arXiv subjects

Avinava Dubey

Publications and source records attributed to Avinava Dubey.

At least 37 records · Page 2Linked to original sources

arXiv2024

Scalable Neural Network Kernels

We introduce the concept of scalable neural network kernels (SNNKs), the replacements of regular feedforward layers (FFLs), capable of approximating the latter, but with favorable computational properties. SNNKs effectively disentangle the inputs from the parameters of the neural network in the FFL, only to connect them in the final computation via the dot-product kernel. They are also strictly more expressive, as allowing to model complicated relationships beyond the functions of the dot-products of parameter-input vectors. We also introduce the neural network bundling process that applies SNNKs to compactify deep neural network architectures, resulting in additional compression gains. In its extreme version, it leads to the fully bundled network whose optimal parameters can be expressed via explicit formulae for several loss functions (e.g. mean squared error), opening a possibility to bypass backpropagation. As a by-product of our analysis, we introduce the mechanism of the universal random features (or URFs), applied to instantiate several SNNK variants, and interesting on its own in the context of scalable kernel methods. We provide rigorous theoretical analysis of all these concepts as well as an extensive empirical evaluation, ranging from point-wise kernel estimation to Transformers' fine-tuning with novel adapter layers inspired by SNNKs. Our mechanism provides up to 5x reduction in the number of trainable parameters, while maintaining competitive accuracy.

cs.LG↗

arXiv2023

SARA-RT: Scaling up Robotics Transformers with Self-Adaptive Robust Attention

We present Self-Adaptive Robust Attention for Robotics Transformers (SARA-RT): a new paradigm for addressing the emerging challenge of scaling up Robotics Transformers (RT) for on-robot deployment. SARA-RT relies on the new method of fine-tuning proposed by us, called up-training. It converts pre-trained or already fine-tuned Transformer-based robotic policies of quadratic time complexity (including massive billion-parameter vision-language-action models or VLAs), into their efficient linear-attention counterparts maintaining high quality. We demonstrate the effectiveness of SARA-RT by speeding up: (a) the class of recently introduced RT-2 models, the first VLA robotic policies pre-trained on internet-scale data, as well as (b) Point Cloud Transformer (PCT) robotic policies operating on large point clouds. We complement our results with the rigorous mathematical analysis providing deeper insight into the phenomenon of SARA.

cs.RO↗

arXiv2023

Robust Concept Erasure via Kernelized Rate-Distortion Maximization

Distributed representations provide a vector space that captures meaningful relationships between data instances. The distributed nature of these representations, however, entangles together multiple attributes or concepts of data instances (e.g., the topic or sentiment of a text, characteristics of the author (age, gender, etc), etc). Recent work has proposed the task of concept erasure, in which rather than making a concept predictable, the goal is to remove an attribute from distributed representations while retaining other information from the original representation space as much as possible. In this paper, we propose a new distance metric learning-based objective, the Kernelized Rate-Distortion Maximizer (KRaM), for performing concept erasure. KRaM fits a transformation of representations to match a specified distance measure (defined by a labeled concept to erase) using a modified rate-distortion function. Specifically, KRaM's objective function aims to make instances with similar concept labels dissimilar in the learned representation space while retaining other information. We find that optimizing KRaM effectively erases various types of concepts: categorical, continuous, and vector-valued variables from data representations across diverse domains. We also provide a theoretical analysis of several properties of KRaM's objective. To assess the quality of the learned representations, we propose an alignment score to evaluate their similarity with the original representation space. Additionally, we conduct experiments to showcase KRaM's efficacy in various settings, from erasing binary gender variables in word embeddings to vector-valued variables in GPT-3 representations.

cs.LG↗

arXiv2023

Unsupervised Opinion Summarization Using Approximate Geodesics

Opinion summarization is the task of creating summaries capturing popular opinions from user reviews. In this paper, we introduce Geodesic Summarizer (GeoSumm), a novel system to perform unsupervised extractive opinion summarization. GeoSumm involves an encoder-decoder based representation learning model, that generates representations of text as a distribution over latent semantic units. GeoSumm generates these representations by performing dictionary learning over pre-trained text representations at multiple decoder layers. We then use these representations to quantify the relevance of review sentences using a novel approximate geodesic distance based scoring mechanism. We use the relevance scores to identify popular opinions in order to compose general and aspect-specific summaries. Our proposed model, GeoSumm, achieves state-of-the-art performance on three opinion summarization datasets. We perform additional experiments to analyze the functioning of our model and showcase the generalization ability of {\X} across different domains.

