Daily Papers

Diffusion Language Models (DLMs) present a compelling alternative to autoregressive models, offering flexible, any-order infilling without specialized prompting design. However, their practical utility is blocked by a critical limitation: the requirement of a fixed-length masked sequence for generation. This constraint severely degrades code infilling performance when the predefined mask size mismatches the ideal completion length. To address this, we propose DreamOn, a novel diffusion framework that enables dynamic, variable-length generation. DreamOn augments the diffusion process with two length control states, allowing the model to autonomously expand or contract the output length based solely on its own predictions. We integrate this mechanism into existing DLMs with minimal modifications to the training objective and no architectural changes. Built upon Dream-Coder-7B and DiffuCoder-7B, DreamOn achieves infilling performance on par with state-of-the-art autoregressive models on HumanEval-Infilling and SantaCoder-FIM and matches oracle performance achieved with ground-truth length. Our work removes a fundamental barrier to the practical deployment of DLMs, significantly advancing their flexibility and applicability for variable-length generation. Our code is available at https://github.com/DreamLM/DreamOn.

Several studies have employed reinforcement learning (RL) to address the challenges of regional adaptive traffic signal control (ATSC) and achieved promising results. In this field, existing research predominantly adopts multi-agent frameworks. However, the adoption of multi-agent frameworks presents challenges for scalability. Instead, the Traffic signal control (TSC) problem necessitates a single-agent framework. TSC inherently relies on centralized management by a single control center, which can monitor traffic conditions across all roads in the study area and coordinate the control of all intersections. This work proposes a single-agent RL-based regional ATSC model compatible with probe vehicle technology. Key components of the RL design include state, action, and reward function definitions. To facilitate learning and manage congestion, both state and reward functions are defined based on queue length, with action designed to regulate queue dynamics. The queue length definition used in this study differs slightly from conventional definitions but is closely correlated with congestion states. More importantly, it allows for reliable estimation using link travel time data from probe vehicles. With probe vehicle data already covering most urban roads, this feature enhances the proposed method's potential for widespread deployment. The method was comprehensively evaluated using the SUMO simulation platform. Experimental results demonstrate that the proposed model effectively mitigates large-scale regional congestion levels via coordinated multi-intersection control.

Building agents with large language models (LLMs) for computer control is a burgeoning research area, where the agent receives computer states and performs actions to complete complex tasks. Previous computer agents have demonstrated the benefits of in-context learning (ICL); however, their performance is hindered by several issues. First, the limited context length of LLMs and complex computer states restrict the number of exemplars, as a single webpage can consume the entire context. Second, the exemplars in current methods, such as high-level plans and multi-choice questions, cannot represent complete trajectories, leading to suboptimal performance in long-horizon tasks. Third, existing computer agents rely on task-specific exemplars and overlook the similarity among tasks, resulting in poor generalization to novel tasks. To address these challenges, we introduce Synapse, a computer agent featuring three key components: i) state abstraction, which filters out task-irrelevant information from raw states, allowing more exemplars within the limited context, ii) trajectory-as-exemplar prompting, which prompts the LLM with complete trajectories of the abstracted states and actions to improve multi-step decision-making, and iii) exemplar memory, which stores the embeddings of exemplars and retrieves them via similarity search for generalization to novel tasks. We evaluate Synapse on MiniWoB++, a standard task suite, and Mind2Web, a real-world website benchmark. In MiniWoB++, Synapse achieves a 99.2% average success rate (a 10% relative improvement) across 64 tasks using demonstrations from only 48 tasks. Notably, Synapse is the first ICL method to solve the book-flight task in MiniWoB++. Synapse also exhibits a 56% relative improvement in average step success rate over the previous state-of-the-art prompting scheme in Mind2Web.

Reasoning language models have shown an uncanny ability to improve performance at test-time by ``thinking longer''-that is, by generating longer chain-of-thought sequences and hence using more compute. However, the length of their chain-of-thought reasoning is not controllable, making it impossible to allocate test-time compute to achieve a desired level of performance. We introduce Length Controlled Policy Optimization (LCPO), a simple reinforcement learning method that optimizes for accuracy and adherence to user-specified length constraints. We use LCPO to train L1, a reasoning language model that produces outputs satisfying a length constraint given in its prompt. L1's length control allows for smoothly trading off computational cost and accuracy on a wide range of tasks, and outperforms the state-of-the-art S1 method for length control. Furthermore, we uncover an unexpected short chain-of-thought capability in models trained with LCPO. For instance, our 1.5B L1 model surpasses GPT-4o at equal reasoning lengths. Overall, LCPO enables precise control over reasoning length, allowing for fine-grained allocation of test-time compute and accuracy. We release code and models at https://www.cmu-l3.github.io/l1

Reinforcement learning substantially improves reasoning in large language models, but it also tends to lengthen chain of thought outputs and increase computational cost during both training and inference. Though length control methods have been proposed, it remains unclear what the optimal output length is for balancing efficiency and performance. In this work, we compare several length control methods on two models, Qwen3-1.7B Base and DeepSeek-R1-Distill-Qwen-1.5B. Our results indicate that length penalties may hinder reasoning acquisition, while properly tuned length control can improve efficiency for models with strong prior reasoning. By extending prior work to RL trained policies, we identify two failure modes, 1) long outputs increase dispersion, and 2) short outputs lead to under-thinking.

