Parallelization techniques have become ubiquitous for accelerating inference and training of deep neural networks. Despite this, several operations are still performed in a sequential manner. For instance, the forward and backward passes are executed layer-by-layer, and the output of diffusion models is produced by applying a sequence of denoising steps. This sequential approach results in a computational cost proportional to the number of steps involved, presenting a potential bottleneck as the number of steps increases. In this work, we introduce DeepPCR, a novel algorithm which parallelizes typically sequential operations in order to speed up inference and training of neural networks. DeepPCR is based on interpreting a sequence of $L$ steps as the solution of a specific system of equations, which we recover using the Parallel Cyclic Reduction algorithm. This reduces the complexity of computing the sequential operations from $\mathcal{O}(L)$ to $\mathcal{O}(\log_2L)$, thus yielding a speedup for large $L$. To verify the theoretical lower complexity of the algorithm, and to identify regimes for speedup, we test the effectiveness of DeepPCR in parallelizing the forward and backward pass in multi-layer perceptrons, and reach speedups of up to $30\times$ for the forward and $200\times$ for the backward pass. We additionally showcase the flexibility of DeepPCR by parallelizing training of ResNets with as many as 1024 layers, and generation in diffusion models, enabling up to $7\times$ faster training and $11\times$ faster generation, respectively, when compared to the sequential approach.

In this paper, we explore the structure of the penultimate Gram matrix in deep neural networks, which contains the pairwise inner products of outputs corresponding to a batch of inputs. In several architectures it has been observed that this Gram matrix becomes degenerate with depth at initialization, which dramatically slows training. Normalization layers, such as batch or layer normalization, play a pivotal role in preventing the rank collapse issue. Despite promising advances, the existing theoretical results do not extend to layer normalization, which is widely used in transformers, and can not quantitatively characterize the role of non-linear activations. To bridge this gap, we prove that layer normalization, in conjunction with activation layers, biases the Gram matrix of a multilayer perceptron towards the identity matrix at an exponential rate with depth at initialization. We quantify this rate using the Hermite expansion of the activation function.

We propose a novel, conceptually simple and general framework for instance segmentation on 3D point clouds. Our method, called 3D-BoNet, follows the simple design philosophy of per-point multilayer perceptrons (MLPs).

Recently, the Weisfeiler-Lehman (WL) graph isomorphism test was used to measure the expressive power of graph neural networks (GNN). It was shown that the popular message passing GNN cannot distinguish between graphs that are indistinguishable by the $1$-WL test \citep{morris2019,xu2019}. Unfortunately, many simple instances of graphs are indistinguishable by the $1$-WL test. In search for more expressive graph learning models we build upon the recent $k$-order invariant and equivariant graph neural networks \citep{maron2019} and present two results: First, we show that such $k$-order networks can distinguish between non-isomorphic graphs as good as the $k$-WL tests, which are provably stronger than the $1$-WL test for $k> 2$. This makes these models strictly stronger than message passing models. Unfortunately, the higher expressiveness of these models comes with a computational cost of processing high order tensors. Second, setting our goal at building a provably stronger, \emph{simple} and \emph{scalable} model we show that a reduced $2$-order network containing just scaled identity operator, augmented with a single quadratic operation (matrix multiplication) has a provable $3$-WL expressive power. Differently put, we suggest a simple model that interleaves applications of standard Multilayer-Perceptron (MLP) applied to the feature dimension and matrix multiplication.

Vision Transformers (ViTs) have shown impressive performance and have become a unified backbone for multiple vision tasks. However, both the attention mechanism and multi-layer perceptrons (MLPs) in ViTs are not sufficiently efficient due to dense multiplications, leading to costly training and inference. To this end, we propose to reparameterize pre-trained ViTs with a mixture of multiplication primitives, e.g., bitwise shifts and additions, towards a new type of multiplication-reduced model, dubbed $\textbf{ShiftAddViT}$, which aims to achieve end-to-end inference speedups on GPUs without requiring training from scratch. Specifically, all $\texttt{MatMuls}$ among queries, keys, and values are reparameterized using additive kernels, after mapping queries and keys to binary codes in Hamming space. The remaining MLPs or linear layers are then reparameterized with shift kernels.

