation methods fine-tune on large, heterogeneous datasets without selection, leading to noisy supervision, higher cost, and negative transfer. To address these issues, we propose SegMoTE, an efficient and adaptive framework for medical image segmentation. SegMoTE preserves SAM's original prompt interface, efficient inference, and zero-shot generalization while introducing only a small number of learnable parameters to dynamically adapt across modalities and tasks. In addition, we design a progressive prompt tokenization mechanism that enables fully automatic segmentation, significantly reducing annotation dependence. Trained on MedSeg-HQ, a curated dataset less than 1% of existing large-scale datasets, SegMoTE achieves SOTA performance across diverse imaging modalities and anatomical tasks. It represents the first efficient, robust, and scalable adaptation of general segmentation models to the medical domain under extremely low annotation cost, advancing the practical deployment of foundation vision models in clinical applications.

Reinforcement learning with verifiable rewards (RLVR) has become standard for improving LLM reasoning. However, existing PPO-style trust-region mechanisms remain position-agnostic by enforcing uniform thresholds across all tokens independently. This pointwise treatment conflicts with autoregressive generation in two critical ways. First, uniform thresholds ignore autoregressive asymmetry. Early-stage deviations produce compounding sequence-level drift, causing static thresholds to under-regulate early divergence and excessively constrain late-stage exploration. Second, evaluating token-level divergence in isolation overlooks cumulative prefix drift, granting the same divergence allowance regardless of how far the conditioning history has already deviated from the rollout policy. To address this limitation, we propose CPPO (Cumulative Prefix-divergence Policy Optimization), a token-level masking rule that aligns updates with a finite-horizon policy-improvement bound via two coupled mechanisms. First, a position-weighted threshold imposes stricter limits at early positions whose effects persist longer, relaxing constraints for late-stage tokens. Second, a cumulative prefix budget tracks historical deviations, dynamically restricting further token-level deviation to prevent compounding errors along the prefix. Empirically, CPPO enhances training stability and significantly improves reasoning accuracy across various model scales.

Inference accounts for the majority of latency and energy consumption in large language model (LLM) deployments, often exceeding 90% of total cost. While training-time efficiency has seen extensive progress, runtime optimization remains a key bottleneck, particularly under autoregressive decoding. Existing approaches -- such as pruning, quantization, early exits, and speculative decoding -- often require retraining, architectural changes, or disrupt decoding compatibility. We introduce QuickSilver, a modular, token-level framework that enables semantic adaptivity at inference time without altering model weights or structure. QuickSilver integrates four synergistic mechanisms: (i) Dynamic Token Halting, which halts computation for tokens with converged representations; (ii) KV Cache Skipping, which selectively suppresses memory writes to reduce attention overhead; and (iii) Contextual Token Fusion, which collapses redundant tokens into shared paths to shrink sequence length. Unlike speculative decoding or MoE routing, QuickSilver operates entirely on frozen, dense models and requires no auxiliary networks. Applied to GPT-2 and Llama-2 across WikiText-103 and C4, QuickSilver achieves up to 39.6% FLOP reduction with negligible perplexity degradation (<=0.2).

Recent advances in multimodal large reasoning models (MLRMs) have substantially improved their ability to solve complex textual and visual tasks. However, these models tend to overthink on simple problems, producing unnecessarily lengthy reasoning traces, while under-exploring on challenging ones, leading to missed solutions. To address this imbalance, we propose ARES, a unified open-source framework for adaptive reasoning that dynamically allocates exploration effort based on task difficulty. Our approach is motivated by two key empirical findings: (i) while single-token entropy is noisy, high window-entropy (HWE) tokens (token-level entropies averaged under a sliding window) can reliably capture reasoning-critical moments; and (ii) reducing HWE usage benefits easy problems, while increasing it is essential for solving hard ones. Building on these insights, ARES introduces a two-stage training pipeline. In the Adaptive Cold-Start stage, we curate multimodal and textual data paired with reasoning traces of length proportional to problem difficulty, equipping the model with initial difficulty awareness. In the second stage, we develop Adaptive Entropy Policy Optimization (AEPO), which uses HWE tokens as exploration triggers to decide when to explore, and a hierarchical entropy reward with dynamic KL control to decide how much to explore. Extensive experiments demonstrate that ARES achieves superior performance and reasoning efficiency across diverse mathematical, logical, and multimodal benchmarks, while closing the gap to leading commercial systems under significantly lower inference costs.

Recent advances in large language models (LLMs) have demonstrated the power of reasoning through self-generated chains of thought. Multiple reasoning agents can collaborate to raise joint reasoning quality above individual outcomes. However, such agents typically interact in a turn-based manner, trading increased latency for improved quality. In this paper, we propose Group Think--a single LLM that acts as multiple concurrent reasoning agents, or thinkers. With shared visibility into each other's partial generation progress, Group Think introduces a new concurrent-reasoning paradigm in which multiple reasoning trajectories adapt dynamically to one another at the token level. For example, a reasoning thread may shift its generation mid-sentence upon detecting that another thread is better positioned to continue. This fine-grained, token-level collaboration enables Group Think to reduce redundant reasoning and improve quality while achieving significantly lower latency. Moreover, its concurrent nature allows for efficient utilization of idle computational resources, making it especially suitable for edge inference, where very small batch size often underutilizes local~GPUs. We give a simple and generalizable modification that enables any existing LLM to perform Group Think on a local GPU. We also present an evaluation strategy to benchmark reasoning latency and empirically demonstrate latency improvements using open-source LLMs that were not explicitly trained for Group Think. We hope this work paves the way for future LLMs to exhibit more sophisticated and more efficient collaborative behavior for higher quality generation.

Frontier LLMs are increasingly utilised across academia, society and industry. A commonly used unit for comparing models, their inputs and outputs, and estimating inference pricing is the token. In general, tokens are used as a stable currency, assumed to be broadly consistent across tokenizers and contexts, enabling direct comparisons. However, tokenization varies significantly across models and domains of text, making naive interpretation of token counts problematic. We quantify this variation by providing a comprehensive empirical analysis of tokenization, exploring the compression of sequences to tokens across different distributions of textual data. Our analysis challenges commonly held heuristics about token lengths, finding them to be overly simplistic. We hope the insights of our study add clarity and intuition toward tokenization in contemporary LLMs.

We study the fractal structure of language, aiming to provide a precise formalism for quantifying properties that may have been previously suspected but not formally shown. We establish that language is: (1) self-similar, exhibiting complexities at all levels of granularity, with no particular characteristic context length, and (2) long-range dependent (LRD), with a Hurst parameter of approximately H=0.70. Based on these findings, we argue that short-term patterns/dependencies in language, such as in paragraphs, mirror the patterns/dependencies over larger scopes, like entire documents. This may shed some light on how next-token prediction can lead to a comprehension of the structure of text at multiple levels of granularity, from words and clauses to broader contexts and intents. We also demonstrate that fractal parameters improve upon perplexity-based bits-per-byte (BPB) in predicting downstream performance. We hope these findings offer a fresh perspective on language and the mechanisms underlying the success of LLMs.