Large language models (LLMs) are increasingly capable of carrying out long-running, real-world tasks. However, as the amount of context grows, their reliability often deteriorates, a phenomenon known as "context rot". Existing long-context benchmarks primarily focus on single-step settings that evaluate a model's ability to retrieve information from a long snippet. In realistic scenarios, however, LLMs often need to act as agents that explore environments, follow instructions and plans, extract useful information, and predict correct actions under a dynamically growing context. To assess language agents in such settings, we introduce LOCA-bench (a benchmark for LOng-Context Agents). Given a task prompt, LOCA-bench leverages automated and scalable control of environment states to regulate the agent's context length. This design enables LOCA-bench to extend the context length potentially to infinity in a controlled way while keeping the underlying task semantics fixed. LOCA-bench evaluates language agents as a combination of models and scaffolds, including various context management strategies. While agent performance generally degrades as the environment states grow more complex, advanced context management techniques can substantially improve the overall success rate. We open-source LOCA-bench to provide a platform for evaluating models and scaffolds in long-context, agentic scenarios: https://github.com/hkust-nlp/LOCA-bench

The target duration of a synthesized human motion is a critical attribute that requires modeling control over the motion dynamics and style. Speeding up an action performance is not merely fast-forwarding it. However, state-of-the-art techniques for human behavior synthesis have limited control over the target sequence length. We introduce the problem of generating length-aware 3D human motion sequences from textual descriptors, and we propose a novel model to synthesize motions of variable target lengths, which we dub "Length-Aware Latent Diffusion" (LADiff). LADiff consists of two new modules: 1) a length-aware variational auto-encoder to learn motion representations with length-dependent latent codes; 2) a length-conforming latent diffusion model to generate motions with a richness of details that increases with the required target sequence length. LADiff significantly improves over the state-of-the-art across most of the existing motion synthesis metrics on the two established benchmarks of HumanML3D and KIT-ML.

Large language models (LLMs) struggle with precise length control, particularly in zero-shot settings. We conduct a comprehensive study evaluating LLMs' length control capabilities across multiple measures and propose practical methods to improve controllability. Our experiments with LLaMA 3 reveal stark differences in length adherence across measures and highlight inherent biases of the model. To address these challenges, we introduce a set of methods: length approximation, target adjustment, sample filtering, and automated revisions. By combining these methods, we demonstrate substantial improvements in length compliance while maintaining or enhancing summary quality, providing highly effective zero-shot strategies for precise length control without the need for model fine-tuning or architectural changes. With our work, we not only advance our understanding of LLM behavior in controlled text generation but also pave the way for more reliable and adaptable summarization systems in real-world applications.

The creation of 3D assets with explicit, editable part structures is crucial for advancing interactive applications, yet most generative methods produce only monolithic shapes, limiting their utility. We introduce OmniPart, a novel framework for part-aware 3D object generation designed to achieve high semantic decoupling among components while maintaining robust structural cohesion. OmniPart uniquely decouples this complex task into two synergistic stages: (1) an autoregressive structure planning module generates a controllable, variable-length sequence of 3D part bounding boxes, critically guided by flexible 2D part masks that allow for intuitive control over part decomposition without requiring direct correspondences or semantic labels; and (2) a spatially-conditioned rectified flow model, efficiently adapted from a pre-trained holistic 3D generator, synthesizes all 3D parts simultaneously and consistently within the planned layout. Our approach supports user-defined part granularity, precise localization, and enables diverse downstream applications. Extensive experiments demonstrate that OmniPart achieves state-of-the-art performance, paving the way for more interpretable, editable, and versatile 3D content.

Large language models (LLMs) like ChatGPT and GPT-4 have attracted great attention given their surprising performance on a wide range of NLP tasks. Length controlled generation of LLMs emerges as an important topic, which enables users to fully leverage the capability of LLMs in more real-world scenarios like generating a proper answer or essay of a desired length. In addition, the autoregressive generation in LLMs is extremely time-consuming, while the ability of controlling this generated length can reduce the inference cost by limiting the length. Therefore, we propose a prompt-based length control method to achieve high-accuracy length controlled generation. In particular, we adopt reinforcement learning with the reward signal given by either trainable or rule-based reward models, which further enhances the length-control ability of LLMs by rewarding outputs that follows pre-defined control instruction. To enable rule-based inference, we also introduce standard prompt extractor to collect the standard control information from users' input. Experiments show that our method significantly improves the accuracy of prompt-based length control for summarization task on popular datasets like CNNDM and NYT. Both the standard prompt extractor and the RL-tuned model have show strong generalization ability to unseen control prompt templates.

