Modern neural sequence models are designed to meet the dual mandate of parallelizable training and fast sequential inference. Recent developments have given rise to various models, such as Gated Linear Attention (GLA) and Mamba, that achieve such ``sequential-parallel duality.'' This raises a natural question: can we characterize the full class of neural sequence models that support near-constant-time parallel evaluation and linear-time, constant-space sequential inference? We begin by describing a broad class of such models -- state space models -- as those whose state updates can be computed using the classic parallel prefix scan algorithm with a custom associative aggregation operator. We then define a more general class, Prefix-Scannable Models (PSMs), by relaxing the state aggregation operator to allow arbitrary (potentially non-associative) functions such as softmax attention. This generalization unifies many existing architectures, including element-wise RNNs (e.g., Mamba) and linear transformers (e.g., GLA, Mamba2, mLSTM), while also introducing new models with softmax-like operators that achieve O(1) amortized compute per token and log(N) memory for sequence length N. We empirically evaluate such models on illustrative small-scale language modeling and canonical synthetic tasks, including state tracking and associative recall. Empirically, we find that PSMs retain the expressivity of transformer-based architectures while matching the inference efficiency of state space models -- in some cases exhibiting better length generalization than either.
State-space models (SSMs) and transformers dominate the language modeling landscape. However, they are constrained to a lower computational complexity than classical recurrent neural networks (RNNs), limiting their expressivity. In contrast, RNNs lack parallelization during training, raising fundamental questions about the trade off between parallelization and expressivity. We propose implicit SSMs, which iterate a transformation until convergence to a fixed point. Theoretically, we show that implicit SSMs implement the non-linear state-transitions of RNNs. Empirically, we find that only approximate fixed-point convergence suffices, enabling the design of a scalable training curriculum that largely retains parallelization, with full convergence required only for a small subset of tokens. Our approach demonstrates superior state-tracking capabilities on regular languages, surpassing transformers and SSMs. We further scale implicit SSMs to natural language reasoning tasks and pretraining of large-scale language models up to 1.3B parameters on 207B tokens representing, to our knowledge, the largest implicit model trained to date. Notably, our implicit models outperform their explicit counterparts on standard benchmarks. Our code is publicly available at http://github.com/microsoft/implicit_languagemodels .
Transformers exhibit proficiency in capturing long-range dependencies, whereas State Space Models (SSMs) facilitate linear-time sequence modeling. Notwithstanding their synergistic potential, the integration of these architectures presents a significant challenge, primarily attributable to a fundamental incongruity in their respective positional encoding mechanisms: Transformers rely on explicit Rotary Position Embeddings (RoPE), while SSMs leverage implicit positional representations via convolutions. This divergence often precipitates discontinuities and suboptimal performance. To address this impediment, we propose a unified rotary position embedding (Unified RoPE) methodology, thereby establishing a consistent positional encoding framework for both self-attention and state-space components. Using this Unified RoPE, we introduce TransXSSM, a hybrid architecture that coherently integrates the Transformer and SSM layers under this unified positional encoding scheme. At a 4K sequence length, TransXSSM exhibits training and inference speeds that are 42.3\% and 29.5\% faster, respectively, relative to standard Transformer models. It also delivers higher accuracy: under comparable settings, it surpasses a Transformer baseline by over 4\% on language modeling benchmarks.TransXSSM furthermore scales more effectively: TransXSSM-1.3B gains 7.22\% in average accuracy over its 320M version (versus about 6\% gains for equivalent Transformers or SSMs). Our results show that unified positional encoding resolves positional incompatibility in hybrid models, enabling efficient, high-performance long-context modeling.
Multi-state spiking neurons such as the adaptive leaky integrate-and-fire (AdLIF) neuron offer compelling alternatives to conventional deep learning models thanks to their sparse binary activations, second-order nonlinear recurrent dynamics, and efficient hardware realizations. However, such internal dynamics can cause instabilities during inference and training, often limiting performance and scalability. Meanwhile, state space models (SSMs) excel in long sequence processing using linear state-intrinsic recurrence resembling spiking neurons' subthreshold regime. Here, we establish a mathematical bridge between SSMs and second-order spiking neuron models. Based on structure and parametrization strategies of diagonal SSMs, we propose two novel spiking neuron models. The first extends the AdLIF neuron through timestep training and logarithmic reparametrization to facilitate training and improve final performance. The second additionally brings initialization and structure from complex-state SSMs, broadening the dynamical regime to oscillatory dynamics. Together, our two models achieve beyond or near state-of-the-art (SOTA) performances for reset-based spiking neuron models across both event-based and raw audio speech recognition datasets. We achieve this with a favorable number of parameters and required dynamic memory while maintaining high activity sparsity. Our models demonstrate enhanced scalability in network size and strike a favorable balance between performance and efficiency with respect to SSM models.