Token-level adaptive computation seeks to reduce inference cost by allocating more computation to harder tokens and less to easier ones. However, prior work is primarily evaluated on natural-language benchmarks using task-level metrics, where token-level difficulty is unobservable and confounded with architectural factors, making it unclear whether compute allocation truly aligns with underlying complexity. We address this gap through three contributions. First, we introduce a complexity-controlled evaluation paradigm using algorithmic and synthetic language tasks with parameterized difficulty, enabling direct testing of token-level compute allocation. Second, we propose ANIRA, a unified recurrent Transformer framework that supports per-token variable-depth computation while isolating compute allocation decisions from other model factors. Third, we use this framework to conduct a systematic analysis of token-level adaptive computation across alignment with complexity, generalization, and decision timing. Our results show that compute allocation aligned with task complexity can emerge without explicit difficulty supervision, but such alignment does not imply algorithmic generalization: models fail to extrapolate to unseen input sizes despite allocating additional computation. We further find that early compute decisions rely on static structural cues, whereas online halting more closely tracks algorithmic execution state.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a leading paradigm for enhancing visual reasoning in Multimodal Large Language Models (MLLMs). However, existing RLVR methods optimize primarily for the reasoning outcome, fundamentally overlooking the fine-grained cross-modal coordination required during the generation process. Through token-level analyses and controlled interventions, we reveal that during Chain-of-Thought (CoT) reasoning, MLLMs frequently fail to dynamically alternate between extracting visual evidence and synthesizing textual context-a coordination breakdown that is causally linked to reasoning failures. Motivated by these findings, we propose DyCo-RL, which integrates dynamic cross-modal coordination into RLVR optimization. Specifically, DyCo-RL uses the Fisher-Rao geodesic distance to measure within-modality attention shifts, assigning tokens to either visually-oriented or text-oriented functional roles. It then evaluates the alignment between a token's actual attention allocation and its assigned role, leveraging this score for alignment-guided advantage reweighting during policy optimization. Extensive experiments demonstrate that the algorithm-agnostic DyCo-RL, when applied to Qwen2.5-VL-3B/7B, consistently improves four representative RLVR algorithms across seven benchmarks spanning visual-centric and mathematical reasoning.

We study how the next-token prediction of an autoregressive Transformer language model changes under small perturbations of earlier input token embeddings. Motivated by operator learning and iterative solvers for differential equations, we investigate how the influence of one token on another decays with distance in a trained model. In multilevel methods for differential equations, such as domain decomposition, multigrid, and multilevel preconditioning, one often exploits a separation between strong local interactions and weaker but essential global interactions. The latter correspond to the long tail of the Green's function and are typically handled by a coarse-level operator. Inspired by this perspective, we compute an empirical, distance-resolved gradient profile of token dependencies using autograd. Experiments on trained Pythia models and Qwen2.5-0.5B show that, over the measured distance range, the median Jacobian sensitivity is much better described by a power-law-type decay than by an exponential alternative: the diagonal-normalized profile is well described by $overline G(r) approx γ+β(r+1)^{-p} with exponents p \approx 0.7--0.9 (typically 0.8--0.9$). This behavior appears on coherent text from Gutenberg and WikiText-103. Token-shuffling experiments show that the power-law profile persists even when syntax and prediction quality collapse, whereas randomly initialized models do not exhibit it. The slowly decaying long-range sensitivity thus appears to be a learned property of trained autoregressive Transformer operators. These findings suggest that hierarchical or coarse-level mechanisms in language models may be able to exploit the long-tailed sensitivity profiles.

We present Dyve, a dynamic process verifier that enhances reasoning error detection in large language models by integrating fast and slow thinking, inspired by Kahneman's Systems Theory. Dyve adaptively applies immediate token-level confirmation System 1 for straightforward steps and comprehensive analysis System 2 for complex ones. Leveraging a novel step-wise consensus-filtered process supervision technique, combining Monte Carlo estimation with LLM based evaluation, Dyve curates high-quality supervision signals from noisy data. Experimental results on ProcessBench and the MATH dataset confirm that Dyve significantly outperforms existing process-based verifiers and boosts performance in Best-of-N settings.

Reinforcement Learning with Verifiable Rewards (RLVR) offers a promising framework for optimizing large language models in reasoning tasks. However, existing RLVR algorithms focus on different granularities, and each has complementary strengths and limitations. Group Relative Policy Optimization (GRPO) updates the policy with token-level importance ratios, which preserves fine-grained credit assignment but often suffers from high variance and instability. In contrast, Group Sequence Policy Optimization (GSPO) applies single sequence-level importance ratios across all tokens in a response that better matches sequence-level rewards, but sacrifices token-wise credit assignment. In this paper, we propose Dynamic Hybrid Policy Optimization (DHPO) to bridge GRPO and GSPO within a single clipped surrogate objective. DHPO combines token-level and sequence-level importance ratios using weighting mechanisms. We explore two variants of the mixing mechanism, including an averaged mixing and an entropy-guided mixing. To further stabilize training, we employ a branch-specific clipping strategy that constrains token-level and sequence-level ratios within separate trust regions before mixing, preventing outliers in either branch from dominating the update. Across seven challenging mathematical reasoning benchmarks, experiments on both dense and MoE models from the Qwen3 series show that DHPO consistently outperforms GRPO and GSPO. We will release our code upon acceptance of this paper.

Reinforcement-learning-based post-training has become a key approach for improving the reasoning ability of large language models, but its token-level learning signals remain poorly understood. This work studies their heterogeneity through attention entropy, which measures how concentrated or diffuse the contextual support is for each response token. We first show that token-level RL objectives are sparsely estimable: uniformly random 20 percent token subsets preserve much of the full-token held-out performance, suggesting substantial redundancy in token-level updates. However, entropy-structured subsets behave very differently. Low-attention-entropy tokens, which we call anchors, rely on concentrated support, produce stable gradients aligned with full-token updates, and provide a reliable optimization backbone, but tend to plateau on harder benchmarks. High-attention-entropy tokens, which we call explorers, aggregate more diffuse context and induce larger but more volatile gradients. Explorer-only training is unstable on average, though rare successful runs suggest that these tokens may contain useful hard-reasoning signals when optimization remains stable. We support this anchor-explorer spectrum with evidence-gathering analyses, entropy dynamics, gradient-geometry diagnostics, and controls showing that position, predictive entropy, and loss normalization do not explain the observed asymmetry. Finally, a dynamic entropy-aware soft-reweighting intervention improves Qwen3-8B-Base from 34.39 to 37.40 held-out average in the strongest setting. These findings suggest that attention entropy reveals optimization-relevant structure in token-level RL signals, and that uniform token averaging can obscure meaningful heterogeneity in reasoning post-training.

Reinforcement Learning from Verifiable Rewards (RLVR) has emerged as a promising framework for enhancing the reasoning capabilities of large language models. However, existing approaches such as GRPO often suffer from zero gradients. This problem arises primarily due to fixed clipping bounds for token-level probability ratios and the standardization of identical rewards, which can lead to ineffective gradient updates and underutilization of generated responses. In this work, we propose Dynamic Clipping Policy Optimization (DCPO), which introduces a dynamic clipping strategy that adaptively adjusts the clipping bounds based on token-specific prior probabilities to enhance token-level exploration, and a smooth advantage standardization technique that standardizes rewards across cumulative training steps to improve the response-level effective utilization of generated responses. DCPO achieved state-of-the-art performance on four benchmarks based on four different models. In particular, DCPO achieved an Avg@1 of 46.7 under greedy decoding and an Avg@32 of 38.8 under 32 times sampling on the AIME24 benchmark, surpassing both DAPO (36.7/31.6) and GRPO (36.7/32.1) on the Qwen2.5-Math-7B model. On the AIME25 benchmark based on Qwen2.5-14B, DCPO achieves a performance of (23.3/19.0), surpassing GRPO (13.3/10.5) and DAPO (20.0/15.3). Furthermore, DCPO achieved an average 28% improvement in the nonzero advantage over GRPO in four models, doubled the training efficiency over DAPO, and significantly reduced the token clipping ratio by an order of magnitude compared to both GRPO and DAPO, while achieving superior performance. These results highlight DCPO's effectiveness in leveraging generated data more efficiently for reinforcement learning in large language models.

