Simulating collisions of deformable objects is a fundamental yet challenging task due to the complexity of modeling solid mechanics and multi-body interactions. Existing data-driven methods often suffer from lack of equivariance to physical symmetries, inadequate handling of collisions, and limited scalability. Here we introduce EqCollide, the first end-to-end equivariant neural fields simulator for deformable objects and their collisions. We propose an equivariant encoder to map object geometry and velocity into latent control points. A subsequent equivariant Graph Neural Network-based Neural Ordinary Differential Equation models the interactions among control points via collision-aware message passing. To reconstruct velocity fields, we query a neural field conditioned on control point features, enabling continuous and resolution-independent motion predictions. Experimental results show that EqCollide achieves accurate, stable, and scalable simulations across diverse object configurations, and our model achieves 24.34% to 35.82% lower rollout MSE even compared with the best-performing baseline model. Furthermore, our model could generalize to more colliding objects and extended temporal horizons, and stay robust to input transformed with group action.

Traditional AI algorithms, such as Genetic Programming and Reinforcement Learning, often require extensive computational resources to simulate real-world physical scenarios effectively. While advancements in multi-core processing have been made, the inherent limitations of parallelizing rigid body dynamics lead to significant communication overheads, hindering substantial performance gains for simple simulations. This paper introduces NeoPhysIx, a novel 3D physical simulator designed to overcome these challenges. By adopting innovative simulation paradigms and focusing on essential algorithmic elements, NeoPhysIx achieves unprecedented speedups exceeding 1000x compared to real-time. This acceleration is realized through strategic simplifications, including point cloud collision detection, joint angle determination, and friction force estimation. The efficacy of NeoPhysIx is demonstrated through its application in training a legged robot with 18 degrees of freedom and six sensors, controlled by an evolved genetic program. Remarkably, simulating half a year of robot lifetime within a mere 9 hours on a single core of a standard mid-range CPU highlights the significant efficiency gains offered by NeoPhysIx. This breakthrough paves the way for accelerated AI development and training in physically-grounded domains.

Casting manipulation has been studied to expand the robot's movable range. In this manipulation, the robot throws and reaches the end effector to a distant target. Usually, a special casting manipulator, which consists of rigid arm links and specific flexible linear objects, is constructed for an effective casting manipulation. However, the special manipulator cannot perform normal manipulations, such as picking and placing, grasping, and operating objects. We propose that the normal robot arm, which can perform normal tasks, picks up an unknown string in the surrounding environment and realizes casting manipulation with it. As the properties of the string are not provided in advance, it is crucial how to reflect it in casting manipulation. This is realized by the motion generation of the robot arm with the simulation of string movement, actual string manipulation by the robot arm, and string parameter estimation from the actual string movement. After repeating these three steps, the simulated string movement approximates the actual to realize casting manipulation with the unknown string. We confirmed the effectiveness of the proposed method through experiments. The try of this study will lead to enhancement of the performance of home service robot, exploration robot, rescue robot and entertainment robot.

Recently, several methods have been proposed for estimating the mutual information from sample data using deep neural networks. These estimators ar referred to as neural mutual information estimation (NMIE)s. NMIEs differ from other approaches as they are data-driven estimators. As such, they have the potential to perform well on a large class of capacity problems. In order to test the performance across various NMIEs, it is desirable to establish a benchmark encompassing the different challenges of capacity estimation. This is the objective of this paper. In particular, we consider three scenarios for benchmarking: (i) the classic AWGN channel, (ii) channels continuous inputs - optical intensity and peak-power constrained AWGN channel (iii) channels with a discrete output-i.e., Poisson channel. We also consider the extension to the multi-terminal case with (iv) the AWGN and optical MAC models. We argue that benchmarking a certain NMIE across these four scenarios provides a substantive test of performance. In this paper we study the performance of mutual information neural estimator (MINE), smoothed mutual information lower-bound estimator (SMILE), and directed information neural estimator (DINE). To summarize our benchmarking results, MINE provides the most reliable performance. Determining the capacity of a channel and the optimal input distribution are problems of fundamental importance in communication scenarios of practical relevance. The value of capacity and the optimal input distribution provide critical insight on the choice of coding rates and input constellation shape, respectively.

A common way of characterizing minimax estimators in point estimation is by moving the problem into the Bayesian estimation domain and finding a least favorable prior distribution. The Bayesian estimator induced by a least favorable prior, under mild conditions, is then known to be minimax. However, finding least favorable distributions can be challenging due to inherent optimization over the space of probability distributions, which is infinite-dimensional. This paper develops a dimensionality reduction method that allows us to move the optimization to a finite-dimensional setting with an explicit bound on the dimension. The benefit of this dimensionality reduction is that it permits the use of popular algorithms such as projected gradient ascent to find least favorable priors. Throughout the paper, in order to make progress on the problem, we restrict ourselves to Bayesian risks induced by a relatively large class of loss functions, namely Bregman divergences.

The normalized maximized likelihood (NML) provides the minimax regret solution in universal data compression, gambling, and prediction, and it plays an essential role in the minimum description length (MDL) method of statistical modeling and estimation. Here we show that the normalized maximum likelihood has a Bayes-like representation as a mixture of the component models, even in finite samples, though the weights of linear combination may be both positive and negative. This representation addresses in part the relationship between MDL and Bayes modeling. This representation has the advantage of speeding the calculation of marginals and conditionals required for coding and prediction applications.