Event cameras unlock new frontiers that were previously unthinkable with standard frame-based cameras. One notable example is low-latency motion estimation (optical flow), which is critical for many real-time applications. In such applications, the computational efficiency of algorithms is paramount. Although recent deep learning paradigms such as CNN, RNN, or ViT have shown remarkable performance, they often lack the desired computational efficiency. Conversely, asynchronous event-based methods including SNNs and GNNs are computationally efficient; however, these approaches fail to capture sufficient spatio-temporal information, a powerful feature required to achieve better performance for optical flow estimation. In this work, we introduce Spatio-Temporal State Space Model (STSSM) module along with a novel network architecture to develop an extremely efficient solution with competitive performance. Our STSSM module leverages state-space models to effectively capture spatio-temporal correlations in event data, offering higher performance with lower complexity compared to ViT, CNN-based architectures in similar settings. Our model achieves 4.5x faster inference and 8x lower computations compared to TMA and 2x lower computations compared to EV-FlowNet with competitive performance on the DSEC benchmark. Our code will be available at https://github.com/AhmedHumais/E-STMFlow
State Space Models (SSMs) have emerged as powerful components for sequence modeling, enabling efficient handling of long-range dependencies via linear recurrence and convolutional computation. However, their effectiveness depends heavily on the choice and initialization of the state matrix. In this work, we build on the SaFARi framework and existing WaLRUS SSMs to introduce a new variant, W4S4 (WaLRUS for S4), a new class of SSMs constructed from redundant wavelet frames. WaLRUS admits a stable diagonalization and supports fast kernel computation without requiring low-rank approximations, making it both theoretically grounded and computationally efficient. We show that WaLRUS retains information over long horizons significantly better than HiPPO-based SSMs, both in isolation and when integrated into deep architectures such as S4. Our experiments demonstrate consistent improvements across delay reconstruction tasks, classification benchmarks, and long-range sequence modeling, confirming that high-quality, structured initialization enabled by wavelet-based state dynamic offers substantial advantages over existing alternatives. WaLRUS provides a scalable and versatile foundation for the next generation of deep SSM-based models.
State Space models (SSMs) such as PointMamba enable efficient feature extraction for point cloud self-supervised learning with linear complexity, outperforming Transformers in computational efficiency. However, existing PointMamba-based methods depend on complex token ordering and random masking, which disrupt spatial continuity and local semantic correlations. We propose ZigzagPointMamba to tackle these challenges. The core of our approach is a simple zigzag scan path that globally sequences point cloud tokens, enhancing spatial continuity by preserving the proximity of spatially adjacent point tokens. Nevertheless, random masking undermines local semantic modeling in self-supervised learning. To address this, we introduce a Semantic-Siamese Masking Strategy (SMS), which masks semantically similar tokens to facilitate reconstruction by integrating local features of original and similar tokens. This overcomes the dependence on isolated local features and enables robust global semantic modeling. Our pre-trained ZigzagPointMamba weights significantly improve downstream tasks, achieving a 1.59% mIoU gain on ShapeNetPart for part segmentation, a 0.4% higher accuracy on ModelNet40 for classification, and 0.19%, 1.22%, and 0.72% higher accuracies respectively for the classification tasks on the OBJ-BG, OBJ-ONLY, and PB-T50-RS subsets of ScanObjectNN.
With the growing demand for deploying large language models (LLMs) across diverse applications, improving their inference efficiency is crucial for sustainable and democratized access. However, retraining LLMs to meet new user-specific requirements is prohibitively expensive and environmentally unsustainable. In this work, we propose a practical and scalable alternative: composing efficient hybrid language models from existing pre-trained models. Our approach, Zebra-Llama, introduces a family of 1B, 3B, and 8B hybrid models by combining State Space Models (SSMs) and Multi-head Latent Attention (MLA) layers, using a refined initialization and post-training pipeline to efficiently transfer knowledge from pre-trained Transformers. Zebra-Llama achieves Transformer-level accuracy with near-SSM efficiency using only 7-11B training tokens (compared to trillions of tokens required for pre-training) and an 8B teacher. Moreover, Zebra-Llama dramatically reduces KV cache size -down to 3.9%, 2%, and 2.73% of the original for the 1B, 3B, and 8B variants, respectively-while preserving 100%, 100%, and >97% of average zero-shot performance on LM Harness tasks. Compared to models like MambaInLLaMA, X-EcoMLA, Minitron, and Llamba, Zebra-Llama consistently delivers competitive or superior accuracy while using significantly fewer tokens, smaller teachers, and vastly reduced KV cache memory. Notably, Zebra-Llama-8B surpasses Minitron-8B in few-shot accuracy by 7% while using 8x fewer training tokens, over 12x smaller KV cache, and a smaller teacher (8B vs. 15B). It also achieves 2.6x-3.8x higher throughput (tokens/s) than MambaInLlama up to a 32k context length. We will release code and model checkpoints upon acceptance.
