arXiv subjects

Aviv Navon

Publications and source records attributed to Aviv Navon.

27 records · Page 2Linked to original sources

arXiv2023

Equivariant Architectures for Learning in Deep Weight Spaces

Designing machine learning architectures for processing neural networks in their raw weight matrix form is a newly introduced research direction. Unfortunately, the unique symmetry structure of deep weight spaces makes this design very challenging. If successful, such architectures would be capable of performing a wide range of intriguing tasks, from adapting a pre-trained network to a new domain to editing objects represented as functions (INRs or NeRFs). As a first step towards this goal, we present here a novel network architecture for learning in deep weight spaces. It takes as input a concatenation of weights and biases of a pre-trained MLP and processes it using a composition of layers that are equivariant to the natural permutation symmetry of the MLP's weights: Changing the order of neurons in intermediate layers of the MLP does not affect the function it represents. We provide a full characterization of all affine equivariant and invariant layers for these symmetries and show how these layers can be implemented using three basic operations: pooling, broadcasting, and fully connected layers applied to the input in an appropriate manner. We demonstrate the effectiveness of our architecture and its advantages over natural baselines in a variety of learning tasks.

cs.LG↗

arXiv2022

Multi-Task Learning as a Bargaining Game

In Multi-task learning (MTL), a joint model is trained to simultaneously make predictions for several tasks. Joint training reduces computation costs and improves data efficiency; however, since the gradients of these different tasks may conflict, training a joint model for MTL often yields lower performance than its corresponding single-task counterparts. A common method for alleviating this issue is to combine per-task gradients into a joint update direction using a particular heuristic. In this paper, we propose viewing the gradients combination step as a bargaining game, where tasks negotiate to reach an agreement on a joint direction of parameter update. Under certain assumptions, the bargaining problem has a unique solution, known as the Nash Bargaining Solution, which we propose to use as a principled approach to multi-task learning. We describe a new MTL optimization procedure, Nash-MTL, and derive theoretical guarantees for its convergence. Empirically, we show that Nash-MTL achieves state-of-the-art results on multiple MTL benchmarks in various domains.

cs.LG↗

arXiv2022

A Study on the Evaluation of Generative Models

Implicit generative models, which do not return likelihood values, such as generative adversarial networks and diffusion models, have become prevalent in recent years. While it is true that these models have shown remarkable results, evaluating their performance is challenging. This issue is of vital importance to push research forward and identify meaningful gains from random noise. Currently, heuristic metrics such as the Inception score (IS) and Frechet Inception Distance (FID) are the most common evaluation metrics, but what they measure is not entirely clear. Additionally, there are questions regarding how meaningful their score actually is. In this work, we study the evaluation metrics of generative models by generating a high-quality synthetic dataset on which we can estimate classical metrics for comparison. Our study shows that while FID and IS do correlate to several f-divergences, their ranking of close models can vary considerably making them problematic when used for fain-grained comparison. We further used this experimental setting to study which evaluation metric best correlates with our probabilistic metrics. Lastly, we look into the base features used for metrics such as FID.

cs.LG↗

arXiv2021

Personalized Federated Learning with Gaussian Processes

Federated learning aims to learn a global model that performs well on client devices with limited cross-client communication. Personalized federated learning (PFL) further extends this setup to handle data heterogeneity between clients by learning personalized models. A key challenge in this setting is to learn effectively across clients even though each client has unique data that is often limited in size. Here we present pFedGP, a solution to PFL that is based on Gaussian processes (GPs) with deep kernel learning. GPs are highly expressive models that work well in the low data regime due to their Bayesian nature. However, applying GPs to PFL raises multiple challenges. Mainly, GPs performance depends heavily on access to a good kernel function, and learning a kernel requires a large training set. Therefore, we propose learning a shared kernel function across all clients, parameterized by a neural network, with a personal GP classifier for each client. We further extend pFedGP to include inducing points using two novel methods, the first helps to improve generalization in the low data regime and the second reduces the computational cost. We derive a PAC-Bayes generalization bound on novel clients and empirically show that it gives non-vacuous guarantees. Extensive experiments on standard PFL benchmarks with CIFAR-10, CIFAR-100, and CINIC-10, and on a new setup of learning under input noise show that pFedGP achieves well-calibrated predictions while significantly outperforming baseline methods, reaching up to 21% in accuracy gain.