cs.CL↗

arXiv2023

Efficient Graph Field Integrators Meet Point Clouds

We present two new classes of algorithms for efficient field integration on graphs encoding point clouds. The first class, SeparatorFactorization(SF), leverages the bounded genus of point cloud mesh graphs, while the second class, RFDiffusion(RFD), uses popular epsilon-nearest-neighbor graph representations for point clouds. Both can be viewed as providing the functionality of Fast Multipole Methods (FMMs), which have had a tremendous impact on efficient integration, but for non-Euclidean spaces. We focus on geometries induced by distributions of walk lengths between points (e.g., shortest-path distance). We provide an extensive theoretical analysis of our algorithms, obtaining new results in structural graph theory as a byproduct. We also perform exhaustive empirical evaluation, including on-surface interpolation for rigid and deformable objects (particularly for mesh-dynamics modeling), Wasserstein distance computations for point clouds, and the Gromov-Wasserstein variant.

cs.LG↗

arXiv2023

RT-2: Vision-Language-Action Models Transfer Web Knowledge to Robotic Control

We study how vision-language models trained on Internet-scale data can be incorporated directly into end-to-end robotic control to boost generalization and enable emergent semantic reasoning. Our goal is to enable a single end-to-end trained model to both learn to map robot observations to actions and enjoy the benefits of large-scale pretraining on language and vision-language data from the web. To this end, we propose to co-fine-tune state-of-the-art vision-language models on both robotic trajectory data and Internet-scale vision-language tasks, such as visual question answering. In contrast to other approaches, we propose a simple, general recipe to achieve this goal: in order to fit both natural language responses and robotic actions into the same format, we express the actions as text tokens and incorporate them directly into the training set of the model in the same way as natural language tokens. We refer to such category of models as vision-language-action models (VLA) and instantiate an example of such a model, which we call RT-2. Our extensive evaluation (6k evaluation trials) shows that our approach leads to performant robotic policies and enables RT-2 to obtain a range of emergent capabilities from Internet-scale training. This includes significantly improved generalization to novel objects, the ability to interpret commands not present in the robot training data (such as placing an object onto a particular number or icon), and the ability to perform rudimentary reasoning in response to user commands (such as picking up the smallest or largest object, or the one closest to another object). We further show that incorporating chain of thought reasoning allows RT-2 to perform multi-stage semantic reasoning, for example figuring out which object to pick up for use as an improvised hammer (a rock), or which type of drink is best suited for someone who is tired (an energy drink).

cs.RO↗

arXiv2023

Mnemosyne: Learning to Train Transformers with Transformers

In this work, we propose a new class of learnable optimizers, called \textit{Mnemosyne}. It is based on the novel spatio-temporal low-rank implicit attention Transformers that can learn to train entire neural network architectures, including other Transformers, without any task-specific optimizer tuning. We show that Mnemosyne: (a) outperforms popular LSTM optimizers (also with new feature engineering to mitigate catastrophic forgetting of LSTMs), (b) can successfully train Transformers while using simple meta-training strategies that require minimal computational resources, (c) matches accuracy-wise SOTA hand-designed optimizers with carefully tuned hyper-parameters (often producing top performing models). Furthermore, Mnemosyne provides space complexity comparable to that of its hand-designed first-order counterparts, which allows it to scale to training larger sets of parameters. We conduct an extensive empirical evaluation of Mnemosyne on: (a) fine-tuning a wide range of Vision Transformers (ViTs) from medium-size architectures to massive ViT-Hs (36 layers, 16 heads), (b) pre-training BERT models and (c) soft prompt-tuning large 11B+ T5XXL models. We complement our results with a comprehensive theoretical analysis of the compact associative memory used by Mnemosyne which we believe was never done before.

cs.LG↗

arXiv2023

FAVOR#: Sharp Attention Kernel Approximations via New Classes of Positive Random Features

The problem of efficient approximation of a linear operator induced by the Gaussian or softmax kernel is often addressed using random features (RFs) which yield an unbiased approximation of the operator's result. Such operators emerge in important applications ranging from kernel methods to efficient Transformers. We propose parameterized, positive, non-trigonometric RFs which approximate Gaussian and softmax-kernels. In contrast to traditional RF approximations, parameters of these new methods can be optimized to reduce the variance of the approximation, and the optimum can be expressed in closed form. We show that our methods lead to variance reduction in practice ($e^{10}$-times smaller variance and beyond) and outperform previous methods in a kernel regression task. Using our proposed mechanism, we also present FAVOR#, a method for self-attention approximation in Transformers. We show that FAVOR# outperforms other random feature methods in speech modelling and natural language processing.