The evolution of sequence modeling architectures, from recurrent neural networks and convolutional models to Transformers and structured state-space models, reflects ongoing efforts to address the diverse temporal dependencies inherent in sequential data. Despite this progress, systematically characterizing the strengths and limitations of these architectures remains a fundamental challenge.In this work, we propose a synthetic benchmarking framework to evaluate how effectively different sequence models capture distinct temporal structures. The core of this approach is to generate synthetic targets, each characterized by a memory function and a parameter that determines the strength of temporal dependence. This setup allows us to produce a continuum of tasks that vary in temporal complexity, enabling fine-grained analysis of model behavior concerning specific memory properties. We focus on four representative memory functions, each corresponding to a distinct class of temporal structures.Experiments on several sequence modeling architectures confirm existing theoretical insights and reveal new findings.These results demonstrate the effectiveness of the proposed method in advancing theoretical understandingand highlight the importance of using controllable targets with clearly defined structures for evaluating sequence modeling architectures.
Real-time decoding of neural activity is central to neuroscience and neurotechnology applications, from closed-loop experiments to brain-computer interfaces, where models are subject to strict latency constraints. Traditional methods, including simple recurrent neural networks, are fast and lightweight but often struggle to generalize to unseen data. In contrast, recent Transformer-based approaches leverage large-scale pretraining for strong generalization performance, but typically have much larger computational requirements and are not always suitable for low-resource or real-time settings. To address these shortcomings, we present POSSM, a novel hybrid architecture that combines individual spike tokenization via a cross-attention module with a recurrent state-space model (SSM) backbone to enable (1) fast and causal online prediction on neural activity and (2) efficient generalization to new sessions, individuals, and tasks through multi-dataset pretraining. We evaluate POSSM's decoding performance and inference speed on intracortical decoding of monkey motor tasks, and show that it extends to clinical applications, namely handwriting and speech decoding in human subjects. Notably, we demonstrate that pretraining on monkey motor-cortical recordings improves decoding performance on the human handwriting task, highlighting the exciting potential for cross-species transfer. In all of these tasks, we find that POSSM achieves decoding accuracy comparable to state-of-the-art Transformers, at a fraction of the inference cost (up to 9x faster on GPU). These results suggest that hybrid SSMs are a promising approach to bridging the gap between accuracy, inference speed, and generalization when training neural decoders for real-time, closed-loop applications.
Deep State Space Models (SSMs) reignite physics-grounded compute paradigms, as RNNs could natively be embodied into dynamical systems. This calls for dedicated learning algorithms obeying to core physical principles, with efficient techniques to simulate these systems and guide their design. We propose Recurrent Hamiltonian Echo Learning (RHEL), an algorithm which provably computes loss gradients as finite differences of physical trajectories of non-dissipative, Hamiltonian systems. In ML terms, RHEL only requires three "forward passes" irrespective of model size, without explicit Jacobian computation, nor incurring any variance in the gradient estimation. Motivated by the physical realization of our algorithm, we first introduce RHEL in continuous time and demonstrate its formal equivalence with the continuous adjoint state method. To facilitate the simulation of Hamiltonian systems trained by RHEL, we propose a discrete-time version of RHEL which is equivalent to Backpropagation Through Time (BPTT) when applied to a class of recurrent modules which we call Hamiltonian Recurrent Units (HRUs). This setting allows us to demonstrate the scalability of RHEL by generalizing these results to hierarchies of HRUs, which we call Hamiltonian SSMs (HSSMs). We apply RHEL to train HSSMs with linear and nonlinear dynamics on a variety of time-series tasks ranging from mid-range to long-range classification and regression with sequence length reaching $\sim 50k$. We show that RHEL consistently matches the performance of BPTT across all models and tasks. This work opens new doors for the design of scalable, energy-efficient physical systems endowed with self-learning capabilities for sequence modelling.
