We show that physics-based simulations can be seamlessly integrated with NeRF to generate high-quality elastodynamics of real-world objects. Unlike existing methods, we discretize nonlinear hyperelasticity in a meshless way, obviating the necessity for intermediate auxiliary shape proxies like a tetrahedral mesh or voxel grid. A quadratic generalized moving least square (Q-GMLS) is employed to capture nonlinear dynamics and large deformation on the implicit model. Such meshless integration enables versatile simulations of complex and codimensional shapes. We adaptively place the least-square kernels according to the NeRF density field to significantly reduce the complexity of the nonlinear simulation. As a result, physically realistic animations can be conveniently synthesized using our method for a wide range of hyperelastic materials at an interactive rate. For more information, please visit our project page at https://fytalon.github.io/pienerf/.

Proximal gradient-based optimization is one of the most common strategies to solve inverse problem of images, and it is easy to implement. However, these techniques often generate heavy artifacts in image reconstruction. One of the most popular refinement methods is to fine-tune the regularization parameter to alleviate such artifacts, but it may not always be sufficient or applicable due to increased computational costs. In this work, we propose a deep geometric incremental learning framework based on the second Nesterov proximal gradient optimization. The proposed end-to-end network not only has the powerful learning ability for high-/low-frequency image features, but also can theoretically guarantee that geometric texture details will be reconstructed from preliminary linear reconstruction. Furthermore, it can avoid the risk of intermediate reconstruction results falling outside the geometric decomposition domains and achieve fast convergence. Our reconstruction framework is decomposed into four modules including general linear reconstruction, cascade geometric incremental restoration, Nesterov acceleration, and post-processing. In the image restoration step, a cascade geometric incremental learning module is designed to compensate for missing texture information from different geometric spectral decomposition domains. Inspired by the overlap-tile strategy, we also develop a post-processing module to remove the block effect in patch-wise-based natural image reconstruction. All parameters in the proposed model are learnable, an adaptive initialization technique of physical parameters is also employed to make model flexibility and ensure converging smoothly. We compare the reconstruction performance of the proposed method with existing state-of-the-art methods to demonstrate its superiority. Our source codes are available at https://github.com/fanxiaohong/Nest-DGIL.

Despite the existence of numerous designs, significant research efforts, and successful applications in the field of control systems, the development of a reliable and secure controller that combines robust theoretical foundations with exceptional performance continues to present a formidable challenge. This challenge has captured the attention of researchers from diverse fields, including robotics [1] and healthcare [2], among others. In the context of control systems, safety is evaluated based on the system state. In this study, we focus on probabilistic safe control, wherein a safe controller is expected to prevent the system from entering hazardous states with an acceptable probability [3-5]. Due to the intricate nature of calculating the safe state space for a general dynamics-driven system, ensuring safety by designing or learning a safe controller is rather complex. Existing safe control strategies include model predictive control [6], reachability analysis [7], and control barrier function (CBF) method [8]. In our research, we build upon the CBF method, which ensures that the system state remains within safe regions by defining a forward invariant set. This set is a subset of the safe region and restricts the system state within its boundaries. Furthermore, we take into account the presence of uncertainty, which not only have a more significant impact on the system state than small disturbances [9], and does not have an analytical format as well [10].

Clustering continues to be a significant and challenging task. Recent studies have demonstrated impressive results by applying clustering to feature representations acquired through self-supervised learning, particularly on small datasets. However, when dealing with datasets containing a large number of clusters, such as ImageNet, current methods struggle to achieve satisfactory clustering performance. In this paper, we introduce a novel method called Contrastive representation Disentanglement for Clustering (CDC) that leverages contrastive learning to directly disentangle the feature representation for clustering. In CDC, we decompose the representation into two distinct components: one component encodes categorical information under an equipartition constraint, and the other component captures instance-specific factors. To train our model, we propose a contrastive loss that effectively utilizes both components of the representation. We conduct a theoretical analysis of the proposed loss and highlight how it assigns different weights to negative samples during the process of disentangling the feature representation. Further analysis of the gradients reveals that larger weights emphasize a stronger focus on hard negative samples. As a result, the proposed loss exhibits strong expressiveness, enabling efficient disentanglement of categorical information. Through experimental evaluation on various benchmark datasets, our method demonstrates either state-of-the-art or highly competitive clustering performance. Notably, on the complete ImageNet dataset, we achieve an accuracy of 53.4%, surpassing existing methods by a substantial margin of +10.2%.

