Sigma simplifies collaboration in economics with a streamlined computational representation.
problem Lack of effective collaboration tools in economics for large-scale projects.
method Introduces Sigma, a domain-specific computational representation for economics based on facets, contributions, and constraints of data.
result Sigma enables sharing and formalizing domain-specific concepts in economics for crowd-based scientific investigations.
RNNs compute by warping neural representations over time.
problem Understanding how RNNs perform task computations.
method Developed a Riemannian geometric framework to derive the manifold topology and geometry of RNNs.
result Dynamic warping is a fundamental feature of RNN computations.
We simplify information measure computation using learned features.
problem Computing information measures from raw data is computationally expensive.
method Developed a separable design for computing information measures from learned feature representations.
result A variety of information measures can be computed efficiently through learned feature representations.
New CR representations are found and shown to be redundant.
problem Identifying and classifying CR representations of 3-manifolds.
method Experimental computation of limit sets and exact computations of triangle groups.
result Many CR representations are redundant and conjugate.
Explores tensor products in hyperdimensional computing.
problem Understanding tensor products in hyperdimensional computing.
method Generalized results from graph embeddings to vector symbolic architectures and hyperdimensional computing.
result Tensor product is the most general and expressive representation with errorless unbinding and detection.
This article reviews statistical methods for learning data representations.
problem Learning meaningful representations of data.
method Statistical perspective on unsupervised and supervised representation learning.
result Recent advances in representation learning from a statistical viewpoint.
Fast algorithm for braid group Hecke representation, applied to knot invariants.
problem Computing topological invariants of knots efficiently.
method Representation-theoretic approach to braid group, leveraging quantum topology.
result Fast algorithm for Hecke representation of braid group, finding non-trivial braids.
InstantEmbedding efficiently generates node representations with less computation and memory.
problem Efficiently generating local node representations for large graphs.
method Local PageRank computations in sublinear time.
result Significantly faster and less memory-intensive than traditional methods.
Symbolic neural network for analyzing and patching complex systems.
problem Analyzing and verifying complex neural networks.
method Symbolic representation of piecewise-linear neural networks for efficient computation.
result Demonstrated applications in weakest preconditions, strongest postconditions, and patching.
Computes dimensions of representation and character varieties for 2 and 3-dimensional orbifolds.
problem Computing dimensions of representation and character varieties for orbifolds.
method Analyzes varieties of representations and characters of hyperbolic and non-hyperbolic orbifolds, provides tools for computation.
result Shows that the dimension of a specific component of characters equals half the dimension of the variety of characters of the boundary.
In this paper we are interested in computing representations of the fundamental group of a 3-manifold into PSL(3;C) (in particular in PSL(2;C); PSL(3;R) and PU(2; 1)). The representations are obtained by gluing decorated tetrahedra of flags. We list complete computations (giving 0-dimensional or 1-dimensional solution …
Researchers compute TQFT representation for sphere with 4 punctures.
problem Computing the representation of mapping class group for a sphere with 4 punctures.
method Non semi-simple TQFT approach, focusing on sphere with 4 punctures.
result The representation is faithful and compared with braid groups.
We give an efficient simplicial formula for the volume and Chern-Simons invariant of a boundary-parabolic PSL(2,C)-representation of a tame 3-manifold. If the representation is the geometric representation of a hyperbolic 3-manifold, our formula computes the volume and Chern-Simons invariant directly from an ideal tria…
New method computes optimal fairness-performance trade-off without complex models.
problem Intrinsic trade-off between fairness and classifier performance.
method Computes optimal Pareto front without training complex models.
result Optimal fair representations have useful structural properties enabling efficient computation.
New method computes knot invariants using free group automorphisms.
problem Computing knot invariants efficiently and accurately.
method Using representations of braid groups by automorphisms of a free group.
result Compared isotopic invariants to Alexander polynomials.
