Unsupervised semantic segmentation is a challenging task that segments images into semantic groups without manual annotation. Prior works have primarily focused on leveraging prior knowledge of semantic consistency or priori concepts from self-supervised learning methods, which often overlook the coherence property of image segments. In this paper, we demonstrate that the smoothness prior, asserting that close features in a metric space share the same semantics, can significantly simplify segmentation by casting unsupervised semantic segmentation as an energy minimization problem. Under this paradigm, we propose a novel approach called SmooSeg that harnesses self-supervised learning methods to model the closeness relationships among observations as smoothness signals. To effectively discover coherent semantic segments, we introduce a novel smoothness loss that promotes piecewise smoothness within segments while preserving discontinuities across different segments. Additionally, to further enhance segmentation quality, we design an asymmetric teacher-student style predictor that generates smoothly updated pseudo labels, facilitating an optimal fit between observations and labeling outputs. Thanks to the rich supervision cues of the smoothness prior, our SmooSeg significantly outperforms STEGO in terms of pixel accuracy on three datasets: COCOStuff (+14.9%),

In continual learning (CL), a learner is faced with a sequence of tasks, arriving one after the other, and the goal is to remember all the tasks once the continual learning experience is finished. The prior art in CL uses episodic memory, parameter regularization or extensible network structures to reduce interference among tasks, but in the end, all the approaches learn different tasks in a joint vector space. We believe this invariably leads to interference among different tasks. We propose to learn tasks in different (low-rank) vector subspaces that are kept orthogonal to each other in order to minimize interference. Further, to keep the gradients of different tasks coming from these subspaces orthogonal to each other, we learn isometric mappings by posing network training as an optimization problem over the Stiefel manifold. To the best of our understanding, we report, for the first time, strong results over experience-replay baseline with and without memory on standard classification benchmarks in continual learning.

Summary and Contributions: This paper studies reinforcement learning (RL) problems on large state and action spaces that are endowed with a metric. They key assumption is that the optimal state-action value function, Q*, is Lipschitz smooth with respect to that metric. The setting is that of an episodic, H-stage Markov decision process, in which the learner must choose an action for each stage of each episode while achieving low regret against an optimal policy. Previously, an algorithm was proposed for this problem based on learning the Q* function on an adaptive discretization of the state-action space that becomes steadily finer on important regions of the space. The regret of this algorithm was thought to depend on the packing number of the state-action space.

This paper is about model-free RL where the state-action state is a metric space. An improved analysis of an existing algorithm (with some modifications) is shown to achieve a regret that scales with the zooming dimension of the metric space, instead of the covering dimesion. A general consensus among reviewers emerged that this theoretical RL paper is well executed, and provides a reasonable though not groundbreaking contribution to the RL literature.

From optimal transport to robust dimensionality reduction, a plethora of machine learning applications can be cast into the min-max optimization problems over Riemannian manifolds. Though many min-max algorithms have been analyzed in the Euclidean setting, it has proved elusive to translate these results to the Riemannian case. Zhang et al. have recently shown that geodesic convex concave Riemannian problems always admit saddle-point solutions. Inspired by this result, we study whether a performance gap between Riemannian and optimal Euclidean space convex-concave algorithms is necessary. We answer this question in the negative--we prove that the Riemannian corrected extragradient (RCEG) method achieves last-iterate convergence at a linear rate in the geodesically stronglyconvex-concave case, matching the Euclidean result. Our results also extend to the stochastic or non-smooth case where RCEG and Riemanian gradient ascent descent (RGDA) achieve near-optimal convergence rates up to factors depending on curvature of the manifold.

Post-feedback update: Thanks for your update. Your additional explanations and results will help improve the paper, and I definitely think this work is strong and should be accepted. The framework itself is new, and the authors make it very clear how prior work fits into the framework as special cases. At the same time, a good case is made for why this framework is useful to have and how it can be better to use than prior losses. Quality: this paper makes a compelling case for the framework it introduces.

We propose in this paper a general framework for deriving loss functions for structured prediction. In our framework, the user chooses a convex set including the output space and provides an oracle for projecting onto that set. Given that oracle, our framework automatically generates a corresponding convex and smooth loss function. As we show, adding a projection as output layer provably makes the loss smaller. We identify the marginal polytope, the output space's convex hull, as the best convex set on which to project. However, because the projection onto the marginal polytope can sometimes be expensive to compute, we allow to use any convex superset instead, with potentially cheaper-to-compute projection. Since efficient projection algorithms are available for numerous convex sets, this allows us to construct loss functions for a variety of tasks. On the theoretical side, when combined with calibrated decoding, we prove that our loss functions can be used as a consistent surrogate for a (potentially non-convex) target loss function of interest. We demonstrate our losses on label ranking, ordinal regression and multilabel classification, confirming the improved accuracy enabled by projections.

All reviewers agreed that this paper make a nice contribution to NeurIPS by providing a novel general framework for generating calibrated surrogate loss functions for structured prediction problems. On the other hand, in discussion, they also stressed that including some baselines (e.g., SSVM/CRF approximation/SPEN) in the experiments and reporting runtimes could make this paper much stronger. The authors should implement their promised changes in the camera-ready version.

Most graph kernels are an instance of the class of R-Convolution kernels, which measure the similarity of objects by comparing their substructures. Despite their empirical success, most graph kernels use a naive aggregation of the final set of substructures, usually a sum or average, thereby potentially discarding valuable information about the distribution of individual components. Furthermore, only a limited instance of these approaches can be extended to continuously attributed graphs. We propose a novel method that relies on the Wasserstein distance between the node feature vector distributions of two graphs, which allows finding subtler differences in data sets by considering graphs as high-dimensional objects rather than simple means. We further propose a Weisfeiler-Lehman-inspired embedding scheme for graphs with continuous node attributes and weighted edges, enhance it with the computed Wasserstein distance, and thereby improve the state-of-the-art prediction performance on several graph classification tasks.

Orthogonal Monte Carlo [43] (OMC) is a very effective sampling algorithm imposing structural geometric conditions (orthogonality) on samples for variance reduction. Due to its simplicity and superior performance as compared to its Quasi Monte Carlo counterparts, OMC is used in a wide spectrum of challenging machine learning applications ranging from scalable kernel methods [18] to predictive recurrent neural networks [11], generative models [36] and reinforcement learning [16]. However theoretical understanding of the method remains very limited. In this paper we shed new light on the theoretical principles behind OMC, applying theory of negatively dependent random variables to obtain several new concentration results. As a corollary, we manage to obtain first uniform convergence results for OMCs and consequently, substantially strengthen best known downstream guarantees for kernel ridge regression via OMCs. We also propose novel extensions of the method leveraging theory of algebraic varieties over finite fields and particle algorithms, called Near-Orthogonal Monte Carlo (NOMC). We show that NOMC is the first algorithm consistently outperforming OMC in applications ranging from kernel methods to approximating distances in probabilistic metric spaces.