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SubscribeCounting Ability of Large Language Models and Impact of Tokenization
Transformers, the backbone of modern large language models (LLMs), face inherent architectural limitations that impede their reasoning capabilities. Unlike recurrent networks, Transformers lack recurrent connections, confining them to constant-depth computation. This restriction places them in the complexity class TC^0, making them theoretically incapable of solving tasks that demand increasingly deep reasoning as input length grows. Counting, a fundamental component of many reasoning tasks, also requires reasoning depth to grow linearly to be performed inductively. While previous studies have established the upper limits of counting ability in Transformer-based expert models (i.e., models specifically trained for counting tasks), these findings do not directly extend to general-purpose LLMs due to differences in reasoning mechanisms. Recent work has highlighted how Chain of Thought (CoT) reasoning can help alleviate some of the architectural limitations of Transformers in counting tasks. However, little attention has been paid to the role of tokenization in these models. Unlike expert models that often use character-level tokenization, LLMs typically rely on byte-level (BPE) tokenizers, which fundamentally alters the way reasoning is processed. Our work investigates the impact of tokenization on the counting abilities of LLMs, uncovering substantial performance variations based on input tokenization differences. We provide both theoretical and experimental analyses, offering insights into how tokenization choices can undermine models' theoretical computability, thereby inspiring the design of new tokenization methods to enhance reasoning in LLMs.
Recurrent Action Transformer with Memory
Recently, the use of transformers in offline reinforcement learning has become a rapidly developing area. This is due to their ability to treat the agent's trajectory in the environment as a sequence, thereby reducing the policy learning problem to sequence modeling. In environments where the agent's decisions depend on past events, it is essential to capture both the event itself and the decision point in the context of the model. However, the quadratic complexity of the attention mechanism limits the potential for context expansion. One solution to this problem is to enhance transformers with memory mechanisms. In this paper, we propose the Recurrent Action Transformer with Memory (RATE) - a model that incorporates recurrent memory. To evaluate our model, we conducted extensive experiments on both memory-intensive environments (VizDoom-Two-Color, T-Maze) and classic Atari games and MuJoCo control environments. The results show that the use of memory can significantly improve performance in memory-intensive environments while maintaining or improving results in classic environments. We hope that our findings will stimulate research on memory mechanisms for transformers applicable to offline reinforcement learning.
Recurrent Attention Networks for Long-text Modeling
Self-attention-based models have achieved remarkable progress in short-text mining. However, the quadratic computational complexities restrict their application in long text processing. Prior works have adopted the chunking strategy to divide long documents into chunks and stack a self-attention backbone with the recurrent structure to extract semantic representation. Such an approach disables parallelization of the attention mechanism, significantly increasing the training cost and raising hardware requirements. Revisiting the self-attention mechanism and the recurrent structure, this paper proposes a novel long-document encoding model, Recurrent Attention Network (RAN), to enable the recurrent operation of self-attention. Combining the advantages from both sides, the well-designed RAN is capable of extracting global semantics in both token-level and document-level representations, making it inherently compatible with both sequential and classification tasks, respectively. Furthermore, RAN is computationally scalable as it supports parallelization on long document processing. Extensive experiments demonstrate the long-text encoding ability of the proposed RAN model on both classification and sequential tasks, showing its potential for a wide range of applications.
Linearly-Recurrent Autoencoder Networks for Learning Dynamics
This paper describes a method for learning low-dimensional approximations of nonlinear dynamical systems, based on neural-network approximations of the underlying Koopman operator. Extended Dynamic Mode Decomposition (EDMD) provides a useful data-driven approximation of the Koopman operator for analyzing dynamical systems. This paper addresses a fundamental problem associated with EDMD: a trade-off between representational capacity of the dictionary and over-fitting due to insufficient data. A new neural network architecture combining an autoencoder with linear recurrent dynamics in the encoded state is used to learn a low-dimensional and highly informative Koopman-invariant subspace of observables. A method is also presented for balanced model reduction of over-specified EDMD systems in feature space. Nonlinear reconstruction using partially linear multi-kernel regression aims to improve reconstruction accuracy from the low-dimensional state when the data has complex but intrinsically low-dimensional structure. The techniques demonstrate the ability to identify Koopman eigenfunctions of the unforced Duffing equation, create accurate low-dimensional models of an unstable cylinder wake flow, and make short-time predictions of the chaotic Kuramoto-Sivashinsky equation.
