Valerii Likhosherstov
now at Waymo
I’m a PhD student supervised by Adrian Weller and advised by José Miguel Hernández-Lobato (started in October 2019, Sidney Sussex College). I am funded by the Department of Engineering and Trust Scholarship. Before entering a PhD program I’ve received a Bachelor’s degree in Computer Science from Ural Federal University (2017, Yekaterinburg, Russia) and Master’s degree in Statistical Learning Theory from Skoltech & HSE (2019, Moscow, Russia). In addition, I’ve graduated from Yandex School of Data Analysis (2017)—a two-year machine learning program which is well known and respectable in Russia. My work experience includes a part-time software engineer position at SKB Kontur in 2016-2017 and a number of summer internships – SKB Kontur (summer 2015), Google Summer of Code (summer 2016), Google UK Ltd (summer 2017), Samsung AI Center Moscow (summer 2018).
As for my research interests, I would indicate statistical machine learning and scalable machine learning algorithms.
Publications
Stochastic Flows and Geometric Optimization on the Orthogonal Group
Krzysztof Choromanski, David Cheikhi, Jared Davis, Valerii Likhosherstov, Achille Nazaret, Achraf Bahamou, Xingyou Song, Mrugank Akarte, Jack Parker-Holder, Jacob Bergquist, Yuan Gao, Aldo Pacchiano, Tamas Sarlos, Adrian Weller, Vikas Sindhwani, 2020. (In 37th International Conference on Machine Learning).
Abstract▼ URL
We present a new class of stochastic, geometrically-driven optimization algorithms on the orthogonal group O(d) and naturally reductive homogeneous manifolds obtained from the action of the rotation group SO(d). We theoretically and experimentally demonstrate that our methods can be applied in various fields of machine learning including deep, convolutional and recurrent neural networks, reinforcement learning, normalizing flows and metric learning. We show an intriguing connection between efficient stochastic optimization on the orthogonal group and graph theory (e.g. matching problem, partition functions over graphs, graph-coloring). We leverage the theory of Lie groups and provide theoretical results for the designed class of algorithms. We demonstrate broad applicability of our methods by showing strong performance on the seemingly unrelated tasks of learning world models to obtain stable policies for the most difficult Humanoid agent from OpenAI Gym and improving convolutional neural networks.
Rethinking Attention with Performers
Krzysztof Marcin Choromanski, Valerii Likhosherstov, David Dohan, Xingyou Song, Andreea Gane, Tamas Sarlos, Peter Hawkins, Jared Quincy Davis, Afroz Mohiuddin, Lukasz Kaiser, David Benjamin Belanger, Lucy J Colwell, Adrian Weller, 2021. (In International Conference on Learning Representations).
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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.
PolyViT: Co-training Vision Transformers on Images, Videos and Audio
Valerii Likhosherstov, Anurag Arnab, Krzysztof Choromanski, Mario Lucic, Yi Tay, Adrian Weller, Mostafa Dehghani, 2021. (CoRR).
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Can we train a single transformer model capable of processing multiple modalities and datasets, whilst sharing almost all of its learnable parameters? We present PolyViT, a model trained on image, audio and video which answers this question. By co-training different tasks on a single modality, we are able to improve the accuracy of each individual task and achieve state-of-the-art results on 5 standard video- and audio-classification datasets. Co-training PolyViT on multiple modalities and tasks leads to a model that is even more parameter-efficient, and learns representations that generalize across multiple domains. Moreover, we show that co-training is simple and practical to implement, as we do not need to tune hyperparameters for each combination of datasets, but can simply adapt those from standard, single-task training.
Sub-Linear Memory: How to Make Performers SLiM
Valerii Likhosherstov, Krzysztof M Choromanski, Jared Quincy Davis, Xingyou Song, Adrian Weller, 2021. (In Advances in Neural Information Processing Systems). Edited by M. Ranzato, A. Beygelzimer, Y. Dauphin, P.S. Liang, J. Wortman Vaughan. Curran Associates, Inc..
