We thank the reviewers for their valuable feedback. As noted in Appendix A, this computation can be amortized across many goal-reaching tasks. Lastly, we agree with R2 that the construction of "good" replay buffers is an We will clarify this in Section 2.3. We will clarify this in Alg. 1. The Atari games fit that mould, as does StarCraft II.

Autonomous drones capable of interpreting and executing high-level language instructions in unstructured environments remain a long-standing goal. Yet existing approaches are constrained by their dependence on hand-crafted skills, extensive parameter tuning, or computationally intensive models unsuitable for onboard use. We introduce GRaD-Nav++, a lightweight Vision-Language-Action (VLA) framework that runs fully onboard and follows natural-language commands in real time. Our policy is trained in a photorealistic 3D Gaussian Splatting (3DGS) simulator via Differentiable Reinforcement Learning (DiffRL), enabling efficient learning of low-level control from visual and linguistic inputs. At its core is a Mixture-of-Experts (MoE) action head, which adaptively routes computation to improve generalization while mitigating forgetting. In multi-task generalization experiments, GRaD-Nav++ achieves a success rate of 83% on trained tasks and 75% on unseen tasks in simulation. When deployed on real hardware, it attains 67% success on trained tasks and 50% on unseen ones. In multi-environment adaptation experiments, GRaD-Nav++ achieves an average success rate of 81% across diverse simulated environments and 67% across varied real-world settings. These results establish a new benchmark for fully onboard Vision-Language-Action (VLA) flight and demonstrate that compact, efficient models can enable reliable, language-guided navigation without relying on external infrastructure.

This paper studies generalization capabilities of neural networks (NNs) using new and improved PyTorch library Loss Landscape Analysis (LLA). LLA facilitates visualization and analysis of loss landscapes along with the properties of NN Hessian. Different approaches to NN loss landscape plotting are discussed with particular focus on normalization techniques showing that conventional methods cannot always ensure correct visualization when batch normalization layers are present in NN architecture. The use of Hessian axes is shown to be able to mitigate this effect, and methods for choosing Hessian axes are proposed. In addition, spectra of Hessian eigendecomposition are studied and it is shown that typical spectra exist for a wide range of NNs. This allows to propose quantitative criteria for Hessian analysis that can be applied to evaluate NN performance and assess its generalization capabilities. Generalization experiments are conducted using ImageNet-1K pre-trained models along with several models trained as part of this study. The experiment include training models on one dataset and testing on another one to maximize experiment similarity to model performance in the Wild. It is shown that when datasets change, the changes in criteria correlate with the changes in accuracy, making the proposed criteria a computationally efficient estimate of generalization ability, which is especially useful for extremely large datasets.

In this paper we present a generative latent variable model for rating-based collaborative filtering called the User Rating Profile model (URP). The generative process which underlies URP is designed to produce complete user rating profiles, an assignment of one rating to each item for each user. Our model represents each user as a mixture of user attitudes, and the mixing proportions are distributed according to a Dirichlet random variable. The rating for each item is generated by selecting a user attitude for the item, and then selecting a rating according to the preference pattern associated with that attitude. URP is related to several models including a multinomial mixture model, the aspect model [7], and LDA [1], but has clear advantages over each.

In this paper we present a generative latent variable model for rating-based collaborative filtering called the User Rating Profile model (URP). The generative process which underlies URP is designed to produce complete user rating profiles, an assignment of one rating to each item for each user. Our model represents each user as a mixture of user attitudes, and the mixing proportions are distributed according to a Dirichlet random variable. The rating for each item is generated by selecting a user attitude for the item, and then selecting a rating according to the preference pattern associated with that attitude. URP is related to several models including a multinomial mixture model, the aspect model [7], and LDA [1], but has clear advantages over each.