Despite the remarkable success of Transformer-based architectures in various sequential modeling tasks, such as natural language processing, computer vision, and robotics, their ability to learn basic sequential models, like Hidden Markov Models (HMMs), is still unclear. This paper investigates the performance of Transformers in learning HMMs and their variants through extensive experimentation and compares them to Recurrent Neural Networks (RNNs). We show that Transformers consistently underperform RNNs in both training speed and testing accuracy across all tested HMM models. There are even challenging HMM instances where Transformers struggle to learn, while RNNs can successfully do so. Our experiments further reveal the relation between the depth of Transformers and the longest sequence length it can effectively learn, based on the types and the complexity of HMMs. To address the limitation of transformers in modeling HMMs, we demonstrate that a variant of the Chain-of-Thought (CoT), called $\textit{block CoT}$ in the training phase, can help transformers to reduce the evaluation error and to learn longer sequences at a cost of increasing the training time. Finally, we complement our empirical findings by theoretical results proving the expressiveness of transformers in approximating HMMs with logarithmic depth.
Memory Limitations of Prompt Tuning in Transformers
Department of Mathematics, National University of Singapore（新加坡国立大学数学系）；IPAL, IRL2955, Singapore（新加坡IPAL）；School of Computing, National University of Singapore（新加坡国立大学计算机学院）；Department of Electrical and Computer Engineering, National University of Singapore（新加坡国立大学电气与计算机工程系）
On the Limitations and Capabilities of Position Embeddings for Length Generalization
State Key Laboratory of General Artificial Intelligence, School of Intelligence Science and Technology, Peking University（人工智能通用基础理论国家重点实验室，智能科学与技术学院，北京大学）；Institute for Artificial Intelligence, Peking University（人工智能研究院，北京大学）；Beijing Institute for General Artificial Intelligence（北京人工智能研究院）；Pazhou Laboratory (Huangpu)（琶洲实验室（黄埔））
Conditional generation of time-dependent data is a task that has much interest, whether for data augmentation, scenario simulation, completing missing data, or other purposes. Recent works proposed a Transformer-based Time series generative adversarial network (TTS-GAN) to address the limitations of recurrent neural networks. However, this model assumes a unimodal distribution and tries to generate samples around the expectation of the real data distribution. One of its limitations is that it may generate a random multivariate time series; it may fail to generate samples in the presence of mul…
David R. Cheriton School of Computer Science（戴维·R·切里顿计算机科学学院）；University of Waterloo（滑铁卢大学）
The ability to perform arithmetic tasks is a remarkable trait of human intelligence and might form a critical component of more complex reasoning tasks. In this work, we investigate if the surface form of a number has any influence on how sequence-to-sequence language models learn simple arithmetic tasks such as addition and subtraction across a wide range of values. We find that how a number is represented in its surface form has a strong influence on the model's accuracy. In particular, the model fails to learn addition of five-digit numbers when using subwords (e.g., "32"), and it struggles…
Facebook AI Research（脸书人工智能研究院）；LORIA（洛林计算机科学及其应用实验室）
Transformers have been successfully applied to sequential, auto-regressive tasks despite being feedforward networks. Unlike recurrent neural networks, Transformers use attention to capture temporal relations while processing input tokens in parallel. While this parallelization makes them computationally efficient, it restricts the model from fully exploiting the sequential nature of the input. The representation at a given layer can only access representations from lower layers, rather than the higher level representations already available. In this work, we propose the Feedback Transformer ar…
Transformers have supplanted recurrent models in a large number of NLP tasks. However, the differences in their abilities to model different syntactic properties remain largely unknown. Past works suggest that LSTMs generalize very well on regular languages and have close connections with counter languages. In this work, we systematically study the ability of Transformers to model such languages as well as the role of its individual components in doing so. We first provide a construction of Transformers for a subclass of counter languages, including well-studied languages such as n-ary Boolean…