Large Language Models (LLMs) are increasingly used in production systems, powering applications such as chatbots, summarization, and question answering. Despite their success, controlling the length of their response remains a significant challenge, particularly for tasks requiring structured outputs or specific levels of detail. In this work, we propose a method to adapt pre-trained decoder-only LLMs for precise control of response length. Our approach incorporates a secondary length-difference positional encoding (LDPE) into the input embeddings, which counts down to a user-set response termination length. Fine-tuning with LDPE allows the model to learn to terminate responses coherently at the desired length, achieving mean token errors of less than 3 tokens. We also introduce Max New Tokens++, an extension that enables flexible upper-bound length control, rather than an exact target. Experimental results on tasks such as question answering and document summarization demonstrate that our method enables precise length control without compromising response quality.

In this paper, we investigate the length-extension of state-space models (SSMs) in language modeling. Length extension involves training models on short sequences and testing them on longer ones. We show that state-space models trained with zero hidden states initialization have difficulty doing length extension. We explain this difficulty by pointing out the length extension is equivalent to polynomial extrapolation. Based on the theory, we propose a simple yet effective method - changing the hidden states initialization scheme - to improve the length extension. Moreover, our method shows that using long training sequence length is beneficial but not necessary to length extension. Changing the hidden state initialization enables the efficient training of long-memory model with a smaller training context length.

In this paper, we propose feedback designs for manipulating a quantum state to a target state by performing sequential measurements. In light of Belavkin's quantum feedback control theory, for a given set of (projective or non-projective) measurements and a given time horizon, we show that finding the measurement selection policy that maximizes the probability of successful state manipulation is an optimal control problem for a controlled Markovian process. The optimal policy is Markovian and can be solved by dynamical programming. Numerical examples indicate that making use of feedback information significantly improves the success probability compared to classical scheme without taking feedback. We also consider other objective functionals including maximizing the expected fidelity to the target state as well as minimizing the expected arrival time. The connections and differences among these objectives are also discussed.

LLM-based auto-annotators have become a key component of the LLM development process due to their cost-effectiveness and scalability compared to human-based evaluation. However, these auto-annotators can introduce complex biases that are hard to remove. Even simple, known confounders such as preference for longer outputs remain in existing automated evaluation metrics. We propose a simple regression analysis approach for controlling biases in auto-evaluations. As a real case study, we focus on reducing the length bias of AlpacaEval, a fast and affordable benchmark for chat LLMs that uses LLMs to estimate response quality. Despite being highly correlated with human preferences, AlpacaEval is known to favor models that generate longer outputs. We introduce a length-controlled AlpacaEval that aims to answer the counterfactual question: "What would the preference be if the model's and baseline's output had the same length?". To achieve this, we first fit a generalized linear model to predict the biased output of interest (auto-annotator preferences) based on the mediators we want to control for (length difference) and other relevant features. We then obtain length-controlled preferences by predicting preferences while conditioning the GLM with a zero difference in lengths. Length-controlling not only improves the robustness of the metric to manipulations in model verbosity, we also find that it increases the Spearman correlation with LMSYS' Chatbot Arena from 0.94 to 0.98. We release the code and leaderboard at https://tatsu-lab.github.io/alpaca_eval/ .

The instruction-following ability of large language models enables humans to interact with AI agents in a natural way. However, when required to generate responses of a specific length, large language models often struggle to meet users' needs due to their inherent difficulty in accurately perceiving numerical constraints. To explore the ability of large language models to control the length of generated responses, we propose the Target Length Generation Task (TLG) and design two metrics, Precise Match (PM) and Flexible Match (FM) to evaluate the model's performance in adhering to specified response lengths. Furthermore, we introduce a novel, model-agnostic approach called Ruler, which employs Meta Length Tokens (MLTs) to enhance the instruction-following ability of large language models under length-constrained instructions. Specifically, Ruler equips LLMs with the ability to generate responses of a specified length based on length constraints within the instructions. Moreover, Ruler can automatically generate appropriate MLT when length constraints are not explicitly provided, demonstrating excellent versatility and generalization. Comprehensive experiments show the effectiveness of Ruler across different LLMs on Target Length Generation Task, e.g., at All Level 27.97 average gain on PM, 29.57 average gain on FM. In addition, we conduct extensive ablation experiments to further substantiate the efficacy and generalization of Ruler. Our code and data is available at https://github.com/Geaming2002/Ruler.

