arXiv subjects

Rong Ge

Publications and source records attributed to Rong Ge.

At least 37 records · Page 2Linked to original sources

arXiv2024

Transfer-Learning-Based Autotuning Using Gaussian Copula

As diverse high-performance computing (HPC) systems are built, many opportunities arise for applications to solve larger problems than ever before. Given the significantly increased complexity of these HPC systems and application tuning, empirical performance tuning, such as autotuning, has emerged as a promising approach in recent years. Despite its effectiveness, autotuning is often a computationally expensive approach. Transfer learning (TL)-based autotuning seeks to address this issue by leveraging the data from prior tuning. Current TL methods for autotuning spend significant time modeling the relationship between parameter configurations and performance, which is ineffective for few-shot (that is, few empirical evaluations) tuning on new tasks. We introduce the first generative TL-based autotuning approach based on the Gaussian copula (GC) to model the high-performing regions of the search space from prior data and then generate high-performing configurations for new tasks. This allows a sampling-based approach that maximizes few-shot performance and provides the first probabilistic estimation of the few-shot budget for effective TL-based autotuning. We compare our generative TL approach with state-of-the-art autotuning techniques on several benchmarks. We find that the GC is capable of achieving 64.37% of peak few-shot performance in its first evaluation. Furthermore, the GC model can determine a few-shot transfer budget that yields up to 33.39$\times$ speedup, a dramatic improvement over the 20.58$\times$ speedup using prior techniques.

cs.LG↗

arXiv2023

FULL-W2V: Fully Exploiting Data Reuse for W2V on GPU-Accelerated Systems

Word2Vec remains one of the highly-impactful innovations in the field of Natural Language Processing (NLP) that represents latent grammatical and syntactical information in human text with dense vectors in a low dimension. Word2Vec has high computational cost due to the algorithm's inherent sequentiality, intensive memory accesses, and the large vocabularies it represents. While prior studies have investigated technologies to explore parallelism and improve memory system performance, they struggle to effectively gain throughput on powerful GPUs. We identify memory data access and latency as the primary bottleneck in prior works on GPUs, which prevents highly optimized kernels from attaining the architecture's peak performance. We present a novel algorithm, FULL-W2V, which maximally exploits the opportunities for data reuse in the W2V algorithm and leverages GPU architecture and resources to reduce access to low memory levels and improve temporal locality. FULL-W2V is capable of reducing accesses to GPU global memory significantly, e.g., by more than 89\%, compared to prior state-of-the-art GPU implementations, resulting in significant performance improvement that scales across successive hardware generations. Our prototype implementation achieves 2.97X speedup when ported from Nvidia Pascal P100 to Volta V100 cards, and outperforms the state-of-the-art by 5.72X on V100 cards with the same embedding quality. In-depth analysis indicates that the reduction of memory accesses through register and shared memory caching and high-throughput shared memory reduction leads to a significantly improved arithmetic intensity. FULL-W2V can potentially benefit many applications in NLP and other domains.

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arXiv2023

Efficient sampling from the Bingham distribution

We give a algorithm for exact sampling from the Bingham distribution $p(x)\propto \exp(x^\top A x)$ on the sphere $\mathcal S^{d-1}$ with expected runtime of $\operatorname{poly}(d, λ_{\max}(A)-λ_{\min}(A))$. The algorithm is based on rejection sampling, where the proposal distribution is a polynomial approximation of the pdf, and can be sampled from by explicitly evaluating integrals of polynomials over the sphere. Our algorithm gives exact samples, assuming exact computation of an inverse function of a polynomial. This is in contrast with Markov Chain Monte Carlo algorithms, which are not known to enjoy rapid mixing on this problem, and only give approximate samples. As a direct application, we use this to sample from the posterior distribution of a rank-1 matrix inference problem in polynomial time.

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arXiv2023

Do Transformers Parse while Predicting the Masked Word?

