Survey on computational models in dynamical systems, including new universality concepts.
problem Understanding the relationship between computational models and dynamical systems.
method Review of recent works on Turing universality, Topological Kleene Field Theories, and dynamical bordisms.
result Introduction of new perspectives on computability through dynamical systems.
The Navier-Stokes equations on certain manifolds can perform universal computation.
problem Computational universality in viscous fluids.
method Cosymplectic geometry and harmonic 1-forms.
result Stationary Navier-Stokes solutions exhibit Turing completeness.
Stochastic reservoir computing is shown to be a universal approximator.
problem Theoretical justification for using stochastic reservoirs in machine learning.
method Investigated stochastic reservoir computing using probabilities of reservoir states as readout.
result Stochastic reservoir computers are universal approximating classes.
Revives Vogel's diagrammatic technique for universal Lie algebra computations.
problem The universality of Lie algebra quantities remains open, despite many being described.
method Diagrammatic algebra based on Vogel's Λ-algebra.
result Diagrammatic technique enables truly universal computations in Lie theory.
We present an algorithm for computing class-specific universal adversarial perturbations for deep neural networks. Such perturbations can induce misclassification in a large fraction of images of a specific class. Unlike previous methods that use iterative optimization for computing a universal perturbation, the propos…
New non-semisimple Ising anyons enable robust universal quantum computation.
problem Limitation of semisimple theories in universal topological quantum computation.
method Developed non-semisimple Ising anyon model with new anyon types indexed by α. result Robust universality of braiding persists over an open interval of α. We prove that the universal Teichmuller space T(1) carries a new structure of a complex Hilbert manifold. We show that the connected component of the identity of T(1), the Hilbert submanifold T_{0}(1), is a topological group. We define a Weil-Petersson metric on T(1) by Hilbert space inner products on tangent spaces, c…
Paper calculates stable cohomology of universal degree d hypersurfaces.
problem Computing stable cohomology of universal degree d hypersurfaces.
method Uses stable cohomology and geometric description of stable classes.
result Geometric description of stable classes of universal degree d hypersurfaces.
Simple construction for universal quantum gates.
problem Designing efficient quantum gates for topological computers.
method Demonstrated a simple construction for unitary solutions of the braided Yang-Baxter equation in any dimension.
result Proved the existence of universal quantum gates in any dimension.
We study the natural Kähler metrics on moduli spaces of stable oriented pairs in a very general framework, and we prove a universal formula expressing the Kähler class of such a moduli space in terms of characteristic classes of the universal bundle. We use these results to compute explicitly the volumina of certain Qu…
We show that the topological modular functor from Witten-Chern-Simons theory is universal for quantum computation in the sense a quantum circuit computation can be efficiently approximated by an intertwining action of a braid on the functor's state space. A computational model based on Chern-Simons theory at a fifth ro…
New derivation of knot invariants from universal invariant.
problem Deriving knot invariants from universal invariant.
method Using Hopf algebra D and a Mathematica implementation to compute ZD(K). result Derivation of large-color expansion from universal invariant.
We compute the rational cohomology of the universal family of smooth cubic surfaces using Vassiliev's method of simplicial resolution. Modulo embedding, the universal family has cohomology isomorphic to that of P2. A consequence of our theorem is that over the finite field Fq, away from finitely…
In this paper, we analyze the Bollobás and Riordan polynomial R for ribbon graphs with half-ribbons introduced in [Combinatorics, Probability and Computing 31, 507-549, 2022]. We prove the universality property of a multivariate version of R whereas R itself turns out to be universal…
We give a new and simple proof for the computation of the oriented and the unoriented fold cobordism groups of Morse functions on surfaces. We also compute similar cobordism groups of Morse functions based on simple stable maps of 3-manifolds into the plane. Furthermore, we show that certain cohomology classes associat…
Survey of universal portfolio techniques for minimizing investment regret.
problem Minimizing investment regret in algorithmic trading.
method Explains various universal portfolio techniques and their proofs.
result Coverage of fundamental concepts and algorithms in regret minimization.
Path signatures adapted for Lie groups improve action recognition in computer vision.
problem Improving action recognition in computer vision with geometric constraints.
method Lifting path signatures to Lie groups and proving universality and characteristic property.
result Path signatures on Lie groups provide comparable performance to shallow learning approaches in action recognition.