Large Language Models (LLMs) demonstrate impressive capabilities across various domains, including role-playing, creative writing, mathematical reasoning, and coding. Despite these advancements, LLMs still encounter challenges with length control, frequently failing to adhere to specific length constraints due to their token-level operations and insufficient training on data with strict length limitations. We identify this issue as stemming from a lack of positional awareness and propose novel approaches--PositionID Prompting and PositionID Fine-Tuning--to address it. These methods enhance the model's ability to continuously monitor and manage text length during generation. Additionally, we introduce PositionID CP Prompting to enable LLMs to perform copy and paste operations accurately. Furthermore, we develop two benchmarks for evaluating length control and copy-paste abilities. Our experiments demonstrate that our methods significantly improve the model's adherence to length constraints and copy-paste accuracy without compromising response quality.

Recently, recurrent models such as state space models and linear attention have become popular due to their linear complexity in the sequence length. Thanks to their recurrent nature, in principle they can process arbitrarily long sequences, but their performance sometimes drops considerably beyond their training context lengths-i.e. they fail to length generalize. In this work, we provide comprehensive empirical and theoretical analysis to support the unexplored states hypothesis, which posits that models fail to length generalize when during training they are only exposed to a limited subset of the distribution of all attainable states (i.e. states that would be attained if the recurrence was applied to long sequences). Furthermore, we investigate simple training interventions that aim to increase the coverage of the states that the model is trained on, e.g. by initializing the state with Gaussian noise or with the final state of a different input sequence. With only 500 post-training steps (sim 0.1% of the pre-training budget), these interventions enable length generalization for sequences that are orders of magnitude longer than the training context (e.g. 2klongrightarrow 128k) and show improved performance in long context tasks, thus presenting a simple and efficient way to enable robust length generalization in general recurrent models.

Aligned instruction following models can better fulfill user requests than their unaligned counterparts. However, it has been shown that there is a length bias in evaluation of such models, and that training algorithms tend to exploit this bias by learning longer responses. In this work we show how to train models that can be controlled at inference time with instructions containing desired length constraints. Such models are superior in length instructed evaluations, outperforming standard instruction following models such as GPT4, Llama 3 and Mixtral.

Existing approaches typically rely on fixed length penalties, but such penalties are hard to tune and fail to adapt to the evolving reasoning abilities of LLMs, leading to suboptimal trade-offs between accuracy and conciseness. To address this challenge, we propose Leash (adaptive LEngth penAlty and reward SHaping), a reinforcement learning framework for efficient reasoning in LLMs. We formulate length control as a constrained optimization problem and employ a Lagrangian primal-dual method to dynamically adjust the penalty coefficient. When generations exceed the target length, the penalty is intensified; when they are shorter, it is relaxed. This adaptive mechanism guides models toward producing concise reasoning without sacrificing task performance. Experiments on Deepseek-R1-Distill-Qwen-1.5B and Qwen3-4B-Thinking-2507 show that Leash reduces the average reasoning length by 60% across diverse tasks - including in-distribution mathematical reasoning and out-of-distribution domains such as coding and instruction following - while maintaining competitive performance. Our work thus presents a practical and effective paradigm for developing controllable and efficient LLMs that balance reasoning capabilities with computational budgets.

Chain-of-Thought significantly enhances a model's reasoning capability, but it also comes with a considerable increase in inference costs due to long chains. With the observation that the reasoning path can be easily compressed under easy tasks but struggle on hard tasks, we explore the feasibility of elastically controlling the length of reasoning paths with only one model, thereby reducing the inference overhead of reasoning models dynamically based on task difficulty. We introduce a new tuning and inference strategy named CoT-Valve, designed to allow models to generate reasoning chains of varying lengths. To achieve this, we propose to identify a direction in the parameter space that, when manipulated, can effectively control the length of generated CoT. Moreover, we show that this property is valuable for compressing the reasoning chain. We construct datasets with chains from long to short for the same questions and explore two enhanced strategies for CoT-Valve: (1) a precise length-compressible CoT tuning method, and (2) a progressive chain length compression approach. Our experiments show that CoT-Valve successfully enables controllability and compressibility of the chain and shows better performance than the prompt-based control. We applied this method to QwQ-32B-Preview, reducing reasoning chains on GSM8K from 741 to 225 tokens with a minor performance drop (95.07% to 94.92%) and on AIME from 6827 to 4629 tokens, with only one additional incorrect answer.

