In 3D computer vision, translation averaging solves for absolute translations given a set of pairwise relative translation directions. While there has been much work on robustness to outliers and studies on the uniqueness of the solution, this paper deals with a distinctly different problem of sensitivity in translation averaging under uncertainty. We first analyze sensitivity in estimating scales corresponding to relative directions under small perturbations of the relative directions. Then, we formally define the conditioning of the translation averaging problem, which assesses the reliability of estimated translations based solely on the input directions. We give a sufficient criterion to ensure that the problem is well-conditioned. Subsequently, we provide an efficient algorithm to identify and remove combinations of directions which make the problem ill-conditioned while ensuring uniqueness of the solution. We demonstrate the utility of such analysis in global structure-from-motion pipelines for obtaining 3D reconstructions, which reveals the benefits of filtering the ill-conditioned set of directions in translation averaging in terms of reduced translation errors, a higher number of 3D points triangulated and faster convergence of bundle adjustment.

Unlike traditional statistical models depending on hand-specified priors, neural processes (NPs) have recently emerged as a class of powerful neural statistical models that combine the strengths of neural networks and stochastic processes. NPs can define a flexible class of stochastic processes well suited for highly non-trivial functions by encoding contextual knowledge into the function space. However, noisy context points introduce challenges to the algorithmic stability that small changes in training data may significantly change the models and yield lower generalization performance. In this paper, we provide theoretical guidelines for deriving stable solutions with high generalization by introducing the notion of algorithmic stability into NPs, which can be flexible to work with various NPs and achieves less biased approximation with theoretical guarantees. To illustrate the superiority of the proposed model, we perform experiments on both synthetic and real-world data, and the results demonstrate that our approach not only helps to achieve more accurate performance but also improves model robustness.

Bayesian neural networks (BNNs) provide a formalism to quantify and calibrate uncertainty in deep learning. Current inference approaches for BNNs often resort to few-sample estimation for scalability, which can harm predictive performance, while its alternatives tend to be computationally prohibitively expensive. We tackle this challenge by revealing a previously unseen connection between inference on BNNs and volume computation problems. With this observation, we introduce a novel collapsed inference scheme that performs Bayesian model averaging using collapsed samples. It improves over a Monte-Carlo sample by limiting sampling to a subset of the network weights while pairing it with some closed-form conditional distribution over the rest. A collapsed sample represents uncountably many models drawn from the approximate posterior and thus yields higher sample efficiency. Further, we show that the marginalization of a collapsed sample can be solved analytically and efficiently despite the non-linearity of neural networks by leveraging existing volume computation solvers. Our proposed use of collapsed samples achieves a balance between scalability and accuracy. On various regression and classification tasks, our collapsed Bayesian deep learning approach demonstrates significant improvements over existing methods and sets a new state of the art in terms of uncertainty estimation as well as predictive performance.

We consider the problem of variational Bayesian inference in a latent variable model where a (possibly complex) observed stochastic process is governed by the unobserved solution of a latent stochastic differential equation (SDE). Motivated by the challenges that arise when trying to learn a latent SDE in $\mathbb{R}^n$ from large-scale data, such as efficient gradient computation, we take a step back and study a specific subclass instead. In our case, the SDE evolves inside a homogeneous latent space and is induced by stochastic dynamics of the corresponding (matrix) Lie group. In the context of learning problems, SDEs on the $n$-dimensional unit sphere are arguably the most relevant incarnation of this setup. For variational inference, the sphere not only facilitates using a uniform prior on the initial state of the SDE, but we also obtain a particularly simple and intuitive expression for the KL divergence between the approximate posterior and prior process in the evidence lower bound. We provide empirical evidence that a latent SDE of the proposed type can be learned efficiently by means of an existing one-step geometric Euler-Maruyama scheme. Despite restricting ourselves to a less diverse class of SDEs, we achieve competitive or even state-of-the-art performance on a collection of time series interpolation and classification benchmarks.

Langevin Monte Carlo (LMC) and its stochastic gradient versions are powerful algorithms for sampling from complex high-dimensional distributions. To sample from a distribution with density $\pi(\theta)\propto \exp(-U(\theta)) $, LMC iteratively generates the next sample by taking a step in the gradient direction $\nabla U$ with added Gaussian perturbations. Expectations w.r.t. the target distribution $\pi$ are estimated by averaging over LMC samples. In ordinary Monte Carlo, it is well known that the estimation error can be substantially reduced by replacing independent random samples by quasi-random samples like low-discrepancy sequences. In this work, we show that the estimation error of LMC can also be reduced by using quasi-random samples. Specifically, we propose to use completely uniformly distributed (CUD) sequences with certain low-discrepancy property to generate the Gaussian perturbations. Under smoothness and convexity conditions, we prove that LMC with a low-discrepancy CUD sequence achieves smaller error than standard LMC. The theoretical analysis is supported by compelling numerical experiments, which demonstrate the effectiveness of our approach.

