State Space Models (SSMs) have emerged as a promising alternative to the popular transformer-based models and have been increasingly gaining attention. Compared to transformers, SSMs excel at tasks with sequential data or longer contexts, demonstrating comparable performances with significant efficiency gains. In this survey, we provide a coherent and systematic overview for SSMs, including their theoretical motivations, mathematical formulations, comparison with existing model classes, and various applications. We divide the SSM series into three main sections, providing a detailed introduction to the original SSM, the structured SSM represented by S4, and the selective SSM typified by Mamba. We put an emphasis on technicality, and highlight the various key techniques introduced to address the effectiveness and efficiency of SSMs. We hope this manuscript serves as an introduction for researchers to explore the theoretical foundations of SSMs.

Hand-object interaction(HOI) is the fundamental link between human and environment, yet its dexterous and complex pose significantly challenges for gesture control. Despite significant advances in AI and robotics, enabling machines to understand and simulate hand-object interactions, capturing the semantics of functional grasping tasks remains a considerable challenge. While previous work can generate stable and correct 3D grasps, they are still far from achieving functional grasps due to unconsidered grasp semantics. To address this challenge, we propose an innovative two-stage framework, Functional Grasp Synthesis Net (FGS-Net), for generating 3D HOI driven by functional text. This framework consists of a text-guided 3D model generator, Functional Grasp Generator (FGG), and a pose optimization strategy, Functional Grasp Refiner (FGR). FGG generates 3D models of hands and objects based on text input, while FGR fine-tunes the poses using Object Pose Approximator and energy functions to ensure the relative position between the hand and object aligns with human intent and remains physically plausible. Extensive experiments demonstrate that our approach achieves precise and high-quality HOI generation without requiring additional 3D annotation data.

The development of intelligent robots seeks to seamlessly integrate them into the human world, providing assistance and companionship in daily life and work, with the ultimate goal of achieving human-robot symbiosis. To realize this vision, robots must continuously learn and evolve through consistent interaction and collaboration with humans, while humans need to gradually develop an understanding of and trust in robots through shared experiences. However, training and testing algorithms directly on physical robots involve substantial costs and safety risks. Moreover, current robotic simulators fail to support real human participation, limiting their ability to provide authentic interaction experiences and gather valuable human feedback. In this paper, we introduce SymbioSim, a novel human-in-the-loop robotic simulation platform designed to enable the safe and efficient development, evaluation, and optimization of human-robot interactions. By leveraging a carefully designed system architecture and modules, SymbioSim delivers a natural and realistic interaction experience, facilitating bidirectional continuous learning and adaptation for both humans and robots. Extensive experiments and user studies demonstrate the platform's promising performance and highlight its potential to significantly advance research on human-robot symbiosis.

Instruction-following made modern large language models (LLMs) helpful assistants. However, the key to taming LLMs on complex instructions remains mysterious, for that there are huge gaps between models trained by open-source community and those trained by leading companies. To bridge the gap, we propose a simple and scalable approach UltraIF for building LLMs that can follow complex instructions with open-source data. UltraIF first decomposes real-world user prompts into simpler queries, constraints, and corresponding evaluation questions for the constraints. Then, we train an UltraComposer to compose constraint-associated prompts with evaluation questions. This prompt composer allows us to synthesize complicated instructions as well as filter responses with evaluation questions. In our experiment, for the first time, we successfully align LLaMA-3.1-8B-Base to catch up with its instruct version on 5 instruction-following benchmarks without any benchmark information, using only 8B model as response generator and evaluator. The aligned model also achieved competitive scores on other benchmarks. Moreover, we also show that UltraIF could further improve LLaMA-3.1-8B-Instruct through self-alignment, motivating broader use cases for the method. Our code will be available at https://github.com/kkk-an/UltraIF.

We introduce OmniRL, a highly generalizable in-context reinforcement learning (ICRL) model that is meta-trained on hundreds of thousands of diverse tasks. These tasks are procedurally generated by randomizing state transitions and rewards within Markov Decision Processes. To facilitate this extensive meta-training, we propose two key innovations: 1. An efficient data synthesis pipeline for ICRL, which leverages the interaction histories of diverse behavior policies; and 2. A novel modeling framework that integrates both imitation learning and reinforcement learning (RL) within the context, by incorporating prior knowledge. For the first time, we demonstrate that in-context learning (ICL) alone, without any gradient-based fine-tuning, can successfully tackle unseen Gymnasium tasks through imitation learning, online RL, or offline RL. Additionally, we show that achieving generalized ICRL capabilities-unlike task identification-oriented few-shot learning-critically depends on long trajectories generated by variant tasks and diverse behavior policies. By emphasizing the potential of ICL and departing from pre-training focused on acquiring specific skills, we further underscore the significance of meta-training aimed at cultivating the ability of ICL itself.

Dense process rewards have proven a more effective alternative to the sparse outcome-level rewards in the inference-time scaling of large language models (LLMs), particularly in tasks requiring complex multi-step reasoning. While dense rewards also offer an appealing choice for the reinforcement learning (RL) of LLMs since their fine-grained rewards have the potential to address some inherent issues of outcome rewards, such as training efficiency and credit assignment, this potential remains largely unrealized. This can be primarily attributed to the challenges of training process reward models (PRMs) online, where collecting high-quality process labels is prohibitively expensive, making them particularly vulnerable to reward hacking. To address these challenges, we propose PRIME (Process Reinforcement through IMplicit rEwards), which enables online PRM updates using only policy rollouts and outcome labels through implict process rewards. PRIME combines well with various advantage functions and forgoes the dedicated reward model training phrase that existing approaches require, substantially reducing the development overhead. We demonstrate PRIME's effectiveness on competitional math and coding. Starting from Qwen2.5-Math-7B-Base, PRIME achieves a 15.1% average improvement across several key reasoning benchmarks over the SFT model. Notably, our resulting model, Eurus-2-7B-PRIME, surpasses Qwen2.5-Math-7B-Instruct on seven reasoning benchmarks with 10% of its training data.