Large Multimodal Models (LMMs) have become a pivotal research focus in deep learning, demonstrating remarkable capabilities in 3D scene understanding. However, current 3D LMMs employing thousands of spatial tokens for multimodal reasoning suffer from critical inefficiencies: excessive computational overhead and redundant information flows. Unlike 2D VLMs processing single images, 3D LMMs exhibit inherent architectural redundancy due to the heterogeneous mechanisms between spatial tokens and visual tokens. To address this challenge, we propose AdaToken-3D, an adaptive spatial token optimization framework that dynamically prunes redundant tokens through spatial contribution analysis. Our method automatically tailors pruning strategies to different 3D LMM architectures by quantifying token-level information flows via attention pattern mining. Extensive experiments on LLaVA-3D (a 7B parameter 3D-LMM) demonstrate that AdaToken-3D achieves 21\% faster inference speed and 63\% FLOPs reduction while maintaining original task accuracy. Beyond efficiency gains, this work systematically investigates redundancy patterns in multimodal spatial information flows through quantitative token interaction analysis. Our findings reveal that over 60\% of spatial tokens contribute minimally (<5\%) to the final predictions, establishing theoretical foundations for efficient 3D multimodal learning.

The quadratic cost of attention hinders the scalability of long-context LLMs, especially in resource-constrained settings. Existing static sparse methods such as sliding windows or global tokens utilizes the sparsity of attention to reduce the cost of attention, but poorly adapts to the content-dependent variations in attention due to their staticity. While previous work has proposed several dynamic approaches to improve flexibility, they still depend on predefined templates or heuristic mechanisms. Such strategies reduce generality and prune tokens that remain contextually important, limiting their accuracy across diverse tasks. To tackle these bottlenecks of existing methods for long-context modeling, we introduce Dynamic Hierarchical Sparse Attention (DHSA), a data-driven framework that dynamically predicts attention sparsity online without retraining. Our proposed DHSA adaptively segments sequences into variable-length chunks, then computes chunk representations by aggregating the token embeddings within each chunk. To avoid the bias introduced by varying chunk lengths, we apply length-normalized aggregation that scales the averaged embeddings by the square root of the chunk size. Finally, DHSA upsamples the chunk-level similarity scores to token level similarities to calculate importance scores that determine which token-level interactions should be preserved. Our experiments on Gemma2 with Needle-in-a-Haystack Test and LongBench show that DHSA matches dense attention in accuracy, while reducing prefill latency by 20-60% and peak memory usage by 35%. Compared to other representative baselines such as block sparse attention, DHSA achieves consistently higher accuracy (6-18% relative gains) with comparable or lower cost, offering an efficient and adaptable solution for long-context on-device LLMs.

Large language models allocate uniform computation across all tokens, ignoring that some sequences are trivially predictable while others require deep reasoning. We introduce ConceptMoE, which dynamically merges semantically similar tokens into concept representations, performing implicit token-level compute allocation. A learnable chunk module identifies optimal boundaries by measuring inter-token similarity, compressing sequences by a target ratio R before they enter the compute-intensive concept model. Crucially, the MoE architecture enables controlled evaluation: we reallocate saved computation to match baseline activated FLOPs (excluding attention map computation) and total parameters, isolating genuine architectural benefits. Under these conditions, ConceptMoE consistently outperforms standard MoE across language and vision-language tasks, achieving +0.9 points on language pretraining, +2.3 points on long context understanding, and +0.6 points on multimodal benchmarks. When converting pretrained MoE during continual training with layer looping, gains reach +5.5 points, demonstrating practical applicability. Beyond performance, ConceptMoE reduces attention computation by up to R^2times and KV cache by Rtimes. At R=2, empirical measurements show prefill speedups reaching 175\% and decoding speedups up to 117\% on long sequences. The minimal architectural modifications enable straightforward integration into existing MoE, demonstrating that adaptive concept-level processing fundamentally improves both effectiveness and efficiency of large language models.

Knowledge-grounded dialogue generation aims to mitigate the issue of text degeneration by incorporating external knowledge to supplement the context. However, the model often fails to internalize this information into responses in a human-like manner. Instead, it simply inserts segments of the provided knowledge into generic responses. As a result, the generated responses tend to be tedious, incoherent, and in lack of interactivity which means the degeneration problem is still unsolved. In this work, we first find that such copying-style degeneration is primarily due to the weak likelihood objective, which allows the model to "cheat" the objective by merely duplicating knowledge segments in a superficial pattern matching based on overlap. To overcome this challenge, we then propose a Multi-level Adaptive Contrastive Learning (MACL) framework that dynamically samples negative examples and subsequently penalizes degeneration behaviors at both the token-level and sequence-level. Extensive experiments on the WoW dataset demonstrate the effectiveness of our approach across various pre-trained models.

Large Language Models (LLMs) apply uniform computation to all tokens, despite language exhibiting highly non-uniform information density. This token-uniform regime wastes capacity on locally predictable spans while under-allocating computation to semantically critical transitions. We propose Dynamic Large Concept Models (DLCM), a hierarchical language modeling framework that learns semantic boundaries from latent representations and shifts computation from tokens to a compressed concept space where reasoning is more efficient. DLCM discovers variable-length concepts end-to-end without relying on predefined linguistic units. Hierarchical compression fundamentally changes scaling behavior. We introduce the first compression-aware scaling law, which disentangles token-level capacity, concept-level reasoning capacity, and compression ratio, enabling principled compute allocation under fixed FLOPs. To stably train this heterogeneous architecture, we further develop a decoupled μP parametrization that supports zero-shot hyperparameter transfer across widths and compression regimes. At a practical setting (R=4, corresponding to an average of four tokens per concept), DLCM reallocates roughly one-third of inference compute into a higher-capacity reasoning backbone, achieving a +2.69\% average improvement across 12 zero-shot benchmarks under matched inference FLOPs.

The scalability of Large Language Models (LLMs) to long contexts is fundamentally constrained by the quadratic complexity of standard attention, motivating the adoption of linear attention mechanisms with sub-quadratic cost. To improve representation capacity under long contexts, recent approaches organize memory in a multi-state manner. However, existing multi-state linear attention methods rely on fixed state merging policies that cannot adapt to dynamically varying token importance, irreversibly obscuring critical tokens and causing severe error accumulation over long sequences. To address this limitation, we propose DLA, a dynamic memory modeling framework for multi-state linear attention. DLA introduces (i) Information-Aware Dynamic State Merging, which adaptively determines state boundaries based on token-level information variation, preserving high-resolution representations around semantic transitions while aggressively summarizing stable regions, and (ii) Capacity-Bounded Memory Modeling, which maintains a fixed-size, chronologically ordered state cache by selectively merging adjacent low-information states to control memory growth with minimal information loss. We pre-train DLA on two different linear attention models and evaluate on 16 datasets across three categories. Experimental results demonstrate the superiority of DLA over state-of-the-art.

Web search provides a promising way for people to obtain information and has been extensively studied. With the surgence of deep learning and large-scale pre-training techniques, various neural information retrieval models are proposed and they have demonstrated the power for improving search (especially, the ranking) quality. All these existing search methods follow a common paradigm, i.e. index-retrieve-rerank, where they first build an index of all documents based on document terms (i.e., sparse inverted index) or representation vectors (i.e., dense vector index), then retrieve and rerank retrieved documents based on similarity between the query and documents via ranking models. In this paper, we explore a new paradigm of information retrieval with neither sparse nor dense index but only a model. Specifically, we propose a pre-training model-based IR system called DynamicRetriever. As for this system, the training stage embeds the token-level and document-level information (especially, document identifiers) of the corpus into the model parameters, then the inference stage directly generates document identifiers for a given query. Compared with existing search methods, the model-based IR system has two advantages: i) it parameterizes the traditional static index with a pre-training model, which converts the document semantic mapping into a dynamic and updatable process; ii) with separate document identifiers, it captures both the term-level and document-level information for each document. Extensive experiments conducted on the public search benchmark MS MARCO verify the effectiveness and potential of our proposed new paradigm for information retrieval.