A new framework for information theory considers computational constraints.
problem Understanding information in complex systems with computational limitations.
method Variational extension of Shannon's information theory with computational constraints.
result Predictive V-information can be created through computation and reliably estimated from data. RPS uses graph-based representation learning for better portfolio optimization.
problem Improving portfolio optimization with better returns and lower risks.
method RPS redefines the distance matrix of financial assets using Representation Learning and Clustering algorithms.
result RPS proposes a heuristic to select closer to the optimal subset of assets.
Extends potential function to non-boundary parabolic representations for computing 3-manifold invariants.
problem Computing invariants of 3-manifolds from representations.
method Extends Cho and Murakami's potential function to non-boundary parabolic representations and derives combinatorial formulas.
result Combinatorial formulas for volume and Chern-Simons invariants of 3-manifolds.
A model learns successor representations in uncertain environments.
problem Learning effective strategies in partially observable, noisy environments.
method Neurally plausible model using distributional successor features.
result Distributional successor features support reinforcement learning in noisy environments.
Complete classification of Deligne-Mostow lattice representations into PGL(3,C).
problem Classifying representations of Deligne-Mostow lattices into PGL(3,C).
method Formal computations in SAGE and MAPLE.
result Local rigidity for all representations with chosen generators.
The paper computes characteristic classes for Lie group representations.
problem Computing characteristic classes for Lie group representations.
method The paper outlines a procedure to compute characteristic classes of irreducible representations of Lie groups, expressing them as polynomial functions in the highest weight.
result The paper expresses characteristic classes of Lie group representations as polynomial functions in the highest weight.
MSA compares neural representations' intrinsic geometry for better understanding.
problem Existing similarity measures fail to capture subtle distinctions between neural network solutions.
method Metric similarity analysis (MSA) using Riemannian geometry.
result MSA can disentangle features of neural computations and compare nonlinear dynamics.
Researchers compute determinants and torsions of Rumin complex in specific Lie group representations.
problem Computing determinants and torsions of Rumin complex in specific Lie group representations.
method Analyzing Schrodinger and generic representations of the (2,3,5) nilpotent Lie group.
result Computed the spectrum and zeta regularized determinant of Rumin differentials in Schrodinger representations and evaluated their alternating product in generic representations.
Novel tRSA combines geometry and topology for brain and model analysis.
problem Traditional RSA overlooks topological information in neural representations.
method Topological RSA (tRSA) using nonlinear monotonic transforms.
result Robust model comparisons and novel insights into neural computation.
New computations show sl(N) homology is related to SU(N) representations of knots.
problem Computing colored sl(N) homology for nontrivial knots and links.
method Using SU(N) representations of knot complements, we compute homology and show isomorphisms.
result Colored sl(N) homology is isomorphic to the cohomology of SU(N) representations of knot complements.
Researchers compute cohomology of mapping class groups with Prym representations, showing instability for large genus.
problem Computing the cohomology of mapping class groups with level structures and Prym representations.
method Using twisted cohomology and Prym representations for any positive integer r.
result Cohomology exhibits instability for large genus, but remains stable for r=0 or r=1.
We simplify matrix computations for block matrices, especially useful for covariance and correlation matrices.
problem Complex computations for block matrices, especially for covariance and correlation matrices.
method Obtained a canonical representation for block matrices, facilitating computation of various matrix operations.
result Simplified computation of matrix operations for block matrices, particularly useful for covariance and correlation matrices.
Secure neural network inference on untrusted platforms using holographic reduced representations.
problem Secure neural network inference on untrusted platforms.
method Connectionist Symbolic Pseudo Secrets using Holographic Reduced Representations (HRR).
result Empirical robustness to attack under various threat models.
New method for high-fidelity shape representations from raw data.
problem Creating accurate shape representations from raw data.
method A simple loss function encouraging neural network to vanish on input point cloud and have unit norm gradient.
result Our method produces high-fidelity, smooth, and natural zero level set surfaces.