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The Transformer architecture has revolutionized deep learning on sequential data, becoming ubiquitous in state-of-the-art solutions for a wide variety of applications. Yet vanilla Transformers are notoriously resource-expensive, requiring 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 perform a thorough analysis of recent Transformer mechanisms with linear self-attention, Performers, in terms of overall computational complexity. We observe a remarkable computational flexibility: forward and backward propagation 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 during training, and still requires O(L) time. This discovered time-memory tradeoff can be used for training or, due to complete backward-compatibility, for fine-tuning on a low-memory device, e.g. a smartphone or an earlier-generation GPU, thus contributing towards decentralized and democratized deep learning.
Chefs’ Random Tables: Non-Trigonometric Random Features
Valerii Likhosherstov, Krzysztof Choromanski, Avinava Dubey, Frederick Liu, Tamas Sarlos, Adrian Weller, 2022. arXiv. DOI: 10.48550/ARXIV.2205.15317.
Abstract▼ URL
We introduce chefs’ random tables (CRTs), a new class of non-trigonometric random features (RFs) to approximate Gaussian and softmax kernels. CRTs are an alternative to standard random kitchen sink (RKS) methods, which inherently rely on the trigonometric maps. We present variants of CRTs where RFs are positive, a key requirement for applications in recent low-rank Transformers. Further variance reduction is possible by leveraging statistics which are simple to compute. One instantiation of CRTs, the optimal positive random features (OPRFs), is to our knowledge the first RF method for unbiased softmax kernel estimation with positive and bounded RFs, resulting in exponentially small tails and much lower variance than its counterparts. As we show, orthogonal random features applied in OPRFs provide additional variance reduction for any dimensionality d (not only asymptotically for sufficiently large d, as for RKS). We test CRTs on many tasks ranging from non-parametric classification to training Transformers for text, speech and image data, obtaining new state-of-the-art results for low-rank text Transformers, while providing linear space and time complexity.
CWY Parametrization: a Solution for Parallelized Optimization of Orthogonal and Stiefel Matrices
Valerii Likhosherstov, Jared Davis, Krzysztof Choromanski, Adrian Weller, 13–15 Apr 2021. (In Proceedings of The 24th International Conference on Artificial Intelligence and Statistics). Edited by Arindam Banerjee, Kenji Fukumizu. PMLR. Proceedings of Machine Learning Research.
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We introduce an efficient approach for optimization over orthogonal groups on highly parallel computation units such as GPUs or TPUs. As in earlier work, we parametrize an orthogonal matrix as a product of Householder reflections. However, to overcome low parallelization capabilities of computing Householder reflections sequentially, we propose employing an accumulation scheme called the compact WY (or CWY) transform – a compact parallelization-friendly matrix representation for the series of Householder reflections. We further develop a novel Truncated CWY (or T-CWY) approach for Stiefel manifold parametrization which has a competitive complexity and, again, yields benefits when computed on GPUs and TPUs. We prove that our CWY and T-CWY methods lead to convergence to a stationary point of the training objective when coupled with stochastic gradient descent. We apply our methods to train recurrent neural network architectures in the tasks of neural machine translation and video prediction.
Debiasing a First-order Heuristic for Approximate Bi-level Optimization
Valerii Likhosherstov, Xingyou Song, Krzysztof Choromanski, Jared Q Davis, Adrian Weller, 18–24 Jul 2021. (In Proceedings of the 38th International Conference on Machine Learning). Edited by Marina Meila, Tong Zhang. PMLR. Proceedings of Machine Learning Research.
Abstract▼ URL
Approximate bi-level optimization (ABLO) consists of (outer-level) optimization problems, involving numerical (inner-level) optimization loops. While ABLO has many applications across deep learning, it suffers from time and memory complexity proportional to the length r of its inner optimization loop. To address this complexity, an earlier first-order method (FOM) was proposed as a heuristic which omits second derivative terms, yielding significant speed gains and requiring only constant memory. Despite FOM’s popularity, there is a lack of theoretical understanding of its convergence properties. We contribute by theoretically characterizing FOM’s gradient bias under mild assumptions. We further demonstrate a rich family of examples where FOM-based SGD does not converge to a stationary point of the ABLO objective. We address this concern by proposing an unbiased FOM (UFOM) enjoying constant memory complexity as a function of r. We characterize the introduced time-variance tradeoff, demonstrate convergence bounds, and find an optimal UFOM for a given ABLO problem. Finally, we propose an efficient adaptive UFOM scheme.