Supervised fine-tuning (SFT) is the predominant method for adapting large language models (LLMs), yet it often struggles with generalization compared to reinforcement learning (RL). In this work, we posit that this performance disparity stems not just from the loss function, but from a more fundamental difference: SFT learns from a fixed, pre-collected dataset, whereas RL utilizes on-policy data sampled from the current policy. Building on this hypothesis, we introduce one-token rollout (OTR), a novel fine-tuning algorithm that guides SFT with the policy gradient method. OTR reframes the autoregressive learning process by treating each token generation as a single-step reinforcement learning trajectory. At each step, it performs a Monte Carlo ``rollout'' by sampling multiple candidate tokens from the current policy's distribution. The ground-truth token from the supervised data is then used to provide a reward signal to these samples. Guided by policy gradient, our algorithm repurposes static, off-policy supervised data into a dynamic, on-policy signal at the token level, capturing the generalization benefits of on-policy learning while bypassing the costly overhead of full sentence generation. Through extensive experiments on a diverse suite of challenging benchmarks spanning mathematical reasoning, code generation, and general domain reasoning, we demonstrate that OTR consistently outperforms standard SFT. Our findings establish OTR as a powerful and practical alternative for fine-tuning LLMs and provide compelling evidence that the on-policy nature of data is a critical driver of generalization, offering a promising new direction for fine-tuning LLMs.

Large Language Models (LLMs) achieve superior performance through Chain-of-Thought (CoT) reasoning, but these token-level reasoning chains are computationally expensive and inefficient. In this paper, we introduce Compressed Latent Reasoning (CoLaR), a novel framework that dynamically compresses reasoning processes in latent space through a two-stage training approach. First, during supervised fine-tuning, CoLaR extends beyond next-token prediction by incorporating an auxiliary next compressed embedding prediction objective. This process merges embeddings of consecutive tokens using a compression factor randomly sampled from a predefined range, and trains a specialized latent head to predict distributions of subsequent compressed embeddings. Second, we enhance CoLaR through reinforcement learning (RL) that leverages the latent head's non-deterministic nature to explore diverse reasoning paths and exploit more compact ones. This approach enables CoLaR to: i) perform reasoning at a dense latent level (i.e., silently), substantially reducing reasoning chain length, and ii) dynamically adjust reasoning speed at inference time by simply prompting the desired compression factor. Extensive experiments across four mathematical reasoning datasets demonstrate that CoLaR achieves 14.1% higher accuracy than latent-based baseline methods at comparable compression ratios, and reduces reasoning chain length by 53.3% with only 4.8% performance degradation compared to explicit CoT method. Moreover, when applied to more challenging mathematical reasoning tasks, our RL-enhanced CoLaR demonstrates performance gains of up to 5.4% while dramatically reducing latent reasoning chain length by 82.8%. The code and models will be released upon acceptance.

Recent video multimodal large language models (MLLMs) increasingly couple step-by-step reasoning with on-demand visual evidence retrieval, allowing models to revisit relevant video segments during inference. However, two structural gaps remain in existing thinking-with-video systems. (i) Sampling density is not a learnable decision: existing methods may let the model decide where to look, but the per-window frame rate is largely fixed. As a result, fine-grained evidence is often recovered through repeated retrieval calls, which increases inference context length and training difficulty. (ii) Retrieval and answer generation are usually optimized with a single trajectory-level advantage, so the "where to look" tokens and the "how to answer" tokens receive the same credit even when one is correct and the other is not. To address these gaps, we present DynFrame, a framework that emits the temporal window and the sampling density as native tokens within a single autoregressive pass. This learnable span-density retrieval enables acquiring multi-granularity evidence with a single retrieval step. Based on the above tokenized retrieval interface, we further introduce Segment-Decoupled GRPO (SD-GRPO), which splits each rollout at the retrieval boundary and assigns role-specific token-level advantages, separately crediting the sampling decision and the answer. Trained on the curated DM-CoT-74k and DM-RL-45k, DynFrame-4B is competitive with strong 7B-8B baselines across six benchmarks (NExT-GQA, Charades-STA, ActivityNet-MR, Video-MME, MLVU, LVBench), and DynFrame-8B sets new state-of-the-art on most metrics. Code is available at https://github.com/zhangguanghao523/DynFrame.

Recent advancements in Large Language Models (LLMs) have achieved robust performance across diverse tasks, but fine-tuning these models for specific domains remains resource-intensive. Parameter-Efficient Fine-Tuning (PEFT) methods like Low-Rank Adaptation (LoRA) address this challenge by fine-tuning a small subset of parameters. However, existing methods for fusing multiple LoRAs lack dynamic fusion based on contextual inputs and often increase inference time due to token-level operations. We propose DLP-LoRA, a Dynamic Lightweight Plugin that employs a mini-MLP module with only 5M parameters to dynamically fuse multiple LoRAs at the sentence level using top-p sampling strategies. This approach reduces inference time to less than twice that of single LoRA inference by leveraging parallel computation. Evaluations across 26 tasks-including multiple-choice questions and question answering-demonstrate that DLP-LoRA achieves an average accuracy of 92.34% on multiple-choice datasets and significant improvements in BLEU and ROUGE scores on QA datasets, outperforming different LLMs backbones under composite task settings. DLP-LoRA effectively balances performance and efficiency, making it a practical solution for dynamic multi-task adaptation in LLMs. Our code is available at https://github.com/MeCuping/DLP-LoRA.

Large language models display remarkable capabilities in logical and mathematical reasoning, allowing them to solve complex tasks. Interestingly, these abilities emerge in networks trained on the simple task of next-token prediction. In this work, we present a theoretical framework for studying auto-regressive next-token predictors. We demonstrate that even simple models such as linear next-token predictors, trained on Chain-of-Thought (CoT) data, can approximate any function efficiently computed by a Turing machine. We introduce a new complexity measure -- length complexity -- which measures the number of intermediate tokens in a CoT sequence required to approximate some target function, and analyze the interplay between length complexity and other notions of complexity. Finally, we show experimentally that simple next-token predictors, such as linear networks and shallow Multi-Layer Perceptrons (MLPs), display non-trivial performance on text generation and arithmetic tasks. Our results demonstrate that the power of language models can be attributed, to a great extent, to the auto-regressive next-token training scheme, and not necessarily to a particular choice of architecture.

Large language models (LLMs) reason over discrete token ID sequences, yet modern subword tokenizers routinely produce non-unique encodings: multiple token ID sequences can detokenize to identical surface strings. This representational mismatch creates an unmeasured fragility wherein reasoning processes can fail. LLMs may treat two internal representations as distinct "words" even when they are semantically identical at the text level. In this work, we show that tokenization can betray LLM reasoning through one-to-many token ID mappings. We introduce a tokenization-consistency probe that requires models to replace designated target words in context while leaving all other content unchanged. The task is intentionally simple at the surface level, enabling us to attribute failures to tokenizer-detokenizer artifacts rather than to knowledge gaps or parameter limitations. Through analysis of over 11000 replacement trials across state-of-the-art open-source LLMs, we find a non-trivial rate of outputs exhibit phantom edits: cases where models operate under the illusion of correct reasoning, a phenomenon arising from tokenizer-induced representational defects. We further analyze these cases and provide a taxonomy of eight systematic tokenizer artifacts, including whitespace-boundary shifts and intra-word resegmentation. These findings indicate that part of apparent reasoning deficiency originates in the tokenizer layer, motivating tokenizer-level remedies before incurring the cost of training ever-larger models on ever-larger corpora.

