Sequential-Parallel Duality in Prefix Scannable Models (2506.10918v1)

Abstract: 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 LLMing 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.

• The paper presents the main contribution of introducing Sequential-Parallel Duality (SPD) by unifying parallel training with constant-space sequential inference.
• It employs an extended prefix scan algorithm that integrates non-associative functions to bridge transformer models, element-wise RNNs, and linear transformers.
• Empirical results show that Prefix-Scannable Models enhance language modeling and algorithmic tasks by outperforming traditional models in both inference efficiency and length generalization.

Sequential-Parallel Duality in Prefix-Scannable Models

The paper "Sequential-Parallel Duality in Prefix-Scannable Models" presents an in-depth examination of modern neural sequence models that are designed to balance two critical aspects: parallelizable training and efficient sequential inference. The authors introduce the concept of "Sequential-Parallel Duality" (SPD) and explore the characteristics and implications of models that support both near-constant-time parallel evaluation and linear-time, constant-space sequential inference.

Background and Motivation

Neural sequence models, especially those based on transformer architectures, have dramatically advanced sequence processing capabilities. Transformers enable parallelizable training over the sequence dimension and handle arbitrary-length sequential dependencies with a constant parameter count. However, transformers also have drawbacks: their computational and memory complexities scale quadratically with sequence length, and they exhibit limited expressivity in handling certain computations.

Recent studies have focused on models that address these limitations, particularly concerning inference time complexity. Several new architectures have been proposed, such as element-wise recurrent models and linear transformers, that achieve linear complexity in inference while maintaining parallelizability during training.

Sequential-Parallel Duality (SPD)

The paper defines the Sequential-Parallel Duality as an attribute of sequence models that can be trained in parallel with nearly constant computational depth while allowing sequential inference with nearly constant space utilization. This duality inherently encompasses the efficiency required for modern language tasks, such as LLMing and associative recall.

Prefix-Scannable Models (PSMs)

To formalize the class of models exhibiting SPD, the authors introduce "Prefix-Scannable Models" (PSMs). PSMs are models whose state updates can be computed using the classic parallel prefix scan algorithm with a custom associative aggregation operator. By extending the prefix scan operations to allow non-associative functions, such as softmax attention, the authors create a more general framework that unifies various architectural approaches, including element-wise RNNs and linear transformers.

Empirical Evaluation

The paper provides empirical evaluations of PSMs through experiments on LLMing tasks and synthetic algorithmic challenges, such as state tracking and associative recall. The results demonstrate that PSMs maintain the expressive capabilities of transformer-based architectures, often surpassing their length generalization capabilities while retaining efficient inference akin to state space models.

Implications and Future Directions

The research outlines a unified framework characterizing diverse sequence model architectures, potentially guiding the development of future models. The theoretical advancement in understanding SPD and prefix scannability opens the door to novel designs that balance expressivity and computational efficiency.

The paper's speculations on future developments in AI suggest that as models continue to grow in complexity and capability, understanding and optimizing sequences' parallel and sequential handling will become increasingly critical. The potential for building models that can seamlessly integrate varying sequence orders and dependencies offers promising avenues for advancing AI in numerous applications, from language processing to complex systems modeling.

In conclusion, this paper provides a structured approach to analyzing and improving neural sequence models, contributing significantly to the ongoing evolution of model architectures in artificial intelligence.