In image processing, solving inverse problems is the task of finding plausible reconstructions of an image that was corrupted by some (usually known) degradation operator. Commonly, this process is done using a generative image model that can guide the reconstruction towards solutions that appear natural. The success of diffusion models over the last few years has made them a leading candidate for this task. However, the sequential nature of diffusion models makes this conditional sampling process challenging. Furthermore, since diffusion models are often defined in the latent space of an autoencoder, the encoder-decoder transformations introduce additional difficulties. To address these challenges, we suggest a novel sampling method based on sequential Monte Carlo (SMC) in the latent space of diffusion models. We name our method LD-SMC. We define a generative model for the data using additional auxiliary observations and perform posterior inference with SMC sampling based on a backward diffusion process. Empirical evaluations on ImageNet and FFHQ show the benefits of LD-SMC over competing methods in various inverse problem tasks and especially in challenging inpainting tasks.

As machine learning becomes more prominent there is a growing demand to perform several inference tasks in parallel. Multi-task learning (MTL) addresses this challenge by learning a single model that solves several tasks simultaneously and efficiently. Often optimizing MTL models entails first computing the gradient of the loss for each task, and then aggregating all the gradients to obtain a combined update direction. However, common methods following this approach do not consider an important aspect, the sensitivity in the dimensions of the gradients. Some dimensions may be more lenient for changes while others may be more restrictive. Here, we introduce a novel gradient aggregation procedure using Bayesian inference. We place a probability distribution over the task-specific parameters, which in turn induce a distribution over the gradients of the tasks. This valuable information allows us to quantify the uncertainty associated with each of the gradients’ dimensions which is factored in when aggregating them. We empirically demonstrate the benefits of our approach in a variety of datasets, achieving state-of-the-art performance.

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.

Combining Gaussian processes with the expressive power of deep neural networks is commonly done nowadays through deep kernel learning (DKL). Unfortunately, due to the kernel optimization process, this often results in losing their Bayesian benefits. In this study, we present a novel approach for learning deep kernels by utilizing infinite-width neural networks. We propose to use the Neural Network Gaussian Process (NNGP) model as a guide to the DKL model in the optimization process. Our approach harnesses the reliable uncertainty estimation of the NNGPs to adapt the DKL target confidence when it encounters novel data points. As a result, we get the best of both worlds, we leverage the Bayesian behavior of the NNGP, namely its robustness to overfitting, and accurate uncertainty estimation, while maintaining the generalization abilities, scalability, and flexibility of deep kernels. Empirically, we show on multiple benchmark datasets of varying sizes and dimensionality, that our method is robust to overfitting, has good predictive performance, and provides reliable uncertainty estimations.

Vertically distributed learning exploits the local features collected by multiple learning workers to form a better global model. However, data exchange between the workers and the model aggregator for parameter training incurs a heavy communication burden, especially when the learning system is built upon capacity-constrained wireless networks. In this paper, we propose a novel hierarchical distributed learning framework, where each worker separately learns a low-dimensional embedding of their local observed data. Then, they perform communication-efficient distributed max-pooling to efficiently transmit the synthesized input to the aggregator. For data exchange over a shared wireless channel, we propose an opportunistic carrier sensing-based protocol to implement the max-pooling of the output of all the workers. Our simulation experiments show that the proposed learning framework is able to achieve almost the same model accuracy as the learning model using the concatenation of all the raw outputs from the learning workers while significantly reducing the communication load.

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.

Bayesian models have many desirable properties, most notable is their ability to generalize from limited data and to properly estimate the uncertainty in their predictions. However, these benefits come at a steep computational cost as Bayesian inference, in most cases, is computationally intractable. One popular approach to alleviate this problem is using a Monte-Carlo estimation with an ensemble of models sampled from the posterior. However, this approach still comes at a significant computational cost, as one needs to store and run multiple models at test time. In this work, we investigate how to best distill an ensemble's predictions using an efficient model. First, we argue that current approaches are limited as they are constrained to classification and the Dirichlet distribution. Second, in many limited data settings, all ensemble members achieve nearly zero training loss, namely, they produce near-identical predictions on the training set which results in sub-optimal distilled models. To address both problems, we propose a novel and general distillation approach, named Functional Ensemble Distillation (FED), and we investigate how to best distill an ensemble in this setting. We find that learning the distilled model via a simple augmentation scheme in the form of mixup augmentation significantly boosts the performance. We evaluated our method on several tasks and showed that it achieves superior results in both accuracy and uncertainty estimation compared to current approaches.

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 P{ó}lya-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.

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.

Self-supervised learning (SSL) is a technique for learning useful representations from unlabeled data. It has been applied effectively to domain adaptation (DA) on images and videos. It is still unknown if and how it can be leveraged for domain adaptation in 3D perception problems. Here we describe the first study of SSL for DA on point clouds. We introduce a new family of pretext tasks, Deformation Reconstruction, inspired by the deformations encountered in sim-to-real transformations. In addition, we propose a novel training procedure for labeled point cloud data motivated by the MixUp method called Point cloud Mixup (PCM). Evaluations on domain adaptations datasets for classification and segmentation, demonstrate a large improvement over existing and baseline methods.