Pre-trained language models have been shown to encode linguistic structures, e.g. dependency and constituency parse trees, in their embeddings while being trained on unsupervised loss functions like masked language modeling. Some doubts have been raised whether the models actually are doing parsing or only some computation weakly correlated with it. We study questions: (a) Is it possible to explicitly describe transformers with realistic embedding dimension, number of heads, etc. that are capable of doing parsing -- or even approximate parsing? (b) Why do pre-trained models capture parsing structure? This paper takes a step toward answering these questions in the context of generative modeling with PCFGs. We show that masked language models like BERT or RoBERTa of moderate sizes can approximately execute the Inside-Outside algorithm for the English PCFG [Marcus et al, 1993]. We also show that the Inside-Outside algorithm is optimal for masked language modeling loss on the PCFG-generated data. We also give a construction of transformers with $50$ layers, $15$ attention heads, and $1275$ dimensional embeddings in average such that using its embeddings it is possible to do constituency parsing with $>70\%$ F1 score on PTB dataset. We conduct probing experiments on models pre-trained on PCFG-generated data to show that this not only allows recovery of approximate parse tree, but also recovers marginal span probabilities computed by the Inside-Outside algorithm, which suggests an implicit bias of masked language modeling towards this algorithm.

cs.CL↗

arXiv2023

The Role of Linguistic Priors in Measuring Compositional Generalization of Vision-Language Models

Compositionality is a common property in many modalities including natural languages and images, but the compositional generalization of multi-modal models is not well-understood. In this paper, we identify two sources of visual-linguistic compositionality: linguistic priors and the interplay between images and texts. We show that current attempts to improve compositional generalization rely on linguistic priors rather than on information in the image. We also propose a new metric for compositionality without such linguistic priors.

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arXiv2023

Hiding Data Helps: On the Benefits of Masking for Sparse Coding

Sparse coding, which refers to modeling a signal as sparse linear combinations of the elements of a learned dictionary, has proven to be a successful (and interpretable) approach in applications such as signal processing, computer vision, and medical imaging. While this success has spurred much work on provable guarantees for dictionary recovery when the learned dictionary is the same size as the ground-truth dictionary, work on the setting where the learned dictionary is larger (or over-realized) with respect to the ground truth is comparatively nascent. Existing theoretical results in this setting have been constrained to the case of noise-less data. We show in this work that, in the presence of noise, minimizing the standard dictionary learning objective can fail to recover the elements of the ground-truth dictionary in the over-realized regime, regardless of the magnitude of the signal in the data-generating process. Furthermore, drawing from the growing body of work on self-supervised learning, we propose a novel masking objective for which recovering the ground-truth dictionary is in fact optimal as the signal increases for a large class of data-generating processes. We corroborate our theoretical results with experiments across several parameter regimes showing that our proposed objective also enjoys better empirical performance than the standard reconstruction objective.

cs.LG↗

arXiv2023

Implicit Regularization Leads to Benign Overfitting for Sparse Linear Regression

In deep learning, often the training process finds an interpolator (a solution with 0 training loss), but the test loss is still low. This phenomenon, known as benign overfitting, is a major mystery that received a lot of recent attention. One common mechanism for benign overfitting is implicit regularization, where the training process leads to additional properties for the interpolator, often characterized by minimizing certain norms. However, even for a simple sparse linear regression problem $y = β^{*\top} x +ξ$ with sparse $β^*$, neither minimum $\ell_1$ or $\ell_2$ norm interpolator gives the optimal test loss. In this work, we give a different parametrization of the model which leads to a new implicit regularization effect that combines the benefit of $\ell_1$ and $\ell_2$ interpolators. We show that training our new model via gradient descent leads to an interpolator with near-optimal test loss. Our result is based on careful analysis of the training dynamics and provides another example of implicit regularization effect that goes beyond norm minimization.

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arXiv2023

Smoothing the Landscape Boosts the Signal for SGD: Optimal Sample Complexity for Learning Single Index Models

We focus on the task of learning a single index model $σ(w^\star \cdot x)$ with respect to the isotropic Gaussian distribution in $d$ dimensions. Prior work has shown that the sample complexity of learning $w^\star$ is governed by the information exponent $k^\star$ of the link function $σ$, which is defined as the index of the first nonzero Hermite coefficient of $σ$. Ben Arous et al. (2021) showed that $n \gtrsim d^{k^\star-1}$ samples suffice for learning $w^\star$ and that this is tight for online SGD. However, the CSQ lower bound for gradient based methods only shows that $n \gtrsim d^{k^\star/2}$ samples are necessary. In this work, we close the gap between the upper and lower bounds by showing that online SGD on a smoothed loss learns $w^\star$ with $n \gtrsim d^{k^\star/2}$ samples. We also draw connections to statistical analyses of tensor PCA and to the implicit regularization effects of minibatch SGD on empirical losses.

