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Miscellaneous Aspects of Machine Learning/Scalable Algorithms

Joshua Engels, Benjamin Coleman, Vihan Lakshman, Anshumali Shrivastava

We study the problem of $\text{\emph{vector set search}}$ with $\text{\emph{vector set queries}}$. This task is analogous to traditional near-neighbor search, with the exception that both the query and each element in the collection are $\text{\textit{sets}}$ of vectors. We identify this problem as a core subroutine for semantic search applications and find that existing solutions are unacceptably slow. Towards this end, we present a new approximate search algorithm, DESSERT ($\text{\bf D}$ESSERT $\text{\bf E}$ffeciently $\text{\bf S}$earches $\text{\bf S}$ets of $\text{\bf E}$mbeddings via $\text{\bf R}$etrieval $\text{\bf T}$ables). DESSERT is a general tool with strong theoretical guarantees and excellent empirical performance. When we integrate DESSERT into ColBERT, a state-of-the-art semantic search model, we find a 2-5x speedup on the MS MARCO and LoTTE retrieval benchmarks with minimal loss in recall, underscoring the effectiveness and practical applicability of our proposal.

Miscellaneous Aspects of Machine Learning/Scalable Algorithms

Logan M Bhamidipaty, Tommy Bruzzese, Caryn Tran, Rami Ratl Mrad, Maxinder S. Kanwal

Modeling complex dynamical systems poses significant challenges, with traditional methods struggling to work on a variety of systems and scale to high-dimensional dynamics. In response, we present DynaDojo, a novel benchmarking platform designed for data-driven dynamical system identification. DynaDojo provides diagnostics on three ways an algorithm’s performance scales: across the number of training samples, the complexity of a dynamical system, and a target error to achieve. Furthermore, DynaDojo enables studying out-of-distribution generalization (by providing unique test conditions for each system) and active learning (by supporting closed-loop control). Through its user-friendly and easily extensible API, DynaDojo accommodates a wide range of user-defined \texttt{Algorithms}, \texttt{Systems}, and \texttt{Challenges} (evaluation metrics). The platform also prioritizes resource-efficient training with parallel processing strategies for running on a cluster. To showcase its utility, in DynaDojo 0.9, we include implementations of 7 baseline algorithms and 20 dynamical systems, along with several demos exhibiting insights researchers can glean using our platform. This work aspires to make DynaDojo a unifying benchmarking platform for system identification, paralleling the role of OpenAI’s Gym in reinforcement learning.

Miscellaneous Aspects of Machine Learning/Scalable Algorithms

Yihua Zhang, Yimeng Zhang, Aochuan Chen, jinghan jia, Jiancheng Liu, Gaowen Liu, Mingyi Hong, Shiyu Chang, Sijia Liu

Massive data is often considered essential for deep learning applications, but it also incurs significant computational and infrastructural costs. Therefore, dataset pruning (DP) has emerged as an effective way to improve data efficiency by identifying and removing redundant training samples without sacrificing performance. In this work, we aim to address the problem of DP for transfer learning, i.e., how to prune a source dataset for improved pretraining efficiency and lossless finetuning accuracy on downstream target tasks. To our best knowledge, the problem of DP for transfer learning remains open, as previous studies have primarily addressed DP and transfer learning as separate problems. By contrast, we establish a unified viewpoint to integrate DP with transfer learning and find that existing DP methods are not suitable for the transfer learning paradigm. We then propose two new DP methods, label mapping and feature mapping, for supervised and self-supervised pretraining settings respectively, by revisiting the DP problem through the lens of source-target domain mapping. Furthermore, we demonstrate the effectiveness of our approach on numerous transfer learning tasks. We show that source data classes can be pruned by up to $40\%\sim 80\%$ without sacrificing the downstream performance, resulting in a significant $2\sim 5\times$ speed-up during the pretraining stage. Besides, our proposal exhibits broad applicability and can improve other computationally intensive transfer learning techniques, such as adversarial pretraining.

