Absence of spurious solutions far from ground truth: A low-rank analysis with high-order losses

Matrix sensing problems exhibit pervasive non-convexity, plaguing optimization with a proliferation of suboptimal spurious solutions. Avoiding convergence to these critical points poses a major challenge. This work provides new theoretical insights that help demystify the intricacies of the non-convex landscape. In this work, we prove that under certain conditions, critical points sufficiently distant from the ground truth matrix exhibit favorable geometry by being strict saddle points rather than troublesome local minima. Moreover, we introduce the notion of higher-order losses for the matrix sensing problem and show that the incorporation of such losses into the objective function amplifies the negative curvature around those distant critical points. This implies that increasing the complexity of the objective function via high-order losses accelerates the escape from such critical points and acts as a desirable alternative to increasing the complexity of the optimization problem via over-parametrization. By elucidating key characteristics of the non-convex optimization landscape, this work makes progress towards a comprehensive framework for tackling broader machine learning objectives plagued by non-convexity.

MixedNUTS: Training-Free Accuracy-Robustness Balance via Nonlinearly Mixed Classifiers

Adversarial robustness often comes at the cost of degraded accuracy, impeding the real-life application of robust classification models. Training-based solutions for better trade-offs are limited by incompatibilities with already-trained high-performance large models, necessitating the exploration of training-free ensemble approaches. Observing that robust models are more confident in correct predictions than in incorrect ones on clean and adversarial data alike, we speculate amplifying this "benign confidence property" can reconcile accuracy and robustness in an ensemble setting. To achieve so, we propose "MixedNUTS", a training-free method where the output logits of a robust classifier and a standard non-robust classifier are processed by nonlinear transformations with only three parameters, which are optimized through an efficient algorithm. MixedNUTS then converts the transformed logits into probabilities and mixes them as the overall output. On CIFAR-10, CIFAR-100, and ImageNet datasets, experimental results with custom strong adaptive attacks demonstrate MixedNUTS's vastly improved accuracy and near-SOTA robustness -- it boosts CIFAR-100 clean accuracy by 7.86 points, sacrificing merely 0.87 points in robust accuracy.

Let's Go Shopping (LGS) -- Web-Scale Image-Text Dataset for Visual Concept Understanding

Vision and vision-language applications of neural networks, such as image classification and captioning, rely on large-scale annotated datasets that require non-trivial data-collecting processes. This time-consuming endeavor hinders the emergence of large-scale datasets, limiting researchers and practitioners to a small number of choices. Therefore, we seek more efficient ways to collect and annotate images. Previous initiatives have gathered captions from HTML alt-texts and crawled social media postings, but these data sources suffer from noise, sparsity, or subjectivity. For this reason, we turn to commercial shopping websites whose data meet three criteria: cleanliness, informativeness, and fluency. We introduce the Let's Go Shopping (LGS) dataset, a large-scale public dataset with 15 million image-caption pairs from publicly available e-commerce websites. When compared with existing general-domain datasets, the LGS images focus on the foreground object and have less complex backgrounds. Our experiments on LGS show that the classifiers trained on existing benchmark datasets do not readily generalize to e-commerce data, while specific self-supervised visual feature extractors can better generalize. Furthermore, LGS's high-quality e-commerce-focused images and bimodal nature make it advantageous for vision-language bi-modal tasks: LGS enables image-captioning models to generate richer captions and helps text-to-image generation models achieve e-commerce style transfer.

Mixing Classifiers to Alleviate the Accuracy-Robustness Trade-Off

Machine learning models have recently found tremendous success in data-driven control systems. However, standard learning models often suffer from an accuracy-robustness trade-off, which is a limitation that must be overcome in the control of safety-critical systems that require both high performance and rigorous robustness guarantees. In this work, we build upon the recent "locally biased smoothing" method to develop classifiers that simultaneously inherit high accuracy from standard models and high robustness from robust models. Specifically, we extend locally biased smoothing to the multi-class setting, and then overcome its performance bottleneck by generalizing the formulation to "mix" the outputs of a standard neural network and a robust neural network. We prove that when the robustness of the robust base model is certifiable, within a closed-form $\ell_p$ radius, no alteration or attack on an input can result in misclassification of the mixed classifier; the proposed model inherits the certified robustness. Moreover, we use numerical experiments on the CIFAR-10 benchmark dataset to verify that the mixed model noticeably improves the accuracy-robustness trade-off.

Algorithmic Regularization in Tensor Optimization: Towards a Lifted Approach in Matrix Sensing

Gradient descent (GD) is crucial for generalization in machine learning models, as it induces implicit regularization, promoting compact representations. In this work, we examine the role of GD in inducing implicit regularization for tensor optimization, particularly within the context of the lifted matrix sensing framework. This framework has been recently proposed to address the non-convex matrix sensing problem by transforming spurious solutions into strict saddles when optimizing over symmetric, rank-1 tensors. We show that, with sufficiently small initialization scale, GD applied to this lifted problem results in approximate rank-1 tensors and critical points with escape directions. Our findings underscore the significance of the tensor parametrization of matrix sensing, in combination with first-order methods, in achieving global optimality in such problems.

