In this paper, we comprehensively study the inductive biases of two major approaches to augmenting Transformers with a recurrent mechanism: (1) the approach of incorporating a depth-wise recurrence similar to Universal Transformers; and (2) the approach of incorporating a chunk-wise temporal recurrence like Temporal Latent Bottleneck. Furthermore, we propose and investigate novel ways to extend and combine the above methods - for example, we propose a global mean-based dynamic halting mechanism for Universal Transformers and an augmentation of Temporal Latent Bottleneck with elements from Universal Transformer. We compare the models and probe their inductive biases in several diagnostic tasks, such as Long Range Arena (LRA), flip-flop language modeling, ListOps, and Logical Inference. The code is released in: https://github.com/JRC1995/InvestigatingRecurrentTransformers/tree/main
Investigating deep learning language models has always been a significant research area due to the ``black box" nature of most advanced models. With the recent advancements in pre-trained language models based on transformers and their increasing integration into daily life, addressing this issue has become more pressing. In order to achieve an explainable AI model, it is essential to comprehend the procedural steps involved and compare them with human thought processes. Thus, in this paper, we use simple, well-understood non-language tasks to explore these models' inner workings. Specifically, we apply a pre-trained language model to constrained arithmetic problems with hierarchical structure, to analyze their attention weight scores and hidden states. The investigation reveals promising results, with the model addressing hierarchical problems in a moderately structured manner, similar to human problem-solving strategies. Additionally, by inspecting the attention weights layer by layer, we uncover an unconventional finding that layer 10, rather than the model's final layer, is the optimal layer to unfreeze for the least parameter-intensive approach to fine-tune the model. We support these findings with entropy analysis and token embeddings similarity analysis. The attention analysis allows us to hypothesize that the model can generalize to longer sequences in ListOps dataset, a conclusion later confirmed through testing on sequences longer than those in the training set. Lastly, by utilizing a straightforward task in which the model predicts the winner of a Tic Tac Toe game, we identify limitations in attention analysis, particularly its inability to capture 2D patterns.
We propose Beam Tree Recursive Cell (BT-Cell) - a backpropagation-friendly framework to extend Recursive Neural Networks (RvNNs) with beam search for latent structure induction. We further extend this framework by proposing a relaxation of the hard top-k operators in beam search for better propagation of gradient signals. We evaluate our proposed models in different out-of-distribution splits in both synthetic and realistic data. Our experiments show that BTCell achieves near-perfect performance on several challenging structure-sensitive synthetic tasks like ListOps and logical inference while maintaining comparable performance in realistic data against other RvNN-based models. Additionally, we identify a previously unknown failure case for neural models in generalization to unseen number of arguments in ListOps. The code is available at: https://github.com/JRC1995/BeamTreeRecursiveCells.
Efficiently capturing the long-range patterns in sequential data sources salient to a given task -- such as classification and generative modeling -- poses a fundamental challenge. Popular approaches in the space tradeoff between the memory burden of brute-force enumeration and comparison, as in transformers, the computational burden of complicated sequential dependencies, as in recurrent neural networks, or the parameter burden of convolutional networks with many or large filters. We instead take inspiration from wavelet-based multiresolution analysis to define a new building block for sequence modeling, which we call a MultiresLayer. The key component of our model is the multiresolution convolution, capturing multiscale trends in the input sequence. Our MultiresConv can be implemented with shared filters across a dilated causal convolution tree. Thus it garners the computational advantages of convolutional networks and the principled theoretical motivation of wavelet decompositions. Our MultiresLayer is straightforward to implement, requires significantly fewer parameters, and maintains at most a $\mathcal{O}(N\log N)$ memory footprint for a length $N$ sequence. Yet, by stacking such layers, our model yields state-of-the-art performance on a number of sequence classification and autoregressive density estimation tasks using CIFAR-10, ListOps, and PTB-XL datasets.
The design choices in the Transformer attention mechanism, including weak inductive bias and quadratic computational complexity, have limited its application for modeling long sequences. In this paper, we introduce Mega, a simple, theoretically grounded, single-head gated attention mechanism equipped with (exponential) moving average to incorporate inductive bias of position-aware local dependencies into the position-agnostic attention mechanism. We further propose a variant of Mega that offers linear time and space complexity yet yields only minimal quality loss, by efficiently splitting the whole sequence into multiple chunks with fixed length. Extensive experiments on a wide range of sequence modeling benchmarks, including the Long Range Arena, neural machine translation, auto-regressive language modeling, and image and speech classification, show that Mega achieves significant improvements over other sequence models, including variants of Transformers and recent state space models.
