Neural Information Processing Systems http://nips.cc/

Although the multi-jointed underactuated manipulator is highly dexterous, its grasping capacity does not match that of the parallel jaw gripper. This work introduces a fractal gripper to enhance the grasping capacity of multi-joint underactuated manipulators, preserving their passive clamping features. We describe in detail the working principle and manufacturing process of the fractal gripper. This work, inspired by the 'Fractal Vise' structure, resulted in the invention of a fractal gripper with mode switching capabilities. The fractal gripper inherits the inherent adaptive properties of the fractal structure and realizes the self-resetting function by integrating spring into the original design, thereby enhancing the efficiency of object grasping tasks. The fractal gripper prevents object damage by distributing pressure evenly and applying it at multiple points through its fractal structure during closure. Objects of various shapes are effectively grasped by the fractal gripper, which ensures a safe and secure grasp. The superior performance was provided by the force distribution characteristics of the fractal gripper. By applying the flexible polymer PDMS, which possesses superior elasticity, to the fractal structure's wrapping surface, potential scratching during grasping is effectively prevented, thus protecting the object's geometric surface. Grab experiments with objects of diverse shapes and sizes confirm fractal gripper multi-scale adaptability and superior grasping stability.

We propose a novel stochastic network model, called Fractal Gaussian Network (FGN), that embodies well-defined and analytically tractable fractal structures. Such fractal structures have been empirically observed in diverse applications. FGNs interpolate continuously between the popular purely random geometric graphs (a.k.a. the Poisson Boolean network), and random graphs with increasingly fractal behavior. In fact, they form a parametric family of sparse random geometric graphs that are parametrized by a fractality parameter $\nu$ which governs the strength of the fractal structure. FGNs are driven by the latent spatial geometry of Gaussian Multiplicative Chaos (GMC), a canonical model of fractality in its own right. We asymptotically characterize the expected number of edges and triangle in FGNs. We then examine the natural question of detecting the presence of fractality and the problem of parameter estimation based on observed network data, in addition to fundamental properties of the FGN as a random graph model. We also explore fractality in community structures by unveiling a natural stochastic block model in the setting of FGNs.

This may come as a surprise because computers seem like they can understand time series data. After all, aren't self-driving cars, AlphaStar and recurrent neural networks all evidence that today's ML can handle time series data? Self-driving cars use a hybrid of ML and procedural programming. ML (statistical programming) handles the low-level stuff like recognizing pedestrians. Procedural (nonstatistical) programming handles high-level stuff like navigation.

Understanding the power of depth in feed-forward neural networks is an ongoing challenge in the field of deep learning theory. While current works account for the importance of depth for the expressive power of neural-networks, it remains an open question whether these benefits are exploited during a gradient-based optimization process. In this work we explore the relation between expressivity properties of deep networks and the ability to train them efficiently using gradient-based algorithms. We give a depth separation argument for distributions with fractal structure, showing that they can be expressed efficiently by deep networks, but not with shallow ones. These distributions have a natural coarse-to-fine structure, and we show that the balance between the coarse and fine details has a crucial effect on whether the optimization process is likely to succeed. We prove that when the distribution is concentrated on the fine details, gradient-based algorithms are likely to fail. Using this result we prove that, at least in some distributions, the success of learning deep networks depends on whether the distribution can be well approximated by shallower networks, and we conjecture that this property holds in general.