Large language models (LLMs) trained on huge corpora of text datasets demonstrate intriguing capabilities, achieving state-of-the-art performance on tasks they were not explicitly trained for. The precise nature of LLM capabilities is often mysterious, and different prompts can elicit different capabilities through in-context learning. We propose a framework that enables us to analyze in-context learning dynamics to understand latent concepts underlying LLMs' behavioral patterns. This provides a more nuanced understanding than success-or-failure evaluation benchmarks, but does not require observing internal activations as a mechanistic interpretation of circuits would. Inspired by the cognitive science of human randomness perception, we use random binary sequences as context and study dynamics of in-context learning by manipulating properties of context data, such as sequence length. In the latest GPT-3.5+ models, we find emergent abilities to generate seemingly random numbers and learn basic formal languages, with striking in-context learning dynamics where model outputs transition sharply from seemingly random behaviors to deterministic repetition.

This paper introduces a continuous-time stochastic dynamical framework for understanding how large language models (LLMs) may self-amplify latent biases or toxicity through their own chain-of-thought reasoning. The model posits an instantaneous "severity" variable x(t) in [0,1] evolving under a stochastic differential equation (SDE) with a drift term μ(x) and diffusion σ(x). Crucially, such a process can be consistently analyzed via the Fokker--Planck approach if each incremental step behaves nearly Markovian in severity space. The analysis investigates critical phenomena, showing that certain parameter regimes create phase transitions from subcritical (self-correcting) to supercritical (runaway severity). The paper derives stationary distributions, first-passage times to harmful thresholds, and scaling laws near critical points. Finally, it highlights implications for agents and extended LLM reasoning models: in principle, these equations might serve as a basis for formal verification of whether a model remains stable or propagates bias over repeated inferences.

Vision-Language Models (VLMs) have demonstrated strong capability in a wide range of tasks such as visual recognition, document parsing, and visual grounding. Nevertheless, recent work shows that while VLMs often manage to capture the correct image region corresponding to the question, they do not necessarily produce the correct answers. In this work, we demonstrate that this misalignment could be attributed to suboptimal information flow within VLMs, where text tokens distribute too much attention to irrelevant visual tokens, leading to incorrect answers. Based on the observation, we show that modulating the information flow during inference can improve the perception capability of VLMs. The idea is that text tokens should only be associated with important visual tokens during decoding, eliminating the interference of irrelevant regions. To achieve this, we propose a token dynamics-based method to determine the importance of visual tokens, where visual tokens that exhibit distinct activation patterns during different decoding stages are viewed as important. We apply our approach to representative open-source VLMs and evaluate on various datasets, including visual question answering, visual grounding and counting, optical character recognition, and object hallucination. The results show that our approach significantly improves the performance of baselines. Project page: https://cxliu0.github.io/AIF/.

Tokenization imposes a fixed granularity on the input text, freezing how a language model operates on data and how far in the future it predicts. Byte Pair Encoding (BPE) and similar schemes split text once, build a static vocabulary, and leave the model stuck with that choice. We relax this rigidity by introducing an autoregressive U-Net that learns to embed its own tokens as it trains. The network reads raw bytes, pools them into words, then pairs of words, then up to 4 words, giving it a multi-scale view of the sequence. At deeper stages, the model must predict further into the future -- anticipating the next few words rather than the next byte -- so deeper stages focus on broader semantic patterns while earlier stages handle fine details. When carefully tuning and controlling pretraining compute, shallow hierarchies tie strong BPE baselines, and deeper hierarchies have a promising trend. Because tokenization now lives inside the model, the same system can handle character-level tasks and carry knowledge across low-resource languages.

A popular approach to post-training control of large language models (LLMs) is the steering of intermediate latent representations. Namely, identify a well-chosen direction depending on the task at hand and perturbs representations along this direction at inference time. While many propositions exist to pick this direction, considerably less is understood about how to choose the magnitude of the move, whereas its importance is clear: too little and the intended behavior does not emerge, too much and the model's performance degrades beyond repair. In this work, we propose the first theoretical analysis of steering strength. We characterize its effect on next token probability, presence of a concept, and cross-entropy, deriving precise qualitative laws governing these quantities. Our analysis reveals surprising behaviors, including non-monotonic effects of steering strength. We validate our theoretical predictions empirically on eleven language models, ranging from a small GPT architecture to modern models.

Large Language Models (LLMs) have made significant strides in natural language processing, and a precise understanding of the internal mechanisms driving their success is essential. In this work, we analyze the trajectories of token embeddings as they pass through transformer blocks, linearizing the system along these trajectories through their Jacobian matrices. By examining the relationships between these block Jacobians, we uncover the phenomenon of transformer block coupling in a multitude of LLMs, characterized by the coupling of their top singular vectors across tokens and depth. Our findings reveal that coupling positively correlates with model performance, and that this relationship is stronger than with other hyperparameters such as parameter count, model depth, and embedding dimension. We further investigate how these properties emerge during training, observing a progressive development of coupling, increased linearity, and layer-wise exponential growth in token trajectories. Additionally, experiments with Vision Transformers (ViTs) corroborate the emergence of coupling and its relationship with generalization, reinforcing our findings in LLMs. Collectively, these insights offer a novel perspective on token interactions in transformers, opening new directions for studying their mechanisms as well as improving training and generalization.

State-of-the-art language models are autoregressive and operate on subword units known as tokens. Specifically, one must encode the conditioning string into a list of tokens before passing to the language models for next-token prediction. We show that popular encoding schemes, such as maximum prefix encoding (MPE) and byte-pair-encoding (BPE), induce a sampling bias that cannot be mitigated with more training or data. To counter this universal problem, for each encoding scheme above, we propose a novel algorithm to obtain unbiased estimates from any language model trained on tokenized data. Our methods do not require finetuning the model, and the complexity, defined as the number of model runs, scales linearly with the sequence length in the case of MPE. As a result, we show that one can simulate token-free behavior from a tokenized language model. We empirically verify the correctness of our method through a Markov-chain setup, where it accurately recovers the transition probabilities, as opposed to the conventional method of directly prompting tokens into the language model.

How should hidden states generated autoregressively be collapsed into a representation that reflects a language model's internal state? Despite tokens being generated under causal masking, we find that mean pooling across their hidden states yields more semantic representations than any individual token alone. We quantify this through kernel alignment to reference spaces in language, vision, and protein domains. The improvement through mean pooling is consistent with information being distributed across generated tokens rather than localized to a single position. Furthermore, representations derived from generated tokens outperform those from prompt tokens, and alignment across generation reveals interpretable dynamics in model behavior.

One of the most striking findings in modern research on large language models (LLMs) is that scaling up compute during training leads to better results. However, less attention has been given to the benefits of scaling compute during inference. This survey focuses on these inference-time approaches. We explore three areas under a unified mathematical formalism: token-level generation algorithms, meta-generation algorithms, and efficient generation. Token-level generation algorithms, often called decoding algorithms, operate by sampling a single token at a time or constructing a token-level search space and then selecting an output. These methods typically assume access to a language model's logits, next-token distributions, or probability scores. Meta-generation algorithms work on partial or full sequences, incorporating domain knowledge, enabling backtracking, and integrating external information. Efficient generation methods aim to reduce token costs and improve the speed of generation. Our survey unifies perspectives from three research communities: traditional natural language processing, modern LLMs, and machine learning systems.

State Space Models (SSMs) have recently emerged as efficient alternatives to Transformer-Based Models (TBMs) for long-sequence processing, offering linear scaling and lower memory use. Yet, how contextual information flows across layers and tokens in these architectures remains understudied. We present the first unified, token- and layer-level analysis of representation propagation in SSMs and TBMs. Using centered kernel alignment, stability metrics, and probing, we characterize how representations evolve within and across layers. We find a key divergence: TBMs rapidly homogenize token representations, with diversity reemerging only in later layers, while SSMs preserve token uniqueness early but converge to homogenization deeper. Theoretical analysis and parameter randomization further reveal that oversmoothing in TBMs stems from architectural design, whereas in SSMs it arises mainly from training dynamics. These insights clarify the inductive biases of both architectures and inform future model and training designs for long-context reasoning.