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arXiv2023

Depth Separation with Multilayer Mean-Field Networks

Depth separation -- why a deeper network is more powerful than a shallower one -- has been a major problem in deep learning theory. Previous results often focus on representation power. For example, arXiv:1904.06984 constructed a function that is easy to approximate using a 3-layer network but not approximable by any 2-layer network. In this paper, we show that this separation is in fact algorithmic: one can learn the function constructed by arXiv:1904.06984 using an overparameterized network with polynomially many neurons efficiently. Our result relies on a new way of extending the mean-field limit to multilayer networks, and a decomposition of loss that factors out the error introduced by the discretization of infinite-width mean-field networks.

cs.LG↗

arXiv2023

Understanding The Robustness of Self-supervised Learning Through Topic Modeling

Self-supervised learning has significantly improved the performance of many NLP tasks. However, how can self-supervised learning discover useful representations, and why is it better than traditional approaches such as probabilistic models are still largely unknown. In this paper, we focus on the context of topic modeling and highlight a key advantage of self-supervised learning - when applied to data generated by topic models, self-supervised learning can be oblivious to the specific model, and hence is less susceptible to model misspecification. In particular, we prove that commonly used self-supervised objectives based on reconstruction or contrastive samples can both recover useful posterior information for general topic models. Empirically, we show that the same objectives can perform on par with posterior inference using the correct model, while outperforming posterior inference using misspecified models.

cs.CL↗

arXiv2023

Understanding Edge-of-Stability Training Dynamics with a Minimalist Example

Recently, researchers observed that gradient descent for deep neural networks operates in an ``edge-of-stability'' (EoS) regime: the sharpness (maximum eigenvalue of the Hessian) is often larger than stability threshold $2/η$ (where $η$ is the step size). Despite this, the loss oscillates and converges in the long run, and the sharpness at the end is just slightly below $2/η$. While many other well-understood nonconvex objectives such as matrix factorization or two-layer networks can also converge despite large sharpness, there is often a larger gap between sharpness of the endpoint and $2/η$. In this paper, we study EoS phenomenon by constructing a simple function that has the same behavior. We give rigorous analysis for its training dynamics in a large local region and explain why the final converging point has sharpness close to $2/η$. Globally we observe that the training dynamics for our example has an interesting bifurcating behavior, which was also observed in the training of neural nets.

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arXiv2023

Plateau in Monotonic Linear Interpolation -- A "Biased" View of Loss Landscape for Deep Networks

Monotonic linear interpolation (MLI) - on the line connecting a random initialization with the minimizer it converges to, the loss and accuracy are monotonic - is a phenomenon that is commonly observed in the training of neural networks. Such a phenomenon may seem to suggest that optimization of neural networks is easy. In this paper, we show that the MLI property is not necessarily related to the hardness of optimization problems, and empirical observations on MLI for deep neural networks depend heavily on biases. In particular, we show that interpolating both weights and biases linearly leads to very different influences on the final output, and when different classes have different last-layer biases on a deep network, there will be a long plateau in both the loss and accuracy interpolation (which existing theory of MLI cannot explain). We also show how the last-layer biases for different classes can be different even on a perfectly balanced dataset using a simple model. Empirically we demonstrate that similar intuitions hold on practical networks and realistic datasets.

stat.ML↗

arXiv2022

Outlier-Robust Sparse Estimation via Non-Convex Optimization

We explore the connection between outlier-robust high-dimensional statistics and non-convex optimization in the presence of sparsity constraints, with a focus on the fundamental tasks of robust sparse mean estimation and robust sparse PCA. We develop novel and simple optimization formulations for these problems such that any approximate stationary point of the associated optimization problem yields a near-optimal solution for the underlying robust estimation task. As a corollary, we obtain that any first-order method that efficiently converges to stationarity yields an efficient algorithm for these tasks. The obtained algorithms are simple, practical, and succeed under broader distributional assumptions compared to prior work.