Miscellaneous Aspects of Machine Learning/Scalable Algorithms

Jin Li, Yaoming Wang, XIAOPENG ZHANG, Bowen Shi, Dongsheng Jiang, Chenglin Li, Wenrui Dai, Hongkai Xiong, Qi Tian

Vision transformers (ViTs) have emerged as a prevalent architecture for vision tasks owing to their impressive performance. However, their complexity dramatically increases when handling long token sequences, particularly for dense prediction tasks that require high-resolution input. Notably, dense prediction tasks, such as semantic segmentation or object detection, emphasize more on the contours or shapes of objects, while the texture inside objects is less informative. Motivated by this observation, we propose to apply adaptive resolution for different regions in the image according to their importance. Specifically, at the intermediate layer of the ViT, we select anchors from the token sequence using the proposed spatial-aware density-based clustering algorithm. Tokens that are adjacent to anchors are merged to form low-resolution regions, while others are preserved independently as high-resolution. This strategy could significantly reduce the number of tokens, and the following layers only handle the reduced token sequence for acceleration. At the output end, the resolution of the feature map is recovered by unfolding merged tokens for task prediction. Consequently, we can considerably accelerate ViTs for dense prediction tasks. The proposed method is evaluated across three different datasets and demonstrates promising performance. For instance, "Segmenter ViT-L" can be accelerated by 48\% FPS without fine-tuning, while maintaining the performance. Moreover, our method can also be applied to accelerate fine-tuning. Experiments indicate that we can save 52\% training time while accelerating 2.46$\times$ FPS with only a 0.09\% performance drop.

Miscellaneous Aspects of Machine Learning/Scalable Algorithms

Yi-Chung Chen, Hsi-Wen Chen, Shun-Gui Wang, Ming-syan Chen

The evaluation of participant contribution in federated learning (FL) has recently gained significant attention due to its applicability in various domains, such as incentive mechanisms, robustness enhancement, and client selection. Previous approaches have predominantly relied on the widely adopted Shapley value for participant evaluation. However, the computation of the Shapley value is expensive, despite using techniques like gradient-based model reconstruction and truncating unnecessary evaluations. Therefore, we present an efficient approach called Single-round Participants Amalgamation for Contribution Evaluation (SPACE). SPACE incorporates two novel components, namely Federated Knowledge Amalgamation and Prototype-based Model Evaluation to reduce the evaluation effort by eliminating the dependence on the size of the validation set and enabling participant evaluation within a single communication round. Experimental results demonstrate that SPACE outperforms state-of-the-art methods in terms of both running time and Pearson’s Correlation Coefficient (PCC). Furthermore, extensive experiments conducted on applications, client reweighting, and client selection highlight the effectiveness of SPACE. The code is available at https://github.com/culiver/SPACE.

Miscellaneous Aspects of Machine Learning/Scalable Algorithms

Guillaume Mahey, Laetitia Chapel, Gilles Gasso, Clément Bonet, Nicolas Courty

Wasserstein distance (WD) and the associated optimal transport plan have been proven useful in many applications where probability measures are at stake. In this paper, we propose a new proxy of the squared WD, coined $\textnormal{min-SWGG}$, that is based on the transport map induced by an optimal one-dimensional projection of the two input distributions. We draw connections between $\textnormal{min-SWGG}$, and Wasserstein generalized geodesics in which the pivot measure is supported on a line. We notably provide a new closed form for the exact Wasserstein distance in the particular case of one of the distributions supported on a line allowing us to derive a fast computational scheme that is amenable to gradient descent optimization. We show that $\textnormal{min-SWGG}$, is an upper bound of WD and that it has a complexity similar to as Sliced-Wasserstein, with the additional feature of providing an associated transport plan. We also investigate some theoretical properties such as metricity, weak convergence, computational and topological properties. Empirical evidences support the benefits of $\textnormal{min-SWGG}$, in various contexts, from gradient flows, shape matching and image colorization, among others.