Tight Certified Robustness via Min-Max Representations of ReLU Neural Networks

The reliable deployment of neural networks in control systems requires rigorous robustness guarantees. In this paper, we obtain tight robustness certificates over convex attack sets for min-max representations of ReLU neural networks by developing a convex reformulation of the nonconvex certification problem. This is done by "lifting" the problem to an infinite-dimensional optimization over probability measures, leveraging recent results in distributionally robust optimization to solve for an optimal discrete distribution, and proving that solutions of the original nonconvex problem are generated by the discrete distribution under mild boundedness, nonredundancy, and Slater conditions. As a consequence, optimal (worst-case) attacks against the model may be solved for exactly. This contrasts prior state-of-the-art that either requires expensive branch-and-bound schemes or loose relaxation techniques. Experiments on robust control and MNIST image classification examples highlight the benefits of our approach.

Soft Convex Quantization: Revisiting Vector Quantization with Convex Optimization

Vector Quantization (VQ) is a well-known technique in deep learning for extracting informative discrete latent representations. VQ-embedded models have shown impressive results in a range of applications including image and speech generation. VQ operates as a parametric K-means algorithm that quantizes inputs using a single codebook vector in the forward pass. While powerful, this technique faces practical challenges including codebook collapse, non-differentiability and lossy compression. To mitigate the aforementioned issues, we propose Soft Convex Quantization (SCQ) as a direct substitute for VQ. SCQ works like a differentiable convex optimization (DCO) layer: in the forward pass, we solve for the optimal convex combination of codebook vectors that quantize the inputs. In the backward pass, we leverage differentiability through the optimality conditions of the forward solution. We then introduce a scalable relaxation of the SCQ optimization and demonstrate its efficacy on the CIFAR-10, GTSRB and LSUN datasets. We train powerful SCQ autoencoder models that significantly outperform matched VQ-based architectures, observing an order of magnitude better image reconstruction and codebook usage with comparable quantization runtime.

Tempo Adaption in Non-stationary Reinforcement Learning

We first raise and tackle ``time synchronization'' issue between the agent and the environment in non-stationary reinforcement learning (RL), a crucial factor hindering its real-world applications. In reality, environmental changes occur over wall-clock time ($\mathfrak{t}$) rather than episode progress ($k$), where wall-clock time signifies the actual elapsed time within the fixed duration $\mathfrak{t} \in [0, T]$. In existing works, at episode $k$, the agent rollouts a trajectory and trains a policy before transitioning to episode $k+1$. In the context of the time-desynchronized environment, however, the agent at time $\mathfrak{t}_k$ allocates $\Delta \mathfrak{t}$ for trajectory generation and training, subsequently moves to the next episode at $\mathfrak{t}_{k+1}=\mathfrak{t}_{k}+\Delta \mathfrak{t}$. Despite a fixed total episode ($K$), the agent accumulates different trajectories influenced by the choice of \textit{interaction times} ($\mathfrak{t}_1,\mathfrak{t}_2,...,\mathfrak{t}_K$), significantly impacting the sub-optimality gap of policy. We propose a Proactively Synchronizing Tempo (ProST) framework that computes optimal $\{ \mathfrak{t}_1,\mathfrak{t}_2,...,\mathfrak{t}_K \} (= \{ \mathfrak{t} \}_{1:K})$. Our main contribution is that we show optimal $\{ \mathfrak{t} \}_{1:K}$ trades-off between the policy training time (agent tempo) and how fast the environment changes (environment tempo). Theoretically, this work establishes an optimal $\{ \mathfrak{t} \}_{1:K}$ as a function of the degree of the environment's non-stationarity while also achieving a sublinear dynamic regret. Our experimental evaluation on various high dimensional non-stationary environments shows that the ProST framework achieves a higher online return at optimal $\{ \mathfrak{t} \}_{1:K}$ than the existing methods.

Projected Randomized Smoothing for Certified Adversarial Robustness

Randomized smoothing is the current state-of-the-art method for producing provably robust classifiers. While randomized smoothing typically yields robust $\ell_2$-ball certificates, recent research has generalized provable robustness to different norm balls as well as anisotropic regions. This work considers a classifier architecture that first projects onto a low-dimensional approximation of the data manifold and then applies a standard classifier. By performing randomized smoothing in the low-dimensional projected space, we characterize the certified region of our smoothed composite classifier back in the high-dimensional input space and prove a tractable lower bound on its volume. We show experimentally on CIFAR-10 and SVHN that classifiers without the initial projection are vulnerable to perturbations that are normal to the data manifold and yet are captured by the certified regions of our method. We compare the volume of our certified regions against various baselines and show that our method improves on the state-of-the-art by many orders of magnitude.

Accelerating Diffusion-Based Text-to-Audio Generation with Consistency Distillation

Diffusion models power a vast majority of text-to-audio (TTA) generation methods. Unfortunately, these models suffer from slow inference speed due to iterative queries to the underlying denoising network, thus unsuitable for scenarios with inference time or computational constraints. This work modifies the recently proposed consistency distillation framework to train TTA models that require only a single neural network query. In addition to incorporating classifier-free guidance into the distillation process, we leverage the availability of generated audio during distillation training to fine-tune the consistency TTA model with novel loss functions in the audio space, such as the CLAP score. Our objective and subjective evaluation results on the AudioCaps dataset show that consistency models retain diffusion models' high generation quality and diversity while reducing the number of queries by a factor of 400.