Models using structured state space sequence (S4) layers have achieved state-of-the-art performance on long-range sequence modeling tasks. An S4 layer combines linear state space models (SSMs), the HiPPO framework, and deep learning to achieve high performance. We build on the design of the S4 layer and introduce a new state space layer, the S5 layer. Whereas an S4 layer uses many independent single-input, single-output SSMs, the S5 layer uses one multi-input, multi-output SSM. We establish a connection between S5 and S4, and use this to develop the initialization and parameterization used by the S5 model. The result is a state space layer that can leverage efficient and widely implemented parallel scans, allowing S5 to match the computational efficiency of S4, while also achieving state-of-the-art performance on several long-range sequence modeling tasks. S5 averages 87.4% on the long range arena benchmark, and 98.5% on the most difficult Path-X task.
While deep generative models have succeeded in image processing, natural language processing, and reinforcement learning, training that involves discrete random variables remains challenging due to the high variance of its gradient estimation process. Monte Carlo is a common solution used in most variance reduction approaches. However, this involves time-consuming resampling and multiple function evaluations. We propose a Gapped Straight-Through (GST) estimator to reduce the variance without incurring resampling overhead. This estimator is inspired by the essential properties of Straight-Through Gumbel-Softmax. We determine these properties and show via an ablation study that they are essential. Experiments demonstrate that the proposed GST estimator enjoys better performance compared to strong baselines on two discrete deep generative modeling tasks, MNIST-VAE and ListOps.
Vision Transformer (ViT) and its variants (e.g., Swin, PVT) have achieved great success in various computer vision tasks, owing to their capability to learn long-range contextual information. Layer Normalization (LN) is an essential ingredient in these models. However, we found that the ordinary LN makes tokens at different positions similar in magnitude because it normalizes embeddings within each token. It is difficult for Transformers to capture inductive bias such as the positional context in an image with LN. We tackle this problem by proposing a new normalizer, termed Dynamic Token Normalization (DTN), where normalization is performed both within each token (intra-token) and across different tokens (inter-token). DTN has several merits. Firstly, it is built on a unified formulation and thus can represent various existing normalization methods. Secondly, DTN learns to normalize tokens in both intra-token and inter-token manners, enabling Transformers to capture both the global contextual information and the local positional context. {Thirdly, by simply replacing LN layers, DTN can be readily plugged into various vision transformers, such as ViT, Swin, PVT, LeViT, T2T-ViT, BigBird and Reformer. Extensive experiments show that the transformer equipped with DTN consistently outperforms baseline model with minimal extra parameters and computational overhead. For example, DTN outperforms LN by $0.5\%$ - $1.2\%$ top-1 accuracy on ImageNet, by $1.2$ - $1.4$ box AP in object detection on COCO benchmark, by $2.3\%$ - $3.9\%$ mCE in robustness experiments on ImageNet-C, and by $0.5\%$ - $0.8\%$ accuracy in Long ListOps on Long-Range Arena.} Codes will be made public at \url{https://github.com/wqshao126/DTN}
The ability to reason with multiple hierarchical structures is an attractive and desirable property of sequential inductive biases for natural language processing. Do the state-of-the-art Transformers and LSTM architectures implicitly encode for these biases? To answer this, we propose ORCHARD, a diagnostic dataset for systematically evaluating hierarchical reasoning in state-of-the-art neural sequence models. While there have been prior evaluation frameworks such as ListOps or Logical Inference, our work presents a novel and more natural setting where our models learn to reason with multiple explicit hierarchical structures instead of only one, i.e., requiring the ability to do both long-term sequence memorizing, relational reasoning while reasoning with hierarchical structure. Consequently, backed by a set of rigorous experiments, we show that (1) Transformer and LSTM models surprisingly fail in systematic generalization, and (2) with increased references between hierarchies, Transformer performs no better than random.
A central goal of sequence modeling is designing a single principled model that can address sequence data across a range of modalities and tasks, particularly on long-range dependencies. Although conventional models including RNNs, CNNs, and Transformers have specialized variants for capturing long dependencies, they still struggle to scale to very long sequences of $10000$ or more steps. A promising recent approach proposed modeling sequences by simulating the fundamental state space model (SSM) \( x'(t) = Ax(t) + Bu(t), y(t) = Cx(t) + Du(t) \), and showed that for appropriate choices of the state matrix \( A \), this system could handle long-range dependencies mathematically and empirically. However, this method has prohibitive computation and memory requirements, rendering it infeasible as a general sequence modeling solution. We propose the Structured State Space sequence model (S4) based on a new parameterization for the SSM, and show that it can be computed much more efficiently than prior approaches while preserving their theoretical strengths. Our technique involves conditioning \( A \) with a low-rank correction, allowing it to be diagonalized stably and reducing the SSM to the well-studied computation of a Cauchy kernel. S4 achieves strong empirical results across a diverse range of established benchmarks, including (i) 91\% accuracy on sequential CIFAR-10 with no data augmentation or auxiliary losses, on par with a larger 2-D ResNet, (ii) substantially closing the gap to Transformers on image and language modeling tasks, while performing generation $60\times$ faster (iii) SoTA on every task from the Long Range Arena benchmark, including solving the challenging Path-X task of length 16k that all prior work fails on, while being as efficient as all competitors.
