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Publications
Realistic Evaluation of Transductive Few-Shot Learning - Supplementary Material
In the main tables of the paper, we did not include the performances of α-TIM in the standard balanced setting. Here, we emphasize that α-… (see more)TIM is a generalization of TIM [1] as when α → 1 (i.e., the α-entropies tend to the Shannon entropies), α-TIM tends to TIM. Therefore, in the standard setting, where optimal hyper-parameter α is obtained over validation tasks that are balanced (as in the standard validation tasks of the original TIM and the other existing methods), the performance of α-TIM is the same as TIM. When α is tuned on balanced validation tasks, we obtain an optimal value of α very close to 1, and our α-mutual information approaches the standard mutual information. When the validation tasks are uniformly random, as in our new setting and in the validation plots we provided in the main figure, one can see that the performance of α-TIM remains competitive when we tend to balanced testing tasks (i.e., when a is increasing), but is significantly better than TIM when we tend to uniformly-random testing tasks (a = 1). These results illustrate the flexibility of α-divergences, and are in line with the technical analysis provided in the main paper.
Recipe for a General, Powerful, Scalable Graph Transformer
We propose a recipe on how to build a general, powerful, scalable (GPS) graph Transformer with linear complexity and state-of-the-art result… (see more)s on a diverse set of benchmarks. Graph Transformers (GTs) have gained popularity in the field of graph representation learning with a variety of recent publications but they lack a common foundation about what constitutes a good positional or structural encoding, and what differentiates them. In this paper, we summarize the different types of encodings with a clearer definition and categorize them as being
Graph Neural Networks (GNNs) extend basic Neural Networks (NNs) by using graph structures based on the relational inductive bias (homophily … (see more)assumption). While GNNs have been commonly believed to outperform NNs in real-world tasks, recent work has identified a non-trivial set of datasets where their performance compared to NNs is not satisfactory. Heterophily has been considered the main cause of this empirical observation and numerous works have been put forward to address it. In this paper, we first revisit the widely used homophily metrics and point out that their consideration of only graph-label consistency is a shortcoming. Then, we study heterophily from the perspective of post-aggregation node similarity and define new homophily metrics, which are potentially advantageous compared to existing ones. Based on this investigation, we prove that some harmful cases of heterophily can be effectively addressed by local diversification operation. Then, we propose the Adaptive Channel Mixing (ACM), a framework to adaptively exploit aggregation, diversification and identity channels node-wisely to extract richer localized information for diverse node heterophily situations. ACM is more powerful than the commonly used uni-channel framework for node classification tasks on heterophilic graphs and is easy to be implemented in baseline GNN layers. When evaluated on 10 benchmark node classification tasks, ACM-augmented baselines consistently achieve significant performance gain, exceeding state-of-the-art GNNs on most tasks without incurring significant computational burden.
Diffusion models are recent state-of-the-art methods for image generation and likelihood estimation. In this work, we generalize continuous-… (see more)time diffusion models to arbitrary Riemannian manifolds and derive a variational framework for likelihood estimation. Computationally, we propose new methods for computing the Riemannian divergence which is needed for likelihood estimation. Moreover, in generalizing the Euclidean case, we prove that maximizing this variational lower-bound is equivalent to Riemannian score matching. Empirically, we demonstrate the expressive power of Riemannian diffusion models on a wide spectrum of smooth manifolds, such as spheres, tori, hyperboloids, and orthogonal groups. Our proposed method achieves new state-of-the-art likelihoods on all benchmarks.
Reinforcement learning (RL) agents need to be robust to variations in safety-critical environments. While system identification methods prov… (see more)ide a way to infer the variation from online experience, they can fail in settings where fast identification is not possible. Another dominant approach is robust RL which produces a policy that can handle worst-case scenarios, but these methods are generally designed to achieve robustness to a single uncertainty set that must be specified at train time. Towards a more general solution, we formulate the multi-set robustness problem to learn a policy robust to different perturbation sets. We then design an algorithm that enjoys the benefits of both system identification and robust RL: it reduces uncertainty where possible given a few interactions, but can still act robustly with respect to the remaining uncertainty. On a diverse set of control tasks, our approach demonstrates improved worst-case performance on new environments compared to prior methods based on system identification and on robust RL alone.
In this article, we consider the problem of allocating human operators in a system with multiple semiautonomous robots. Each robot is requir… (see more)ed to perform an independent sequence of tasks, subject to a chance of failing and getting stuck in a fault state at every task. If and when required, a human operator can assist or teleoperate a robot. Conventional dynamic programming-based techniques used to solve such problems face scalability issues due to an exponential growth of state and action spaces with the number of robots and operators. In this article, we derive conditions under which the operator allocation problem satisfies a technical condition called indexability, thereby enabling the use of the Whittle index heuristic. The conditions are easy to check, and we show that they hold for a wide range of problems of interest. Our key insight is to leverage the structure of the value function of individual robots, resulting in conditions that can be verified separately for each state of each robot. We apply these conditions to two types of transitions commonly seen in remote robot supervision systems. Through numerical simulations, we demonstrate the efficacy of Whittle index policy as a near-optimal and scalable approach that outperforms existing scalable methods.
2022-01-01
IEEE Transactions on Control of Network Systems (published)
