Transformer architectures have become very popular yet the original implementation requires O(L2) in serial time and memory as functions of input length L. Recent works proposed various linear self-attention mechanisms, scaling only as O(L) for serial computation. We conduct a thorough complexity analysis of Performers, a class which includes most recent linear Transformer mechanisms. We note a remarkable computational flexibility: the gradient computation can be performed with no approximations using sublinear memory as a function of L (in addition to negligible storage for the input sequence), at a cost of greater time complexity in the parallel setting. In the extreme case, a Performer consumes only O(1) memory, and still requires O(L) time. Due to complete backwardcompatibility, this discovered time-memory tradeoff can be used for fine-tuning on low-memory devices in a decentralized fashion without any server computations.

Deep neural networks are powerful machines for visual pattern recognition, but reasoning tasks that are easy for humans may still be difficult for neural models. Humans possess the ability to extrapolate reasoning strategies learned on simple problems to solve harder examples, often by thinking for longer. For example, a person who has learned to solve small mazes can easily extend the very same search techniques to solve much larger mazes by spending more time. In computers, this behavior is often achieved through the use of algorithms, which scale to arbitrarily hard problem instances at the cost of more computation. In contrast, the sequential computing budget of feed-forward neural networks is limited by their depth, and networks trained on simple problems have no way of extending their reasoning to accommodate harder problems. In this work, we show that recurrent networks trained to solve simple problems with few recurrent steps can indeed solve much more complex problems simply by performing additional recurrences during inference. We demonstrate this algorithmic behavior of recurrent networks on prefix sum computation, mazes, and chess. In all three domains, networks trained on simple problem instances are able to extend their reasoning abilities at test time simply by "thinking for longer."

In this paper, we follow Rodomanov and Nesterov [19]'s work to study quasiNewton methods. We focus on the common SR1 and BFGS quasi-Newton methods to establish better explicit (local) superlinear convergence rates. First, based on the greedy quasi-Newton update which greedily selects the direction to maximize a certain measure of progress, we improve the convergence rate to a conditionnumber-free superlinear convergence rate. Second, based on the random quasiNewton update that selects the direction randomly from a spherically symmetric distribution, we show the same superlinear convergence rate established as above. Our analysis is closely related to the approximation of a given Hessian matrix, unconstrained quadratic objective, as well as the general strongly convex, smooth and strongly self-concordant functions.

In this paper, we follow Rodomanov and Nesterov [19]'s work to study quasiNewton methods. We focus on the common SR1 and BFGS quasi-Newton methods to establish better explicit (local) superlinear convergence rates. First, based on the greedy quasi-Newton update which greedily selects the direction to maximize a certain measure of progress, we improve the convergence rate to a conditionnumber-free superlinear convergence rate. Second, based on the random quasiNewton update that selects the direction randomly from a spherically symmetric distribution, we show the same superlinear convergence rate established as above. Our analysis is closely related to the approximation of a given Hessian matrix, unconstrained quadratic objective, as well as the general strongly convex, smooth and strongly self-concordant functions.

Recent works (Shah et al., 2020; Chen et al., 2021) have demonstrated that neural networks exhibit extreme simplicity bias (SB). That is, they learn only the simplest features to solve a task at hand, even in the presence of other, more robust but more complex features. Due to the lack of a general and rigorous definition of features, these works showcase SB on semi-synthetic datasets such as Color-MNIST, MNISTCIFAR where defining features is relatively easier. In this work, we rigorously define as well as thoroughly establish SB for one hidden layer neural networks. More concretely, (i) we define SB as the network essentially being a function of a low dimensional projection of the inputs (ii) theoretically, in the infinite width regime, we show that when the data is linearly separable, the network primarily depends on only the linearly separable (1-dimensional) subspace even in the presence of an arbitrarily large number of other, more complex features which could have led to a significantly more robust classifier, (iii) empirically, we show that models trained on real datasets such as Imagenet and WaterbirdsLandbirds indeed depend on a low dimensional projection of the inputs, thereby demonstrating SB on these datasets, iv) finally, we present a natural ensemble approach that encourages diversity in models by training successive models on features not used by earlier models, and demonstrate that it yields models that are significantly more robust to Gaussian noise.

Neural Transducer (e.g., RNN-T) has been widely used in automatic speech recognition (ASR) due to its capabilities of efficiently modeling monotonic alignments between input and output sequences and naturally supporting streaming inputs. Considering that monotonic alignments are also critical to text to speech (TTS) synthesis and streaming TTS is also an important application scenario, in this work, we explore the possibility of applying Transducer to TTS and more. However, it is challenging because it is difficult to trade off the emission (continuous melspectrogram prediction) probability and transition (ASRTransducer predicts blank token to indicate transition to next input) probability when calculating the output probability lattice in Transducer, and it is not easy to learn the alignments between text and speech through the output probability lattice. We propose SpeechTransducer (Speech-T for short), a Transformer based Transducer model that 1) uses a new forward algorithm to separate the transition prediction from the continuous mel-spectrogram prediction when calculating the output probability lattice, and uses a diagonal constraint in the probability lattice to help the alignment learning; 2) supports both full-sentence or streaming TTS by adjusting the look-ahead context; and 3) further supports both TTS and ASR together for the first time, which enjoys several advantages including fewer parameters as well as streaming synthesis and recognition in a single model. Experiments on LJSpeech datasets demonstrate that Speech-T 1) is more robust than the attention based autoregressive TTS model due to its inherent monotonic alignments between text and speech; 2) naturally supports streaming TTS with good voice quality; and 3) enjoys the benefit of joint modeling TTS and ASR in a single network.

We study the problem of sequential prediction in the stochastic setting with an1 adversary that is allowed to inject clean-label adversarial (or out-of-distribution)2 examples. Algorithms designed to handle purely stochastic data tend to fail in the3 presence of such adversarial examples, often leading to erroneous predictions. This4 is undesirable in many high-stakes applications such as medical recommendations,5 where abstaining from predictions on adversarial examples is preferable to mis-6 classification. On the other hand, assuming fully adversarial data leads to very7 pessimistic bounds that are often vacuous in practice.8 To capture this motivation, we propose a new model of sequential prediction that9 sits between the purely stochastic and fully adversarial settings by allowing the10 learner to abstain from making a prediction at no cost on adversarial examples.11