Autoregressive language models generate text one token at a time, yet natural language is inherently structured in multi-token units, including phrases, n-grams, and collocations that carry meaning jointly. This one-token bottleneck limits both the expressiveness of the model during pre-training and its throughput at inference time. Existing remedies such as speculative decoding or diffusion-based language models either leave the underlying bottleneck intact or sacrifice the causal structure essential to language modeling. We propose BitLM, a language model that represents each token as a fixed-length binary code and employs a lightweight diffusion head to denoise multiple tokens in parallel within each block. Crucially, BitLM preserves left-to-right causal attention across blocks while making joint lexical decisions within each block, combining the reliability of autoregressive modeling with the parallelism of iterative refinement. By replacing the large-vocabulary softmax with bitwise denoising, BitLM reframes token generation as iterative commitment in a compact binary space, enabling more efficient pre-training and substantially faster inference without altering the causal foundation that makes language models effective. Our results demonstrate that the one-token-at-a-time paradigm is not a fundamental requirement but an interface choice, and that changing it can yield a stronger and faster language model. We hope BitLM points toward a promising direction for next-generation language model architectures.

Entropy-based deep reasoning has emerged as a promising direction for improving the reasoning capabilities of Large Language Models (LLMs), but existing methods often either increase response length indiscriminately or shorten responses at the cost of accuracy. To better balance this trade-off, we introduce Conditional Entropy Shaping (CES), a framework that dynamically controls token-level response entropy, enabling LLMs to produce concise solutions on simple problems while encouraging deeper exploration on hard ones. Built on DAPO, CES uses token-level entropy as an uncertainty signal and applies a conditional bidirectional policy: it penalizes high-entropy "forking point" tokens on correct reasoning paths to improve conciseness, and rewards them on incorrect paths to encourage exploration and error correction. We implement CES on DeepSeek-R1-Distill-7B and evaluate it on 12 mathematical benchmarks. CES consistently improves average accuracy while reducing response length relative to DAPO, and supplementary experiments show similar trends on a smaller 1.5B backbone and on out-of-domain benchmarks.

Finetuning large language models (LLMs) enables user-specific customization but introduces critical safety risks: even a few harmful examples can compromise safety alignment. A common mitigation strategy is to update the model more strongly on examples deemed safe, while downweighting or excluding those flagged as unsafe. However, because safety context can shift within a single example, updating the model equally on both harmful and harmless parts of a response is suboptimal-a coarse treatment we term static safety shaping. In contrast, we propose dynamic safety shaping (DSS), a framework that uses fine-grained safety signals to reinforce learning from safe segments of a response while suppressing unsafe content. To enable such fine-grained control during finetuning, we introduce a key insight: guardrail models, traditionally used for filtering, can be repurposed to evaluate partial responses, tracking how safety risk evolves throughout the response, segment by segment. This leads to the Safety Trajectory Assessment of Response (STAR), a token-level signal that enables shaping to operate dynamically over the training sequence. Building on this, we present STAR-DSS, guided by STAR scores, that robustly mitigates finetuning risks and delivers substantial safety improvements across diverse threats, datasets, and model families-all without compromising capability on intended tasks. We encourage future safety research to build on dynamic shaping principles for stronger mitigation against evolving finetuning risks.

On-policy distillation (OPD) offers superior capacity transfer by supervising student-sampled trajectories with dense token-level signals. To furnish high-quality supervision sources and thereby elevate the performance frontier of distillation, an intuitive direction is to infuse privileged information to either teacher or student itself. However, this additional input induces a potential failure mode we dub privilege illusion: a pattern that conflates the transferable capability gap that students are meant to close, and the information asymmetry gap that can only be mimicked but never replicated. This issue is further amplified by the inherent non-uniformity of token-level supervision, where only a small subset of tokens carries pivotal capability-bearing signals. To this end, we propose DOPD, an advantage-aware dual distillation paradigm that dynamically routes token-level supervision between privileged teacher and privileged student policies based on their advantage gap and relative probabilities. Each token receives supervision of different strength, objective, and strategy from either teacher or student itself, which transfers credible capability while simultaneously receiving auxiliary signals, to alleviate privilege illusion. Extensive experiments on both large language model (LLM) and vision-language model (VLM) settings demonstrate that DOPD consistently outperforms Vanilla OPD and other counterparts. Further results on stability, robustness, continual learning, and out-of-distribution tasks validate its superiority.

Large language models have shown strong potential for Arabic medical text generation; however, traditional fine-tuning objectives treat all medical cases uniformly, ignoring differences in clinical severity. This limitation is particularly critical in healthcare settings, where errors in severe cases contain higher clinical risk. In this work, we propose a severity-aware weighted loss for fine-tuning Arabic language models on medical complaint-response data. The method depends on soft severity probabilities to dynamically scale token-level loss contributions during optimization, thereby prioritizing clinically critical interactions without modifying model architectures. Experiments are conducted using the MAQA dataset, which provides Arabic medical complaints and trusted human responses. Severity labels and probabilistic scores are automatically derived using a fine-tuned AraBERT-based classifier and incorporated exclusively at the loss level. The proposed approach is evaluated across ten Arabic large language models of varying architectures and parameter scales. While standard cross-entropy fine-tuning yields only modest improvements, severity-aware optimization consistently achieves larger gains. Using a balanced weighting configuration, performance improves from 54.04% to 66.14% for AraGPT2-Base, from 59.16% to 67.18% for AraGPT2-Medium, and from 57.83% to 66.86% for Qwen2.5-0.5B, with peak performance reaching 67.18%. Overall, severity-aware fine-tuning delivers improvements of up to 12.10% over non-fine-tuned baselines, demonstrating robust and architecture-consistent gains.

Large Language Models (LLMs) have achieved remarkable progress across reasoning, generation, and decision-making tasks, yet deploying them on mobile, embedded, and edge devices remains particularly challenging. On-device LLM inference is heavily constrained by the memory and bandwidth overhead of the key-value (KV) cache, which grows linearly with context length and often dominates decoding cost. Existing KV-cache quantization schemes typically rely on fixed precision or hand-crafted heuristics, thereby wasting bits on low-impact tokens while over-compressing informative ones, leading to avoidable accuracy degradation. Inspired by Huffman coding's principle of variable-length allocation, we propose adaptive KV-cache quantization, a learned policy that assigns bit-width proportional to token importance, minimizing expected memory and latency without sacrificing competitive accuracy. Our framework extracts lightweight token-level features, including token frequency, quality score, attention variance, and entropy-based uncertainty, and feeds them into a compact data-driven controller that dynamically selects KV precision from {2-bit, 4-bit, 8-bit, FP16} during decoding. This adaptive precision policy reduces KV memory footprint and latency while improving accuracy compared to static KV quantization and rule-based baselines, and maintaining competitive accuracy close to FP16 inference across standard LLM benchmarks. Extensive experiments across multiple commonsense reasoning benchmarks using SmolLM-135M, SmolLM-360M, and SmolLM-1.7B demonstrate that our controller consistently improves the accuracy-latency trade-off. For instance, with SmolLM-360M on HellaSwag, our method reduces decoding latency (ms/token) by 17.75% relative to static KV quantization, improves accuracy by 7.60 points, and remains within only 0.30 points of FP16 inference.

Large language models (LLMs) have significantly advanced in reasoning tasks through reinforcement learning (RL) optimization, achieving impressive capabilities across various challenging benchmarks. However, our empirical analysis reveals a critical drawback: reasoning-oriented RL fine-tuning significantly increases the prevalence of hallucinations. We theoretically analyze the RL training dynamics, identifying high-variance gradient, entropy-induced randomness, and susceptibility to spurious local optima as key factors leading to hallucinations. To address this drawback, we propose Factuality-aware Step-wise Policy Optimization (FSPO), an innovative RL fine-tuning algorithm incorporating explicit factuality verification at each reasoning step. FSPO leverages automated verification against given evidence to dynamically adjust token-level advantage values, incentivizing factual correctness throughout the reasoning process. Experiments across mathematical reasoning and hallucination benchmarks using Qwen2.5 and Llama models demonstrate that FSPO effectively reduces hallucinations while enhancing reasoning accuracy, substantially improving both reliability and performance.