The sparse representation of graphs has shown great potential for accelerating the computation of graph applications (e.g., Social Networks, Knowledge Graphs) on traditional computing architectures (CPU, GPU, or TPU). But the exploration of large-scale sparse graph computing on processing-in-memory (PIM) platforms (typically with memristive crossbars) is still in its infancy. To implement the computation or storage of large-scale or batch graphs on memristive crossbars, a natural assumption is that a large-scale crossbar is demanded, but with low utilization. Some recent works question this assumption, to avoid the waste of storage and computational resource, the fixed-size or progressively scheduled ''block partition'' schemes are proposed. However, these methods are coarse-grained or static, and are not effectively sparsity-aware. This work proposes the dynamic sparsity-aware mapping scheme generating method that models the problem with a sequential decision-making model, and optimizes it by reinforcement learning (RL) algorithm (REINFORCE). Our generating model (LSTM, combined with the dynamic-fill scheme) generates remarkable mapping performance on a small-scale graph/matrix data (complete mapping costs 43% area of the original matrix) and two large-scale matrix data (costing 22.5% area on qh882 and 17.1% area on qh1484). Our method may be extended to sparse graph computing on other PIM architectures, not limited to the memristive device-based platforms.

Deep neural networks have strong capabilities of memorizing the underlying training data, which can be a serious privacy concern. An effective solution to this problem is to train models with differential privacy, which provides rigorous privacy guarantees by injecting random noise to the gradients. This paper focuses on the scenario where sensitive data are distributed among multiple participants, who jointly train a model through federated learning (FL), using both secure multiparty computation (MPC) to ensure the confidentiality of each gradient update, and differential privacy to avoid data leakage in the resulting model. A major challenge in this setting is that common mechanisms for enforcing DP in deep learning, which inject real-valued noise, are fundamentally incompatible with MPC, which exchanges finite-field integers among the participants. Consequently, most existing DP mechanisms require rather high noise levels, leading to poor model utility. Motivated by this, we propose Skellam mixture mechanism (SMM), an approach to enforce DP on models built via FL. Compared to existing methods, SMM eliminates the assumption that the input gradients must be integer-valued, and, thus, reduces the amount of noise injected to preserve DP. Further, SMM allows tight privacy accounting due to the nice composition and sub-sampling properties of the Skellam distribution, which are key to accurate deep learning with DP. The theoretical analysis of SMM is highly non-trivial, especially considering (i) the complicated math of differentially private deep learning in general and (ii) the fact that the mixture of two Skellam distributions is rather complex, and to our knowledge, has not been studied in the DP literature. Extensive experiments on various practical settings demonstrate that SMM consistently and significantly outperforms existing solutions in terms of the utility of the resulting model.

Recent breakthroughs in Vision-Language (V&L) joint research have achieved remarkable results in various text-driven tasks. High-quality Text-to-video (T2V), a task that has been long considered mission-impossible, was proven feasible with reasonably good results in latest works. However, the resulting videos often have undesired artifacts largely because the system is purely data-driven and agnostic to the physical laws. To tackle this issue and further push T2V towards high-level physical realism, we present an autonomous data generation technique and a dataset, which intend to narrow the gap with a large number of multi-modal, 3D Text-to-Video/Simulation (T2V/S) data. In the dataset, we provide high-resolution 3D physical simulations for both solids and fluids, along with textual descriptions of the physical phenomena. We take advantage of state-of-the-art physical simulation methods (i) Incremental Potential Contact (IPC) and (ii) Material Point Method (MPM) to simulate diverse scenarios, including elastic deformations, material fractures, collisions, turbulence, etc. Additionally, high-quality, multi-view rendering videos are supplied for the benefit of T2V, Neural Radiance Fields (NeRF), and other communities. This work is the first step towards fully automated Text-to-Video/Simulation (T2V/S). Live examples and subsequent work are at https://sites.google.com/view/tpa-net.