We propose Generative Well-intentioned Networks (GWINs), a novel framework for increasing the accuracy of certainty-based, closed-world classifiers. A conditional generative network recovers the distribution of observations that the classifier labels correctly with high certainty. We introduce a reject option to the classifier during inference, allowing the classifier to reject an observation instance rather than predict an uncertain label. These rejected observations are translated by the generative network to high-certainty representations, which are then relabeled by the classifier. This architecture allows for any certainty-based classifier or rejection function and is not limited to multilayer perceptrons. The capability of this framework is assessed using benchmark classification datasets and shows that GWINs significantly improve the accuracy of uncertain observations.

In recent computer vision research, the advent of the Vision Transformer (ViT) has rapidly revolutionized various architectural design efforts: ViT achieved state-of-the-art image classification performance using self-attention found in natural language processing, and MLP-Mixer achieved competitive performance using simple multi-layer perceptrons. In contrast, several studies have also suggested that carefully redesigned convolutional neural networks (CNNs) can achieve advanced performance comparable to ViT without resorting to these new ideas. Against this background, there is growing interest in what inductive bias is suitable for computer vision. Here we propose Sequencer, a novel and competitive architecture alternative to ViT that provides a new perspective on these issues.

Wide neural networks with random weights and biases are Gaussian processes, as observed by Neal (1995) for shallow networks, and more recently by Lee et al.~(2018) and Matthews et al.~(2018) for deep fully-connected networks, as well as by Novak et al.~(2019) and Garriga-Alonso et al.~(2019) for deep convolutional networks. We show that this Neural Network-Gaussian Process correspondence surprisingly extends to all modern feedforward or recurrent neural networks composed of multilayer perceptron, RNNs (e.g. LSTMs, GRUs), (nD or graph) convolution, pooling, skip connection, attention, batch normalization, and/or layer normalization. More generally, we introduce a language for expressing neural network computations, and our result encompasses all such expressible neural networks. This work serves as a tutorial on the \emph{tensor programs} technique formulated in Yang (2019) and elucidates the Gaussian Process results obtained there. We provide open-source implementations of the Gaussian Process kernels of simple RNN, GRU, transformer, and batchnorm+ReLU network at github.com/thegregyang/GP4A. Please see our arxiv version for the complete and up-to-date version of this paper.

Chain-of-thought (CoT) is a method that enables language models to handle complex reasoning tasks by decomposing them into simpler steps. Despite its success, the underlying mechanics of CoT are not yet fully understood. In an attempt to shed light on this, our study investigates the impact of CoT on the ability of transformers to in-context learn a simple to study, yet general family of compositional functions: multi-layer perceptrons (MLPs). In this setting, we find that the success of CoT can be attributed to breaking down in-context learning of a compositional function into two distinct phases: focusing on and filtering data related to each step of the composition and in-context learning the single-step composition function. Through both experimental and theoretical evidence, we demonstrate how CoT significantly reduces the sample complexity of in-context learning (ICL) and facilitates the learning of complex functions that non-CoT methods struggle with. Furthermore, we illustrate how transformers can transition from vanilla in-context learning to mastering a compositional function with CoT by simply incorporating additional layers that perform the necessary data-filtering for CoT via the attention mechanism. In addition to these test-time benefits, we show CoT helps accelerate pretraining by learning shortcuts to represent complex functions and filtering plays an important role in this process. These findings collectively provide insights into the mechanics of CoT, inviting further investigation of its role in complex reasoning tasks.

Convolutional Neural Networks (CNNs) are the go-to model for computer vision. Recently, attention-based networks, such as the Vision Transformer, have also become popular. In this paper we show that while convolutions and attention are both sufficient for good performance, neither of them are necessary. We present MLP-Mixer, an architecture based exclusively on multi-layer perceptrons (MLPs). MLP-Mixer contains two types of layers: one with MLPs applied independently to image patches (i.e.