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1. The Illusion of State in State-Space Models

   Merrill, William; Petty, Jackson; Sabharwal, Ashish (July 2024, International Conference on Machine Learning (ICML) 2024)

   State-space models (SSMs) have emerged as a potential alternative architecture for building large language models (LLMs) compared to the previously ubiquitous transformer architecture. One theoretical weakness of transformers is that they cannot express certain kinds of sequential computation and state tracking (Merrill & Sabharwal, 2023), which SSMs are explicitly designed to address via their close architectural similarity to recurrent neural networks (RNNs). But do SSMs truly have an advantage (over transformers) in expressive power for state tracking? Surprisingly, the answer is no. Our analysis reveals that the expressive power of SSMs is limited very similarly to transformers: SSMs cannot express computation outside the complexity class 𝖳𝖢0. In particular, this means they cannot solve simple state-tracking problems like permutation composition. It follows that SSMs are provably unable to accurately track chess moves with certain notation, evaluate code, or track entities in a long narrative. To supplement our formal analysis, we report experiments showing that Mamba-style SSMs indeed struggle with state tracking. Thus, despite its recurrent formulation, the "state" in an SSM is an illusion: SSMs have similar expressiveness limitations to non-recurrent models like transformers, which may fundamentally limit their ability to solve real-world state-tracking problems. 

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2. MambaByte: Token-free Selective State Space Model

   Wang, Junxiong; Gangavarapu, Tushaar; Yan, Jing Nathan; Rush, Alexander M (October 2024, COLM)

   Token-free language models learn directly from raw bytes and remove the inductive bias of subword tokenization. Operating on bytes, however, results in significantly longer sequences. In this setting, standard autoregressive Transformers scale poorly as the effective memory required grows with sequence length. The recent development of the Mamba state space model (SSM) offers an appealing alternative approach with a fixed-sized memory state and efficient decoding. We propose MambaByte, a token-free adaptation of the Mamba SSM trained autoregressively on byte sequences. In terms of modeling, we show MambaByte to be competitive with, and even to outperform, state-of-the-art subword Transformers on language modeling tasks while maintaining the benefits of token-free language models, such as robustness to noise. In terms of efficiency, we develop an adaptation of speculative decoding with tokenized drafting and byte-level verification. This results in a 2.6× inference speedup to the standard MambaByte implementation, showing similar decoding efficiency as the subword Mamba. These findings establish the viability of SSMs in enabling token-free language modeling. 

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3. The Mamba in the Llama: Distilling and Accelerating Hybrid Models

   Wang, Junxiong; Paliotta, Daniele; May, Avner; Rush, Alexander M; Dao, Tri (December 2024, NeurIPS)

   Linear RNN architectures, like Mamba, can be competitive with Transformer models in language modeling while having advantageous deployment characteristics. Given the focus on training large-scale Transformer models, we consider the challenge of converting these pretrained models for deployment. We demonstrate that it is feasible to distill large Transformers into linear RNNs by reusing the linear projection weights from attention layers with academic GPU resources. The resulting hybrid model, which incorporates a quarter of the attention layers, achieves performance comparable to the original Transformer in chat benchmarks and outperforms open-source hybrid Mamba models trained from scratch with trillions of tokens in both chat benchmarks and general benchmarks. Moreover, we introduce a hardware-aware speculative decoding algorithm that accelerates the inference speed of Mamba and hybrid models. Overall we show how, with limited computation resources, we can remove many of the original attention layers and generate from the resulting model more efficiently. Our top-performing model, distilled from Llama3-8B-Instruct, achieves a 29.61 length-controlled win rate on AlpacaEval 2 against GPT-4 and 7.35 on MT-Bench, surpassing the best 8B scale instruction-tuned linear RNN model. We also find that the distilled model has natural length extrapolation, showing almost perfect accuracy in the needle-in-a-haystack test at 20x the distillation length. 

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4. Task Descriptors Help Transformers Learn Linear Models In-Context

   Huang, Ruomin; Ge, Rong (April 2025, ICLR 2025)

   Large language models (LLMs) exhibit strong in-context learning (ICL) ability, which allows the model to make predictions on new examples based on the given prompt. Recently, a line of research (Von Oswald et al., 2023; Aky¨urek et al., 2023; Ahn et al., 2023; Mahankali et al., 2023; Zhang et al., 2024) considered ICL for a simple linear regression setting and showed that the forward pass of Transformers is simulating some variants of gradient descent (GD) algorithms on the in-context examples. In practice, the input prompt usually contains a task descriptor in addition to in-context examples. We investigate how the task description helps ICL in the linear regression setting. Consider a simple setting where the task descriptor describes the mean of input in linear regression. Our results show that gradient flow converges to a global minimum for a linear Transformer. At the global minimum, the Transformer learns to use the task descriptor effectively to improve its performance. Empirically, we verify our results by showing that the weights converge to the predicted global minimum and Transformers indeed perform better with task descriptors. 

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5. Characterizing State Space Model (SSM) and SSM-Transformer Hybrid Language Model Performance with Long Context Length

   Mitra, Saptarshi; Karami, Rachid; Xu, Haocheng; Huang, Sitao; Kwon, Hyoukjun (July 2025, arXiv preprint)

   The demand for machine intelligence capable of processing continuous, long-context inputs on local devices is growing rapidly. However, the quadratic complexity and memory requirements of traditional Transformer architectures make them inefficient and often unusable for these tasks. This has spurred a paradigm shift towards new architectures like State Space Models (SSMs) and hybrids, which promise near-linear scaling. While most current research focuses on the accuracy and theoretical throughput of these models, a systematic performance characterization on practical consumer hardware is critically needed to guide system-level optimization and unlock new applications. To address this gap, we present a comprehensive, comparative benchmarking of carefully selected Transformer, SSM, and hybrid models specifically for long-context inference on consumer and embedded GPUs. Our analysis reveals that SSMs are not only viable but superior for this domain, capable of processing sequences up to 220K tokens on a 24GB consumer GPU-approximately 4x longer than comparable Transformers. While Transformers may be up to 1.8x faster at short sequences, SSMs demonstrate a dramatic performance inversion, becoming up to 4x faster at very long contexts (~57K tokens). Our operator-level analysis reveals that custom, hardware-aware SSM kernels dominate the inference runtime, accounting for over 55% of latency on edge platforms, identifying them as a primary target for future hardware acceleration. We also provide detailed, device-specific characterization results to guide system co-design for the edge. 

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