Despite progress across a broad range of applications, Transformers have limited success in systematic generalization. The situation is especially frustrating in the case of algorithmic tasks, where they often fail to find intuitive solutions that route relevant information to the right node/operation at the right time in the grid represented by Transformer columns. To facilitate the learning of useful control flow, we propose two modifications to the Transformer architecture, copy gate and geometric attention. Our novel Neural Data Router (NDR) achieves 100% length generalization accuracy on the classic compositional table lookup task, as well as near-perfect accuracy on the simple arithmetic task and a new variant of ListOps testing for generalization across computational depths. NDR's attention and gating patterns tend to be interpretable as an intuitive form of neural routing. Our code is public.
Transformers with linearised attention (''linear Transformers'') have demonstrated the practical scalability and effectiveness of outer product-based Fast Weight Programmers (FWPs) from the '90s. However, the original FWP formulation is more general than the one of linear Transformers: a slow neural network (NN) continually reprograms the weights of a fast NN with arbitrary architecture. In existing linear Transformers, both NNs are feedforward and consist of a single layer. Here we explore new variations by adding recurrence to the slow and fast nets. We evaluate our novel recurrent FWPs (RFWPs) on two synthetic algorithmic tasks (code execution and sequential ListOps), Wikitext-103 language models, and on the Atari 2600 2D game environment. Our models exhibit properties of Transformers and RNNs. In the reinforcement learning setting, we report large improvements over LSTM in several Atari games. Our code is public.
Recursive Neural Networks (RvNNs), which compose sequences according to their underlying hierarchical syntactic structure, have performed well in several natural language processing tasks compared to similar models without structural biases. However, traditional RvNNs are incapable of inducing the latent structure in a plain text sequence on their own. Several extensions have been proposed to overcome this limitation. Nevertheless, these extensions tend to rely on surrogate gradients or reinforcement learning at the cost of higher bias or variance. In this work, we propose Continuous Recursive Neural Network (CRvNN) as a backpropagation-friendly alternative to address the aforementioned limitations. This is done by incorporating a continuous relaxation to the induced structure. We demonstrate that CRvNN achieves strong performance in challenging synthetic tasks such as logical inference and ListOps. We also show that CRvNN performs comparably or better than prior latent structure models on real-world tasks such as sentiment analysis and natural language inference.
Transformers do not scale very well to long sequence lengths largely because of quadratic self-attention complexity. In the recent months, a wide spectrum of efficient, fast Transformers have been proposed to tackle this problem, more often than not claiming superior or comparable model quality to vanilla Transformer models. To this date, there is no well-established consensus on how to evaluate this class of models. Moreover, inconsistent benchmarking on a wide spectrum of tasks and datasets makes it difficult to assess relative model quality amongst many models. This paper proposes a systematic and unified benchmark, LRA, specifically focused on evaluating model quality under long-context scenarios. Our benchmark is a suite of tasks consisting of sequences ranging from $1K$ to $16K$ tokens, encompassing a wide range of data types and modalities such as text, natural, synthetic images, and mathematical expressions requiring similarity, structural, and visual-spatial reasoning. We systematically evaluate ten well-established long-range Transformer models (Reformers, Linformers, Linear Transformers, Sinkhorn Transformers, Performers, Synthesizers, Sparse Transformers, and Longformers) on our newly proposed benchmark suite. LRA paves the way towards better understanding this class of efficient Transformer models, facilitates more research in this direction, and presents new challenging tasks to tackle. Our benchmark code will be released at https://github.com/google-research/long-range-arena.
Stack-augmented recurrent neural networks (RNNs) have been of interest to the deep learning community for some time. However, the difficulty of training memory models remains a problem obstructing the widespread use of such models. In this paper, we propose the Ordered Memory architecture. Inspired by Ordered Neurons (Shen et al., 2018), we introduce a new attention-based mechanism and use its cumulative probability to control the writing and erasing operation of the memory. We also introduce a new Gated Recursive Cell to compose lower-level representations into higher-level representation. We demonstrate that our model achieves strong performance on the logical inference task (Bowman et al., 2015)and the ListOps (Nangia and Bowman, 2018) task. We can also interpret the model to retrieve the induced tree structure, and find that these induced structures align with the ground truth. Finally, we evaluate our model on the Stanford SentimentTreebank tasks (Socher et al., 2013), and find that it performs comparatively with the state-of-the-art methods in the literature.