However, existing work either applies predefined filter weights or learns them without necessary constraints, which may lead to oversimplified or ill-posed filters. To overcome these issues, we propose BernNet, a novel graph neural network with theoretical support that provides a simple but effective scheme for designing and learning arbitrary graph spectral filters. In particular, for any filter over the normalized Laplacian spectrum of a graph, our BernNet estimates it by an order-K Bernstein polynomial approximation and designs its spectral property by setting the coefficients of the Bernstein basis. Moreover, we can learn the coefficients (and the corresponding filter weights) based on observed graphs and their associated signals and thus achieve the BernNet specialized for the data. Our experiments demonstrate that BernNet can learn arbitrary spectral filters, including complicated band-rejection and comb filters, and it achieves superior performance in real-world graph modeling tasks. Code is available at https://github.com/ivam-he/BernNet.

Physics-informed neural networks (PINNs) are infamous for being hard to train. Recently, second-order methods based on natural gradient and Gauss-Newton methods have shown promising performance, improving the accuracy achieved by first-order methods by several orders of magnitude. While promising, the proposed methods only scale to networks with a few thousand parameters due to the high computational cost to evaluate, store, and invert the curvature matrix. We propose Kronecker-factored approximate curvature (KFAC) for PINN losses that greatly reduces the computational cost and allows scaling to much larger networks. Our approach goes beyond the established KFAC for traditional deep learning problems as it captures contributions from a PDE's differential operator that are crucial for optimization. To establish KFAC for such losses, we use Taylor-mode automatic differentiation to describe the differential operator's computation graph as a forward network with shared weights. This allows us to apply KFAC thanks to a recently developed general formulation for networks with weight sharing. Empirically, we find that our KFAC-based optimizers are competitive with expensive second-order methods on small problems, scale more favorably to higher-dimensional neural networks and PDEs, and consistently outperform first-order methods and LBFGS.

Personalized Federated Graph Learning (pFGL) facilitates the decentralized training of Graph Neural Networks (GNNs) without compromising privacy while accommodating personalized requirements for non-IID participants. In crossdomain scenarios, structural heterogeneity poses significant challenges for pFGL. Nevertheless, previous pFGL methods incorrectly share non-generic knowledge globally and fail to tailor personalized solutions locally under domain structural shift. We innovatively reveal that the spectral nature of graphs can well reflect inherent domain structural shifts. Correspondingly, our method overcomes it by sharing generic spectral knowledge. Moreover, we indicate the biased messagepassing schemes for graph structures and propose the personalized preference module. Combining both strategies, we propose our pFGL framework FedSSP which Shares generic Spectral knowledge while satisfying graph Preferences. Furthermore, We perform extensive experiments on cross-dataset and cross-domain settings to demonstrate the superiority of our framework. The code is available at https://github.com/OakleyTan/FedSSP.

The convergence of stochastic gradient descent is highly dependent on the step-size, especially on non-convex problems such as neural network training. Step decay step-size schedules (constant and then cut) are widely used in practice because of their excellent convergence and generalization qualities, but their theoretical properties are not yet well understood. We provide convergence results for step decay in the non-convex regime, ensuring that the gradient norm vanishes at an O(ln T/ T) rate. We also provide near-optimal (and sometimes provably tight) convergence guarantees for general, possibly non-smooth, convex and strongly convex problems. The practical efficiency of the step decay step-size is demonstrated in several large-scale deep neural network training tasks.

The convergence of stochastic gradient descent is highly dependent on the step-size, especially on non-convex problems such as neural network training. Step decay step-size schedules (constant and then cut) are widely used in practice because of their excellent convergence and generalization qualities, but their theoretical properties are not yet well understood. We provide convergence results for step decay in the non-convex regime, ensuring that the gradient norm vanishes at an O(ln T/ T) rate. We also provide near-optimal (and sometimes provably tight) convergence guarantees for general, possibly non-smooth, convex and strongly convex problems. The practical efficiency of the step decay step-size is demonstrated in several large-scale deep neural network training tasks.

Web-scale visual entity recognition, the task of associating images with their corresponding entities within vast knowledge bases like Wikipedia, presents significant challenges due to the lack of clean, large-scale training data. In this paper, we propose a novel methodology to curate such a dataset, leveraging a multimodal large language model (LLM) for label verification, metadata generation, and rationale explanation. Instead of relying on the multimodal LLM to directly annotate data, which we found to be suboptimal, we prompt it to reason about potential candidate entity labels by accessing additional contextually relevant information (such as Wikipedia), resulting in more accurate annotations. We further use the multimodal LLM to enrich the dataset by generating question-answer pairs and a grounded finegrained textual description (referred to as "rationale") that explains the connection between images and their assigned entities. Experiments demonstrate that models trained on this automatically curated data achieve state-of-the-art performance on web-scale visual entity recognition tasks (e.g.

In this section, we describe the details of MiniRTS Environment and human dataset. The data do not contain any personally identifiable information or offensive content. Figure 1: MiniRTS [2] implements the rockpaper-scissors Figure 2: Building units can produce different attack graph, each army type army units using resources. "workshop" can produce has some units it is effective against and vulnerable "archer", "dragon" and "catapult" while other to. For example, "swordman" restrains buildings can build one unit type. Only "peasant" "spearman" but is retrained by "cavarly". Game Units There are 3 kinds of units in MiniRTS, including resource units, building units, and army units. Resource Units: Resource units are stationary and neutral. Resource units cannot be constructed by anyone and are created at the beginning of a game. One mine action could gather resources from the resource units, and the mined resources are necessary to build new building units or army units.

We consider the problem of building a reinforcement learning (RL) agent that can both accomplish non-trivial tasks, like winning a real-time strategy game, and strictly follow high-level language commands from humans, like "attack", even if a command is sub-optimal. We call this novel yet important problem, Grounded Reinforcement Learning (GRL). Compared with other language grounding tasks, GRL is particularly non-trivial and cannot be simply solved by pure RL or behavior cloning (BC). From the RL perspective, it is extremely challenging to derive a precise reward function for human preferences since the commands are abstract and the valid behaviors are highly complicated and multi-modal. From the BC perspective, it is impossible to obtain perfect demonstrations since human strategies in complex games are typically sub-optimal. We tackle GRL via a simple, tractable, and practical constrained RL objective and develop an iterative RL algorithm, REinforced demonstration Distillation (RED), to obtain a strong GRL policy. We evaluate the policies derived by RED, BC and pure RL methods on a simplified real-time strategy game, MiniRTS. Experiment results and human studies show that the RED policy is able to consistently follow human commands and, at the same time, achieve a higher win rate than the baselines. We release our code and present more examples at https://sites.google.com/view/grounded-rl.