arXiv subjects

Itay Griniasty

Publications and source records attributed to Itay Griniasty.

17 recordsLinked to original sources

arXiv2026

Multistable energy landscapes for adaptive microscopic machines

The past few years have seen great strides in our ability to build synthetic microscopic machines. However, the function of such machines is often controlled directly by externally applied fields that deterministically specify the instantaneous machine dynamics. A crucial step towards machines that can respond adaptively to changes in their environment is the ability to program multiple functions that actuate under the same external driving field, so that their internal state dictates which function is executed. Here, we demonstrate that energy landscapes with designed multistability enable the same externally applied field to drive multiple configurations and dynamic responses in microscopic machines, enabling increasing levels of autonomy. We show three examples. First, we write a bistable energy landscape into a microscopic device, enabling the device to exhibit two stable mechanical configurations under the same external magnetic field. Next, adding a second degree of freedom enables differing dynamic responses to the same external magnetic field, which we direct into net displacement of the environment. Finally, we demonstrate how a microscopic machine with a continuous symmetry autonomously channels a single degree-of-freedom magnetic actuation into locomotion and adaptively responds to forces induced by other machines.

cond-mat.soft↗

arXiv2025

An Analytical Characterization of Sloppiness in Neural Networks: Insights from Linear Models

Recent experiments have shown that training trajectories of multiple deep neural networks with different architectures, optimization algorithms, hyper-parameter settings, and regularization methods evolve on a remarkably low-dimensional "hyper-ribbon-like" manifold in the space of probability distributions. Inspired by the similarities in the training trajectories of deep networks and linear networks, we analytically characterize this phenomenon for the latter. We show, using tools in dynamical systems theory, that the geometry of this low-dimensional manifold is controlled by (i) the decay rate of the eigenvalues of the input correlation matrix of the training data, (ii) the relative scale of the ground-truth output to the weights at the beginning of training, and (iii) the number of steps of gradient descent. By analytically computing and bounding the contributions of these quantities, we characterize phase boundaries of the region where hyper-ribbons are to be expected. We also extend our analysis to kernel machines and linear models that are trained with stochastic gradient descent.

cs.LG↗

arXiv2024

Programming evolution of geometry in shape-morphing sheets via spatiotemporal activation

Shape-programmed sheets morph from one surface into another upon activation by stimuli such as illumination, and have attracted much interest for their potential engineering applications, especially in soft robotics. Complex shape changes can be achieved by patterning a simple local active deformation (e.g. isotropic swelling), to generate differential growth. Usually the material itself is designed $\unicode{x2014}$ for example by patterning a molecular director $\unicode{x2014}$ such that a particular shape change occurs upon exposure to a spatially uniform stimulus. A limitation of this paradigm is that typically only one target geometry can be attained as the stimulus is adjusted. Here we show that this limitation can be overcome by patterning the stimulus itself, thereby exercising spatiotemporal control over local deformation magnitudes. Thus a single physical sample can be induced to traverse a continuous family of target geometries, opening the door to precise shape adjustments, new functionalities, and designable non-reciprocal loops in shape space. We illustrate these possibilities with examples including active parabolic reflectors, chiral flow guides, and bending channels. Finding the necessary patterns of activation involves solving families of metric inverse problems; we solve these by reduction to ODEs in an axisymmetric setting, then present a novel numerical scheme to solve them in generality.

cond-mat.soft↗

arXiv2024

The Training Process of Many Deep Networks Explores the Same Low-Dimensional Manifold

We develop information-geometric techniques to analyze the trajectories of the predictions of deep networks during training. By examining the underlying high-dimensional probabilistic models, we reveal that the training process explores an effectively low-dimensional manifold. Networks with a wide range of architectures, sizes, trained using different optimization methods, regularization techniques, data augmentation techniques, and weight initializations lie on the same manifold in the prediction space. We study the details of this manifold to find that networks with different architectures follow distinguishable trajectories but other factors have a minimal influence; larger networks train along a similar manifold as that of smaller networks, just faster; and networks initialized at very different parts of the prediction space converge to the solution along a similar manifold.

