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.

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.

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.

With the development of artificial intelligence, its contribution to science is evolving from simulating a complex problem to automating entire research processes and producing novel discoveries. Achieving this advancement requires both specialized general models grounded in real-world scientific data and iterative, exploratory frameworks that mirror human scientific methodologies. In this paper, we present PROTEUS, a fully automated system for scientific discovery from raw proteomics data. PROTEUS uses large language models (LLMs) to perform hierarchical planning, execute specialized bioinformatics tools, and iteratively refine analysis workflows to generate high-quality scientific hypotheses. The system takes proteomics datasets as input and produces a comprehensive set of research objectives, analysis results, and novel biological hypotheses without human intervention. We evaluated PROTEUS on 12 proteomics datasets collected from various biological samples (e.g. immune cells, tumors) and different sample types (single-cell and bulk), generating 191 scientific hypotheses. These were assessed using both automatic LLM-based scoring on 5 metrics and detailed reviews from human experts. Results demonstrate that PROTEUS consistently produces reliable, logically coherent results that align well with existing literature while also proposing novel, evaluable hypotheses. The system's flexible architecture facilitates seamless integration of diverse analysis tools and adaptation to different proteomics data types. By automating complex proteomics analysis workflows and hypothesis generation, PROTEUS has the potential to considerably accelerate the pace of scientific discovery in proteomics research, enabling researchers to efficiently explore large-scale datasets and uncover biological insights.

Improving the effectiveness and efficiency of large language models (LLMs) simultaneously is a critical yet challenging research goal. In this paper, we find that low-rank pre-training, normally considered as efficient methods that will compromise performance, can be scalably effective when reduced parameters are precisely targeted. Specifically, applying the low-dimensional module only to the attention layer -- resolves this issue and enhances both effectiveness and efficiency. We refer to this structure as Low-dimensional Projected Attention (LPA) and provide an explanatory analysis. Through extensive experimentation at parameter scales of 130M, 370M, and scaling up to 3B, we have validated the effectiveness and scalability of LPA. Our results show that LPA model can save up to 12.4% in time while achieving an approximate 5% improvement in test perplexity (ppl) and on downstream tasks compared with the vanilla Transformer.

Large Language Models (LLMs) have demonstrated remarkable capabilities across various domains and are moving towards more specialized areas. Recent advanced proprietary models such as GPT-4 and Gemini have achieved significant advancements in biomedicine, which have also raised privacy and security challenges. The construction of specialized generalists hinges largely on high-quality datasets, enhanced by techniques like supervised fine-tuning and reinforcement learning from human or AI feedback, and direct preference optimization. However, these leading technologies (e.g., preference learning) are still significantly limited in the open source community due to the scarcity of specialized data. In this paper, we present the UltraMedical collections, which consist of high-quality manual and synthetic datasets in the biomedicine domain, featuring preference annotations across multiple advanced LLMs. By utilizing these datasets, we fine-tune a suite of specialized medical models based on Llama-3 series, demonstrating breathtaking capabilities across various medical benchmarks. Moreover, we develop powerful reward models skilled in biomedical and general reward benchmark, enhancing further online preference learning within the biomedical LLM community.

Supervised Fine-Tuning (SFT) and Preference Optimization (PO) are two fundamental processes for enhancing the capabilities of Language Models (LMs) post pre-training, aligning them better with human preferences. Although SFT advances in training efficiency, PO delivers better alignment, thus they are often combined. However, common practices simply apply them sequentially without integrating their optimization objectives, ignoring the opportunities to bridge their paradigm gap and take the strengths from both. To obtain a unified understanding, we interpret SFT and PO with two sub-processes -- Preference Estimation and Transition Optimization -- defined at token level within the Markov Decision Process (MDP) framework. This modeling shows that SFT is only a specialized case of PO with inferior estimation and optimization. PO evaluates the quality of model's entire generated answer, whereas SFT only scores predicted tokens based on preceding tokens from target answers. Therefore, SFT overestimates the ability of model, leading to inferior optimization. Building on this view, we introduce Intuitive Fine-Tuning (IFT) to integrate SFT and Preference Optimization into a single process. IFT captures LMs' intuitive sense of the entire answers through a temporal residual connection, but it solely relies on a single policy and the same volume of non-preference-labeled data as SFT. Our experiments show that IFT performs comparably or even superiorly to sequential recipes of SFT and some typical Preference Optimization methods across several tasks, particularly those requires generation, reasoning, and fact-following abilities. An explainable Frozen Lake game further validates the effectiveness of IFT for getting competitive policy.

Underlying data distributions of natural language, programming code, and mathematical symbols vary vastly, presenting a complex challenge for large language models (LLMs) that strive to achieve high performance across all three domains simultaneously. Achieving a very high level of proficiency for an LLM within a specific domain often requires extensive training with relevant corpora, which is typically accompanied by a sacrifice in performance in other domains. In this paper, we propose to fuse models that are already highly-specialized directly. The proposed fusing framework, UltraFuser, consists of three distinct specialists that are already sufficiently trained on language, coding, and mathematics. A token-level gating mechanism is introduced to blend the specialists' outputs. A two-stage training strategy accompanied by balanced sampling is designed to ensure stability. To effectively train the fused model, we further construct a high-quality supervised instruction tuning dataset, UltraChat 2, which includes text, code, and mathematical content. This dataset comprises approximately 300,000 instructions and covers a wide range of topics in each domain. Experiments show that our model could simultaneously achieve mastery of the three crucial domains.

Fine-tuning pre-trained large language models in a parameter-efficient manner is widely studied for its effectiveness and efficiency. The popular method of low-rank adaptation (LoRA) offers a notable approach, hypothesizing that the adaptation process is intrinsically low-dimensional. Although LoRA has demonstrated commendable performance, it is implemented with a fixed and unalterable intrinsic rank that might not always be the ideal choice. Recognizing the need for more flexible adaptation, we extend the methodology of LoRA to an innovative approach we call sparse low-rank adaptation (SoRA) that enables dynamic adjustments to the intrinsic rank during the adaptation process. We achieve this through the incorporation of a gate unit optimized with proximal gradient method in the training stage, controlling the cardinality of rank under the sparsity of the gate. In the subsequent inference stage, we eliminate the parameter blocks corresponding to the zeroed-out ranks, to reduce each SoRA module back to a concise yet rank-optimal LoRA. Our approach strengthens the representation power of LoRA by initializing it with a higher rank, while efficiently taming a temporarily increased number of parameters via updating in a sparse way. We further introduce a sparsifying scheduler for SoRA, aiming to examine the impact of the number of non-zero parameters on the model's memorization and generalization. Our experimental results demonstrate that SoRA can outperform other baselines even with 70% retained parameters and 70% training time.