Miscellaneous Aspects of Machine Learning/Scalable Algorithms

Aditya Bhaskara, Sepideh Mahabadi, Ali Vakilian

Given a set of points of interest, a volumetric spanner is a subset of the points using which all the points can be expressed using "small" coefficients (measured in an appropriate norm). Formally, given a set of vectors $X = [v_1, v_2, \dots, v_n]$, the goal is to find $T \subseteq [n]$ such that every $v \in X$ can be expressed as $\sum_{i\in T} \alpha_i v_i$, with $\Vert \alpha \Vert$ being small. This notion, which has also been referred to as a well-conditioned basis, has found several applications, including bandit linear optimization, determinant maximization, and matrix low rank approximation. In this paper, we give almost optimal bounds on the size of volumetric spanners for all $\ell_p$ norms, and show that they can be constructed using a simple local search procedure. We then show the applications of our result to other tasks and in particular the problem of finding coresets for the Minimum Volume Enclosing Ellipsoid (MVEE) problem.

Miscellaneous Aspects of Machine Learning/Scalable Algorithms

Philip Sun, David Simcha, Dave Dopson, Ruiqi Guo, Sanjiv Kumar

This paper introduces SOAR: **S**pilling with **O**rthogonality-**A**mplified **R**esiduals, a novel data indexing technique for approximate nearest neighbor (ANN) search. SOAR extends upon previous approaches to ANN search, such as spill trees, that utilize multiple redundant representations while partitioning the data to reduce the probability of missing a nearest neighbor during search. Rather than training and computing these redundant representations independently, however, SOAR uses an *orthogonality-amplified residual* loss, which optimizes each representation to compensate for cases where other representations perform poorly. This drastically improves the overall index quality, resulting in state-of-the-art ANN benchmark performance while maintaining fast indexing times and low memory consumption.

Miscellaneous Aspects of Machine Learning/Scalable Algorithms

Meyer Scetbon, Michal Klein, Giovanni Palla, Marco Cuturi

The relevance of optimal transport methods to machine learning has long been hindered by two salient limitations.First, the $O(n^3)$ computational cost of standard sample-based solvers (when used on batches of $n$ samples) is prohibitive.Second, the mass conservation constraint makes OT solvers too rigid in practice: because they must match \textit{all} points from both measures, their output can be heavily influenced by outliers.A flurry of recent works in OT has addressed these computational and modelling limitations, but has resulted in two separate strains of methods:While the computational outlook was much improved by entropic regularization, more recent $O(n)$ linear-time \textit{low-rank} solvers hold the promise to scale up OT further.On the other hand, modelling rigidities have been eased owing to unbalanced variants of OT, that rely on penalization terms to promote, rather than impose, mass conservation.The goal of this paper is to merge these two strains, to achieve the promise of \textit{both} versatile/scalable unbalanced/low-rank OT solvers. We propose custom algorithms to implement these extensions for the linear OT problem and its Fused-Gromov-Wasserstein generalization, and demonstrate their practical relevance to challenging spatial transcriptomics matching problems.

Miscellaneous Aspects of Machine Learning/Scalable Algorithms

Weiwei Kong, Andres Munoz Medina

A well-known numerical bottleneck in the differentially-private stochastic gradient descent (DP-SGD) algorithm is the computation of the gradient norm for each example in a large input batch. When the loss function in DP-SGD is consists of an intermediate linear operation, existing methods in the literature have proposed decompositions of gradients that are amenable to fast norm computations. In this paper, we present a framework that generalizes the above approach to arbitrary (possibly nonlinear) intermediate operations. Moreover, we show that for certain operations, such as fully-connected and embedding layer computations, further improvements to the runtime and storage costs of existing decompositions can be deduced using certain components of our framework. Finally, preliminary numerical experiments are given to demonstrate the substantial effects of the aforementioned improvements.

Miscellaneous Aspects of Machine Learning/Scalable Algorithms

Jerry Chee, Yaohui Cai, Volodymyr Kuleshov, Christopher De Sa

This work studies post-training parameter quantization in large language models (LLMs). We introduce quantization with incoherence processing (QuIP), a new method based on the insight that quantization benefits from incoherent weight and Hessian matrices, i.e., from the weights being even in magnitude and the directions in which it is important to round them accurately being unaligned with the coordinate axes. QuIP consists of two steps: (1) an adaptive rounding procedure minimizing a quadratic proxy objective; (2) efficient pre- and post-processing that ensures weight and Hessian incoherence via multiplication by random orthogonal matrices. We complement QuIP with the first theoretical analysis for an LLM-scale quantization algorithm, and show that our theory also applies to an existing method, OPTQ. Empirically, we find that our incoherence preprocessing improves several existing quantization algorithms and yields the first LLM quantization methods that produce viable results using only two bits per weight. Our code can be found at https://github.com/Cornell-RelaxML/QuIP.