cs.LG↗

arXiv2023

A picture of the space of typical learnable tasks

We develop information geometric techniques to understand the representations learned by deep networks when they are trained on different tasks using supervised, meta-, semi-supervised and contrastive learning. We shed light on the following phenomena that relate to the structure of the space of tasks: (1) the manifold of probabilistic models trained on different tasks using different representation learning methods is effectively low-dimensional; (2) supervised learning on one task results in a surprising amount of progress even on seemingly dissimilar tasks; progress on other tasks is larger if the training task has diverse classes; (3) the structure of the space of tasks indicated by our analysis is consistent with parts of the Wordnet phylogenetic tree; (4) episodic meta-learning algorithms and supervised learning traverse different trajectories during training but they fit similar models eventually; (5) contrastive and semi-supervised learning methods traverse trajectories similar to those of supervised learning. We use classification tasks constructed from the CIFAR-10 and Imagenet datasets to study these phenomena.

cs.LG↗

arXiv2023

Universal scaling of shear thickening transitions

Nearly all dense suspensions undergo dramatic and abrupt thickening transitions in their flow behaviour when sheared at high stresses. Such transitions occur when the dominant interactions between the suspended particles shift from hydrodynamic to frictional. Here, we interpret abrupt shear thickening as a precursor to a rigidity transition and give a complete theory of the viscosity in terms of a universal crossover scaling function from the frictionless jamming point to a rigidity transition associated with friction, anisotropy, and shear. Strikingly, we find experimentally that for two different systems -- cornstarch in glycerol and silica spheres in glycerol -- the viscosity can be collapsed onto a single universal curve over a wide range of stresses and volume fractions. The collapse reveals two separate scaling regimes, due to a crossover between frictionless isotropic jamming and frictional shear jamming, with different critical exponents. The material-specific behaviour due to the microscale particle interactions is incorporated into a scaling variable governing the proximity to shear jamming that depends on both stress and volume fraction. This reformulation opens the door to importing the vast theoretical machinery developed to understand equilibrium critical phenomena to elucidate fundamental physical aspects of the shear thickening transition.

cond-mat.soft↗

arXiv2023

Bifurcation instructed design of multistate machines

We propose a novel design paradigm for multistate machines where transitions from one state to another are organized by bifurcations of multiple equilibria of the energy landscape describing the collective interactions of the machine components. This design paradigm is attractive since, near bifurcations, small variations in a few control parameters can result in large changes to the system's state providing an emergent lever mechanism. Further, the topological configuration of transitions between states near such bifurcations ensures robust operation, making the machine less sensitive to fabrication errors and noise. To design such machines, we develop and implement a new efficient algorithm that searches for interactions between the machine components that give rise to energy landscapes with these bifurcation structures. We demonstrate a proof of concept for this approach by designing magneto elastic machines whose motions are primarily guided by their magnetic energy landscapes and show that by operating near bifurcations we can achieve multiple transition pathways between states. This proof of concept demonstration illustrates the power of this approach, which could be especially useful for soft robotics and at the microscale where typical macroscale designs are difficult to implement.

cond-mat.soft↗

arXiv2022

Discontinuous metric programming in liquid crystalline elastomers

Liquid crystalline elastomers (LCEs) are shape-changing materials that exhibit large deformations in response to applied stimuli. Local control of the orientation of LCEs spatially directs the deformation of these materials to realize spontaneous shape change in response to stimuli. Prior approaches to shape programming in LCEs utilize patterning techniques that involve the detailed inscription of spatially varying nematic fields to produce sheets. These patterned sheets deform into elaborate geometries with complex Gaussian curvatures. Here, we present an alternative approach to realize shape-morphing in LCEs where spatial patterning of the crosslink density locally regulates the material deformation magnitude on either side of a prescribed interface curve. We also present a simple mathematical model describing the behavior of these materials. Further experiments coupled with the mathematical model demonstrate the control of the sign of Gaussian curvature, which is used in combination with heat transfer effects to design LCEs that self-clean as a result of temperature-dependent actuation properties.

cond-mat.soft↗

arXiv2022

Incorporating tunability into a universal scaling framework for shear thickening

Recently, we proposed a universal scaling framework that shows shear thickening in dense suspensions is governed by the crossover between two critical points: one associated with frictionless isotropic jamming and a second corresponding to frictional shear jamming. Here, we show that orthogonal perturbations to the flows, an effective method for tuning shear thickening, can also be folded into this universal scaling framework. Specifically, we show that the effect of adding in orthogonal shear perturbations (OSP) can be incorporated by simply altering the scaling variable to include a multiplicative term that decreases with the normalized OSP strain rate. These results demonstrate the broad applicability of our scaling framework, and illustrate how it can be modified to incorporate other complex flow fields.

