Liam Collins

Liam Collins, Hamed Hassani, Aryan Mokhtari et al.

The Federated Averaging (FedAvg) algorithm, which consists of alternating between a few local stochastic gradient updates at client nodes, followed by a model averaging update at the server, is perhaps the most commonly used method in Federated Learning. Notwithstanding its simplicity, several empirical studies have illustrated that the output model of FedAvg, after a few fine-tuning steps, leads to a model that generalizes well to new unseen tasks. This surprising performance of such a simple method, however, is not fully understood from a theoretical point of view. In this paper, we formally investigate this phenomenon in the multi-task linear representation setting. We show that the reason behind generalizability of the FedAvg's output is its power in learning the common data representation among the clients' tasks, by leveraging the diversity among client data distributions via local updates. We formally establish the iteration complexity required by the clients for proving such result in the setting where the underlying shared representation is a linear map. To the best of our knowledge, this is the first such result for any setting. We also provide empirical evidence demonstrating FedAvg's representation learning ability in federated image classification with heterogeneous data.

Advait Parulekar, Liam Collins, Karthikeyan Shanmugam et al.

The goal of contrasting learning is to learn a representation that preserves underlying clusters by keeping samples with similar content, e.g. the ``dogness'' of a dog, close to each other in the space generated by the representation. A common and successful approach for tackling this unsupervised learning problem is minimizing the InfoNCE loss associated with the training samples, where each sample is associated with their augmentations (positive samples such as rotation, crop) and a batch of negative samples (unrelated samples). To the best of our knowledge, it was unanswered if the representation learned by minimizing the InfoNCE loss preserves the underlying data clusters, as it only promotes learning a representation that is faithful to augmentations, i.e., an image and its augmentations have the same representation. Our main result is to show that the representation learned by InfoNCE with a finite number of negative samples is also consistent with respect to clusters in the data, under the condition that the augmentation sets within clusters may be non-overlapping but are close and intertwined, relative to the complexity of the learning function class.

Liam Collins, Hamed Hassani, Mahdi Soltanolkotabi et al.

An increasingly popular machine learning paradigm is to pretrain a neural network (NN) on many tasks offline, then adapt it to downstream tasks, often by re-training only the last linear layer of the network. This approach yields strong downstream performance in a variety of contexts, demonstrating that multitask pretraining leads to effective feature learning. Although several recent theoretical studies have shown that shallow NNs learn meaningful features when either (i) they are trained on a {\em single} task or (ii) they are {\em linear}, very little is known about the closer-to-practice case of {\em nonlinear} NNs trained on {\em multiple} tasks. In this work, we present the first results proving that feature learning occurs during training with a nonlinear model on multiple tasks. Our key insight is that multi-task pretraining induces a pseudo-contrastive loss that favors representations that align points that typically have the same label across tasks. Using this observation, we show that when the tasks are binary classification tasks with labels depending on the projection of the data onto an $r$-dimensional subspace within the $d\gg r$-dimensional input space, a simple gradient-based multitask learning algorithm on a two-layer ReLU NN recovers this projection, allowing for generalization to downstream tasks with sample and neuron complexity independent of $d$. In contrast, we show that with high probability over the draw of a single task, training on this single task cannot guarantee to learn all $r$ ground-truth features.

Liam Collins, Shanshan Wu, Sewoong Oh et al.

In many applications of federated learning (FL), clients desire models that are personalized using their local data, yet are also robust in the sense that they retain general global knowledge. However, the presence of data heterogeneity across clients induces a fundamental trade-off between personalization (i.e., adaptation to a local distribution) and robustness (i.e., not forgetting previously learned general knowledge). It is critical to understand how to navigate this personalization vs robustness trade-off when designing federated systems, which are increasingly moving towards a paradigm of fine-tuning large foundation models. Due to limited computational and communication capabilities in most federated settings, this foundation model fine-tuning must be done using parameter-efficient fine-tuning (PEFT) approaches. While some recent work has studied federated approaches to PEFT, the personalization vs robustness trade-off of federated PEFT has been largely unexplored. In this work, we take a step towards bridging this gap by benchmarking fundamental FL algorithms -- FedAvg and FedSGD plus personalization (via client local fine-tuning) -- applied to one of the most ubiquitous PEFT approaches to large language models (LLMs) -- prompt tuning -- in a multitude of hyperparameter settings under varying levels of data heterogeneity. Our results show that federated-trained prompts can be surprisingly robust when using a small learning rate with many local epochs for personalization, especially when using an adaptive optimizer as the client optimizer during federated training. We also demonstrate that simple approaches such as adding regularization and interpolating two prompts are effective in improving the personalization vs robustness trade-off in computation-limited settings with few local updates allowed for personalization.

Huanhuan Zhao, Connor Vernachio, Laxmi Bhurtel et al.

