Federated Learning (FL) has demonstrated a promising future in privacy-friendly collaboration but it faces the data heterogeneity problem. Knowledge Distillation (KD) can serve as an effective method to address this issue. However, challenges arise from the unreliability of existing distillation methods in multi-domain scenarios. Prevalent distillation solutions primarily aim to fit the distributions of the global model directly by minimizing forward Kullback-Leibler divergence (KLD). This results in significant bias when the outputs of the global model are multi-peaked, which indicates the unreliability of distillation pathway. Meanwhile, cross-domain update conflicts can notably reduce the accuracy of the global model (teacher model) in certain domains, reflecting the unreliability of the teacher model in these domains.

Efficient sampling of unnormalized probability densities such as the Boltzmann distribution of molecular systems is a longstanding challenge. Next to conventional approaches like molecular dynamics or Markov chain Monte Carlo, variational approaches, such as training normalizing flows with the reverse Kullback-Leibler divergence, have been introduced. However, such methods are prone to mode collapse and often do not learn to sample the full configurational space. Here, we present temperature-annealed Boltzmann generators (TA-BG) to address this challenge. First, we demonstrate that training a normalizing flow with the reverse Kullback-Leibler divergence at high temperatures is possible without mode collapse. Furthermore, we introduce a reweighting-based training objective to anneal the distribution to lower target temperatures. We apply this methodology to three molecular systems of increasing complexity and, compared to the baseline, achieve better results in almost all metrics while requiring up to three times fewer target energy evaluations. For the largest system, our approach is the only method that accurately resolves the metastable states of the system.

We propose ratio divergence (RD) learning for discrete energy-based models, a method that utilizes both training data and a tractable target energy function. We apply RD learning to restricted Boltzmann machines (RBMs), which are a minimal model that satisfies the universal approximation theorem for discrete distributions. RD learning combines the strength of both forward and reverse Kullback-Leibler divergence (KLD) learning, effectively addressing the "notorious" issues of underfitting with the forward KLD and mode-collapse with the reverse KLD. Since the summation of forward and reverse KLD seems to be sufficient to combine the strength of both approaches, we include this learning method as a direct baseline in numerical experiments to evaluate its effectiveness. Numerical experiments demonstrate that RD learning significantly outperforms other learning methods in terms of energy function fitting, mode-covering, and learning stability across various discrete energy-based models. Moreover, the performance gaps between RD learning and the other learning methods become more pronounced as the dimensions of target models increase.

Knowledge Distillation (KD) is a promising technique for reducing the high computational demand of large language models (LLMs). However, previous KD methods are primarily applied to white-box classification models or training small models to imitate black-box model APIs like ChatGPT. How to effectively distill the knowledge from white-box generative LLMs is still under-explored, which becomes more and more important with the prosperity of LLMs. In this work, we propose MiniLLM that distills smaller language models from generative larger language models. We first replace the forward Kullback-Leibler divergence (KLD) objective in the standard KD approaches with reverse KLD, which is more suitable for KD on generative language models, to prevent the student model from overestimating the low-probability regions of the teacher distribution. Then, we derive an effective optimization approach to learn this objective. Extensive experiments in the instruction-following setting show that the MiniLLM models generate more precise responses with the higher overall quality, lower exposure bias, better calibration, and higher long-text generation performance. Our method is also scalable for different model families with 120M to 13B parameters. We will release our code and model checkpoints at https://aka.ms/MiniLLM.

In this paper, we propose a novel loss function for training Generative Adversarial Networks (GANs) aiming towards deeper theoretical understanding as well as improved performance for the underlying optimization problem. The new loss function is based on cumulant generating functions giving rise to \emph{Cumulant GAN}. Relying on a recently-derived variational formula, we show that the corresponding optimization problem is equivalent to R{\'e}nyi divergence minimization, thus offering a (partially) unified perspective of GAN losses: the R{\'e}nyi family encompasses Kullback-Leibler divergence (KLD), reverse KLD, Hellinger distance and $\chi^2$-divergence. Wasserstein GAN is also a member of the proposed cumulant GAN. In terms of stability, we rigorously prove the exponential convergence of cumulant GAN to the Nash equilibrium for a linear discriminator, Gaussian distributions and the standard gradient descent algorithm. Finally, we experimentally demonstrate that image generation is generally more robust relative to Wasserstein GAN and it is substantially improved in terms of inception score when weaker discriminators are considered.