The attention mechanism in Transformers is an important primitive for accurate and scalable sequence modeling. Its quadratic-compute and linear-memory complexity however remain significant bottlenecks. Linear attention and state-space models enable linear-time, constant-memory sequence modeling and can moreover be trained efficiently through matmul-rich parallelization across sequence length. However, at their core these models are still RNNs, and thus their use of a fixed-size hidden state to model the context is a fundamental limitation. This paper develops log-linear attention, an attention mechanism that balances linear attention's efficiency and the expressiveness of softmax attention. Log-linear attention replaces the fixed-size hidden state with a logarithmically growing set of hidden states. We show that with a particular growth function, log-linear attention admits a similarly matmul-rich parallel form whose compute cost is log-linear in sequence length. Log-linear attention is a general framework and can be applied on top of existing linear attention variants. As case studies, we instantiate log-linear variants of two recent architectures -- Mamba-2 and Gated DeltaNet -- and find they perform well compared to their linear-time variants.
Accurate 3D medical image segmentation demands architectures capable of reconciling global context modeling with spatial topology preservation. While State Space Models (SSMs) like Mamba show potential for sequence modeling, existing medical SSMs suffer from encoder-decoder incompatibility: the encoder's 1D sequence flattening compromises spatial structures, while conventional decoders fail to leverage Mamba's state propagation. We present DM-SegNet, a Dual-Mamba architecture integrating directional state transitions with anatomy-aware hierarchical decoding. The core innovations include a quadri-directional spatial Mamba module employing four-directional 3D scanning to maintain anatomical spatial coherence, a gated spatial convolution layer that enhances spatially sensitive feature representation prior to state modeling, and a Mamba-driven decoding framework enabling bidirectional state synchronization across scales. Extensive evaluation on two clinically significant benchmarks demonstrates the efficacy of DM-SegNet: achieving state-of-the-art Dice Similarity Coefficient (DSC) of 85.44% on the Synapse dataset for abdominal organ segmentation and 90.22% on the BraTS2023 dataset for brain tumor segmentation.
Real-time object detection is a fundamental but challenging task in computer vision, particularly when computational resources are limited. Although YOLO-series models have set strong benchmarks by balancing speed and accuracy, the increasing need for richer global context modeling has led to the use of Transformer-based architectures. Nevertheless, Transformers have high computational complexity because of their self-attention mechanism, which limits their practicality for real-time and edge deployments. To overcome these challenges, recent developments in linear state space models, such as Mamba, provide a promising alternative by enabling efficient sequence modeling with linear complexity. Building on this insight, we propose MambaNeXt-YOLO, a novel object detection framework that balances accuracy and efficiency through three key contributions: (1) MambaNeXt Block: a hybrid design that integrates CNNs with Mamba to effectively capture both local features and long-range dependencies; (2) Multi-branch Asymmetric Fusion Pyramid Network (MAFPN): an enhanced feature pyramid architecture that improves multi-scale object detection across various object sizes; and (3) Edge-focused Efficiency: our method achieved 66.6% mAP at 31.9 FPS on the PASCAL VOC dataset without any pre-training and supports deployment on edge devices such as the NVIDIA Jetson Xavier NX and Orin NX.
State space models are emerging as a dominant model class for sequence problems with many relying on the HiPPO framework to initialize their dynamics. However, HiPPO fundamentally assumes data to be noise-free; an assumption often violated in practice. We extend the HiPPO theory with measurement noise and derive an uncertainty-aware initialization for state space model dynamics. In our analysis, we interpret HiPPO as a linear stochastic control problem where the data enters as a noise-free control signal. We then reformulate the problem so that the data become noisy outputs of a latent system and arrive at an alternative dynamics initialization that infers the posterior of this latent system from the data without increasing runtime. Our experiments show that our initialization improves the resistance of state-space models to noise both at training and inference time. Find our implementation at https://cs.cit.tum.de/daml/unhippo.
State-space models (SSMs) offer a promising architecture for sequence modeling, providing an alternative to Transformers by replacing expensive self-attention with linear recurrences. In this paper, we propose a simple yet effective trick to enhance SSMs within given computational budgets by sparsifying them. Our intuition is that tokens in SSMs are highly redundant due to gradual recurrent updates, and dense recurrence operations block the delivery of past information. In particular, we observe that upper layers of SSMs tend to be more redundant as they encode global information, while lower layers encode local information. Motivated by this, we introduce Simba, a hierarchical sparsification method for SSMs based on token pruning. Simba sparsifies upper layers more than lower layers, encouraging the upper layers to behave like highways. To achieve this, we propose a novel token pruning criterion for SSMs, measuring the global impact of tokens on the final output by accumulating local recurrences. We demonstrate that Simba outperforms the baseline model, Mamba, with the same FLOPS in various natural language tasks. Moreover, we illustrate the effect of highways, showing that Simba not only enhances efficiency but also improves the information flow across long sequences. Code is available at https://github.com/woominsong/Simba.