Layerwise Recurrent Router for Mixture-of-Experts
The scaling of large language models (LLMs) has revolutionized their capabilities in various tasks, yet this growth must be matched with efficient computational strategies. The Mixture-of-Experts (MoE) architecture stands out for its ability to scale model size without significantly increasing training costs. Despite their advantages, current MoE models often display parameter inefficiency. For instance, a pre-trained MoE-based LLM with 52 billion parameters might perform comparably to a standard model with 6.7 billion parameters. Being a crucial part of MoE, current routers in different layers independently assign tokens without leveraging historical routing information, potentially leading to suboptimal token-expert combinations and the parameter inefficiency problem. To alleviate this issue, we introduce the Layerwise Recurrent Router for Mixture-of-Experts (RMoE). RMoE leverages a Gated Recurrent Unit (GRU) to establish dependencies between routing decisions across consecutive layers. Such layerwise recurrence can be efficiently parallelly computed for input tokens and introduces negotiable costs. Our extensive empirical evaluations demonstrate that RMoE-based language models consistently outperform a spectrum of baseline models. Furthermore, RMoE integrates a novel computation stage orthogonal to existing methods, allowing seamless compatibility with other MoE architectures. Our analyses attribute RMoE's gains to its effective cross-layer information sharing, which also improves expert selection and diversity. Our code is at https://github.com/qiuzh20/RMoE
Relational recurrent neural networks
Memory-based neural networks model temporal data by leveraging an ability to remember information for long periods. It is unclear, however, whether they also have an ability to perform complex relational reasoning with the information they remember. Here, we first confirm our intuitions that standard memory architectures may struggle at tasks that heavily involve an understanding of the ways in which entities are connected -- i.e., tasks involving relational reasoning. We then improve upon these deficits by using a new memory module -- a Relational Memory Core (RMC) -- which employs multi-head dot product attention to allow memories to interact. Finally, we test the RMC on a suite of tasks that may profit from more capable relational reasoning across sequential information, and show large gains in RL domains (e.g. Mini PacMan), program evaluation, and language modeling, achieving state-of-the-art results on the WikiText-103, Project Gutenberg, and GigaWord datasets.
Recurrent Graph Syntax Encoder for Neural Machine Translation
Syntax-incorporated machine translation models have been proven successful in improving the model's reasoning and meaning preservation ability. In this paper, we propose a simple yet effective graph-structured encoder, the Recurrent Graph Syntax Encoder, dubbed RGSE, which enhances the ability to capture useful syntactic information. The RGSE is done over a standard encoder (recurrent or self-attention encoder), regarding recurrent network units as graph nodes and injects syntactic dependencies as edges, such that RGSE models syntactic dependencies and sequential information (i.e., word order) simultaneously. Our approach achieves considerable improvements over several syntax-aware NMT models in EnglishRightarrowGerman and EnglishRightarrowCzech translation tasks. And RGSE-equipped big model obtains competitive result compared with the state-of-the-art model in WMT14 En-De task. Extensive analysis further verifies that RGSE could benefit long sentence modeling, and produces better translations.
LCIRC: A Recurrent Compression Approach for Efficient Long-form Context and Query Dependent Modeling in LLMs
While large language models (LLMs) excel in generating coherent and contextually rich outputs, their capacity to efficiently handle long-form contexts is limited by fixed-length position embeddings. Additionally, the computational cost of processing long sequences increases quadratically, making it challenging to extend context length. To address these challenges, we propose Long-form Context Injection with Recurrent Compression (LCIRC), a method that enables the efficient processing long-form sequences beyond the model's length limit through recurrent compression without retraining the entire model. We further introduce query dependent context modeling, which selectively compresses query-relevant information, ensuring that the model retains the most pertinent content. Our empirical results demonstrate that Query Dependent LCIRC (QD-LCIRC) significantly improves LLM's ability to manage extended contexts, making it well-suited for tasks that require both comprehensive context understanding and query relevance.