cs.LG↗

arXiv2021

GP-Tree: A Gaussian Process Classifier for Few-Shot Incremental Learning

Gaussian processes (GPs) are non-parametric, flexible, models that work well in many tasks. Combining GPs with deep learning methods via deep kernel learning (DKL) is especially compelling due to the strong representational power induced by the network. However, inference in GPs, whether with or without DKL, can be computationally challenging on large datasets. Here, we propose GP-Tree, a novel method for multi-class classification with Gaussian processes and DKL. We develop a tree-based hierarchical model in which each internal node of the tree fits a GP to the data using the Pólya Gamma augmentation scheme. As a result, our method scales well with both the number of classes and data size. We demonstrate the effectiveness of our method against other Gaussian process training baselines, and we show how our general GP approach achieves improved accuracy on standard incremental few-shot learning benchmarks.

cs.LG↗

arXiv2021

Auxiliary Learning by Implicit Differentiation

Training neural networks with auxiliary tasks is a common practice for improving the performance on a main task of interest. Two main challenges arise in this multi-task learning setting: (i) designing useful auxiliary tasks; and (ii) combining auxiliary tasks into a single coherent loss. Here, we propose a novel framework, AuxiLearn, that targets both challenges based on implicit differentiation. First, when useful auxiliaries are known, we propose learning a network that combines all losses into a single coherent objective function. This network can learn non-linear interactions between tasks. Second, when no useful auxiliary task is known, we describe how to learn a network that generates a meaningful, novel auxiliary task. We evaluate AuxiLearn in a series of tasks and domains, including image segmentation and learning with attributes in the low data regime, and find that it consistently outperforms competing methods.

cs.CV↗

arXiv2021

Learning the Pareto Front with Hypernetworks

Multi-objective optimization (MOO) problems are prevalent in machine learning. These problems have a set of optimal solutions, called the Pareto front, where each point on the front represents a different trade-off between possibly conflicting objectives. Recent MOO methods can target a specific desired ray in loss space however, most approaches still face two grave limitations: (i) A separate model has to be trained for each point on the front; and (ii) The exact trade-off must be known before the optimization process. Here, we tackle the problem of learning the entire Pareto front, with the capability of selecting a desired operating point on the front after training. We call this new setup Pareto-Front Learning (PFL). We describe an approach to PFL implemented using HyperNetworks, which we term Pareto HyperNetworks (PHNs). PHN learns the entire Pareto front simultaneously using a single hypernetwork, which receives as input a desired preference vector and returns a Pareto-optimal model whose loss vector is in the desired ray. The unified model is runtime efficient compared to training multiple models and generalizes to new operating points not used during training. We evaluate our method on a wide set of problems, from multi-task regression and classification to fairness. PHNs learn the entire Pareto front at roughly the same time as learning a single point on the front and at the same time reach a better solution set. Furthermore, we show that PHNs can scale to generate large models like ResNet18. PFL opens the door to new applications where models are selected based on preferences that are only available at run time.

cs.LG↗

arXiv2021

Personalized Federated Learning using Hypernetworks

Personalized federated learning is tasked with training machine learning models for multiple clients, each with its own data distribution. The goal is to train personalized models in a collaborative way while accounting for data disparities across clients and reducing communication costs. We propose a novel approach to this problem using hypernetworks, termed pFedHN for personalized Federated HyperNetworks. In this approach, a central hypernetwork model is trained to generate a set of models, one model for each client. This architecture provides effective parameter sharing across clients, while maintaining the capacity to generate unique and diverse personal models. Furthermore, since hypernetwork parameters are never transmitted, this approach decouples the communication cost from the trainable model size. We test pFedHN empirically in several personalized federated learning challenges and find that it outperforms previous methods. Finally, since hypernetworks share information across clients we show that pFedHN can generalize better to new clients whose distributions differ from any client observed during training.

cs.LG↗

arXiv2019

Capturing Between-Tasks Covariance and Similarities Using Multivariate Linear Mixed Models

We consider the problem of predicting several response variables using the same set of explanatory variables. This setting naturally induces a group structure over the coefficient matrix, in which every explanatory variable corresponds to a set of related coefficients. Most of the existing methods that utilize this group formation assume that the similarities between related coefficients arise solely through a joint sparsity structure. In this paper, we propose a procedure for constructing an estimator of a multivariate regression coefficient matrix that directly models and captures the within-group similarities, by employing a multivariate linear mixed model formulation, with a joint estimation of covariance matrices for coefficients and errors via penalized likelihood. Our approach, which we term Multivariate random Regression with Covariance Estimation (MrRCE) encourages structured similarity in parameters, in which coefficients for the same variable in related tasks sharing the same sign and similar magnitude. We illustrate the benefits of our approach in synthetic and real examples, and show that the proposed method outperforms natural competitors and alternative estimators under several model settings.

stat.ME↗