We introduce MedXpertQA, a highly challenging and comprehensive benchmark to evaluate expert-level medical knowledge and advanced reasoning. MedXpertQA includes 4,460 questions spanning 17 specialties and 11 body systems. It includes two subsets, Text for text evaluation and MM for multimodal evaluation. Notably, MM introduces expert-level exam questions with diverse images and rich clinical information, including patient records and examination results, setting it apart from traditional medical multimodal benchmarks with simple QA pairs generated from image captions. MedXpertQA applies rigorous filtering and augmentation to address the insufficient difficulty of existing benchmarks like MedQA, and incorporates specialty board questions to improve clinical relevance and comprehensiveness. We perform data synthesis to mitigate data leakage risk and conduct multiple rounds of expert reviews to ensure accuracy and reliability. We evaluate 16 leading models on MedXpertQA. Moreover, medicine is deeply connected to real-world decision-making, providing a rich and representative setting for assessing reasoning abilities beyond mathematics and code. To this end, we develop a reasoning-oriented subset to facilitate the assessment of o1-like models.

Extending the context length of Language Models (LMs) by improving Rotary Position Embedding (RoPE) has become a trend. While existing works mainly address RoPE's limitations within attention mechanism, this paper provides an analysis across nearly all parts of LMs, uncovering their adverse effects on length generalization for RoPE-based attention. Using Discrete Signal Processing theory, we show that RoPE enables periodic attention by implicitly achieving Non-Uniform Discrete Fourier Transform. However, this periodicity is undermined by the spectral damage caused by: 1) linear layers and activation functions outside of attention; 2) insufficiently trained frequency components brought by time-domain truncation. Building on our observations, we propose Fourier Position Embedding (FoPE), which enhances attention's frequency-domain properties to improve both its periodic extension and length generalization. FoPE constructs Fourier Series and zero-outs the destructive frequency components, increasing model robustness against the spectrum damage. Experiments across various model scales show that, within varying context windows, FoPE can maintain a more stable perplexity and a more consistent accuracy in a needle-in-haystack task compared to RoPE and ALiBi. Several analyses and ablations bring further support to our method and theoretical modeling.

Model collapse in synthetic data indicates that iterative training on self-generated data leads to a gradual decline in performance. With the proliferation of AI models, synthetic data will fundamentally reshape the web data ecosystem. Future GPT-{n} models will inevitably be trained on a blend of synthetic and humanproduced data. In this paper, we focus on two questions: what is the impact of synthetic data on language model training, and how to synthesize data without model collapse? We further conduct statistical analysis on synthetic data to uncover distributional shift phenomenon and over-concentration of n-gram features. Inspired by the above findings, we propose token editing on human-produced data to obtain semi-synthetic data. As a proof of concept, we theoretically demonstrate that token-level editing can prevent model collapse, as the test error is constrained by a finite upper bound. We conduct extensive experiments on pre-training from scratch, continual pre-training, and supervised finetuning. The results validate our theoretical proof that token-level editing improves data quality and enhances model performance. As generative artificial intelligence (AI) (Rombach et al., 2021; Achiam et al., 2023) becomes increasingly prevalent in research and industry, synthetic data will proliferate throughout the web data ecosystem. Consequently, future training of GPT-{n} on a mixture of synthetic and humanproduced data will be inevitable. Thus, model collapse is a critical concern that must be considered when training models on synthetic data. Model collapse refers to a degenerative process in which the output data of learned generative models contaminates the training sets of subsequent generations. As shown in Figure 1, iterative training coupled with data synthesis induces a progressive accumulation of test errors (Shumailov et al., 2024; Dohmatob et al., 2024a). Consequently, generative models increasingly overfit to synthetic data distributions, failing to capture the complexity in human-produced data.

Different from its counterpart outcome reward models (ORMs), which evaluate the entire responses, a process reward model (PRM) scores a reasoning trajectory step by step, providing denser and more fine grained rewards. However, training a PRM requires labels annotated at every intermediate step, presenting significant challenges for both manual and automatic data collection. This paper aims to address this challenge. Both theoretically and empirically, we show that an \textit{implicit PRM} can be obtained at no additional cost, by simply training an ORM on the cheaper response-level labels. The only assumption is to parameterize the outcome reward as the log-likelihood ratios of the policy and reference models, which can be optimized regardless of the specific choice of loss objectives. In experiments, we instantiate our implicit PRMs with various objectives and evaluate their performance on MATH. We show that our implicit PRM outperforms a strong MCTS-based baseline \textit{\'a la} Math-Shepherd using less than $1/38$ of the training data. Its performance can be further improved with majority voting. We further find that scaling up instructions and responses benefits our implicit PRM, and the latter brings a larger gain. Particularly, we find that our implicit PRM, when instantiated with the cross-entropy (CE) loss, is more data-efficient and can keep improving generation models even when trained with only one response per instruction, the setup that suffers from extreme data scarcity and imbalance. Further, instructions should be relevant to downstream tasks while the diversity of responses does not bring gains. Surprisingly, training on extra Math-Shepherd step labels brings no further improvements to our implicit PRM trained on only outcome data. We hope that our work will encourage a rethinking of PRM training approaches and contribute to making training PRMs more accessible.