We introduce Performers, Transformer architectures which can estimate regular (softmax) full-rank-attention Transformers with provable accuracy, but using only linear (as opposed to quadratic) space and time complexity, without relying on any priors such as sparsity or low-rankness. To approximate softmax attention-kernels, Performers use a novel Fast Attention Via positive Orthogonal Random features approach (FAVOR+), which may be of independent interest for scalable kernel methods. FAVOR+ can be also used to efficiently model kernelizable attention mechanisms beyond softmax. This representational power is crucial to accurately compare softmax with other kernels for the first time on large-scale tasks, beyond the reach of regular Transformers, and investigate optimal attention-kernels. Performers are linear architectures fully compatible with regular Transformers and with strong theoretical guarantees: unbiased or nearly-unbiased estimation of the attention matrix, uniform convergence and low estimation variance. We tested Performers on a rich set of tasks stretching from pixel-prediction through text models to protein sequence modeling. We demonstrate competitive results with other examined efficient sparse and dense attention methods, showcasing effectiveness of the novel attention-learning paradigm leveraged by Performers.

pdf/rethinking-attention-with-performers-1tqtwobvqw.pdf

Rethinking Attention with Performers

We introduce Performers, Transformer architectures which can estimate regular (softmax) full-rank-attention Transformers with provable accuracy, but using only linear (as opposed to quadratic) space and time complexity, without relying on any priors such as sparsity or low-rankness. To approximate softmax attention-kernels, Performers use a novel Fast Attention Via positive Orthogonal Random features approach (FAVOR+), which may be of independent interest for scalable kernel methods. FAVOR+ can also be used to efficiently model kernelizable attention mechanisms beyond softmax. This representational power is crucial to accurately compare softmax with other kernels for the first time on large-scale tasks, beyond the reach of regular Transformers, and investigate optimal attention-kernels. Performers are linear architectures fully compatible with regular Transformers and with strong theoretical guarantees: unbiased or nearly-unbiased estimation of the attention matrix, uniform convergence and low estimation variance. We tested Performers on a rich set of tasks stretching from pixel-prediction through text models to protein sequence modeling. We demonstrate competitive results with other examined efficient sparse and dense attention methods, showcasing effectiveness of the novel attention-learning paradigm leveraged by Performers.

/pdf/rethinking-attention-with-performers-1bxectc8vh.pdf

Transformer models have achieved state-of-the-art results across a diverse range of domains. However, concern over the cost of training the attention mechanism to learn complex dependencies between distant inputs continues to grow. In response, solutions that exploit the structure and sparsity of the learned attention matrix have blossomed. However, real-world applications that involve long sequences, such as biological sequence analysis, may fall short of meeting these assumptions, precluding exploration of these models. To address this challenge, we present a new Transformer architecture, Performer, based on Fast Attention Via Orthogonal Random features (FAVOR). Our mechanism scales linearly rather than quadratically in the number of tokens in the sequence, is characterized by sub-quadratic space complexity and does not incorporate any sparsity pattern priors. Furthermore, it provides strong theoretical guarantees: unbiased estimation of the attention matrix and uniform convergence. It is also backwards-compatible with pre-trained regular Transformers. We demonstrate its effectiveness on the challenging task of protein sequence modeling and provide detailed theoretical analysis.

pdf/masked-language-modeling-for-proteins-via-linearly-scalable-xxwncp1sbd.pdf

Masked Language Modeling for Proteins via Linearly Scalable Long-Context Transformers

Spatio-temporal scene-graph approaches to video-based reasoning tasks, such as video question-answering (QA), typically construct such graphs for every video frame. These approaches often ignore the fact that videos are essentially sequences of 2D ``views'' of events happening in a 3D space, and that the semantics of the 3D scene can thus be carried over from frame to frame. Leveraging this insight, we propose a (2.5+1)D scene graph representation to better capture the spatio-temporal information flows inside the videos. Specifically, we first create a 2.5D (pseudo-3D) scene graph by transforming every 2D frame to have an inferred 3D structure using an off-the-shelf 2D-to-3D transformation module, following which we register the video frames into a shared (2.5+1)D spatio-temporal space and ground each 2D scene graph within it. Such a (2.5+1)D graph is then segregated into a static sub-graph and a dynamic sub-graph, corresponding to whether the objects within them usually move in the world. The nodes in the dynamic graph are enriched with motion features capturing their interactions with other graph nodes. Next, for the video QA task, we present a novel transformer-based reasoning pipeline that embeds the (2.5+1)D graph into a spatio-temporal hierarchical latent space, where the sub-graphs and their interactions are captured at varied granularity. To demonstrate the effectiveness of our approach, we present experiments on the NExT-QA and AVSD-QA datasets. Our results show that our proposed (2.5+1)D representation leads to faster training and inference, while our hierarchical model showcases superior performance on the video QA task versus the state of the art.

