Sequence Modeling with Multiresolution Convolutional Memory (2305.01638v2)

Abstract: 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 paper introduces MultiresLayer, a novel architecture that leverages multiresolution convolution to capture long-range dependencies in sequential data.
• It demonstrates superior parameter efficiency and state-of-the-art performance on sequence classification and autoregressive density estimation tasks.
• The approach bridges convolutional networks and wavelet theory, providing a solid foundation for future applications in image, video, and complex sequences.

Sequence Modeling with Multiresolution Convolutional Memory

The paper "Sequence Modeling with Multiresolution Convolutional Memory" presents an innovative framework for sequence modeling inspired by multiresolution analysis (MRA) and wavelets. The proposed architecture, termed MultiresLayer, addresses a fundamental challenge in sequence modeling: efficiently capturing long-range dependencies in sequential data. This methodology significantly contributes to the landscape of neural network architectures designed for tasks such as classification and generative modeling by integrating the strengths of convolutional networks and wavelet-based multiresolution analysis.

The essence of the paper lies in its formulation of MultiresLayer, which utilizes MultiresConv, a multiresolution convolution operation that mirrors wavelet decomposition. This operation is designed to capture multiscale trends in input sequences. Implemented via shared filters across a dilated causal convolution tree, MultiresConv allows the model to perform computations linearly with respect to input length. This design choice contrasts with conventional methods that often struggle with parameter inefficiency or computational overhead.

The paper provides a comprehensive evaluation of MultiresNet, a deep architecture derived from stacking MultiresLayer blocks, across various tasks. MultiresNet demonstrates state-of-the-art performance on sequence classification and autoregressive density estimation tasks using CIFAR-10, ListOps, and PTB-XL datasets. Particularly notable is its ability to achieve this with significantly fewer parameters compared to competing models. For instance, in pixel-level CIFAR-10 classification, MultiresNet outperforms recent models with a parameter count around 1.4M, whereas others exceed this significantly.

The paper's empirical results underscore the advantages of MultiresNet in terms of parameter efficiency and computational simplicity. The model delivers robust performance on challenging tasks known for requiring the modeling of hierarchical or long-range dependencies, such as ListOps and autoregressive generative modeling of CIFAR-10. These successes highlight MultiresNet's potent memory mechanism, where structural patterns at varying resolutions are memorized and utilized throughout the sequence.

In examining theoretical implications, the paper strengthens the understanding of convolutional networks by providing them with a principled foundation grounded in wavelet theory. This approach not only facilitates a better theoretical understanding of existing architectures, such as WaveNet, but also offers avenues for further improvements by leveraging insights from the extensive MRA and wavelet literature.

The proposed model also expands the scope of sequence modeling approaches, providing an architecture that maintains key benefits—such as computational efficiency and interpretability—while addressing limitations seen in models reliant on heavy parameterization or sophisticated initialization schemes (e.g., those utilizing state-space models).

Looking forward, the research lays a promising groundwork for further exploration into the multiresolution properties of data beyond sequences. Potential future developments, as suggested by the paper, involve adapting MultiresLayer for applications in image and video data or further enhancing shift-invariant properties through advanced wavelet techniques. Such extensions could significantly broaden the model's applicability and performance across diverse domains.

Overall, the proposed MultiresLayer and its integration within MultiresNet represent a solid advancement in sequence modeling, demonstrating the potential for convolutional networks inspired by theoretical constructs from signal processing to redefine efficiency and performance benchmarks in the field.