Drinfel'd used associators to construct families of universal representations of braid groups. We consider semi-associators (i.e., we drop the pentagonal axiom and impose a normalization in degree one). We show that the process may be reversed, to obtain semi-associators from universal representations of 3-braids. We v…
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48 results for “universal representation”
Study extends Vogel's universality to torus knots in adjoint representation.
problem Applying Vogel's universality to knot invariants in adjoint representation theory.
method Extending Vogel's parameters to include torus knots and focusing on with odd .
result Unified description of adjoint invariants for torus knots with odd .
We present a universal knot polynomials for 2- and 3-strand torus knots in adjoint representation, by universalization of appropriate Rosso-Jones formula. According to universality, these polynomials coincide with adjoined colored HOMFLY and Kauffman polynomials at SL and SO/Sp lines on Vogel's plane, and give their ex…
Based on the analogies between knot theory and number theory, we study a deformation theory for SL_2-representations of knot groups, following after Mazur's deformation theory of Galois representations. Firstly, by employing the pseudo-SL_2-representations, we prove the existence of the universal deformation of a given…
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.
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.
Universal connection constructed using diffeology theory.
problem Natural connection on bundles of paths on manifolds.
method Diffeological construction of Singer's universal connection.
result Functorial equivalence between holonomy categories and diffeological bundle-connection pairs.
We study the twisted knot module for the universal deformation of an -representation of a knot group, and introduce an associated -function, which may be seen as an analogue of the algebraic -adic -function associated to the Selmer module for the universal deformation of a Galois representation. We…
By now it is well established that the quantum dimensions of descendants of the adjoint representation can be described in a universal form, independent of a particular family of simple Lie algebras. The Rosso-Jones formula then implies a universal description of the adjoint knot polynomials for torus knots, which in p…
Sharp lower bound on GHHs' representation power of CPWL functions.
problem Proving the minimum number of nestings for GHHs to represent arbitrary CPWL functions.
method Using a key lemma about finite sums of periodic functions, proving necessity of n nestings.
result Proving necessity of n nestings for GHHs to achieve universal representation power.
This research classifies singular foliations and finds a universal deformation.
problem Classifying singular foliations on .
method Topological universal deformation through fixed invariants.
result Every equisingular deformation uniquely factors through the topological universal deformation.
This paper fine-tunes LLMs for stock return prediction using financial news.
problem Improving stock return forecasting accuracy using LLMs.
method Fine-tuning LLMs with text and forecasting modules, comparing encoder-only and decoder-only models, and integrating token-level representations.
result LLMs' aggregated token-level embeddings enhance return predictions for long-only and long-short portfolios.
CF-INNs can approximate any invertible function, resolving a long-standing problem.
problem Whether CF-INNs can approximate any invertible function.
method Demonstrated CF-INNs are universal approximators for invertible functions by showing a convenient criterion.
result CF-INNs are universal approximators for invertible functions.
URT layer improves few-shot image classification across diverse domains.
problem Few-shot image classification in multi-domain settings.
method Meta-learns to dynamically re-weight and compose domain-specific representations.
result Sets new state-of-the-art on Meta-Dataset.
Refines a tangle invariant using XC-algebras.
problem Building a refined tangle invariant using XC-algebras.
method Constructing a canonical strict monoidal functor that refines the Kerler-Kauffman-Radford invariant.
result Preserves the braiding, twist, and open trace.
Derives adjoint polynomials of torus knots in explicit form.
problem Understanding adjoint invariants of torus knots.
method Closed-form double sum expression derivation.
result Explicit double sum form of adjoint polynomials.
INNs can approximate diverse functions despite layer restrictions.
problem Can INNs approximate sufficiently diverse functions?
method Developed a theoretical framework based on differential geometry to simplify the approximation problem of diffeomorphisms.
result INNs have the universal approximation property.
Unified theorem for deep and shallow joint-equivariant machines.
problem Universal approximation of joint-equivariant machines.
method Constructive universal approximation theorem based on ridgelet transform.
result Unified approximation of deep and shallow networks.