The success of Deepseek-R1 has drawn the LLM community's attention to reinforcement learning (RL) methods like GRPO. However, such rule-based 0/1 outcome reward methods lack the capability to regulate the intermediate reasoning processes during chain-of-thought (CoT) generation, leading to severe overthinking phenomena. In response, recent studies have designed reward functions to reinforce models' behaviors in producing shorter yet correct completions. Nevertheless, we observe that these length-penalty reward functions exacerbate RL training instability: as the completion length decreases, model accuracy abruptly collapses, often occurring early in training. To address this issue, we propose a simple yet effective solution GRPO-lambda, an efficient and stabilized variant of GRPO, which dynamically adjusts the reward strategy by monitoring the correctness ratio among completions within each query-sampled group. A low correctness ratio indicates the need to avoid length penalty that compromises CoT quality, triggering a switch to length-agnostic 0/1 rewards that prioritize reasoning capability. A high ratio maintains length penalties to boost efficiency. Experimental results show that our approach avoids training instability caused by length penalty while maintaining the optimal accuracy-efficiency trade-off. On the GSM8K, GPQA, MATH-500, AMC 2023, and AIME 2024 benchmarks, it improves average accuracy by 1.48% while reducing CoT sequence length by 47.3%.

A control technique is developed via Reinforcement Learning that allows arbitrary controlling of the position of an acoustic cavitation bubble in a dual-frequency standing acoustic wave field. The agent must choose the optimal pressure amplitude values to manipulate the bubble position in the range of x/lambda_0in[0.05, 0.25]. To train the agent an actor-critic off-policy algorithm (Deep Deterministic Policy Gradient) was used that supports continuous action space, which allows setting the pressure amplitude values continuously within 0 and 1, bar. A shaped reward function is formulated that minimizes the distance between the bubble and the target position and implicitly encourages the agent to perform the position control within the shortest amount of time. In some cases, the optimal control can be 7 times faster than the solution expected from the linear theory.

Recent applications of Reinforcement Learning with Verifiable Rewards (RLVR) to Large Language Models (LLMs) and Vision-Language Models (VLMs) have demonstrated significant success in enhancing reasoning capabilities for complex tasks. During RLVR training, an increase in response length is often regarded as a key factor contributing to the growth of reasoning ability. However, the patterns of change in response length vary significantly across different RLVR algorithms during the training process. To provide a fundamental explanation for these variations, this paper conducts an in-depth analysis of the components of mainstream RLVR algorithms. We present a theoretical analysis of the factors influencing response length and validate our theory through extensive experimentation. Building upon these theoretical findings, we propose the Length-Unbiased Sequence Policy Optimization (LUSPO) algorithm. Specifically, we rectify the length bias inherent in Group Sequence Policy Optimization (GSPO), rendering its loss function unbiased with respect to response length and thereby resolving the issue of response length collapse. We conduct extensive experiments across mathematical reasoning benchmarks and multimodal reasoning scenarios, where LUSPO consistently achieves superior performance. Empirical results demonstrate that LUSPO represents a novel, state-of-the-art optimization strategy compared to existing methods such as GRPO and GSPO.

Large Reasoning Models (LRMs) have achieved impressive performance on complex reasoning tasks by generating detailed chain-of-thought (CoT) explanations. However, these responses are often excessively long, containing redundant reasoning steps that inflate inference cost and reduce usability. Controlling the length of generated reasoning without sacrificing accuracy remains an open challenge. Through a systematic empirical analysis, we reveal a consistent positive correlation between model entropy and response length at different reasoning stages across diverse LRMs: the thinking phase exhibits higher entropy, reflecting exploratory behavior of longer responses, while the final answer phase shows lower entropy, indicating a more deterministic solution. This observation suggests that entropy at different reasoning stages can serve as a control knob for balancing conciseness and performance. Based on this insight, this paper introduces Phase Entropy Aware Reward (PEAR), a reward mechanism that incorporating phase-dependent entropy into the reward design. Instead of treating all tokens uniformly, PEAR penalize excessive entropy during the thinking phase and allowing moderate exploration at the final answer phase, which encourages models to generate concise reasoning traces that retain sufficient flexibility to solve the task correctly. This enables adaptive control of response length without relying on explicit length targets or rigid truncation rules. Extensive experiments across four benchmarks demonstrate that PEAR consistently reduces response length while sustaining competitive accuracy across model scales. In addition, PEAR demonstrates strong out-of-distribution (OOD) robustness beyond the training distribution. Our code is available at: https://github.com/iNLP-Lab/PEAR.