Deep neural networks (DNNs) could be very useful in blockchain applications such as DeFi and NFT trading. However, training / running large-scale DNNs as part of a smart contract is infeasible on today's blockchain platforms, due to two fundamental design issues of these platforms. First, blockchains nowadays typically require that each node maintain the complete world state at any time, meaning that the node must execute all transactions in every block. This is prohibitively expensive for computationally intensive smart contracts involving DNNs. Second, existing blockchain platforms expect smart contract transactions to have deterministic, reproducible results and effects. In contrast, DNNs are usually trained / run lock-free on massively parallel computing devices such as GPUs, TPUs and / or computing clusters, which often do not yield deterministic results. This paper proposes novel platform designs, collectively called A New Hope (ANH), that address the above issues. The main ideas are (i) computing-intensive smart contract transactions are only executed by nodes who need their results, or by specialized serviced providers, and (ii) a non-deterministic smart contract transaction leads to uncertain results, which can still be validated, though at a relatively high cost; specifically for DNNs, the validation cost can often be reduced by verifying properties of the results instead of their exact values. In addition, we discuss various implications of ANH, including its effects on token fungibility, sharding, private transactions, and the fundamental meaning of a smart contract.

While the superior performance of second-order optimization methods such as Newton's method is well known, they are hardly used in practice for deep learning because neither assembling the Hessian matrix nor calculating its inverse is feasible for large-scale problems. Existing second-order methods resort to various diagonal or low-rank approximations of the Hessian, which often fail to capture necessary curvature information to generate a substantial improvement. On the other hand, when training becomes batch-based (i.e., stochastic), noisy second-order information easily contaminates the training procedure unless expensive safeguard is employed. In this paper, we adopt a numerical algorithm for second-order neural network training. We tackle the practical obstacle of Hessian calculation by using the complex-step finite difference (CSFD) -- a numerical procedure adding an imaginary perturbation to the function for derivative computation. CSFD is highly robust, efficient, and accurate (as accurate as the analytic result). This method allows us to literally apply any known second-order optimization methods for deep learning training. Based on it, we design an effective Newton Krylov procedure. The key mechanism is to terminate the stochastic Krylov iteration as soon as a disturbing direction is found so that unnecessary computation can be avoided. During the optimization, we monitor the approximation error in the Taylor expansion to adjust the step size. This strategy combines advantages of line search and trust region methods making our method preserves good local and global convergency at the same time. We have tested our methods in various deep learning tasks. The experiments show that our method outperforms exiting methods, and it often converges one-order faster. We believe our method will inspire a wide-range of new algorithms for deep learning and numerical optimization.

We solve a challenging yet practically useful variant of 3D Bin Packing Problem (3D-BPP). In our problem, the agent has limited information about the items to be packed into the bin, and an item must be packed immediately after its arrival without buffering or readjusting. The item's placement also subjects to the constraints of collision avoidance and physical stability. We formulate this online 3D-BPP as a constrained Markov decision process. To solve the problem, we propose an effective and easy-to-implement constrained deep reinforcement learning (DRL) method under the actor-critic framework. In particular, we introduce a feasibility predictor to predict the feasibility mask for the placement actions and use it to modulate the action probabilities output by the actor during training. Such supervisions and transformations to DRL facilitate the agent to learn feasible policies efficiently. Our method can also be generalized e.g., with the ability to handle lookahead or items with different orientations. We have conducted extensive evaluation showing that the learned policy significantly outperforms the state-of-the-art methods. A user study suggests that our method attains a human-level performance.