We present core attention disaggregation (CAD), a technique that improves long-context large language model training by decoupling the core attention computation, softmax(QK^T)V, from the rest of the model and executing it on a separate pool of devices. In existing systems, core attention is colocated with other layers; at long context lengths, its quadratic compute growth compared to the near-linear growth of other components causes load imbalance and stragglers across data and pipeline parallel groups. CAD is enabled by two observations. First, core attention is stateless: it has no trainable parameters and only minimal transient data, so balancing reduces to scheduling compute-bound tasks. Second, it is composable: modern attention kernels retain high efficiency when processing fused batches of token-level shards with arbitrary lengths. CAD partitions core attention into token-level tasks and dispatches them to dedicated attention servers, which dynamically rebatch tasks to equalize compute without sacrificing kernel efficiency. We implement CAD in a system called DistCA, which uses a ping-pong execution scheme to fully overlap communication with computation and in-place execution on attention servers to reduce memory use. On 512 H200 GPUs and context lengths up to 512k tokens, DistCA improves end-to-end training throughput by up to 1.35x, eliminates data and pipeline parallel stragglers, and achieves near-perfect compute and memory balance.

While linear attention reduces the quadratic complexity of standard Transformers to linear time, it often lags behind in expressivity due to the removal of softmax normalization. This omission eliminates global competition, a critical mechanism that enables models to sharply focus on relevant information amidst long-context noise. In this work, we propose Softmax Linear Attention (SLA), a framework designed to restore this competitive selection without sacrificing efficiency. By lifting the softmax operation from the token level to the head level, SLA leverages attention heads as coarse semantic slots, applying a competitive gating mechanism to dynamically select the most relevant subspaces. This reintroduces the ``winner-take-all'' dynamics essential for precise retrieval and robust long-context understanding. Distinct from prior methods that focus on refining local kernel functions, SLA adopts a broader perspective by exploiting the higher-level multi-head aggregation structure. Extensive experiments demonstrate that SLA consistently enhances state-of-the-art linear baselines (RetNet, GLA, GDN) across language modeling and long-context benchmarks, particularly in challenging retrieval scenarios where it significantly boosts robustness against noise, validating its capability to restore precise focus while maintaining linear complexity.

Current critic-free RL methods for large reasoning models suffer from severe inefficiency when training on positive homogeneous prompts (where all rollouts are correct), resulting in waste of rollouts due to zero advantage estimates. We introduce a radically simple yet powerful solution to Mine intrinsic mastery (Miner), that repurposes the policy's intrinsic uncertainty as a self-supervised reward signal, with no external supervision, auxiliary models, or additional inference cost. Our method pioneers two key innovations: (1) a token-level focal credit assignment mechanism that dynamically amplifies gradients on critical uncertain tokens while suppressing overconfident ones, and (2) adaptive advantage calibration to seamlessly integrate intrinsic and verifiable rewards. Evaluated across six reasoning benchmarks on Qwen3-4B and Qwen3-8B base models, Miner achieves state-of-the-art performance among the other four algorithms, yielding up to 4.58 absolute gains in Pass@1 and 6.66 gains in Pass@K compared to GRPO. Comparison with other methods targeted at exploration enhancement further discloses the superiority of the two newly proposed innovations. This demonstrates that latent uncertainty exploitation is both necessary and sufficient for efficient and scalable RL training of reasoning models.

Multi-hop question answering (QA) requires models to retrieve and reason over multiple pieces of evidence. While Retrieval-Augmented Generation (RAG) has made progress in this area, existing methods often suffer from two key limitations: (1) fixed or overly frequent retrieval steps, and (2) ineffective use of previously retrieved knowledge. We propose MIND (Memory-Informed and INteractive Dynamic RAG), a framework that addresses these challenges through: (i) prompt-based entity extraction to identify reasoning-relevant elements, (ii) dynamic retrieval triggering based on token-level entropy and attention signals, and (iii) memory-aware filtering, which stores high-confidence facts across reasoning steps to enable consistent multi-hop generation.

Recent works have argued that high-level semantic concepts are encoded "linearly" in the representation space of large language models. In this work, we study the origins of such linear representations. To that end, we introduce a simple latent variable model to abstract and formalize the concept dynamics of the next token prediction. We use this formalism to show that the next token prediction objective (softmax with cross-entropy) and the implicit bias of gradient descent together promote the linear representation of concepts. Experiments show that linear representations emerge when learning from data matching the latent variable model, confirming that this simple structure already suffices to yield linear representations. We additionally confirm some predictions of the theory using the LLaMA-2 large language model, giving evidence that the simplified model yields generalizable insights.

The increasing size of generative Pre-trained Language Models (PLMs) has greatly increased the demand for model compression. Despite various methods to compress BERT or its variants, there are few attempts to compress generative PLMs, and the underlying difficulty remains unclear. In this paper, we compress generative PLMs by quantization. We find that previous quantization methods fail on generative tasks due to the homogeneous word embeddings caused by reduced capacity, and varied distribution of weights. Correspondingly, we propose a token-level contrastive distillation to learn distinguishable word embeddings, and a module-wise dynamic scaling to make quantizers adaptive to different modules. Empirical results on various tasks show that our proposed method outperforms the state-of-the-art compression methods on generative PLMs by a clear margin. With comparable performance with the full-precision models, we achieve 14.4x and 13.4x compression rates on GPT-2 and BART, respectively.

Alignment has greatly improved large language models (LLMs)' output quality at the cost of diversity, yielding highly similar outputs across generations. We propose Base-Aligned Model Collaboration (BACo), an inference-time token-level model collaboration framework that dynamically combines a base LLM with its aligned counterpart to optimize diversity and quality. Inspired by prior work (Fei et al., 2025), BACo employs routing strategies that determine, at each token, from which model to decode based on next-token prediction uncertainty and predicted contents' semantic role. Prior diversity-promoting methods, such as retraining, prompt engineering, and multi-sampling methods, improve diversity but often degrade quality or require costly decoding or post-training. In contrast, BACo achieves both high diversity and quality post hoc within a single pass, while offering strong controllability. We explore a family of routing strategies, across three open-ended generation tasks and 13 metrics covering diversity and quality, BACo consistently surpasses state-of-the-art inference-time baselines. With our best router, BACo achieves a 21.3% joint improvement in diversity and quality. Human evaluations also mirror these improvements. The results suggest that collaboration between base and aligned models can optimize and control diversity and quality.

Activation steering offers a promising approach to controlling the behavior of Large Language Models by directly manipulating their internal activations. However, most existing methods struggle to jointly steer multiple attributes, often resulting in interference and undesirable trade-offs. To address this challenge, we propose Multi-Subspace Representation Steering (MSRS), a novel framework for effective multi-attribute steering via subspace representation fine-tuning. MSRS reduces inter-attribute interference by allocating orthogonal subspaces to each attribute, isolating their influence within the model's representation space. MSRS also incorporates a hybrid subspace composition strategy: it combines attribute-specific subspaces for unique steering directions with a shared subspace for common steering directions. A dynamic weighting function learns to efficiently integrate these components for precise control. During inference, MSRS introduces a token-level steering mechanism that dynamically identifies and intervenes on the most semantically relevant tokens, enabling fine-grained behavioral modulation. Experimental results show that MSRS significantly reduces attribute conflicts, surpasses existing methods across a range of attributes, and generalizes effectively to diverse downstream tasks.

