电网优化

Physics-informed neural networks (PINNs) are attracting significant attention for solving partial differential equation (PDE) based inverse problems, including electrical impedance tomography (EIT). EIT is non-linear and especially its inverse problem is highly ill-posed. Therefore, successful training of PINN is extremely sensitive to interplay between different loss terms and hyper-parameters, including the learning rate. In this work, we propose a Bayesian approach through data-driven energy-based model (EBM) as a prior, to improve the overall accuracy and quality of tomographic reconstruction. In particular, the EBM is trained over the possible solutions of the PDEs with different boundary conditions. By imparting such prior onto physics-based training, PINN convergence is expedited by more than ten times faster to the PDE’s solution. Evaluation outcome shows that our proposed method is more robust for solving the EIT problem. Our code is available at: https://rooshenasgroup.github.io/eit_ebprior.

Sampling from a target measure whose density is only known up to a normalization constant is a fundamental problem in computational statistics and machine learning. In this paper, we present a new optimization-based method for sampling called mollified interaction energy descent (MIED). MIED minimizes a new class of energies on probability measures called mollified interaction energies (MIEs). These energies rely on mollifier functions---smooth approximations of the Dirac delta originated from PDE theory. We show that as the mollifier approaches the Dirac delta, the MIE converges to the chi-square divergence with respect to the target measure and the gradient flow of the MIE agrees with that of the chi-square divergence. Optimizing this energy with proper discretization yields a practical first-order particle-based algorithm for sampling in both unconstrained and constrained domains. We show experimentally that for unconstrained sampling problems our algorithm performs on par with existing particle-based algorithms like SVGD, while for constrained sampling problems our method readily incorporates constrained optimization techniques to handle more flexible constraints with strong performance compared to alternatives.

To afford flexible behaviour, the brain must build internal representations that mirror the structure of variables in the external world. For example, 2D space obeys rules: the same set of actions combine in the same way everywhere (step north, then south, and you won't have moved, wherever you start). We suggest the brain must represent this consistent meaning of actions across space, as it allows you to find new short-cuts and navigate in unfamiliar settings. We term this representation an `actionable representation'. We formulate actionable representations using group and representation theory, and show that, when combined with biological and functional constraints - non-negative firing, bounded neural activity, and precise coding - multiple modules of hexagonal grid cells are the optimal representation of 2D space. We support this claim with intuition, analytic justification, and simulations. Our analytic results normatively explain a set of surprising grid cell phenomena, and make testable predictions for future experiments. Lastly, we highlight the generality of our approach beyond just understanding 2D space. Our work characterises a new principle for understanding and designing flexible internal representations: they should be actionable, allowing animals and machines to predict the consequences of their actions, rather than just encode.

Real-world data generation often involves complex inter-dependencies among instances, violating the IID-data hypothesis of standard learning paradigms and posing a challenge for uncovering the geometric structures for learning desired instance representations. To this end, we introduce an energy constrained diffusion model which encodes a batch of instances from a dataset into evolutionary states that progressively incorporate other instances' information by their interactions. The diffusion process is constrained by descent criteria w.r.t. a principled energy function that characterizes the global consistency of instance representations over latent structures. We provide rigorous theory that implies closed-form optimal estimates for the pairwise diffusion strength among arbitrary instance pairs, which gives rise to a new class of neural encoders, dubbed as DIFFormer (diffusion-based Transformers), with two instantiations: a simple version with linear complexity for prohibitive instance numbers, and an advanced version for learning complex structures. Experiments highlight the wide applicability of our model as a general-purpose encoder backbone with superior performance in various tasks, such as node classification on large graphs, semi-supervised image/text classification, and spatial-temporal dynamics prediction. The codes are available at https://github.com/qitianwu/DIFFormer.