Although transformers are remarkably effective for many tasks, there are some surprisingly easy-looking regular languages that they struggle with. Hahn shows that for languages where acceptance depends on a single input symbol, a transformer's classification decisions become less and less confident (that is, with cross-entropy approaching 1 bit per string) as input strings get longer and longer. We examine this limitation using two languages: PARITY, the language of bit strings with an odd number of 1s, and FIRST, the language of bit strings starting with a 1. We demonstrate three ways of over…
Department of Applied Mathematics, University of Waterloo（滑铁卢大学应用数学系）；University of Waterloo（滑铁卢大学）
We use neural ordinary differential equations to formulate a variant of the Transformer that is depth-adaptive in the sense that an input-dependent number of time steps is taken by the ordinary differential equation solver. Our goal in proposing the N-ODE Transformer is to investigate whether its depth-adaptivity may aid in overcoming some specific known theoretical limitations of the Transformer in handling nonlocal effects. Specifically, we consider the simple problem of determining the parity of a binary sequence, for which the standard Transformer has known limitations that can only be ove…
Theoretical Constraints on the Expressive Power of $\mathsf{RoPE}$-based Tensor Attention Transformers
The University of Hong Kong（香港大学）；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；The Simons Institute for the Theory of Computing at UC Berkeley（加州大学伯克利分校西蒙斯理论计算研究所）；Anhui University（安徽大学）
Many real-world tasks are plagued by limitations on data: in some instances very little data is available and in others, data is protected by privacy enforcing regulations (e.g. GDPR). We consider limitations posed specifically on time-series data and present a model that can generate synthetic time-series which can be used in place of real data. A model that generates synthetic time-series data has two objectives: 1) to capture the stepwise conditional distribution of real sequences, and 2) to faithfully model the joint distribution of entire real sequences. Autoregressive models trained via …
Transformers are emerging as the new workhorse of NLP, showing great success across tasks. Unlike LSTMs, transformers process input sequences entirely through self-attention. Previous work has suggested that the computational capabilities of self-attention to process hierarchical structures are limited. In this work, we mathematically investigate the computational power of self-attention to model formal languages. Across both soft and hard attention, we show strong theoretical limitations of the computational abilities of self-attention, finding that it cannot model periodic finite-state langu…
Idiap Research Institute（伊迪亚普研究所）；EPFL（洛桑联邦理工学院）；University of Washington（华盛顿大学）；University of Geneva（日内瓦大学）
Transformers achieve remarkable performance in several tasks but due to their quadratic complexity, with respect to the input's length, they are prohibitively slow for very long sequences. To address this limitation, we express the self-attention as a linear dot-product of kernel feature maps and make use of the associativity property of matrix products to reduce the complexity from $\mathcal{O}\left(N^2\right)$ to $\mathcal{O}\left(N\right)$, where $N$ is the sequence length. We show that this formulation permits an iterative implementation that dramatically accelerates autoregressive transfo…
Aristotle University of Thessaloniki（塞萨洛尼基亚里士多德大学）
In the last decade, the field of Neural Language Modelling has witnessed enormous changes, with the development of novel models through the use of Transformer architectures. However, even these models struggle to model long sequences due to memory constraints and increasing computational complexity. Coreference annotations over the training data can provide context far beyond the modelling limitations of such language models. In this paper we present an extension over the Transformer-block architecture used in neural language models, specifically in GPT2, in order to incorporate entity annotat…
Transformers are being used extensively across several sequence modeling tasks. Significant research effort has been devoted to experimentally probe the inner workings of Transformers. However, our conceptual and theoretical understanding of their power and inherent limitations is still nascent. In particular, the roles of various components in Transformers such as positional encodings, attention heads, residual connections, and feedforward networks, are not clear. In this paper, we take a step towards answering these questions. We analyze the computational power as captured by Turing-complete…
Designing Time Series Experiments in A/B Testing with Transformer Reinforcement Learning
School of Mathematical Sciences（数学科学学院）；Zhejiang University（浙江大学）；Yunnan Key Laboratory of Statistical Modeling and Data Analysis（云南统计建模与数据分析重点实验室）；Yunnan University（云南大学）；School of Statistics（统计学系）；East China Normal University（华东师范大学）；University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校）；London School of Economics and Political Science（伦敦政治经济学院）