Agentic language models must learn when to call tools, when to consume tool responses, and when to answer directly. This makes multi-teacher on-policy distillation a natural training strategy: one teacher can specialize in tool calls, another in direct responses, and the student can learn from both on its own generated distribution. We show that this strategy can induce a behavior shift that is invisible from aggregate losses alone. In a two-teacher tool-use setting, vanilla generalized knowledge distillation improves tool-call recall but also moves the model toward over-calling, where it calls tools on examples that should be answered directly. Aggregate explanations are insufficient: tool-call samples do not receive more token exposure, and full-sequence per-token divergence is not larger for the tool-call teacher. We instead analyze behavior leverage imbalance: local token-level signals at mode- entry and structural positions, such as <tool_call> and function names, can have disproportionate control over the global generation mode. We propose Soft Clamp, a per-token divergence calibration method that dynamically compresses extreme token-level Jensen-Shannon divergence while preserving nonzero gradients. On APIGen-MT, Soft Clamp reduces over-calling from 13.7% to 9.0% relative to vanilla GKD while matching its decision accuracy. In a BFCL multi-turn diagnostic, it also lowers tool-call loops and repeated calls among GKD variants. These results suggest that multi-teacher OPD should monitor where teacher signals act, not only how large they are in aggregate.

Large Language Models (LLMs) demonstrate exceptional capabilities in various scenarios. However, they suffer from much redundant information and tend to be lost in the middle in long context scenarios, leading to inferior performance. To address these challenges, we present Perception Compressor, a training-free prompt compression method. It includes a dual-slope ratio allocator to dynamically assign compression ratios and open-book ratios, a perception retriever that leverages guiding questions and instruction to retrieve the most relevant demonstrations, and a semi-guided iterative compression that retains key information at the token level while removing tokens that distract the LLM. We conduct extensive experiments on long context benchmarks, i.e., NaturalQuestions, LongBench, and MuSiQue. Experiment results show that Perception Compressor outperforms existing methods by a large margin, achieving state-of-the-art performance.

Jailbreak attacks pose a serious threat to the safety of Large Language Models (LLMs) by crafting adversarial prompts that bypass alignment mechanisms, causing the models to produce harmful, restricted, or biased content. In this paper, we propose SafeLLM, a novel unlearning-based defense framework that unlearn the harmful knowledge from LLMs while preserving linguistic fluency and general capabilities. SafeLLM employs a three-stage pipeline: (1) dynamic unsafe output detection using a hybrid approach that integrates external classifiers with model-internal evaluations; (2) token-level harmful content tracing through feedforward network (FFN) activations to localize harmful knowledge; and (3) constrained optimization to suppress unsafe behavior without degrading overall model quality. SafeLLM achieves targeted and irreversible forgetting by identifying and neutralizing FFN substructures responsible for harmful generation pathways. Extensive experiments on prominent LLMs (Vicuna, LLaMA, and GPT-J) across multiple jailbreak benchmarks show that SafeLLM substantially reduces attack success rates while maintaining high general-purpose performance. Compared to standard defense methods such as supervised fine-tuning and direct preference optimization, SafeLLM offers stronger safety guarantees, more precise control over harmful behavior, and greater robustness to unseen attacks. Moreover, SafeLLM maintains the general performance after the harmful knowledge unlearned. These results highlight unlearning as a promising direction for scalable and effective LLM safety.

Code generation using large language models (LLMs) is highly sensitive to the choice of tokens during decoding, especially at points of uncertainty that critically affect the generated program's logic. Conventional decoding methods such as greedy search and beam search apply uniform treatment to all tokens, neglecting the unique uncertainty characteristics inherent in code generation, which can result in suboptimal outputs. In this work, we conduct an empirical analysis demonstrating that a significant portion of generation errors arises from incorrect token ranking at high-uncertainty steps, where the ground truth token exists in the candidate set but fails to be ranked first. Inspired by this insight, we introduce AdaDec, an adaptive decoding framework guided by token-level uncertainty quantified via Shannon entropy. AdaDec dynamically learns uncertainty thresholds tailored to each model and employs a pause-then-rerank mechanism with lookahead when the uncertainty surpasses these thresholds. Evaluation on the HumanEval and MBPP benchmarks reveals that AdaDec achieves up to a 15.5% improvement in Pass@1 accuracy compared to greedy decoding, matches or outperforms traditional beam search, and reduces both computational overhead and latency through targeted, selective pausing. Our findings suggest that uncertainty-aware adaptive decoding holds considerable potential for enhancing both the reliability and efficiency of code generation with LLMs.

Image compression for machines calls for a unified codec that serves multiple downstream vision tasks. Existing approaches either adopt task-specific end-to-end designs, raising parameter and deployment overhead, or rely on transfer-based adaptations that remain externally attached and heuristic task design. A key limitation shared by both lines of work is their largely static computation pattern, which applies similar transformations across tokens despite the fact that different image regions exhibit markedly different semantic importance and complexity for machine perception. We propose MoECodec, a token-aware image compression framework that supports multiple downstream tasks within a single model. MoECodec replaces the FFN layers in transformer-based compression model token-wise Mixture-of-Experts (MoE), enabling dynamic, token-level computation conditioned on the input content and task objective. To make MoE effective in compression model, we introduce a stable routing strategy that combines expert-choice routing with spatial total variation regularization to encourage spatially coherent assignments, and we propose a lightweight expert architecture, Group Shuffle MLP (GShMLP), to control parameter growth. Extensive experiments show consistent improvement against baselines on both conventional image reconstruction and machine tasks.

Recent studies have successfully shown that large language models (LLMs) can be successfully used for generative error correction (GER) on top of the automatic speech recognition (ASR) output. Specifically, an LLM is utilized to carry out a direct mapping from the N-best hypotheses list generated by an ASR system to the predicted output transcription. However, despite its effectiveness, GER introduces extra data uncertainty since the LLM is trained without taking into account acoustic information available in the speech signal. In this work, we aim to overcome such a limitation by infusing acoustic information before generating the predicted transcription through a novel late fusion solution termed Uncertainty-Aware Dynamic Fusion (UADF). UADF is a multimodal fusion approach implemented into an auto-regressive decoding process and works in two stages: (i) It first analyzes and calibrates the token-level LLM decision, and (ii) it then dynamically assimilates the information from the acoustic modality. Experimental evidence collected from various ASR tasks shows that UADF surpasses existing fusion mechanisms in several ways. It yields significant improvements in word error rate (WER) while mitigating data uncertainty issues in LLM and addressing the poor generalization relied with sole modality during fusion. We also demonstrate that UADF seamlessly adapts to audio-visual speech recognition.

We present Ring-1T, the first open-source, state-of-the-art thinking model with a trillion-scale parameter. It features 1 trillion total parameters and activates approximately 50 billion per token. Training such models at a trillion-parameter scale introduces unprecedented challenges, including train-inference misalignment, inefficiencies in rollout processing, and bottlenecks in the RL system. To address these, we pioneer three interconnected innovations: (1) IcePop stabilizes RL training via token-level discrepancy masking and clipping, resolving instability from training-inference mismatches; (2) C3PO++ improves resource utilization for long rollouts under a token budget by dynamically partitioning them, thereby obtaining high time efficiency; and (3) ASystem, a high-performance RL framework designed to overcome the systemic bottlenecks that impede trillion-parameter model training. Ring-1T delivers breakthrough results across critical benchmarks: 93.4 on AIME-2025, 86.72 on HMMT-2025, 2088 on CodeForces, and 55.94 on ARC-AGI-v1. Notably, it attains a silver medal-level result on the IMO-2025, underscoring its exceptional reasoning capabilities. By releasing the complete 1T parameter MoE model to the community, we provide the research community with direct access to cutting-edge reasoning capabilities. This contribution marks a significant milestone in democratizing large-scale reasoning intelligence and establishes a new baseline for open-source model performance.