In a backdoor attack, an adversary injects corrupted data into a model's training dataset in order to gain control over its predictions on images with a specific attacker-defined trigger. A typical corrupted training example requires altering both the image, by applying the trigger, and the label. Models trained on clean images, therefore, were considered safe from backdoor attacks. However, in some common machine learning scenarios, the training labels are provided by potentially malicious third-parties. This includes crowd-sourced annotation and knowledge distillation. We, hence, investigate a fundamental question: can we launch a successful backdoor attack by only corrupting labels? We introduce a novel approach to design label-only backdoor attacks, which we call FLIP, and demonstrate its strengths on three datasets (CIFAR-10, CIFAR-100, and Tiny-ImageNet) and four architectures (ResNet-32, ResNet-18, VGG-19, and Vision Transformer). With only 2% of CIFAR-10 labels corrupted, FLIP achieves a near-perfect attack success rate of 99.4% while suffering only a 1.8% drop in the clean test accuracy. Our approach builds upon the recent advances in trajectory matching, originally introduced for dataset distillation.

Distributional shifts pose a significant challenge to achieving robustness in contemporary machine learning. To overcome this challenge, robust satisficing (RS) seeks a robust solution to an unspecified distributional shift while achieving a utility above a desired threshold. This paper focuses on the problem of RS in contextual Bayesian optimization when there is a discrepancy between the true and reference distributions of the context. We propose a novel robust Bayesian satisficing algorithm called RoBOS for noisy black-box optimization.

Large conferences such as NeurIPS and AAAI serve as crossroads of various AI fields, since they attract submissions from a vast number of communities. However, in some cases, this has resulted in a poor reviewing experience for some communities, whose submissions get assigned to less qualified reviewers outside of their communities. An often-advocated solution is to break up any such large conference into smaller conferences, but this can lead to isolation of communities and harm interdisciplinary research. We tackle this challenge by introducing a notion of group fairness, called the core, which requires that every possible community (subset of researchers) to be treated in a way that prevents them from unilaterally benefiting by withdrawing from a large conference. We study a simple peer review model, prove that it always admits a reviewing assignment in the core, and design an efficient algorithm to find one such assignment. We use real data from CVPR and ICLR conferences to compare our algorithm to existing reviewing assignment algorithms on a number of metrics.

We present an approach for analyzing message passing graph neural networks (MPNNs) based on an extension of graphon analysis to a so called graphon-signal analysis. A MPNN is a function that takes a graph and a signal on the graph (a graph-signal) and returns some value. Since the input space of MPNNs is non-Euclidean, i.e., graphs can be of any size and topology, properties such as generalization are less well understood for MPNNs than for Euclidean neural networks. We claim that one important missing ingredient in past work is a meaningful notion of graph-signal similarity measure, that endows the space of inputs to MPNNs with a regular structure. We present such a similarity measure, called the graphon-signal cut distance, which makes the space of all graph-signals a dense subset of a compact metric space -- the graphon-signal space.

Low-rank matrix recovery is a fundamental problem in machine learning with numerous applications. In practice, the problem can be solved by convex optimization namely nuclear norm minimization, or by non-convex optimization as it is well-known that for low-rank matrix problems like matrix sensing and matrix completion, all local optima of the natural non-convex objectives are also globally optimal under certain ideal assumptions.In this paper, we study new approaches for matrix sensing in a semi-random model where an adversary can add any number of arbitrary sensing matrices. More precisely, the problem is to recover a low-rank matrix $X^\star$ from linear measurements $b_i = \langle A_i, X^\star \rangle$, where an unknown subset of the sensing matrices satisfies the Restricted Isometry Property (RIP) and the rest of the $A_i$'s are chosen adversarially.It is known that in the semi-random model, existing non-convex objectives can have bad local optima. To fix this, we present a descent-style algorithm that provably recovers the ground-truth matrix $X^\star$. For the closely-related problem of semi-random matrix completion, prior work [CG18] showed that all bad local optima can be eliminated by reweighting the input data. However, the analogous approach for matrix sensing requires reweighting a set of matrices to satisfy RIP, which is a condition that is NP-hard to check. Instead, we build on the framework proposed in [KLL$^+$23] for semi-random sparse linear regression, where the algorithm in each iteration reweights the input based on the current solution, and then takes a weighted gradient step that is guaranteed to work well locally. Our analysis crucially exploits the connection between sparsity in vector problems and low-rankness in matrix problems, which may have other applications in obtaining robust algorithms for sparse and low-rank problems.