An official website of the United States government
Fast linear transforms are ubiquitous in machine learning, including the discrete Fourier transform, discrete cosine transform, and other structured transformations such as convolutions. All of these transforms can be represented by dense matrix-vector multiplication, yet each has a specialized and highly efficient (subquadratic) algorithm. We ask to what extent hand-crafting these algorithms and implementations is necessary, what structural prior they encode, and how much knowledge is required to automatically learn a fast algorithm for a provided structured transform. Motivated by a characterization of fast matrix-vector multiplication as products of sparse matrices, we introduce a parameterization of divide-and-conquer methods that is capable of representing a large class of transforms. This generic formulation can automatically learn an efficient algorithm for many important transforms; for example, it recovers the O(N logN) Cooley-Tukey FFT algorithm to machine precision, for dimensions N up to 1024. Furthermore, our method can be incorporated as a lightweight replacement of generic matrices in machine learning pipelines to learn efficient and compressible transformations. On a standard task of compressing a single hidden-layer network, our method exceeds the classification accuracy of unconstrained matrices on CIFAR-10 by 3.9 points—the first time a structured approach has done so—with 4X faster inference speed and 40X fewer parameters.
more »
« less
Kaleidoscope: An Efficient, Learnable Representation For All Structured Linear Maps
Modern neural network architectures use structured linear transformations, such as low-rank matrices, sparse matrices, permutations, and the Fourier transform, to improve inference speed and reduce memory usage compared to general linear maps. However, choosing which of the myriad structured transformations to use (and its associated parameterization) is a laborious task that requires trading off speed, space, and accuracy. We consider a different approach: we introduce a family of matrices called kaleidoscope matrices (K-matrices) that provably capture any structured matrix with near-optimal space (parameter) and time (arithmetic operation) complexity. We empirically validate that K-matrices can be automatically learned within end-to-end pipelines to replace hand-crafted procedures, in order to improve model quality. For example, replacing channel shuffles in ShuffleNet improves classification accuracy on ImageNet by up to 5%. K-matrices can also simplify hand-engineered pipelines---we replace filter bank feature computation in speech data preprocessing with a learnable kaleidoscope layer, resulting in only 0.4% loss in accuracy on the TIMIT speech recognition task. In addition, K-matrices can capture latent structure in models: for a challenging permuted image classification task, adding a K-matrix to a standard convolutional architecture can enable learning the latent permutation and improve accuracy by over 8 points. We provide a practically efficient implementation of our approach, and use K-matrices in a Transformer network to attain 36% faster end-to-end inference speed on a language translation task.
more »
« less
- Award ID(s):
- 1763481
- PAR ID:
- 10137133
- Date Published:
- Journal Name:
- Eighth International Conference on Learning Representations
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Recurrent neural networks (RNNs), temporal convolutions, and neural differential equations (NDEs) are popular families of deep learning models for time-series data, each with unique strengths and tradeoffs in modeling power and computational efficiency. We introduce a simple sequence model inspired by control systems that generalizes these approaches while addressing their shortcomings. The Linear State-Space Layer (LSSL) maps a sequence u↦y by simply simulating a linear continuous-time state-space representation ˙x=Ax+Bu,y=Cx+Du. Theoretically, we show that LSSL models are closely related to the three aforementioned families of models and inherit their strengths. For example, they generalize convolutions to continuous-time, explain common RNN heuristics, and share features of NDEs such as time-scale adaptation. We then incorporate and generalize recent theory on continuous-time memorization to introduce a trainable subset of structured matrices A that endow LSSLs with long-range memory. Empirically, stacking LSSL layers into a simple deep neural network obtains state-of-the-art results across time series benchmarks for long dependencies in sequential image classification, real-world healthcare regression tasks, and speech. On a difficult speech classification task with length-16000 sequences, LSSL outperforms prior approaches by 24 accuracy points, and even outperforms baselines that use hand-crafted features on 100x shorter sequences.more » « less
-
null (Ed.)This paper presents a ternary low-density parity-check (LDPC) error correction system for wireless electrocardiogram sensors to improve the accuracy of arrhythmia classification. The classification system is based on ternary Delta-modulated bitstreams and rotation linear kernel support vector machines, which identifies the supraventricular ectopic beat (SVEB) and the ventricular ectopic beat (VEB) over the normal heartbeats. We model errors using a ternary symmetric channel with probability parameter p and construct a variety of ternary LDPC codes with different coding rates by concatenating two-component sub-matrices to form a parity-check matrix with a quasi-cyclic structure that facilitates the hardware design. In particular, a hardware-friendly LDPC encoder circuit is proposed that leverages the highly structured parity-check matrix to perform serial generation of the parity symbols using an accumulator and a look-up table. The encoder circuits are implemented on FPGA and synthesized on ASIC using a 32 nm CMOS process. Simulation results show that the ternary LDPC codes can significantly improve classification accuracy in the presence of errors. For example, with an error probability of up to 21% in the sensor output bitstreams, the classification accuracy remains above 99% with the proposed error correction system.more » « less
-
End-to-end spoken language understanding (SLU) systems are typically trained on large amounts of data. In many practical scenarios, the amount of labeled speech is often limited as opposed to text. In this study, we investigate the use of non-parallel speech and text to improve the performance of dialog act recognition as an example SLU task. We propose a multiview architecture that can handle each modality separately. To effectively train on such data, this model enforces the internal speech and text encodings to be similar using a shared classifier. On the Switchboard Dialog Act corpus, we show that pretraining the classifier using large amounts of text helps learning better speech encodings, resulting in up to 40% relatively higher classification accuracies. We also show that when the speech embeddings from an automatic speech recognition (ASR) system are used in this framework, the speech-only accuracy exceeds the performance of ASR-text based tests up to 15% relative and approaches the performance of using true transcripts.more » « less
-
Real-world tasks often exhibit a compositional structure that contains a sequence of simpler sub-tasks. For instance, opening a door requires reaching, grasping, rotating, and pulling the door knob. Such compositional tasks require an agent to reason about the sub-task at hand while orchestrating global behavior accordingly. This can be cast as an online task inference problem, where the current task identity, represented by a context variable, is estimated from the agent’s past experiences with probabilistic inference. Previous approaches have employed simple latent distributions, e.g., Gaussian, to model a single context for the entire task. However, this formulation lacks the expressiveness to capture the composition and transition of the sub-tasks. We propose a variational inference framework OCEAN to perform online task inference for compositional tasks. OCEAN models global and local context variables in a joint latent space, where the global variables represent a mixture of subtasks required for the task, while the local variables capture the transitions between the subtasks. Our framework supports flexible latent distributions based on prior knowledge of the task structure and can be trained in an unsupervised manner. Experimental results show that OCEAN provides more effective task inference with sequential context adaptation and thus leads to a performance boost on complex, multi-stage tasks.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- The DOI is not currently available.