Miscellaneous Aspects of Machine Learning/Scalable Algorithms

Federico Danieli, Miguel Sarabia, Xavier Suau Cuadros, Pau Rodriguez, Luca Zappella

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.

Miscellaneous Aspects of Machine Learning/Scalable Algorithms

Hoang Pham, The Anh Ta, Shiwei Liu, Lichuan Xiang, Dung Le, Hongkai Wen, Long Tran-Thanh

Pruning at initialization (PaI) aims to remove weights of neural networks before training in pursuit of training efficiency besides the inference. While off-the-shelf PaI methods manage to find trainable subnetworks that outperform random pruning, their performance in terms of both accuracy and computational reduction is far from satisfactory compared to post-training pruning and the understanding of PaI is missing. For instance, recent studies show that existing PaI methods only able to find good layerwise sparsities not weights, as the discovered subnetworks are surprisingly resilient against layerwise random mask shuffling and weight re-initialization.In this paper, we study PaI from a brand-new perspective -- the topology of subnetworks. In particular, we propose a principled framework for analyzing the performance of Pruning and Initialization (PaI) methods with two quantities, namely, the number of effective paths and effective nodes. These quantities allow for a more comprehensive understanding of PaI methods, giving us an accurate assessment of different subnetworks at initialization. We systematically analyze the behavior of various PaI methods through our framework and observe a guiding principle for constructing effective subnetworks: *at a specific sparsity, the top-performing subnetwork always presents a good balance between the number of effective nodes and the number of effective paths.*Inspired by this observation, we present a novel data-agnostic pruning method by solving a multi-objective optimization problem. By conducting extensive experiments across different architectures and datasets, our results demonstrate that our approach outperforms state-of-the-art PaI methods while it is able to discover subnetworks that have much lower inference FLOPs (up to 3.4$\times$). Code will be fully released.

Miscellaneous Aspects of Machine Learning/Scalable Algorithms

Mengzhao Wang, Lingwei Lv, Xiaoliang Xu, Yuxiang Wang, Qiang Yue, Jiongkang Ni

This paper introduces an efficient and robust framework for hybrid query (HQ) processing, which combines approximate nearest neighbor search (ANNS) with attribute constraint. HQ aims to find objects that are similar to a feature vector and match some structured attributes. Existing methods handle ANNS and attribute filtering separately, leading to inefficiency and inaccuracy. Our framework, called native hybrid query (NHQ), builds a composite index based on proximity graph (PG) and applies joint pruning for HQ. We can easily adapt existing PGs to this framework for efficient HQ processing. We also propose two new navigable PGs (NPGs) with optimized edge selection and routing, which improve the overall ANNS performance. We implement five HQ methods based on the proposed NPGs and existing PGs in NHQ, and show that they outperform the state-of-the-art methods on 10 real-world datasets (up to 315$\times$ faster with the same accuracy).

Miscellaneous Aspects of Machine Learning/Scalable Algorithms

Rylan Schaeffer, Brando Miranda, Sanmi Koyejo

Recent work claims that large language models display \textit{emergent abilities}, abilities not present in smaller-scale models that are present in larger-scale models.What makes emergent abilities intriguing is two-fold: their \textit{sharpness}, transitioning seemingly instantaneously from not present to present, and their \textit{unpredictability}, appearing at seemingly unforeseeable model scales.Here, we present an alternative explanation for emergent abilities: that for a particular task and model family, when analyzing fixed model outputs, emergent abilities appear due the researcher’s choice of metric rather than due to fundamental changes in model behavior with scale. Specifically, nonlinear or discontinuous metrics produce apparent emergent abilities, whereas linear or continuous metrics produce smooth, continuous, predictable changes in model performance.We present our alternative explanation in a simple mathematical model, then test it in three complementary ways: we (1) make, test and confirm three predictions on the effect of metric choice using the InstructGPT/GPT-3 family on tasks with claimed emergent abilities, (2) make, test and confirm two predictions about metric choices in a meta-analysis of emergent abilities on BIG-Bench; and (3) show how to choose metrics to produce never-before-seen seemingly emergent abilities in multiple vision tasks across diverse deep networks.Via all three analyses, we provide evidence that alleged emergent abilities evaporate with different metrics or with better statistics, and may not be a fundamental property of scaling AI models.

