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Cenk Baykal, Dylan J Cutler, Nishanth Dikkala, Nikhil Ghosh, Rina Panigrahy, Xin Wang

One way of introducing sparsity into deep networks is by attaching an external table of parameters that is sparsely looked up at different layers of the network. By storing the bulk of the parameters in the external table, one can increase the capacity of the model without necessarily increasing the inference time. Two crucial questions in this setting are then: what is the lookup function for accessing the table and how are the contents of the table consumed? Prominent methods for accessing the table include 1) using words/wordpieces token-ids as table indices, 2) LSH hashing the token vector in each layer into a table of buckets, and 3) learnable softmax style routing to a table entry. The ways to consume the contents include adding/concatenating to input representation, and using the contents as expert networks that specialize to different inputs. In this work, we conduct rigorous experimental evaluations of existing ideas and their combinations. We also introduce a new method, alternating updates, that enables access to an increased token dimension without increasing the computation time, and demonstrate its effectiveness in language modeling.

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Cenk Baykal, Dylan Cutler, Nishanth Dikkala, Nikhil Ghosh, Rina Panigrahy, Xin Wang

It is well established that increasing scale in deep transformer networks leads to improved quality and performance. This increase in scale often comes with an increase in compute cost and inference latency. Consequently, research into methods which help realize the benefits of increased scale without leading to an increase in the compute cost becomes important. We introduce Alternating Updates (AltUp), a simple-to-implement method to increase a model's capacity without the computational burden. AltUp enables the widening of the learned representation without increasing the computation time by working on a subblock of the representation at each layer. Our experiments on various transformer models and language tasks demonstrate the consistent effectiveness of alternating updates on a diverse set of benchmarks. Finally, we present extensions of AltUp to the sequence dimension, and demonstrate how AltUp can be synergistically combined with existing approaches, such as Sparse Mixture-of-Experts models, to obtain efficient models with even higher capacity.

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Cenk Baykal, Nishanth Dikkala, Rina Panigrahy, Cyrus Rashtchian, Xin Wang

Deep and wide neural networks successfully fit very complex functions today, but dense models are starting to be prohibitively expensive for inference. To mitigate this, one promising direction is networks that activate a sparse subgraph of the network. The subgraph is chosen by a data-dependent routing function, enforcing a fixed mapping of inputs to subnetworks (e.g., the Mixture of Experts (MoE) paradigm in Switch Transformers). However, prior work is largely empirical, and while existing routing functions work well in practice, they do not lead to theoretical guarantees on approximation ability. We aim to provide a theoretical explanation for the power of sparse networks. As our first contribution, we present a formal model of data-dependent sparse networks that captures salient aspects of popular architectures. We then introduce a routing function based on locality sensitive hashing (LSH) that enables us to reason about how well sparse networks approximate target functions. After representing LSH-based sparse networks with our model, we prove that sparse networks can match the approximation power of dense networks on Lipschitz functions. Applying LSH on the input vectors means that the experts interpolate the target function in different subregions of the input space. To support our theory, we define various datasets based on Lipschitz target functions, and we show that sparse networks give a favorable trade-off between number of active units and approximation quality.

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Shaojin Ding, Weiran Wang, Ding Zhao, Tara N. Sainath, Yanzhang He, Robert David, Rami Botros, Xin Wang, Rina Panigrahy, Qiao Liang, Dongseong Hwang, Ian McGraw, Rohit Prabhavalkar, Trevor Strohman

In this paper, we propose a dynamic cascaded encoder Automatic Speech Recognition (ASR) model, which unifies models for different deployment scenarios. Moreover, the model can significantly reduce model size and power consumption without loss of quality. Namely, with the dynamic cascaded encoder model, we explore three techniques to maximally boost the performance of each model size: 1) Use separate decoders for each sub-model while sharing the encoders; 2) Use funnel-pooling to improve the encoder efficiency; 3) Balance the size of causal and non-causal encoders to improve quality and fit deployment constraints. Overall, the proposed large-medium model has 30% smaller size and reduces power consumption by 33%, compared to the baseline cascaded encoder model. The triple-size model that unifies the large, medium, and small models achieves 37% total size reduction with minimal quality loss, while substantially reducing the engineering efforts of having separate models.