Deep networks have recently been shown to be vulnerable to universal perturbations: there exist very small image-agnostic perturbations that cause most natural images to be misclassified by such classifiers. In this paper, we propose the first quantitative analysis of the robustness of classifiers to universal perturba…
A new method inflates and deflates data manifolds to estimate densities without losing universality.
problem Density estimation on low-dimensional manifolds with non-Euclidean support.
method Inflation-deflation approach using Normalizing Flows with added noise.
result Exact estimation of densities on manifolds with sufficient conditions and Gaussian noise approximation.
Given a biquandle (X,S), a function τ with certain compatibility and a pair of {\em non commutative cocyles} f,h:X×X→G with values in a non necessarily commutative group G, we give an invariant for singular knots / links. Given (X,S,τ), we also define a universal group Uncfh(X) and universa…
MAT combines meta-learning and adversarial training to defend against universal patches.
problem Defending against universal patches that fool models in various contexts.
method Meta adversarial training (MAT) integrates meta-learning with adversarial training.
result MAT increases robustness against universal patch attacks on image classification and traffic-light detection.
Estimating symmetric properties of a distribution, e.g. support size, coverage, entropy, distance to uniformity, are among the most fundamental problems in algorithmic statistics. While each of these properties have been studied extensively and separate optimal estimators are known for each, in striking recent work, Ac…
Large-scale deep neural networks are both memory intensive and computation-intensive, thereby posing stringent requirements on the computing platforms. Hardware accelerations of deep neural networks have been extensively investigated in both industry and academia. Specific forms of binary neural networks (BNNs) and sto…
Given a state-of-the-art deep neural network classifier, we show the existence of a universal (image-agnostic) and very small perturbation vector that causes natural images to be misclassified with high probability. We propose a systematic algorithm for computing universal perturbations, and show that state-of-the-art …
Optical ESNs enable flexible, efficient machine learning with reduced energy.
problem Implementing universal computational capabilities in machine learning.
method Optical implementation of ESNs leveraging stimulated Brillouin scattering.
result Efficient, scalable, and memory-capable optical reservoir computing.
Simple technique turns any adversarial attack into a universal one using few test examples.
problem Creating universal adversarial attacks with minimal data.
method Universalization technique using few adversarial test examples and spectral properties.
result Simple universalization technique achieves comparable fooling rates to state-of-the-art methods.
Dubrovin duality connects two F-manifolds on the universal curve.
problem Connecting two F-manifolds on the universal curve.
method Proving natural extension of Dubrovin dual to F-manifolds with compatible flat connection.
result Equips the universal curve with two F-manifolds with compatible flat structure.
Prototype rules simplify multiclass classification in metric spaces, achieving consistency and reduced complexity.
problem Multiclass classification in metric spaces, focusing on universal consistency and convergence rates.
method Novel Proto-NN and hybrid rules for multiclass classification in metric spaces, analyzing convergence rates.
result Proto-NN is universally consistent and simpler to implement, with similar computational advantages.
Sumformer simplifies Transformers to handle long sequences efficiently.
problem Quadratic complexity of Transformers limits their use with long sequences.
method Introducing Sumformer, a simple architecture that universally approximates equivariant sequence-to-sequence functions.
result Sumformer achieves the first universal approximation results for Linformer and Performer.
Given a state-of-the-art deep neural network text classifier, we show the existence of a universal and very small perturbation vector (in the embedding space) that causes natural text to be misclassified with high probability. Unlike images on which a single fixed-size adversarial perturbation can be found, text is of …
Proves a formula for push-forward of polynomial Chern forms in universal vector bundles.
problem Positivity of characteristic forms in vector bundles.
method Explicit computation of Chern curvature and use of flag bundles.
result Positivity of polynomials in Chern forms for Griffiths semipositive bundles.
The study of linguistic typology is rooted in the implications we find between linguistic features, such as the fact that languages with object-verb word ordering tend to have post-positions. Uncovering such implications typically amounts to time-consuming manual processing by trained and experienced linguists, which p…
Enhances generative models by improving expressivity without high computational cost.
problem Improving expressivity in generative models without increasing computational complexity.
method Proposes a new family of generative flows on an augmented data space, proving they can approximate a Hamiltonian ODE as a universal transport map.
result Demonstrates state-of-the-art performance on flow-based generative modeling benchmarks.