The paper proves impossibilities and positive results for universal machine translation.
problem Learning shared sentence representations across multiple language pairs.
method Formal proofs and analysis of natural generative processes.
result Lower bound on translation error and positive results under natural structure.
This paper describes a language representation model which combines the Bidirectional Encoder Representations from Transformers (BERT) learning mechanism described in Devlin et al. (2018) with a generalization of the Universal Transformer model described in Dehghani et al. (2018). We further improve this model by addin…
When a bilingual student learns to solve word problems in math, we expect the student to be able to solve these problem in both languages the student is fluent in,even if the math lessons were only taught in one language. However, current representations in machine learning are language dependent. In this work, we pres…
G5 universal GRAPH-BERT learns graph representations across different datasets.
problem Learning graph representations across diverse graph datasets with distinct input and output configurations.
method G5 introduces a pluggable model architecture with input and output components for each graph data source, connected via a unified layer and fusion layer.
result G5 removes obstacles for cross-graph representation learning and transfer, even for sparse data.
We investigate how one can twist L^2-invariants such as L^2-Betti numbers and L^2-torsion with finite-dimensional representations. As a special case we assign to the universal covering of a finite connected CW-complex X together with an element phi in H^1(X;R) a phi-twisted L^2-torsion function from R^{>0} to R, provid…
We prove universality theorems ("Murphy's Laws") for representation schemes of fundamental groups of closed 3-dimensional manifolds. We show that germs of SL(2,C)-representation schemes of such groups are essentially the same as germs of schemes of over rational numbers.
Deep Ridgelet Transform: Voice with Koopman Operator Proves Universality of Formal Deep Networkscs.LG
Deep neural networks are proven universally powerful using Koopman operator.
problem Proving the universality of deep neural networks.
method Formal deep network as a dual voice transform with Koopman operator, using group actions and Schur's lemma.
result Simple proof of the universality of DNNs.
We present a simple proof for the universality of invariant and equivariant tensorized graph neural networks. Our approach considers a restricted intermediate hypothetical model named Graph Homomorphism Model to reach the universality conclusions including an open case for higher-order output. We find that our proposed…
The objective of transfer reinforcement learning is to generalize from a set of previous tasks to unseen new tasks. In this work, we focus on the transfer scenario where the dynamics among tasks are the same, but their goals differ. Although general value function (Sutton et al., 2011) has been shown to be useful for k…
SNNs can represent complex functions efficiently.
problem Understanding the representational power of SNNs.
method Viewed as sequence-to-sequence processors, analyzed using spike train functions.
result SNNs have the universal representation property for certain functions.
The universal approximation property of various machine learning models is currently only understood on a case-by-case basis, limiting the rapid development of new theoretically justified neural network architectures and blurring our understanding of our current models' potential. This paper works towards overcoming th…
With the advent of large labelled datasets and high-capacity models, the performance of machine vision systems has been improving rapidly. However, the technology has still major limitations, starting from the fact that different vision problems are still solved by different models, trained from scratch or fine-tuned o…
Study presents a method to induce a generalized neural network from joint group invariant functions.
problem Encoding rule of neural network internal data representation.
method Systematic method using joint group invariant function on data-parameter domain.
result Induces a generalized neural network and its inverse operator (ridgelet transform).
We prove geometric and cohomological stabilization results for the universal smooth degree hypersurface section of a fixed smooth projective variety as goes to infinity. We show that relative configuration spaces of the universal smooth hypersurface section stabilize in the completed Grothendieck ring of variet…
The abstract proves the existence of universal lottery tickets without needing further training.
problem The existence of universal sparse subnetworks in large neural networks.
method Theoretical proofs and technical innovations in pruning and subset sum results.
result Universal tickets exist and do not require further training.