Miscellaneous Aspects of Machine Learning/Scalable Algorithms

Dan Busbridge, Jason Ramapuram, Pierre Ablin, Tatiana Likhomanenko, Eeshan Gunesh Dhekane, Xavier Suau Cuadros, Russell Webb

Preserving training dynamics across batch sizes is an important tool for practical machine learning as it enables the trade-off between batch size and wall-clock time. This trade-off is typically enabled by a scaling rule, for example, in stochastic gradient descent, one should scale the learning rate linearly with the batch size. Another important machine learning tool is the model EMA, a functional copy of a target model, whose parameters move towards those of its target model according to an Exponential Moving Average (EMA) at a rate parameterized by a momentum hyperparameter. This model EMA can improve the robustness and generalization of supervised learning, stabilize pseudo-labeling, and provide a learning signal for Self-Supervised Learning (SSL). Prior works have not considered the optimization of the model EMA when performing scaling, leading to different training dynamics across batch sizes and lower model performance. In this work, we provide a scaling rule for optimization in the presence of a model EMA and demonstrate the rule's validity across a range of architectures, optimizers, and data modalities. We also show the rule's validity where the model EMA contributes to the optimization of the target model, enabling us to train EMA-based pseudo-labeling and SSL methods at small and large batch sizes. For SSL, we enable training of BYOL up to batch size 24,576 without sacrificing performance, a 6$\times$ wall-clock time reduction under idealized hardware settings.

Miscellaneous Aspects of Machine Learning/Scalable Algorithms

Anders Aamand, Justin Chen, Huy Nguyen, Sandeep Silwal, Ali Vakilian

Estimating frequencies of elements appearing in a data stream is a key task in large-scale data analysis. Popular sketching approaches to this problem (e.g., CountMin and CountSketch) come with worst-case guarantees that probabilistically bound the error of the estimated frequencies for any possible input. The work of Hsu et al.~(2019) introduced the idea of using machine learning to tailor sketching algorithms to the specific data distribution they are being run on. In particular, their learning-augmented frequency estimation algorithm uses a learned heavy-hitter oracle which predicts which elements will appear many times in the stream. We give a novel algorithm, which in some parameter regimes, already theoretically outperforms the learning based algorithm of Hsu et al. *without* the use of any predictions. Augmenting our algorithm with heavy-hitter predictions further reduces the error and improves upon the state of the art. Empirically, our algorithms achieve superior performance in all experiments compared to prior approaches.

Miscellaneous Aspects of Machine Learning/Scalable Algorithms

Alaa Maalouf, Murad Tukan, Noel Loo, Ramin Hasani, Mathias Lechner, Daniela Rus

Dataset Distillation is the task of synthesizing small datasets from large ones while still retaining comparable predictive accuracy to the original uncompressed dataset. Despite significant empirical progress in recent years, there is little understanding of the theoretical limitations/guarantees of dataset distillation, specifically, what excess risk is achieved by distillation compared to the original dataset, and how large are distilled datasets? In this work, we take a theoretical view on kernel ridge regression (KRR) based methods of dataset distillation such as Kernel Inducing Points. By transforming ridge regression in random Fourier features (RFF) space, we provide the first proof of the existence of small (size) distilled datasets and their corresponding excess risk for shift-invariant kernels. We prove that a small set of instances exists in the original input space such that its solution in the RFF space coincides with the solution of the original data. We further show that a KRR solution can be generated using this distilled set of instances which gives an approximation towards the KRR solution optimized on the full input data. The size of this set is linear in the dimension of the RFF space of the input set or alternatively near linear in the number of effective degrees of freedom, which is a function of the kernel, number of data points, and the regularization parameter $\lambda$. The error bound of this distilled set is also a function of $\lambda$. We verify our bounds analytically and empirically.