Recent works have shown that language modeling can be effectively used to train reinforcement learning (RL) policies. However, the success of applying existing language models to planning, in which we wish to obtain a trajectory of actions to reach some goal, is less straightforward. The typical autoregressive generation procedures of language models preclude sequential refinement of earlier steps, which limits the effectiveness of a predicted plan. In this paper, we suggest an approach towards integrating planning with language models based on the idea of iterative energy minimization, and illustrate how such a procedure leads to improved RL performance across different tasks. We train a masked language model to capture an implicit energy function over trajectories of actions, and formulate planning as finding a trajectory of actions with minimum energy. We illustrate how this procedure enables improved performance over recent approaches across BabyAI and Atari environments. We further demonstrate unique benefits of our iterative optimization procedure, involving new task generalization, test-time constraints adaptation, and the ability to compose plans together. Project webpage: https://hychen-naza.github.io/projects/LEAP/index.html

We propose preventive learning as the first framework to guarantee Deep Neural Network (DNN) solution feasibility for optimization problems with linear constraints without post-processing, upon satisfying a mild condition on constraint calibration. Without loss of generality, we focus on problems with only inequality constraints. We systematically calibrate the inequality constraints used in training, thereby anticipating DNN prediction errors and ensuring the obtained solutions remain feasible. We characterize the calibration rate and a critical DNN size, based on which we can directly construct a DNN with provable solution feasibility guarantee. We further propose an Adversarial-Sample Aware training algorithm to improve its optimality performance. We apply the framework to develop DeepOPF+ for solving essential DC optimal power flow problems in grid operation. Simulation results over IEEE test cases show that it outperforms existing strong DNN baselines in ensuring 100\% feasibility and attaining consistent optimality loss (<0.19%) and speedup (up to x228) in both light-load and heavy-load regimes, as compared to a state-of-the-art solver. We also apply our framework to a non-convex problem and show its performance advantage over existing schemes.

Out-of-Distribution (OOD) detection is essential for safety-critical applications of deep neural networks. OOD detection is challenging since DNN models may produce very high logits value even for OOD samples. Hence, it is of great difficulty to discriminate OOD data by directly adopting Softmax on output logits as the confidence score. Differently, we detect the OOD sample with Hopfield energy in a store-then-compare paradigm. In more detail, penultimate layer outputs on the training set are considered as the representations of in-distribution (ID) data. Thus they can be transformed into stored patterns that serve as anchors to measure the discrepancy of unseen data for OOD detection. Starting from the energy function defined in Modern Hopfield Network for the discrepancy score calculation, we derive a simplified version SHE with theoretical analysis. In SHE, we utilize only one stored pattern to present each class, and these patterns can be obtained by simply averaging the penultimate layer outputs of training samples within this class. SHE has the advantages of hyperparameterfree and high computational efficiency. The evaluations of nine widely-used OOD datasets show the promising performance of such a simple yet effective approach and its superiority over State-of-the-Art models. Code is available at https://github.com/zjs975584714/SHE ood detection.

An energy-based model (EBM) is a popular generative framework that offers both explicit density and architectural flexibility, but training them is difficult since it is often unstable and time-consuming. In recent years, various training techniques have been developed, e.g., better divergence measures or stabilization in MCMC sampling, but there often exists a large gap between EBMs and other generative frameworks like GANs in terms of generation quality. In this paper, we propose a novel and effective framework for improving EBMs via contrastive representation learning (CRL). To be specific, we consider representations learned by contrastive methods as the true underlying latent variable. This contrastive latent variable could guide EBMs to understand the data structure better, so it can improve and accelerate EBM training significantly. To enable the joint training of EBM and CRL, we also design a new class of latent-variable EBMs for learning the joint density of data and the contrastive latent variable. Our experimental results demonstrate that our scheme achieves lower FID scores, compared to prior-art EBM methods (e.g., additionally using variational autoencoders or diffusion techniques), even with significantly faster and more memory-efficient training. We also show conditional and compositional generation abilities of our latent-variable EBMs as their additional benefits, even without explicit conditional training. The code is available at https://github.com/hankook/CLEL.

Learning energy-based models (EBMs) is known to be difficult especially on discrete data where gradient-based learning strategies cannot be applied directly. Although ratio matching is a sound method to learn discrete EBMs, it suffers from expensive computation and excessive memory requirements, thereby resulting in difficulties in learning EBMs on high-dimensional data. Motivated by these limitations, in this study, we propose ratio matching with gradient-guided importance sampling (RMwGGIS). Particularly, we use the gradient of the energy function w.r.t. the discrete data space to approximately construct the provably optimal proposal distribution, which is subsequently used by importance sampling to efficiently estimate the original ratio matching objective. We perform experiments on density modeling over synthetic discrete data, graph generation, and training Ising models to evaluate our proposed method. The experimental results demonstrate that our method can significantly alleviate the limitations of ratio matching, perform more effectively in practice, and scale to high-dimensional problems. Our implementation is available at https://github.com/divelab/RMwGGIS.