(2.5+1)D Spatio-Temporal Scene Graphs for Video Question Answering

We introduce in this paper the mechanism of graph random features (GRFs). GRFs can be used to construct unbiased randomized estimators of several important kernels defined on graphs' nodes, in particular the regularized Laplacian kernel. As regular RFs for non-graph kernels, they provide means to scale up kernel methods defined on graphs to larger networks. Importantly, they give substantial computational gains also for smaller graphs, while applied in downstream applications. Consequently, GRFs address the notoriously difficult problem of cubic (in the number of the nodes of the graph) time complexity of graph kernels algorithms. We provide a detailed theoretical analysis of GRFs and an extensive empirical evaluation: from speed tests, through Frobenius relative error analysis to kmeans graph-clustering with graph kernels. We show that the computation of GRFs admits an embarrassingly simple distributed algorithm that can be applied if the graph under consideration needs to be split across several machines. We also introduce a (still unbiased) quasi Monte Carlo variant of GRFs, q-GRFs, relying on the so-called reinforced random walks, that might be used to optimize the variance of GRFs. As a byproduct, we obtain a novel approach to solve certain classes of linear equations with positive and symmetric matrices.

Taming graph kernels with random features

Orthogonal Monte Carlo (OMC) is a very effective sampling algorithm imposing structural geometric conditions (orthogonality) on samples for variance reduction. Due to its simplicity and superior performance as compared to its Quasi Monte Carlo counterparts, OMC is used in a wide spectrum of challenging machine learning applications ranging from scalable kernel methods to predictive recurrent neural networks, generative models and reinforcement learning. However theoretical understanding of the method remains very limited. In this paper we shed new light on the theoretical principles behind OMC, applying theory of negatively dependent random variables to obtain several new concentration results. We also propose a novel extensions of the method leveraging number theory techniques and particle algorithms, called Near-Orthogonal Monte Carlo (NOMC). We show that NOMC is the first algorithm consistently outperforming OMC in applications ranging from kernel methods to approximating distances in probabilistic metric spaces.

/pdf/demystifying-orthogonal-monte-carlo-and-beyond-2jfyv1ws0b.pdf

Demystifying Orthogonal Monte Carlo and Beyond

We introduce a new class of graph neural networks (GNNs), by combining several concepts that were so far studied independently - graph kernels, attention-based networks with structural priors and more recently, efficient Transformers architectures applying small memory footprint implicit attention methods via low rank decomposition techniques. The goal of the paper is twofold. Proposed by us Graph Kernel Attention Transformers (or GKATs) are much more expressive than SOTA GNNs as capable of modeling longer-range dependencies within a single layer. Consequently, they can use more shallow architecture design. Furthermore, GKAT attention layers scale linearly rather than quadratically in the number of nodes of the input graphs, even when those graphs are dense, requiring less compute than their regular graph attention counterparts. They achieve it by applying new classes of graph kernels admitting random feature map decomposition via random walks on graphs. As a byproduct of the introduced techniques, we obtain a new class of learnable graph sketches, called graphots, compactly encoding topological graph properties as well as nodes' features. We conducted exhaustive empirical comparison of our method with nine different GNN classes on tasks ranging from motif detection through social network classification to bioinformatics challenges, showing consistent gains coming from GKATs.

Graph Kernel Attention Transformers

We propose a new class of random feature methods for linearizing softmax and Gaussian kernels called hybrid random features (HRFs) that automatically adapt the quality of kernel estimation to provide most accurate approximation in the defined regions of interest. Special instantiations of HRFs lead to well-known methods such as trigonometric (Rahimi and Recht, 2007) or (recently introduced in the context of linear-attention Transformers) positive random features (Choromanski et al., 2021). By generalizing Bochner's Theorem for softmax/Gaussian kernels and leveraging random features for compositional kernels, the HRF-mechanism provides strong theoretical guarantees - unbiased approximation and strictly smaller worst-case relative errors than its counterparts. We conduct exhaustive empirical evaluation of HRF ranging from pointwise kernel estimation experiments, through tests on data admitting clustering structure to benchmarking implicit-attention Transformers (also for downstream Robotics applications), demonstrating its quality in a wide spectrum of machine learning problems.

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Demystifying Orthogonal Monte Carlo and Beyond

Graph Kernel Attention Transformers

Demystifying Orthogonal Monte Carlo and Beyond

Hybrid Random Features