Microscopy such as Scanning Tunneling Microscopy (STM), Atomic Force Microscopy (AFM) and Scanning Electron Microscopy (SEM) are essential tools in material imaging at micro- and nanoscale resolutions to extract physical knowledge and materials structure-property relationships. However, tuning microscopy controls (e.g. scanning speed, current setpoint, tip bias etc.) to obtain a high-quality of images is a non-trivial and time-consuming effort. On the other hand, with sub-standard images, the key features are not accurately discovered due to noise and artifacts, leading to erroneous analysis. Existing denoising models mostly build on generalizing the weak signals as noises while the strong signals are enhanced as key features, which is not always the case in microscopy images, thus can completely erase a significant amount of hidden physical information. To address these limitations, we propose a global denoising model (GDM) to smartly remove artifacts of microscopy images while preserving weaker but physically important features. The proposed model is developed based on 1) first designing a two-imaging input channel of non-pair and goal specific pre-processed images with user-defined trade-off information between two channels and 2) then integrating a loss function of pixel- and fast Fourier-transformed (FFT) based on training the U-net model. We compared the proposed GDM with the non-FFT denoising model over STM-generated images of Copper(Cu) and Silicon(Si) materials, AFM-generated Pantoea sp.YR343 bio-film images and SEM-generated plastic degradation images. We believe this proposed workflow can be extended to improve other microscopy image quality and will benefit the experimentalists with the proposed design flexibility to smartly tune via domain-experts preferences.

Liam Collins, Bhuvesh Kumar, Clark Mingxuan Ju et al.

Modern Sequential Recommendation (SR) models commonly utilize modality features to represent items, motivated in large part by recent advancements in language and vision modeling. To do so, several works completely replace ID embeddings with modality embeddings, claiming that modality embeddings render ID embeddings unnecessary because they can match or even exceed ID embedding performance. On the other hand, many works jointly utilize ID and modality features, but posit that complex fusion strategies, such as multi-stage training and/or intricate alignment architectures, are necessary for this joint utilization. However, underlying both these lines of work is a lack of understanding of the complementarity of ID and modality features. In this work, we address this gap by studying the complementarity of ID- and text-based SR models. We show that these models do learn complementary signals, meaning that either should provide performance gain when used properly alongside the other. Motivated by this, we propose a new SR method that preserves ID-text complementarity through independent model training, then harnesses it through a simple ensembling strategy. Despite this method's simplicity, we show it outperforms several competitive SR baselines, implying that both ID and text features are necessary to achieve state-of-the-art SR performance but complex fusion architectures are not.

Liam Collins, Advait Parulekar, Aryan Mokhtari et al.

A striking property of transformers is their ability to perform in-context learning (ICL), a machine learning framework in which the learner is presented with a novel context during inference implicitly through some data, and tasked with making a prediction in that context. As such, that learner must adapt to the context without additional training. We explore the role of softmax attention in an ICL setting where each context encodes a regression task. We show that an attention unit learns a window that it uses to implement a nearest-neighbors predictor adapted to the landscape of the pretraining tasks. Specifically, we show that this window widens with decreasing Lipschitzness and increasing label noise in the pretraining tasks. We also show that on low-rank, linear problems, the attention unit learns to project onto the appropriate subspace before inference. Further, we show that this adaptivity relies crucially on the softmax activation and thus cannot be replicated by the linear activation often studied in prior theoretical analyses.

Huanhuan Zhao, Ruben Millan-Solsona, Marti Checa et al.

Microscopy is an essential tool in scientific research, enabling the visualization of structures at micro- and nanoscale resolutions. However, the field of microscopy often encounters limitations in field-of-view (FOV), restricting the amount of sample that can be imaged in a single capture. To overcome this limitation, image stitching techniques have been developed to seamlessly merge multiple overlapping images into a single, high-resolution composite. The images collected from microscope need to be optimally stitched before accurate physical information can be extracted from post analysis. However, the existing stitching tools either struggle to stitch images together when the microscopy images are feature sparse or cannot address all the transformations of images. To address these issues, we propose a bi-channel aided feature-based image stitching method and demonstrate its use on AFM generated biofilm images. The topographical channel image of AFM data captures the morphological details of the sample, and a stitched topographical image is desired for researchers. We utilize the amplitude channel of AFM data to maximize the matching features and to estimate the position of the original topographical images and show that the proposed bi-channel aided stitching method outperforms the traditional stitching approach. Furthermore, we found that the differentiation of the topographical images along the x-axis provides similar feature information to the amplitude channel image, which generalizes our approach when the amplitude images are not available. Here we demonstrated the application on AFM, but similar approaches could be employed of optical microscopy with brightfield and fluorescence channels. We believe this proposed workflow will benefit the experimentalist to avoid erroneous analysis and discovery due to incorrect stitching.

Jacob L. Block, Sundararajan Srinivasan, Liam Collins et al.