Generalization without systematicity: On the compositional skills of sequence-to-sequence recurrent networks
Humans can understand and produce new utterances effortlessly, thanks to their compositional skills. Once a person learns the meaning of a new verb "dax," he or she can immediately understand the meaning of "dax twice" or "sing and dax." In this paper, we introduce the SCAN domain, consisting of a set of simple compositional navigation commands paired with the corresponding action sequences. We then test the zero-shot generalization capabilities of a variety of recurrent neural networks (RNNs) trained on SCAN with sequence-to-sequence methods. We find that RNNs can make successful zero-shot generalizations when the differences between training and test commands are small, so that they can apply "mix-and-match" strategies to solve the task. However, when generalization requires systematic compositional skills (as in the "dax" example above), RNNs fail spectacularly. We conclude with a proof-of-concept experiment in neural machine translation, suggesting that lack of systematicity might be partially responsible for neural networks' notorious training data thirst.
Block-Recurrent Dynamics in Vision Transformers
As Vision Transformers (ViTs) become standard vision backbones, a mechanistic account of their computational phenomenology is essential. Despite architectural cues that hint at dynamical structure, there is no settled framework that interprets Transformer depth as a well-characterized flow. In this work, we introduce the Block-Recurrent Hypothesis (BRH), arguing that trained ViTs admit a block-recurrent depth structure such that the computation of the original L blocks can be accurately rewritten using only k ll L distinct blocks applied recurrently. Across diverse ViTs, between-layer representational similarity matrices suggest few contiguous phases. To determine whether these phases reflect genuinely reusable computation, we train block-recurrent surrogates of pretrained ViTs: Recurrent Approximations to Phase-structured TransfORmers (Raptor). In small-scale, we demonstrate that stochastic depth and training promote recurrent structure and subsequently correlate with our ability to accurately fit Raptor. We then provide an empirical existence proof for BRH by training a Raptor model to recover 96% of DINOv2 ImageNet-1k linear probe accuracy in only 2 blocks at equivalent computational cost. Finally, we leverage our hypothesis to develop a program of Dynamical Interpretability. We find i) directional convergence into class-dependent angular basins with self-correcting trajectories under small perturbations, ii) token-specific dynamics, where cls executes sharp late reorientations while patch tokens exhibit strong late-stage coherence toward their mean direction, and iii) a collapse to low rank updates in late depth, consistent with convergence to low-dimensional attractors. Altogether, we find a compact recurrent program emerges along ViT depth, pointing to a low-complexity normative solution that enables these models to be studied through principled dynamical systems analysis.
Fast Training of Recurrent Neural Networks with Stationary State Feedbacks
Recurrent neural networks (RNNs) have recently demonstrated strong performance and faster inference than Transformers at comparable parameter budgets. However, the recursive gradient computation with the backpropagation through time (or BPTT) algorithm remains the major computational bottleneck. In this work, we propose a novel method that replaces BPTT with a fixed gradient feedback mechanism, yielding an efficient approximation of the exact gradient propagation based on the assumption of time stationarity. Our approach leverages state-space model (SSM) principles to define a structured feedback matrix that directly propagates gradients from future time steps. This formulation bypasses the need for recursive gradient backpropagation, significantly reducing training overhead while preserving the network's ability to capture long-term dependencies. The experiments on language modeling benchmarks exhibit competitive perplexity scores, while significantly reducing the training costs. These promising results suggest that designing a feedback method like an SSM can fully exploit the efficiency advantages of RNNs for many practical applications.
Exploring the Relationship Between Model Architecture and In-Context Learning Ability
What is the relationship between model architecture and the ability to perform in-context learning? In this empirical study, we take the first steps toward answering this question. We evaluate twelve model architectures capable of causal language modeling across a suite of synthetic in-context learning tasks. These selected architectures represent a broad range of paradigms, including recurrent and convolution-based neural networks, transformers, state-space model inspired, and other emerging attention alternatives. We discover that all the considered architectures can perform in-context learning under a wider range of conditions than previously documented. Additionally, we observe stark differences in statistical efficiency and consistency by varying context length and task difficulty. We also measure each architecture's predisposition towards in-context learning when presented with alternative routes for task resolution. Finally, and somewhat surprisingly, we find that several attention alternatives are more robust in-context learners than transformers. Given that such approaches have constant-sized memory footprints at inference time, this result opens the possibility of scaling up in-context learning to accommodate vastly larger numbers of in-context examples.
