The main challenge of the LAC problem lies in how to depict relationships between known and augmented classes.

We address your concern as follows. This clearly shows the advantage of our method. We answer your main questions as follows. Q1:"Do we need to commit ourselves to the OVR loss?...considering a loss function such as softmax cross entropy Y ou are absolutely correct! If convexity is not required (e.g., NN implementation), we can use more flexible multiclass loss and binary We will make this clear in the revision. Q2:"How to use the non-negative risk estimator in this problem?" We will add more elaborations about the formulation in the revision. Q3:"My question is have you tried different loss functions?" However, it does not converge in experiments. So we instead use sigmoid loss following Kiryo et al. [24]. Theorem 1 serves as a guide to choose binary loss for OVR scheme. Thus, a consistency guarantee (Theorem 1) is necessary. Thanks for the detailed review and helpful comments. We address your main concerns as follows. For the other minor issues, we will discuss in the paper and revise the paper according to your suggestions. We would like to revise the terminology in the revision if it is allowed. Q2:"Some of the claims made about prior work are not accurate.

Mean field type games (MFTGs) describe Nash equilibria between large coalitions: each coalition consists of a continuum of cooperative agents who maximize the average reward of their coalition while interacting non-cooperatively with a finite number of other coalitions. Although the theory has been extensively developed, we are still lacking efficient and scalable computational methods. Here, we develop reinforcement learning methods for such games in a finite space setting with general dynamics and reward functions. We start by proving that MFTG solution yields approximate Nash equilibria in finite-size coalition games. We then propose two algorithms. The first is based on quantization of mean-field spaces and Nash Q-learning. We provide convergence and stability analysis. We then propose a deep reinforcement learning algorithm, which can scale to larger spaces. Numerical experiments in 5 environments with mean-field distributions of dimension up to $200$ show the scalability and efficiency of the proposed method.

Most existing generative models are limited to learning a single probability distribution from the training data and cannot generalize to novel distributions for unseen data. An architecture that can generate samples from both trained datasets and unseen probability distributions would mark a significant breakthrough. Recently, score-based generative models have gained considerable attention for their comprehensive mode coverage and high-quality image synthesis, as they effectively learn an operator that maps a probability distribution to its corresponding score function. In this work, we introduce the $\emph{Score Neural Operator}$, which learns the mapping from multiple probability distributions to their score functions within a unified framework. We employ latent space techniques to facilitate the training of score matching, which tends to over-fit in the original image pixel space, thereby enhancing sample generation quality. Our trained Score Neural Operator demonstrates the ability to predict score functions of probability measures beyond the training space and exhibits strong generalization performance in both 2-dimensional Gaussian Mixture Models and 1024-dimensional MNIST double-digit datasets. Importantly, our approach offers significant potential for few-shot learning applications, where a single image from a new distribution can be leveraged to generate multiple distinct images from that distribution.

Machine learning society has witnessed the emergence of a myriad of Out-of-Distribution (OoD) algorithms, which address the distribution shift between the training and the testing distribution by searching for a unified predictor or invariant feature representation. However, the task of directly mitigating the distribution shift in the unseen testing set is rarely investigated, due to the unavailability of the testing distribution during the training phase and thus the impossibility of training a distribution translator mapping between the training and testing distribution. In this paper, we explore how to bypass the requirement of testing distribution for distribution translator training and make the distribution translation useful for OoD prediction. We propose a portable Distribution Shift Inversion algorithm, in which, before being fed into the prediction model, the OoD testing samples are first linearly combined with additional Gaussian noise and then transferred back towards the training distribution using a diffusion model trained only on the source distribution. Theoretical analysis reveals the feasibility of our method. Experimental results, on both multiple-domain generalization datasets and single-domain generalization datasets, show that our method provides a general performance gain when plugged into a wide range of commonly used OoD algorithms.