cs.LG↗

arXiv2022

A Fourier Approach to Mixture Learning

We revisit the problem of learning mixtures of spherical Gaussians. Given samples from mixture $\frac{1}{k}\sum_{j=1}^{k}\mathcal{N}(μ_j, I_d)$, the goal is to estimate the means $μ_1, μ_2, \ldots, μ_k \in \mathbb{R}^d$ up to a small error. The hardness of this learning problem can be measured by the separation $Δ$ defined as the minimum distance between all pairs of means. Regev and Vijayaraghavan (2017) showed that with $Δ= Ω(\sqrt{\log k})$ separation, the means can be learned using $\mathrm{poly}(k, d)$ samples, whereas super-polynomially many samples are required if $Δ= o(\sqrt{\log k})$ and $d = Ω(\log k)$. This leaves open the low-dimensional regime where $d = o(\log k)$. In this work, we give an algorithm that efficiently learns the means in $d = O(\log k/\log\log k)$ dimensions under separation $d/\sqrt{\log k}$ (modulo doubly logarithmic factors). This separation is strictly smaller than $\sqrt{\log k}$, and is also shown to be necessary. Along with the results of Regev and Vijayaraghavan (2017), our work almost pins down the critical separation threshold at which efficient parameter learning becomes possible for spherical Gaussian mixtures. More generally, our algorithm runs in time $\mathrm{poly}(k)\cdot f(d, Δ, ε)$, and is thus fixed-parameter tractable in parameters $d$, $Δ$ and $ε$. Our approach is based on estimating the Fourier transform of the mixture at carefully chosen frequencies, and both the algorithm and its analysis are simple and elementary. Our positive results can be easily extended to learning mixtures of non-Gaussian distributions, under a mild condition on the Fourier spectrum of the distribution.

cs.LG↗

arXiv2022

On Learning the Transformer Kernel

In this work we introduce KERNELIZED TRANSFORMER, a generic, scalable, data driven framework for learning the kernel function in Transformers. Our framework approximates the Transformer kernel as a dot product between spectral feature maps and learns the kernel by learning the spectral distribution. This not only helps in learning a generic kernel end-to-end, but also reduces the time and space complexity of Transformers from quadratic to linear. We show that KERNELIZED TRANSFORMERS achieve performance comparable to existing efficient Transformer architectures, both in terms of accuracy as well as computational efficiency. Our study also demonstrates that the choice of the kernel has a substantial impact on performance, and kernel learning variants are competitive alternatives to fixed kernel Transformers, both in long as well as short sequence tasks.

cs.LG↗

arXiv2022

Chefs' Random Tables: Non-Trigonometric Random Features

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.

cs.LG↗

arXiv2021

Scalable Hierarchical Agglomerative Clustering

The applicability of agglomerative clustering, for inferring both hierarchical and flat clustering, is limited by its scalability. Existing scalable hierarchical clustering methods sacrifice quality for speed and often lead to over-merging of clusters. In this paper, we present a scalable, agglomerative method for hierarchical clustering that does not sacrifice quality and scales to billions of data points. We perform a detailed theoretical analysis, showing that under mild separability conditions our algorithm can not only recover the optimal flat partition, but also provide a two-approximation to non-parametric DP-Means objective. This introduces a novel application of hierarchical clustering as an approximation algorithm for the non-parametric clustering objective. We additionally relate our algorithm to the classic hierarchical agglomerative clustering method. We perform extensive empirical experiments in both hierarchical and flat clustering settings and show that our proposed approach achieves state-of-the-art results on publicly available clustering benchmarks. Finally, we demonstrate our method's scalability by applying it to a dataset of 30 billion queries. Human evaluation of the discovered clusters show that our method finds better quality of clusters than the current state-of-the-art.

cs.LG↗

arXiv2021

Exact and Approximate Hierarchical Clustering Using A*

Hierarchical clustering is a critical task in numerous domains. Many approaches are based on heuristics and the properties of the resulting clusterings are studied post hoc. However, in several applications, there is a natural cost function that can be used to characterize the quality of the clustering. In those cases, hierarchical clustering can be seen as a combinatorial optimization problem. To that end, we introduce a new approach based on A* search. We overcome the prohibitively large search space by combining A* with a novel \emph{trellis} data structure. This combination results in an exact algorithm that scales beyond previous state of the art, from a search space with $10^{12}$ trees to $10^{15}$ trees, and an approximate algorithm that improves over baselines, even in enormous search spaces that contain more than $10^{1000}$ trees. We empirically demonstrate that our method achieves substantially higher quality results than baselines for a particle physics use case and other clustering benchmarks. We describe how our method provides significantly improved theoretical bounds on the time and space complexity of A* for clustering.