We propose Self-Control, a novel method utilizing suffix gradients to control the behavior of large language models (LLMs) without explicit human annotations. Given a guideline expressed in suffix string and the model's self-assessment of adherence, Self-Control computes the gradient of this self-judgment concerning the model's hidden states, directly influencing the auto-regressive generation process towards desired behaviors. To enhance efficiency, we introduce Self-Control_{prefix}, a compact module that encapsulates the learned representations from suffix gradients into a Prefix Controller, facilitating inference-time control for various LLM behaviors. Our experiments demonstrate Self-Control's efficacy across multiple domains, including emotional modulation, ensuring harmlessness, and enhancing complex reasoning. Especially, Self-Control_{prefix} enables a plug-and-play control and jointly controls multiple attributes, improving model outputs without altering model parameters or increasing inference-time costs.

Recent work on enhancing the reasoning abilities of large language models (LLMs) has introduced explicit length control as a means of constraining computational cost while preserving accuracy. However, existing approaches rely on fixed-length training budgets, which do not take advantage of the natural progression from exploration to compression during learning. In this work, we propose a curriculum learning strategy for length-controlled reasoning using Group Relative Policy Optimization (GRPO). Our method starts with generous token budgets and gradually tightens them over training, encouraging models to first discover effective solution strategies and then distill them into more concise reasoning traces. We augment GRPO with a reward function that balances three signals: task correctness (via verifier feedback), length efficiency, and formatting adherence (via structural tags). Experiments on GSM8K, MATH500, SVAMP, College Math, and GSM+ demonstrate that curriculum-based training consistently outperforms fixed-budget baselines at the same final budget, achieving higher accuracy and significantly improved token efficiency. We further ablate the impact of reward weighting and decay schedule design, showing that progressive constraint serves as a powerful inductive bias for training efficient reasoning models. Our code and checkpoints are released at: https://github.com/hammoudhasan/curriculum_grpo.

We introduce controlgym, a library of thirty-six safety-critical industrial control settings, and ten infinite-dimensional partial differential equation (PDE)-based control problems. Integrated within the OpenAI Gym/Gymnasium (Gym) framework, controlgym allows direct applications of standard reinforcement learning (RL) algorithms like stable-baselines3. Our control environments complement those in Gym with continuous, unbounded action and observation spaces, motivated by real-world control applications. Moreover, the PDE control environments uniquely allow the users to extend the state dimensionality of the system to infinity while preserving the intrinsic dynamics. This feature is crucial for evaluating the scalability of RL algorithms for control. This project serves the learning for dynamics & control (L4DC) community, aiming to explore key questions: the convergence of RL algorithms in learning control policies; the stability and robustness issues of learning-based controllers; and the scalability of RL algorithms to high- and potentially infinite-dimensional systems. We open-source the controlgym project at https://github.com/xiangyuan-zhang/controlgym.

Recent research enhances language model reasoning by scaling test-time compute via longer chain-of-thought traces. This often improves accuracy but also introduces redundancy and high computational cost, especially for small language models distilled with supervised fine-tuning (SFT). In this work, we propose new algorithms to improve token-efficient reasoning with small-scale models by effectively trading off accuracy and computation. We first show that the post-SFT model fails to determine the optimal stopping point of the reasoning process, resulting in verbose and repetitive outputs. Verbosity also significantly varies across wrong vs correct responses. To address these issues, we propose two solutions: (1) Temperature scaling (TS) to control the stopping point for the thinking phase and thereby trace length, and (2) TLDR: a length-regularized reinforcement learning method based on GRPO that facilitates multi-level trace length control (e.g. short, medium, long reasoning). Experiments on four reasoning benchmarks, MATH500, AMC, AIME24 and OlympiadBench, demonstrate that TS is highly effective compared to s1's budget forcing approach and TLDR significantly improves token efficiency by about 50% with minimal to no accuracy loss over the SFT baseline. Moreover, TLDR also facilitates flexible control over the response length, offering a practical and effective solution for token-efficient reasoning in small models. Ultimately, our work reveals the importance of stopping time control, highlights shortcomings of pure SFT, and provides effective algorithmic recipes.

Since the release of Deepseek-R1, reinforcement learning with verifiable rewards (RLVR) has become a central approach for training large language models (LLMs) on reasoning tasks. Recent work has largely focused on modifying loss functions to make RLVR more efficient and effective. In this paper, motivated by studies of overthinking in LLMs, we propose Length-aware Sampling for Policy Optimization (LSPO), a novel meta-RLVR algorithm that dynamically selects training data at each step based on the average response length. We evaluate LSPO across multiple base models and datasets, demonstrating that it consistently improves learning effectiveness. In addition, we conduct a detailed ablation study to examine alternative ways of incorporating length signals into dynamic sampling, offering further insights and highlighting promising directions for future research.

