However, existing watermarking methods for meshes, point clouds, and implicit radiance fields cannot be directly applied to 3DGS models, as 3DGS models use explicit 3D Gaussians with distinct structures and do not rely on neural networks. Naively embedding the watermark on a pre-trained 3DGS can cause obvious distortion in rendered images. In our work, we propose an uncertaintybased method that constrains the perturbation of model parameters to achieve invisible watermarking for 3DGS.

If causal relationships are linear and acyclic and noise terms are independent and Gaussian, causal orientation is not identified from observational data -- even if faithfulness is satisfied (Spirtes et al., 2002). Shimizu et al. (2006) showed that acyclic, linear, non-Gaussian (LiNGAM) causal models are identified from observational data, so long as no latent confounders are present. That holds even when faithfulness fails. Genin and Mayo-Wilson (2020) refine that result: not only are causal relationships identified, but causal orientation is statistically decidable. That means that for every ϵ > 0, there is a method that converges in probability to the correct orientation and, at every sample size, outputs an incorrect orientation with probability less than ϵ. These results naturally raise questions about what happens in the presence of latent confounders. Hoyer et al. (2008) and Salehkaleybar et al. (2020) show that, although the causal model is not uniquely identified, causal orientation among observed variables is identified in the presence of latent confounders, so long as faithfulness is satisfied. This paper refines these results: although it is possible to converge to the right orientation in the limit, causal orientation is no longer statistically decidable--it is not possible to converge to the correct orientation with finite-sample bounds on the probability of orientation errors, even if faithfulness is satisfied. However, that limiting result suggests several adjustments to the LiNGAM model that may recover decidability.

Proteins are essential for almost all biological processes and derive their diverse functions from complex 3D structures, which are in turn determined by their amino acid sequences.

Lemma 3. Let l be any positive integer. The sequence r(k) defined by (14) is a strictly increasing sequence. Appendix B.9 Lemma 7. Let m Appendix B.11. Lemma 9. Let f If Definition 1 is satisfied for a non-affine function, then every nonempty subset has a nonempty intersection with the other subset or at least one of the other subsets. The number of closed connected subsets satisfying Definition 1 is a minimum. The interior and frontier (boundary) of a set X are denoted as IntX and FrX, respectively.

Normalizing flows are a class of probabilistic generative models which allow for both fast density computation and efficient sampling and are effective at modelling complex distributions like images. A drawback among current methods is their significant training cost, sometimes requiring months of GPU training time to achieve state-of-the-art results. This paper introduces Wavelet Flow, a multi-scale, normalizing flow architecture based on wavelets. A Wavelet Flow has an explicit representation of signal scale that inherently includes models of lower resolution signals and conditional generation of higher resolution signals, i.e., super resolution. A major advantage of Wavelet Flow is the ability to construct generative models for high resolution data (e.g., 1024 1024 images) that are impractical with previous models. Furthermore, Wavelet Flow is competitive with previous normalizing flows in terms of bits per dimension on standard (low resolution) benchmarks while being up to 15 faster to train.

In view of training increasingly complex learning architectures, we establish a nonsmooth implicit function theorem with an operational calculus. Our result applies to most practical problems (i.e., definable problems) provided that a nonsmooth form of the classical invertibility condition is fulfilled. This approach allows for formal subdifferentiation: for instance, replacing derivatives by Clarke Jacobians in the usual differentiation formulas is fully justified for a wide class of nonsmooth problems. Moreover this calculus is entirely compatible with algorithmic differentiation (e.g., backpropagation). We provide several applications such as training deep equilibrium networks, training neural nets with conic optimization layers, or hyperparameter-tuning for nonsmooth Lasso-type models. To show the sharpness of our assumptions, we present numerical experiments showcasing the extremely pathological gradient dynamics one can encounter when applying implicit algorithmic differentiation without any hypothesis.

Despite significant progress on multi-agent reinforcement learning (MARL) in recent years, coordination in complex domains remains a challenge. Work in MARL often focuses on solving tasks where agents interact with all other agents and entities in the environment; however, we observe that real-world tasks are often composed of several isolated instances of local agent interactions (subtasks), and each agent can meaningfully focus on one subtask to the exclusion of all else in the environment. In these composite tasks, successful policies can often be decomposed into two levels of decision-making: agents are allocated to specific subtasks and each agent acts productively towards their assigned subtask alone. This decomposed decision making provides a strong structural inductive bias, significantly reduces agent observation spaces, and encourages subtask-specific policies to be reused and composed during training, as opposed to treating each new composition of subtasks as unique. We introduce ALMA, a general learning method for taking advantage of these structured tasks. ALMA simultaneously learns a high-level subtask allocation policy and low-level agent policies. We demonstrate that ALMA learns sophisticated coordination behavior in a number of challenging environments, outperforming strong baselines. ALMA's modularity also enables it to better generalize to new environment configurations. Finally, we find that while ALMA can integrate separately trained allocation and action policies, the best performance is obtained only by training all components jointly.

Visual Reinforcement Learning (RL) methods often require extensive amounts of data. As opposed to model-free RL, model-based RL (MBRL) offers a potential solution with efficient data utilization through planning. Additionally, RL lacks generalization capabilities for real-world tasks. Prior work has shown that incorporating pre-trained visual representations (PVRs) enhances sample efficiency and generalization. While PVRs have been extensively studied in the context of model-free RL, their potential in MBRL remains largely unexplored.