cs.LG↗

arXiv2022

Dissecting Hessian: Understanding Common Structure of Hessian in Neural Networks

Hessian captures important properties of the deep neural network loss landscape. Previous works have observed low rank structure in the Hessians of neural networks. In this paper, we propose a decoupling conjecture that decomposes the layer-wise Hessians of a network as the Kronecker product of two smaller matrices. We can analyze the properties of these smaller matrices and prove the structure of top eigenspace random 2-layer networks. The decoupling conjecture has several other interesting implications - top eigenspaces for different models have surprisingly high overlap, and top eigenvectors form low rank matrices when they are reshaped into the same shape as the corresponding weight matrix. All of these can be verified empirically for deeper networks. Finally, we use the structure of layer-wise Hessian to get better explicit generalization bounds for neural networks.

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arXiv2022

Online Algorithms with Multiple Predictions

This paper studies online algorithms augmented with multiple machine-learned predictions. While online algorithms augmented with a single prediction have been extensively studied in recent years, the literature for the multiple predictions setting is sparse. In this paper, we give a generic algorithmic framework for online covering problems with multiple predictions that obtains an online solution that is competitive against the performance of the best predictor. Our algorithm incorporates the use of predictions in the classic potential-based analysis of online algorithms. We apply our algorithmic framework to solve classical problems such as online set cover, (weighted) caching, and online facility location in the multiple predictions setting. Our algorithm can also be robustified, i.e., the algorithm can be simultaneously made competitive against the best prediction and the performance of the best online algorithm (without prediction).

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arXiv2022

A Regression Approach to Learning-Augmented Online Algorithms

The emerging field of learning-augmented online algorithms uses ML techniques to predict future input parameters and thereby improve the performance of online algorithms. Since these parameters are, in general, real-valued functions, a natural approach is to use regression techniques to make these predictions. We introduce this approach in this paper, and explore it in the context of a general online search framework that captures classic problems like (generalized) ski rental, bin packing, minimum makespan scheduling, etc. We show nearly tight bounds on the sample complexity of this regression problem, and extend our results to the agnostic setting. From a technical standpoint, we show that the key is to incorporate online optimization benchmarks in the design of the loss function for the regression problem, thereby diverging from the use of off-the-shelf regression tools with standard bounds on statistical error.

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arXiv2022

Customizing ML Predictions for Online Algorithms

A popular line of recent research incorporates ML advice in the design of online algorithms to improve their performance in typical instances. These papers treat the ML algorithm as a black-box, and redesign online algorithms to take advantage of ML predictions. In this paper, we ask the complementary question: can we redesign ML algorithms to provide better predictions for online algorithms? We explore this question in the context of the classic rent-or-buy problem, and show that incorporating optimization benchmarks in ML loss functions leads to significantly better performance, while maintaining a worst-case adversarial result when the advice is completely wrong. We support this finding both through theoretical bounds and numerical simulations.

cs.LG↗

arXiv2022

Towards Understanding the Data Dependency of Mixup-style Training

In the Mixup training paradigm, a model is trained using convex combinations of data points and their associated labels. Despite seeing very few true data points during training, models trained using Mixup seem to still minimize the original empirical risk and exhibit better generalization and robustness on various tasks when compared to standard training. In this paper, we investigate how these benefits of Mixup training rely on properties of the data in the context of classification. For minimizing the original empirical risk, we compute a closed form for the Mixup-optimal classification, which allows us to construct a simple dataset on which minimizing the Mixup loss can provably lead to learning a classifier that does not minimize the empirical loss on the data. On the other hand, we also give sufficient conditions for Mixup training to also minimize the original empirical risk. For generalization, we characterize the margin of a Mixup classifier, and use this to understand why the decision boundary of a Mixup classifier can adapt better to the full structure of the training data when compared to standard training. In contrast, we also show that, for a large class of linear models and linearly separable datasets, Mixup training leads to learning the same classifier as standard training.

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