New method for curvature computation in sub-Riemannian geometry.
problem Computing curvature in sub-Riemannian manifolds.
method Using compatible affine connections and induced tensors.
result Universal Bonnet-Myers theorem for sub-Riemannian geometry.
ELF simplifies normalizing flows, making them more efficient and universal.
problem Computational inefficiency of normalizing flows.
method ELF introduces a simple, one-layer network with closed-form Lipschitz constants, combining the ease of residual flows with the performance of autoregressive flows.
result ELF is a provably universal density approximator, more efficient computationally and parameter-wise.
New universal automorphic functions capture monstrous moonshine.
problem Developing a universal framework for automorphic functions.
method Reformulating old results, constructing new coordinates, and defining central extensions.
result New invariant 1-forms and representations for universal Teichmüller space.
The paper presents a chain complex for 3-manifold covers, including surface bundles and surgeries.
problem Calculating linking forms and Dijkgraaf-Witten invariants for specific 3-manifold covers.
method Presentation of cellular chain complexes for universal covers of 3-manifolds in a specified class.
result Established a formula for linking forms and developed procedures for Dijkgraaf-Witten invariants.
The paper studies orbifold splice quotients and log covers of surface pairs.
problem Understanding orbifold splice quotients and log covers of surface pairs.
method Analyzes orbifold homology and constructs pairs with universal abelian log covers.
result Computes orbifold homology from resolutions and constructs orbifold splice quotients.
Physics: Similar long-distance properties can mask vastly different short-distance metrics.
problem Classifying homogeneous metrics on group manifolds by long-distance properties.
method Apply universality concept to geometry, focusing on metrics on Lie groups.
result Many metrics on low-dimensional Lie groups have similar long-distance properties despite differing short-distance properties.
Estimates means in metric spaces using quantization.
problem No practical estimator for Fréchet means in all metric spaces.
method Introduced estimators based on random quantization and data-driven partitioning.
result Universal consistency of estimators across separable metric spaces and Banach spaces.
A single qubit may be represented on the Bloch sphere or similarly on the 3-sphere S3. Our goal is to dress this correspondence by converting the language of universal quantum computing (UQC) to that of 3-manifolds. A magic state and the Pauli group acting on it define a model of UQC as a positive operator-value…
We show how to use Bar-Natan's `divide and conquer' approach to computations to efficiently compute the universal sl(2) dotted foam cohomology groups, even for big knots and links. We also describe a purely topological version of the sl(2) foam theory, in the sense that no dots are needed on foams.
Paper relaxes symmetry conditions for universal feature selection in noisy data.
problem Feature selection in noisy data with weak symmetry.
method Developed a universal feature selection framework using singular value decomposition of canonical dependence matrix.
result Selected features achieve asymptotically optimal error exponents up to a residual term.
The paper introduces surface signatures for irregular surfaces and rough surfaces.
problem Characterizing and integrating highly irregular paths and surfaces.
method Introducing surface signatures and proving extension theorems.
result Surface signatures are universal for surface holonomy and rough surfaces.
Transformers can approximate any sequence-to-sequence function, surprising given their complexity.
problem Understanding the expressive power of Transformer models for sequence-to-sequence functions.
method Established that Transformers are universal approximators of continuous permutation equivariant sequence-to-sequence functions with compact support, and extended this to arbitrary functions using positional encodings.
result Transformers are universal approximators of arbitrary continuous sequence-to-sequence functions on a compact domain.
A new machine-learned CG model predicts protein structures efficiently.
problem Developing a universal, computationally efficient protein simulation model.
method Combining deep learning with all-atom protein simulations to create a transferable CG force field.
result The model predicts protein structures, intermediates, and fluctuations efficiently.
Quantum reservoir computing tackles noisy quantum computers for temporal tasks.
problem Efficiently process input sequences on noisy quantum computers.
method Quantum reservoir computing using dissipative quantum dynamics.
result Small and noisy quantum reservoirs can handle high-order nonlinear temporal tasks.
We present a universal algorithm for online trading in Stock Market which performs asymptotically at least as good as any stationary trading strategy that computes the investment at each step using a fixed function of the side information that belongs to a given RKHS (Reproducing Kernel Hilbert Space). Using a universa…