cs.LG↗

arXiv2021

Big Bird: Transformers for Longer Sequences

Transformers-based models, such as BERT, have been one of the most successful deep learning models for NLP. Unfortunately, one of their core limitations is the quadratic dependency (mainly in terms of memory) on the sequence length due to their full attention mechanism. To remedy this, we propose, BigBird, a sparse attention mechanism that reduces this quadratic dependency to linear. We show that BigBird is a universal approximator of sequence functions and is Turing complete, thereby preserving these properties of the quadratic, full attention model. Along the way, our theoretical analysis reveals some of the benefits of having $O(1)$ global tokens (such as CLS), that attend to the entire sequence as part of the sparse attention mechanism. The proposed sparse attention can handle sequences of length up to 8x of what was previously possible using similar hardware. As a consequence of the capability to handle longer context, BigBird drastically improves performance on various NLP tasks such as question answering and summarization. We also propose novel applications to genomics data.

cs.LG↗

arXiv2020

Contextual Explanation Networks

Modern learning algorithms excel at producing accurate but complex models of the data. However, deploying such models in the real-world requires extra care: we must ensure their reliability, robustness, and absence of undesired biases. This motivates the development of models that are equally accurate but can be also easily inspected and assessed beyond their predictive performance. To this end, we introduce contextual explanation networks (CEN)---a class of architectures that learn to predict by generating and utilizing intermediate, simplified probabilistic models. Specifically, CENs generate parameters for intermediate graphical models which are further used for prediction and play the role of explanations. Contrary to the existing post-hoc model-explanation tools, CENs learn to predict and to explain simultaneously. Our approach offers two major advantages: (i) for each prediction valid, instance-specific explanation is generated with no computational overhead and (ii) prediction via explanation acts as a regularizer and boosts performance in data-scarce settings. We analyze the proposed framework theoretically and experimentally. Our results on image and text classification and survival analysis tasks demonstrate that CENs are not only competitive with the state-of-the-art methods but also offer additional insights behind each prediction, that can be valuable for decision support. We also show that while post-hoc methods may produce misleading explanations in certain cases, CENs are consistent and allow to detect such cases systematically.

cs.LG↗

arXiv2020

Distributed, partially collapsed MCMC for Bayesian Nonparametrics

Bayesian nonparametric (BNP) models provide elegant methods for discovering underlying latent features within a data set, but inference in such models can be slow. We exploit the fact that completely random measures, which commonly used models like the Dirichlet process and the beta-Bernoulli process can be expressed as, are decomposable into independent sub-measures. We use this decomposition to partition the latent measure into a finite measure containing only instantiated components, and an infinite measure containing all other components. We then select different inference algorithms for the two components: uncollapsed samplers mix well on the finite measure, while collapsed samplers mix well on the infinite, sparsely occupied tail. The resulting hybrid algorithm can be applied to a wide class of models, and can be easily distributed to allow scalable inference without sacrificing asymptotic convergence guarantees.

stat.ML↗

arXiv2018

Transformation Autoregressive Networks

The fundamental task of general density estimation $p(x)$ has been of keen interest to machine learning. In this work, we attempt to systematically characterize methods for density estimation. Broadly speaking, most of the existing methods can be categorized into either using: \textit{a}) autoregressive models to estimate the conditional factors of the chain rule, $p(x_{i}\, |\, x_{i-1}, \ldots)$; or \textit{b}) non-linear transformations of variables of a simple base distribution. Based on the study of the characteristics of these categories, we propose multiple novel methods for each category. For example we proposed RNN based transformations to model non-Markovian dependencies. Further, through a comprehensive study over both real world and synthetic data, we show for that jointly leveraging transformations of variables and autoregressive conditional models, results in a considerable improvement in performance. We illustrate the use of our models in outlier detection and image modeling. Finally we introduce a novel data driven framework for learning a family of distributions.

stat.ML↗

arXiv2018

Bayesian Nonparametric Kernel-Learning

Kernel methods are ubiquitous tools in machine learning. However, there is often little reason for the common practice of selecting a kernel a priori. Even if a universal approximating kernel is selected, the quality of the finite sample estimator may be greatly affected by the choice of kernel. Furthermore, when directly applying kernel methods, one typically needs to compute a $N \times N$ Gram matrix of pairwise kernel evaluations to work with a dataset of $N$ instances. The computation of this Gram matrix precludes the direct application of kernel methods on large datasets, and makes kernel learning especially difficult. In this paper we introduce Bayesian nonparmetric kernel-learning (BaNK), a generic, data-driven framework for scalable learning of kernels. BaNK places a nonparametric prior on the spectral distribution of random frequencies allowing it to both learn kernels and scale to large datasets. We show that this framework can be used for large scale regression and classification tasks. Furthermore, we show that BaNK outperforms several other scalable approaches for kernel learning on a variety of real world datasets.

stat.ML↗