Frame-Recurrent Video Super-Resolution
Recent advances in video super-resolution have shown that convolutional neural networks combined with motion compensation are able to merge information from multiple low-resolution (LR) frames to generate high-quality images. Current state-of-the-art methods process a batch of LR frames to generate a single high-resolution (HR) frame and run this scheme in a sliding window fashion over the entire video, effectively treating the problem as a large number of separate multi-frame super-resolution tasks. This approach has two main weaknesses: 1) Each input frame is processed and warped multiple times, increasing the computational cost, and 2) each output frame is estimated independently conditioned on the input frames, limiting the system's ability to produce temporally consistent results. In this work, we propose an end-to-end trainable frame-recurrent video super-resolution framework that uses the previously inferred HR estimate to super-resolve the subsequent frame. This naturally encourages temporally consistent results and reduces the computational cost by warping only one image in each step. Furthermore, due to its recurrent nature, the proposed method has the ability to assimilate a large number of previous frames without increased computational demands. Extensive evaluations and comparisons with previous methods validate the strengths of our approach and demonstrate that the proposed framework is able to significantly outperform the current state of the art.
Flow Equivariant Recurrent Neural Networks
Data arrives at our senses as a continuous stream, smoothly transforming from one instant to the next. These smooth transformations can be viewed as continuous symmetries of the environment that we inhabit, defining equivalence relations between stimuli over time. In machine learning, neural network architectures that respect symmetries of their data are called equivariant and have provable benefits in terms of generalization ability and sample efficiency. To date, however, equivariance has been considered only for static transformations and feed-forward networks, limiting its applicability to sequence models, such as recurrent neural networks (RNNs), and corresponding time-parameterized sequence transformations. In this work, we extend equivariant network theory to this regime of `flows' -- one-parameter Lie subgroups capturing natural transformations over time, such as visual motion. We begin by showing that standard RNNs are generally not flow equivariant: their hidden states fail to transform in a geometrically structured manner for moving stimuli. We then show how flow equivariance can be introduced, and demonstrate that these models significantly outperform their non-equivariant counterparts in terms of training speed, length generalization, and velocity generalization, on both next step prediction and sequence classification. We present this work as a first step towards building sequence models that respect the time-parameterized symmetries which govern the world around us.
MossFormer2: Combining Transformer and RNN-Free Recurrent Network for Enhanced Time-Domain Monaural Speech Separation
Our previously proposed MossFormer has achieved promising performance in monaural speech separation. However, it predominantly adopts a self-attention-based MossFormer module, which tends to emphasize longer-range, coarser-scale dependencies, with a deficiency in effectively modelling finer-scale recurrent patterns. In this paper, we introduce a novel hybrid model that provides the capabilities to model both long-range, coarse-scale dependencies and fine-scale recurrent patterns by integrating a recurrent module into the MossFormer framework. Instead of applying the recurrent neural networks (RNNs) that use traditional recurrent connections, we present a recurrent module based on a feedforward sequential memory network (FSMN), which is considered "RNN-free" recurrent network due to the ability to capture recurrent patterns without using recurrent connections. Our recurrent module mainly comprises an enhanced dilated FSMN block by using gated convolutional units (GCU) and dense connections. In addition, a bottleneck layer and an output layer are also added for controlling information flow. The recurrent module relies on linear projections and convolutions for seamless, parallel processing of the entire sequence. The integrated MossFormer2 hybrid model demonstrates remarkable enhancements over MossFormer and surpasses other state-of-the-art methods in WSJ0-2/3mix, Libri2Mix, and WHAM!/WHAMR! benchmarks.
Handwritten digit string recognition by combination of residual network and RNN-CTC
Recurrent neural network (RNN) and connectionist temporal classification (CTC) have showed successes in many sequence labeling tasks with the strong ability of dealing with the problems where the alignment between the inputs and the target labels is unknown. Residual network is a new structure of convolutional neural network and works well in various computer vision tasks. In this paper, we take advantage of the architectures mentioned above to create a new network for handwritten digit string recognition. First we design a residual network to extract features from input images, then we employ a RNN to model the contextual information within feature sequences and predict recognition results. At the top of this network, a standard CTC is applied to calculate the loss and yield the final results. These three parts compose an end-to-end trainable network. The proposed new architecture achieves the highest performances on ORAND-CAR-A and ORAND-CAR-B with recognition rates 89.75% and 91.14%, respectively. In addition, the experiments on a generated captcha dataset which has much longer string length show the potential of the proposed network to handle long strings.