In this paper, we present efficient quantum algorithms that are exponentially faster than classical algorithms for solving the quantum optimal control problem. This problem involves finding the control variable that maximizes a physical quantity at time T, where the system is governed by a time-dependent Schr\"odinger equation. This type of control problem also has an intricate relation with machine learning. Our algorithms are based on a time-dependent Hamiltonian simulation method and a fast gradient-estimation algorithm. We also provide a comprehensive error analysis to quantify the total error from various steps, such as the finite-dimensional representation of the control function, the discretization of the Schr\"odinger equation, the numerical quadrature, and optimization. Our quantum algorithms require fault-tolerant quantum computers.

Large reasoning models have achieved remarkable performance through extended chain-of-thought sequences, yet this computational freedom leads to excessive token generation even for simple problems. We present Length-Adaptive Policy Optimization (LAPO), a novel framework that transforms reasoning length control from an external constraint into an intrinsic model capability. Unlike existing approaches that impose rigid limits or rely on post-hoc interventions, LAPO enables models to internalize an understanding of appropriate reasoning depth through a two-stage reinforcement learning process. In the first stage, models learn natural reasoning patterns by discovering the statistical distribution of successful solution lengths. The second stage leverages these patterns as meta-cognitive guidance, embedding them directly within the model's reasoning context to ensure inference-time flexibility. Experiments on mathematical reasoning benchmarks demonstrate that LAPO reduces token usage by up to 40.9\% while improving accuracy by 2.3\%. Our analysis reveals that models trained with LAPO develop emergent abilities to allocate computational resources based on problem complexity, achieving efficient reasoning without sacrificing quality.

In this work, we study the issue of reward hacking on the response length, a challenge emerging in Reinforcement Learning from Human Feedback (RLHF) on LLMs. A well-formatted, verbose but less helpful response from the LLMs can often deceive LLMs or even human evaluators to achieve high scores. The same issue also holds for some reward models in RL. To address the challenges in both training and evaluation, we establish a more reliable evaluation protocol for comparing different training configurations, which inspects the trade-off between LLM evaluation score and response length obtained by varying training hyperparameters. Based on this evaluation, we conduct large-scale studies, where the results shed insights into the efficacy of hyperparameters and tricks used in RL on mitigating length bias. We further propose to improve the reward model by jointly training two linear heads on shared feature representations to predict the rewards, one trained to correlate with length, and the other trained to decorrelate with length and therefore focus more on the actual content. We then discard the length head in RL to prevent reward hacking on length. Experiments demonstrate that our approach almost eliminates the reward correlation with length, and improves the obtained policy by a significant margin.

Great successes have been reported using Reinforcement Learning from Human Feedback (RLHF) to align large language models. Open-source preference datasets and reward models have enabled wider experimentation beyond generic chat settings, particularly to make systems more "helpful" for tasks like web question answering, summarization, and multi-turn dialogue. When optimizing for helpfulness, RLHF has been consistently observed to drive models to produce longer outputs. This paper demonstrates that optimizing for response length is a significant factor behind RLHF's reported improvements in these settings. First, we study the relationship between reward and length for reward models trained on three open-source preference datasets for helpfulness. Here, length correlates strongly with reward, and improvements in reward score are driven in large part by shifting the distribution over output lengths. We then explore interventions during both RL and reward model learning to see if we can achieve the same downstream improvements as RLHF without increasing length. While our interventions mitigate length increases, they aren't uniformly effective across settings. Furthermore, we find that even running RLHF with a reward based solely on length can reproduce most of the downstream improvements over the initial policy model, showing that reward models in these settings have a long way to go.

Living systems face both environmental complexity and limited access to free-energy resources. Survival under these conditions requires a control system that can activate, or deploy, available perception and action resources in a context specific way. We show here that when systems are described as executing active inference driven by the free-energy principle (and hence can be considered Bayesian prediction-error minimizers), their control flow systems can always be represented as tensor networks (TNs). We show how TNs as control systems can be implmented within the general framework of quantum topological neural networks, and discuss the implications of these results for modeling biological systems at multiple scales.

Over the past three decades, numerous controllers have been developed to regulate complex chemical processes, but they have certain limitations. Traditional PI/PID controllers often require customized tuning for various set-point scenarios. On the other hand, MPC frameworks involve resource-intensive steps, and the utilization of black-box machine learning (ML) models can lead to issues such as local minima and infeasibility. Thus, there is a need for an alternative controller paradigm that combines the simplicity of a PI controller with the grade-to-grade (G2G) transferability of an MPC approach. To this end, we developed a novel LSTM controller (LSTMc) as a model-free data-driven controller framework. The LSTMc considers an augmented input tensor that incorporates information on state evolution and error dynamics for the current and previous W time steps, to predict the manipulated input at the next step (u_{t+1}). To demonstrate LSTMc, batch crystallization of dextrose was taken as a representative case study. The desired output for set-point tracking was the mean crystal size (L), with the manipulated input being the jacket temperature (T_j). Extensive training data, encompassing 7000+ different operating conditions, was compiled to ensure comprehensive training of LSTMc across a wide state space region. For comparison, we also designed a PI controller and an LSTM-MPC for different set-point tracking cases. The results consistently showed that LSTMc achieved the lowest set-point deviation (<2\%), three times lower than the MPC. Remarkably, LSTMc maintained this superior performance across all set points, even when sensor measurements contained noise levels of 10\% to 15\%. In summary, by effectively leveraging process data and utilizing sequential ML models, LSTMc offers a superior controller design approach.