cond-mat.soft↗

arXiv2021

Multi-valued inverse design: multiple surface geometries from one flat sheet

Designing flat sheets that can be made to deform into 3D shapes is an area of intense research with applications in micromachines, soft robotics, and medical implants. Thus far, such sheets were designed to adopt a single target shape. Here, we show that through anisotropic deformation applied inhomogenously throughout a sheet, it is possible to design a single sheet that can deform into multiple surface geometries upon different actuations. The key to our approach is development of an analytical method for solving this multi-valued inverse problem. Such sheets open the door to fabricating machines that can perform complex tasks through cyclic transitions between multiple shapes. As a proof of concept we design a simple swimmer capable of moving through a fluid at low Reynolds numbers.

cond-mat.soft↗

arXiv2020

Explicit symmetric DGLA models of 3-cells

We give explicit formulae for differential graded Lie algebra (DGLA) models of 3-cells. In particular, for a cube and an $n$-faceted banana-shaped 3-cell with two vertices, $n$ edges each joining those two vertices and $n$ bi-gon 2-cells, we construct a model symmetric under the geometric symmetries of the cell fixing two antipodal vertices. The cube model is to be used in forthcoming work for discrete analogues of differential geometry on cubulated manifolds.

math.AT↗

arXiv2019

Curved geometries from planar director fields - Solving the two-dimensional inverse problem

Thin nematic elastomers, composite hydrogels and plant tissues are among many systems that display uniform anisotropic deformation upon external actuation. In these materials, the spatial orientation variation of a local director field induces intricate global shape changes. Despite extensive recent efforts, to date, there is no general solution to the inverse design problem: how to design a director field that deforms exactly into a desired surface geometry upon actuation, or whether such a field exists. In this work, we phrase this inverse problem as a hyperbolic system of differential equations. We prove that the inverse problem is locally integrable, provide an algorithm for its integration, and derive bounds on global solutions. We classify the set of director fields that deform into a given surface, thus paving the way to finding optimized fields.

cond-mat.soft↗

arXiv2018

An explicit symmetric DGLA model of a triangle

We give explicit formulae for a differential graded Lie algebra (DGLA) model of the triangle which is symmetric under the geometric symmetries of the cell. This follows the work of Lawrence-Sullivan on the (unique) DGLA model of the interval and of Gadish-Griniasty-Lawrence on an explicit symmetric model of the bi-gon. As in the case of the bi-gon, the essential intermediate step is the construction of a symmetric point. Although in this warped geometry of points given by solutions of the Maurer-Cartan equation and lines given by a gauge transformation by Lie algebra elements of grading zero, the medians of a triangle are not concurrent, various other geometric constructions can be carried out. The construction can similarly be applied to give symmetric model of arbitrary $k$-gons.

math.AT↗

arXiv2017

Classical analogue of the Unruh effect

In the Unruh effect an observer with constant acceleration perceives the quantum vacuum as thermal radiation. The Unruh effect has been believed to be a pure quantum phenomenon, but here we show theoretically how the effect arises from the classical correlation of noise. We demonstrate this idea with a simple experiment on water waves where we see the first indications of a Planck spectrum in the correlation energy.

gr-qc↗

arXiv2017

An explicit symmetric DGLA model of a bi-gon

We give explicit formulae for a DGLA model of the bi-gon which is symmetric under the geometric symmetries of the cell. This follows the work of Lawrence-Sullivan on the (unique) DGLA model of the interval and its construction uses deeper knowledge of the structure of such models and their localisations for non-simply connected spaces.

math.AT↗

arXiv2017

Casimir stress inside planar materials

Current theory is able to predict the Casimir force between macroscopic bodies with an accuracy only limited by the knowledge of the material parameters. Yet surprisingly after almost 70 years of research, while theory describes the Casimir force between bodies, the force inside macroscopic bodies is poorly understood. In this paper, we develop from a physically intuitive picture the macroscopic theory of the Casimir stress inside inhomogeneous planar media. Our result agrees with a previous ad hoc procedure [T. G. Philbin et al., Ann. Phys. (New York) 325, 579 (2010)], giving both mathematical and physical justification to a conjecture that was only tested numerically so far. Our theory is likely to be extendable; it may open the gate to the computation of Casimir forces inside arbitrary materials.

quant-ph↗

arXiv2017

Casimir stress in materials: hard divergency at soft walls

The Casimir force between macroscopic bodies is well understood, but not the Casimir stress inside bodies. Suppose empty space or a uniform medium meets a soft wall where the refractive index is continuous but its derivative jumps. For this situation we predict a characteristic power law for the stress inside the soft wall and close to its edges. Our result shows that such edges are not tolerated in the aggregation of liquids at surfaces, regardless whether the liquid is attracted or repelled.

quant-ph↗