Samba: Simple Hybrid State Space Models for Efficient Unlimited Context Language Modeling
Efficiently modeling sequences with infinite context length has been a long-standing problem. Past works suffer from either the quadratic computation complexity or the limited extrapolation ability on length generalization. In this work, we present Samba, a simple hybrid architecture that layer-wise combines Mamba, a selective State Space Model (SSM), with Sliding Window Attention (SWA). Samba selectively compresses a given sequence into recurrent hidden states while still maintaining the ability to precisely recall memories with the attention mechanism. We scale Samba up to 3.8B parameters with 3.2T training tokens and show that Samba substantially outperforms the state-of-the-art models based on pure attention or SSMs on a wide range of benchmarks. When trained on 4K length sequences, Samba can be efficiently extrapolated to 256K context length with perfect memory recall and show improved token predictions up to 1M context length. As a linear-time sequence model, Samba enjoys a 3.73x higher throughput compared to Transformers with grouped-query attention when processing user prompts of 128K length, and 3.64x speedup when generating 64K tokens with unlimited streaming. A sample implementation of Samba is publicly available in https://github.com/microsoft/Samba.
StateX: Enhancing RNN Recall via Post-training State Expansion
While Transformer-based models have demonstrated remarkable language modeling performance, their high complexities result in high costs when processing long contexts. In contrast, recurrent neural networks (RNNs) such as linear attention and state space models have gained popularity due to their constant per-token complexities. However, these recurrent models struggle with tasks that require accurate recall of contextual information from long contexts, because all contextual information is compressed into a constant-size recurrent state. Previous works have shown that recall ability is positively correlated with the recurrent state size, yet directly training RNNs with larger recurrent states results in high training costs. In this paper, we introduce StateX, a training pipeline for efficiently expanding the states of pre-trained RNNs through post-training. For two popular classes of RNNs, linear attention and state space models, we design post-training architectural modifications to scale up the state size with no or negligible increase in model parameters. Experiments on models up to 1.3B parameters demonstrate that StateX efficiently enhances the recall and in-context learning ability of RNNs without incurring high post-training costs or compromising other capabilities.
Resona: Improving Context Copying in Linear Recurrence Models with Retrieval
Recent shifts in the space of large language model (LLM) research have shown an increasing focus on novel architectures to compete with prototypical Transformer-based models that have long dominated this space. Linear recurrent models have proven to be a viable competitor due to their computational efficiency. However, such models still demonstrate a sizable gap compared to Transformers in terms of in-context learning among other tasks that require recalling information from a context. In this work, we introduce __Resona__, a simple and scalable framework for augmenting linear recurrent models with retrieval. __Resona__~augments models with the ability to integrate retrieved information from the provided input context, enabling tailored behavior to diverse task requirements. Experiments on a variety of linear recurrent models demonstrate that __Resona__-augmented models observe significant performance gains on a variety of synthetic as well as real-world natural language tasks, highlighting its ability to act as a general purpose method to improve the in-context learning and language modeling abilities of linear recurrent LLMs.
The Illusion of State in State-Space Models
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 and 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 TC^0. 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.
Attention as an RNN
The advent of Transformers marked a significant breakthrough in sequence modelling, providing a highly performant architecture capable of leveraging GPU parallelism. However, Transformers are computationally expensive at inference time, limiting their applications, particularly in low-resource settings (e.g., mobile and embedded devices). Addressing this, we (1) begin by showing that attention can be viewed as a special Recurrent Neural Network (RNN) with the ability to compute its many-to-one RNN output efficiently. We then (2) show that popular attention-based models such as Transformers can be viewed as RNN variants. However, unlike traditional RNNs (e.g., LSTMs), these models cannot be updated efficiently with new tokens, an important property in sequence modelling. Tackling this, we (3) introduce a new efficient method of computing attention's many-to-many RNN output based on the parallel prefix scan algorithm. Building on the new attention formulation, we (4) introduce Aaren, an attention-based module that can not only (i) be trained in parallel (like Transformers) but also (ii) be updated efficiently with new tokens, requiring only constant memory for inferences (like traditional RNNs). Empirically, we show Aarens achieve comparable performance to Transformers on 38 datasets spread across four popular sequential problem settings: reinforcement learning, event forecasting, time series classification, and time series forecasting tasks while being more time and memory-efficient.