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Zihao Deng, Zee Fryer, Brendan Juba, Rina Panigrahy, Xin Wang

We propose a modular architecture for the lifelong learning of hierarchically structured tasks. Specifically, we prove that our architecture is theoretically able to learn tasks that can be solved by functions that are learnable given access to functions for other, previously learned tasks as subroutines. We empirically show that some tasks that we can learn in this way are not learned by standard training methods in practice; indeed, prior work suggests that some such tasks cannot be learned by any efficient method without the aid of the simpler tasks. We also consider methods for identifying the tasks automatically, without relying on explicitly given indicators.

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Atish Agarwala, Abhimanyu Das, Brendan Juba, Rina Panigrahy, Vatsal Sharan, Xin Wang, Qiuyi Zhang

Can deep learning solve multiple tasks simultaneously, even when they are unrelated and very different? We investigate how the representations of the underlying tasks affect the ability of a single neural network to learn them jointly. We present theoretical and empirical findings that a single neural network is capable of simultaneously learning multiple tasks from a combined data set, for a variety of methods for representing tasks -- for example, when the distinct tasks are encoded by well-separated clusters or decision trees over certain task-code attributes. More concretely, we present a novel analysis that shows that families of simple programming-like constructs for the codes encoding the tasks are learnable by two-layer neural networks with standard training. We study more generally how the complexity of learning such combined tasks grows with the complexity of the task codes; we find that combining many tasks may incur a sample complexity penalty, even though the individual tasks are easy to learn. We provide empirical support for the usefulness of the learning bounds by training networks on clusters, decision trees, and SQL-style aggregation.

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Nishanth Dikkala, Gal Kaplun, Rina Panigrahy

It is well established that training deep neural networks gives useful representations that capture essential features of the inputs. However, these representations are poorly understood in theory and practice. In the context of supervised learning an important question is whether these representations capture features informative for classification, while filtering out non-informative noisy ones. We explore a formalization of this question by considering a generative process where each class is associated with a high-dimensional manifold and different classes define different manifolds. Under this model, each input is produced using two latent vectors: (i) a "manifold identifier" $\gamma$ and; (ii)~a "transformation parameter" $\theta$ that shifts examples along the surface of a manifold. E.g., $\gamma$ might represent a canonical image of a dog, and $\theta$ might stand for variations in pose, background or lighting. We provide theoretical and empirical evidence that neural representations can be viewed as LSH-like functions that map each input to an embedding that is a function of solely the informative $\gamma$ and invariant to $\theta$, effectively recovering the manifold identifier $\gamma$. An important consequence of this behavior is one-shot learning to unseen classes.

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Atish Agarwala, Abhimanyu Das, Rina Panigrahy, Qiuyi Zhang

Large neural network models have been successful in learning functions of importance in many branches of science, including physics, chemistry and biology. Recent theoretical work has shown explicit learning bounds for wide networks and kernel methods on some simple classes of functions, but not on more complex functions which arise in practice. We extend these techniques to provide learning bounds for analytic functions on the sphere for any kernel method or equivalent infinitely-wide network with the corresponding activation function trained with SGD. We show that a wide, one-hidden layer ReLU network can learn analytic functions with a number of samples proportional to the derivative of a related function. Many functions important in the sciences are therefore efficiently learnable. As an example, we prove explicit bounds on learning the many-body gravitational force function given by Newton's law of gravitation. Our theoretical bounds suggest that very wide ReLU networks (and the corresponding NTK kernel) are better at learning analytic functions as compared to kernel learning with Gaussian kernels. We present experimental evidence that the many-body gravitational force function is easier to learn with ReLU networks as compared to networks with exponential activations.

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Rina Panigrahy

How we store information in our mind has been a major intriguing open question. We approach this question not from a physiological standpoint as to how information is physically stored in the brain, but from a conceptual and algorithm standpoint as to the right data structures to be used to organize and index information. Here we propose a memory architecture directly based on the recursive sketching ideas from the paper "Recursive Sketches for Modular Deep Networks", ICML 2019 (arXiv:1905.12730), to store information in memory as concise sketches. We also give a high level, informal exposition of the recursive sketching idea from the paper that makes use of subspace embeddings to capture deep network computations into a concise sketch. These sketches form an implicit knowledge graph that can be used to find related information via sketches from the past while processing an event.

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