The U-shaped encoder-decoder architecture with skip connections has become a prevailing paradigm in medical image segmentation due to its simplicity and effectiveness. While many recent works aim to improve this framework by designing more powerful encoders and decoders, employing advanced convolutional neural networks (CNNs) for local feature extraction, Transformers or state space models (SSMs) such as Mamba for global context modeling, or hybrid combinations of both, these methods often struggle to fully utilize pretrained vision backbones (e.g., ResNet, ViT, VMamba) due to structural mismatches. To bridge this gap, we introduce ACM-UNet, a general-purpose segmentation framework that retains a simple UNet-like design while effectively incorporating pretrained CNNs and Mamba models through a lightweight adapter mechanism. This adapter resolves architectural incompatibilities and enables the model to harness the complementary strengths of CNNs and SSMs-namely, fine-grained local detail extraction and long-range dependency modeling. Additionally, we propose a hierarchical multi-scale wavelet transform module in the decoder to enhance feature fusion and reconstruction fidelity. Extensive experiments on the Synapse and ACDC benchmarks demonstrate that ACM-UNet achieves state-of-the-art performance while remaining computationally efficient. Notably, it reaches 85.12% Dice Score and 13.89mm HD95 on the Synapse dataset with 17.93G FLOPs, showcasing its effectiveness and scalability. Code is available at: https://github.com/zyklcode/ACM-UNet.
We investigate whether hidden states from Structured State Space Models (SSMs) can be merged post-hoc to support downstream reasoning. Inspired by model souping, we propose a strategy where documents are encoded independently and their representations are pooled -- via simple operations like averaging -- into a single context state. This approach, which we call document souping, enables modular encoding and reuse without reprocessing the full input for each query. We finetune Mamba2 models to produce soupable representations and find that they support multi-hop QA, sparse retrieval, and long-document reasoning with strong accuracy. On HotpotQA, souping ten independently encoded documents nearly matches the performance of a cross-encoder trained on the same inputs.
In-context learning, the ability of large language models to perform tasks using only examples provided in the prompt, has recently been adapted for time series forecasting. This paradigm enables zero-shot prediction, where past values serve as context for forecasting future values, making powerful forecasting tools accessible to non-experts and increasing the performance when training data are scarce. Most existing zero-shot forecasting approaches rely on transformer architectures, which, despite their success in language, often fall short of expectations in time series forecasting, where recurrent models like LSTMs frequently have the edge. Conversely, while LSTMs are well-suited for time series modeling due to their state-tracking capabilities, they lack strong in-context learning abilities. We introduce TiRex that closes this gap by leveraging xLSTM, an enhanced LSTM with competitive in-context learning skills. Unlike transformers, state-space models, or parallelizable RNNs such as RWKV, TiRex retains state-tracking, a critical property for long-horizon forecasting. To further facilitate its state-tracking ability, we propose a training-time masking strategy called CPM. TiRex sets a new state of the art in zero-shot time series forecasting on the HuggingFace benchmarks GiftEval and Chronos-ZS, outperforming significantly larger models including TabPFN-TS (Prior Labs), Chronos Bolt (Amazon), TimesFM (Google), and Moirai (Salesforce) across both short- and long-term forecasts.
We use the fertile ground of betting markets to study the anticipation of major news in financial markets. While there is a considerable body of literature on the accuracy and efficiency of betting markets after important in-match events, there are no studies dealing with the anticipation of such events. This paper tracks bookmaker odds and betting stakes to provide insights into the movement of both prior to goals. Utilising high-resolution (1 Hz) data from a leading European bookmaker for a full season of the top German football league, we analyse whether market participants anticipate major news. In particular, we consider the case of the first goal scored within a match, with its strong impact on the match outcome. Using regression models and state-space models (SSMs) accounting for an underlying market activity level, we investigate whether the bookmaker adjusts odds and bettors tend to place higher stakes on the scoring team right before the first goal is scored. Our results indicate that neither side of the market anticipates goals by significantly adjusting their behaviour.