We derive the quantum Teichmüller space, previously constructed by Kashaev and by Fock and Chekhov, from tensor products of a single canonical representation of the modular double of the quantum plane. We show that the quantum dilogarithm function appears naturally in the decomposition of the tensor square, the quantum…
Identifiable Energy-based Representations: An Application to Estimating Heterogeneous Causal Effectscs.LG
EBM reduces dimensionality for estimating heterogeneous CATEs.
problem Estimating CATEs requires many confounding variables, increasing sample complexity.
method Proposes an EBM that learns a low-dimensional representation of variables.
result EBM representations keep CATE estimates consistent and perform better than other methods.
The book explains deep learning theory and how networks learn nontrivial representations.
problem Understanding and optimizing deep neural networks.
method Developed RG flow to characterize signal propagation, solved layer-to-layer equations, and analyzed representation learning.
result Predictions of trained networks are nearly-Gaussian, with depth-to-width ratio controlling deviations.
We present a data-driven framework for learning fair universal representations (FUR) that guarantee statistical fairness for any learning task that may not be known a priori. Our framework leverages recent advances in adversarial learning to allow a data holder to learn representations in which a set of sensitive attri…
We prove that there are no nontrivial finite-dimensional Lie representations of certain Poisson algebras of polynomials on a compact symplectic manifold. This result is used to establish the existence of a universal obstruction to quantizing a compact symplectic manifold, regardless of the dimensionality of the represe…
This work establishes universality for deep equivariant networks, overcoming limitations of previous approaches.
problem Rarity of universality results for equivariant neural networks, especially in high-dimensional settings.
method Develops a more general account of universality for equivariant networks, introducing entry-wise separability and readout layers.
result Deep equivariant networks achieve universality under entry-wise separability, with or without readout layers.
The study characterizes quasiperiodic surfaces in pseudo-hyperbolic spaces with curvature conditions.
problem Characterizing quasiperiodic surfaces in pseudo-hyperbolic spaces.
method Curvature conditions, Gromov hyperbolicity, conformal hyperbolicity.
result Limit curves of quasiperiodic surfaces in the Einstein Universe have canonical quasisymmetric parametrizations.
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.
In this paper, we show that a simple coloring scheme can improve, both theoretically and empirically, the expressive power of Message Passing Neural Networks(MPNNs). More specifically, we introduce a graph neural network called Colored Local Iterative Procedure (CLIP) that uses colors to disambiguate identical node att…
Study non-acyclic SL2-representations of twist knots and their L-functions.
problem Characterize SL2-representations of twist knots and their properties.
method Character variety, Reidemeister torsion, Chebyshev polynomials, and L-functions.
result Non-acyclic SL2-representations lie on the line x=y in character variety, and their orders are related to (-3)-Dehn surgery.
A key challenge in complex visuomotor control is learning abstract representations that are effective for specifying goals, planning, and generalization. To this end, we introduce universal planning networks (UPN). UPNs embed differentiable planning within a goal-directed policy. This planning computation unrolls a for…
We construct a certain cross product of two copies of the braided dual of a quasitriangular Hopf algebra , which we call the elliptic double , and which we use to construct representations of the punctured elliptic braid group extending the well-known representations of the planar braid group attache…
Universal approximations of permutation invariant/equivariant functions by deep neural networkscs.LG
In this paper, we develop a theory about the relationship between -invariant/equivariant functions and deep neural networks for finite group . Especially, for a given -invariant/equivariant function, we construct its universal approximator by deep neural network whose layers equip -actions and each affine t…
Improves shared encoder representations for better multi-task learning performance.
problem Improving quality of shared encoder representations in multi-task learning.
method Dummy Gradient norm Regularization (DGR) to decrease gradient norm of dummy task-specific predictors.
result DGR improves multi-task prediction performances and superior performance compared to existing methods.
New neural architectures invariant to sign flips and basis symmetries for graph representation learning.
problem Learning invariant graph representations from eigenvectors.
method SignNet and BasisNet neural architectures that are invariant to sign flips and basis symmetries.
result Proven to be universal, approximating any continuous function of eigenvectors with desired invariances.