Despite the remarkable practical success of transformer-based language models, recent work has raised concerns about their ability to perform state tracking. In particular, a growing body of literature has shown this limitation primarily through failures in out-of-distribution (OOD) generalization, such as length extrapolation. In this work, we shift attention to the in-distribution implications of these limitations. We conduct a large-scale experimental study of the data efficiency of transformers and recurrent neural networks (RNNs) across multiple supervision regimes. We find that the amount of training data required by transformers grows much more rapidly with state-space size and sequence length than for RNNs. Furthermore, we analyze the extent to which learned state-tracking mechanisms are shared across different sequence lengths. We show that transformers exhibit negligible or even detrimental weight sharing across lengths, indicating that they learn length-specific solutions in isolation. In contrast, recurrent models exhibit effective amortized learning by sharing weights across lengths, allowing data from one sequence length to improve performance on others. Together, these results demonstrate that state tracking remains a fundamental challenge for transformers, even when training and evaluation distributions match.

In Reinforcement Learning (RL), an agent acts in an unknown environment to maximize the expected cumulative discounted sum of an external reward signal, i.e., the expected return. In practice, in many tasks of interest, such as policy optimization, the agent usually spends its interaction budget by collecting episodes of fixed length within a simulator (i.e., Monte Carlo simulation). However, given the discounted nature of the RL objective, this data collection strategy might not be the best option. Indeed, the rewards taken in early simulation steps weigh exponentially more than future rewards. Taking a cue from this intuition, in this paper, we design an a-priori budget allocation strategy that leads to the collection of trajectories of different lengths, i.e., truncated. The proposed approach provably minimizes the width of the confidence intervals around the empirical estimates of the expected return of a policy. After discussing the theoretical properties of our method, we make use of our trajectory truncation mechanism to extend Policy Optimization via Importance Sampling (POIS, Metelli et al., 2018) algorithm. Finally, we conduct a numerical comparison between our algorithm and POIS: the results are consistent with our theory and show that an appropriate truncation of the trajectories can succeed in improving performance.

LLMs are not generally able to adjust the length of their outputs based on strict length requirements, a capability that would improve their usefulness in applications that require adherence to diverse user and system requirements. We present an approach to train LLMs to acquire this capability by augmenting existing data and applying existing fine-tuning techniques, which we compare based on the trained models' adherence to the length requirement and overall response quality relative to the baseline model. Our results demonstrate that these techniques can be successfully applied to train LLMs to adhere to length requirements, with the trained models generating texts which better align to the length requirements. Our results indicate that our method may change the response quality when using training data that was not generated by the baseline model. This allows simultaneous alignment to another training objective in certain scenarios, but is undesirable otherwise. Training on a dataset containing the model's own responses eliminates this issue.

Prompt engineering is crucial for deploying LLMs but is poorly understood mathematically. We formalize LLM systems as a class of discrete stochastic dynamical systems to explore prompt engineering through the lens of control theory. We investigate the reachable set of output token sequences R_y(mathbf x_0) for which there exists a control input sequence mathbf u for each mathbf y in R_y(mathbf x_0) that steers the LLM to output mathbf y from initial state sequence mathbf x_0. We offer analytic analysis on the limitations on the controllability of self-attention in terms of reachable set, where we prove an upper bound on the reachable set of outputs R_y(mathbf x_0) as a function of the singular values of the parameter matrices. We present complementary empirical analysis on the controllability of a panel of LLMs, including Falcon-7b, Llama-7b, and Falcon-40b. Our results demonstrate a lower bound on the reachable set of outputs R_y(mathbf x_0) w.r.t. initial state sequences mathbf x_0 sampled from the Wikitext dataset. We find that the correct next Wikitext token following sequence mathbf x_0 is reachable over 97% of the time with prompts of kleq 10 tokens. We also establish that the top 75 most likely next tokens, as estimated by the LLM itself, are reachable at least 85% of the time with prompts of kleq 10 tokens. Intriguingly, short prompt sequences can dramatically alter the likelihood of specific outputs, even making the least likely tokens become the most likely ones. This control-centric analysis of LLMs demonstrates the significant and poorly understood role of input sequences in steering output probabilities, offering a foundational perspective for enhancing language model system capabilities.