The power of foundation models (FMs) lies in their capacity to learn highly expressive representations that can be adapted to a broad spectrum of tasks. However, these pretrained models require additional training stages to become effective for downstream applications. In the multi-task setting, prior works have shown empirically that specific meta-learning approaches for preparing a model for future adaptation through parameter-efficient fine-tuning (PEFT) can outperform standard retraining methods, but the mechanism of the benefits of meta-learning has been largely unexplored. We introduce a framework for generic PEFT-based meta-learning to learn a model that can easily adapt to unseen tasks. For linear models using LoRA, we show that standard retraining is provably suboptimal for finding an adaptable set of parameters and provide strict performance guarantees for our proposed method. We verify these theoretical insights through experiments on synthetic data as well as real-data vision and language tasks. We observe significant performance benefits using a simple implementation of our proposed meta-learning scheme during retraining relative to the conventional approach.

Liam Collins, Aryan Mokhtari, Sewoong Oh et al.

Recent empirical evidence has driven conventional wisdom to believe that gradient-based meta-learning (GBML) methods perform well at few-shot learning because they learn an expressive data representation that is shared across tasks. However, the mechanics of GBML have remained largely mysterious from a theoretical perspective. In this paper, we prove that two well-known GBML methods, MAML and ANIL, as well as their first-order approximations, are capable of learning common representation among a set of given tasks. Specifically, in the well-known multi-task linear representation learning setting, they are able to recover the ground-truth representation at an exponentially fast rate. Moreover, our analysis illuminates that the driving force causing MAML and ANIL to recover the underlying representation is that they adapt the final layer of their model, which harnesses the underlying task diversity to improve the representation in all directions of interest. To the best of our knowledge, these are the first results to show that MAML and/or ANIL learn expressive representations and to rigorously explain why they do so.

Liam Collins, Hamed Hassani, Aryan Mokhtari et al.

Deep neural networks have shown the ability to extract universal feature representations from data such as images and text that have been useful for a variety of learning tasks. However, the fruits of representation learning have yet to be fully-realized in federated settings. Although data in federated settings is often non-i.i.d. across clients, the success of centralized deep learning suggests that data often shares a global feature representation, while the statistical heterogeneity across clients or tasks is concentrated in the labels. Based on this intuition, we propose a novel federated learning framework and algorithm for learning a shared data representation across clients and unique local heads for each client. Our algorithm harnesses the distributed computational power across clients to perform many local-updates with respect to the low-dimensional local parameters for every update of the representation. We prove that this method obtains linear convergence to the ground-truth representation with near-optimal sample complexity in a linear setting, demonstrating that it can efficiently reduce the problem dimension for each client. This result is of interest beyond federated learning to a broad class of problems in which we aim to learn a shared low-dimensional representation among data distributions, for example in meta-learning and multi-task learning. Further, extensive experimental results show the empirical improvement of our method over alternative personalized federated learning approaches in federated environments with heterogeneous data.

Liam Collins, Aryan Mokhtari, Sanjay Shakkottai

Model-Agnostic Meta-Learning (MAML) has become increasingly popular for training models that can quickly adapt to new tasks via one or few stochastic gradient descent steps. However, the MAML objective is significantly more difficult to optimize compared to standard non-adaptive learning (NAL), and little is understood about how much MAML improves over NAL in terms of the fast adaptability of their solutions in various scenarios. We analytically address this issue in a linear regression setting consisting of a mixture of easy and hard tasks, where hardness is related to the rate that gradient descent converges on the task. Specifically, we prove that in order for MAML to achieve substantial gain over NAL, (i) there must be some discrepancy in hardness among the tasks, and (ii) the optimal solutions of the hard tasks must be closely packed with the center far from the center of the easy tasks optimal solutions. We also give numerical and analytical results suggesting that these insights apply to two-layer neural networks. Finally, we provide few-shot image classification experiments that support our insights for when MAML should be used and emphasize the importance of training MAML on hard tasks in practice.

Liam Collins, Aryan Mokhtari, Sanjay Shakkottai

Meta-learning methods have shown an impressive ability to train models that rapidly learn new tasks. However, these methods only aim to perform well in expectation over tasks coming from some particular distribution that is typically equivalent across meta-training and meta-testing, rather than considering worst-case task performance. In this work we introduce the notion of "task-robustness" by reformulating the popular Model-Agnostic Meta-Learning (MAML) objective [Finn et al. 2017] such that the goal is to minimize the maximum loss over the observed meta-training tasks. The solution to this novel formulation is task-robust in the sense that it places equal importance on even the most difficult and/or rare tasks. This also means that it performs well over all distributions of the observed tasks, making it robust to shifts in the task distribution between meta-training and meta-testing. We present an algorithm to solve the proposed min-max problem, and show that it converges to an $ε$-accurate point at the optimal rate of $\mathcal{O}(1/ε^2)$ in the convex setting and to an $(ε, δ)$-stationary point at the rate of $\mathcal{O}(\max\{1/ε^5, 1/δ^5\})$ in nonconvex settings. We also provide an upper bound on the new task generalization error that captures the advantage of minimizing the worst-case task loss, and demonstrate this advantage in sinusoid regression and image classification experiments.