Proposes a new graph representation method using tensor products.
problem Dynamic graph representation and theoretical properties.
method Bind-and-sum approach in hyperdimensional computing (HDC), tensor product as binding operation.
result Memory vs. size analysis of graph representation size scaling.
Induction of common sense knowledge about prototypical sequences of events has recently received much attention. Instead of inducing this knowledge in the form of graphs, as in much of the previous work, in our method, distributed representations of event realizations are computed based on distributed representations o…
ICLR 2021 challenge in computational geometry and topology attracted 16 teams.
problem Designing and evaluating computational methods in differential geometry and topology.
method Designing and hosting an open-source competition with repositories Geomstats and Giotto-TDA.
result 16 teams participated in the challenge, showcasing innovative contributions to computational geometry and topology.
HAGs eliminate redundant computations in GNNs, improving training efficiency.
problem Redundant computations in GNNs leading to inefficiencies.
method Hierarchically Aggregated computation Graphs (HAGs) to manage and eliminate redundant computations.
result Significant improvement in training efficiency (up to 2.8x) with HAGs.
Proposes a method to learn representations of higher-dimensional simplicial complexes.
problem Lack of methods for representing entire simplicial complexes.
method Geometric message passing schemes for end-to-end learning of simplicial complex representations.
result First method for learning representations of entire simplicial complexes.
INVERT connects neural representations to human-understandable concepts.
problem Lack of understanding and statistical significance in existing explainability methods.
method Inverse Recognition (INVERT) approach that connects learned representations to human-understandable concepts.
result INVERT provides interpretable metrics and statistical significance for representation alignment.
Can we effectively learn a nonlinear representation in time comparable to linear learning? We describe a new algorithm that explicitly and adaptively expands higher-order interaction features over base linear representations. The algorithm is designed for extreme computational efficiency, and an extensive experimental …
Computes the decomposition of rank-three bundles over the projective line with three marked points.
problem Decomposing rank-three bundles over the projective line with three marked points.
method Using the monodromy derivative to compute the roots of the bundles.
result Computes the exact decomposition of rank-three bundles for m=3. New metrics for Anosov representations defined from Thurston's asymmetric metrics.
problem Defining metrics for Anosov representations.
method Generalizing Thurston's asymmetric metric to Anosov representations.
result Provides a (possibly asymmetric) Finsler distance in some cases.
NodeSig efficiently computes binary node embeddings for scalable graph analysis.
problem Scalability issues in graph representation learning models.
method NodeSig uses random walk diffusion probabilities and stable random projections to compute binary node embeddings efficiently.
result NodeSig achieves a good balance between accuracy and efficiency on node classification and link prediction tasks.
New methods compare neural network models using geometric and topological summaries.
problem Comparing deep representations of complex networks in models and brains.
method Develops inference methods based on topological data analysis (TDA) and graph-based techniques.
result New statistical methods enable better model comparison and inference.
Computes cohomological invariants of 3-manifold representations.
problem Computing cohomological invariants for 3-manifold representations.
method Defines and extends a pairing to 3-manifolds with corners, establishes a gluing law, and provides a surgery method.
result Computes Chern-Simons invariant for 3-manifolds via surgery.
FILDNE learns dynamic graph embeddings efficiently.
problem Learning node embeddings on evolving graphs.
method Integrates static graph learning methods into dynamic graphs using convex combination and alignment.
result FILDNE reduces memory and computational costs while improving downstream task performance.
AUC-spec optimizes graph-based SSL for complex label distributions.
problem Training accurate models with scarce labeled data and abundant unlabeled data.
method Computes a low-dimensional representation that maximizes class separation via AUC optimization.
result AUC-spec achieves competitive results on synthetic and real-world datasets.
New Alexander invariant classes computed for knot group representations.
problem Computing Alexander invariants for knot group representations.
method Introducing a new K1-class and comparing it with existing classes. result Showed a relation to Reidemeister torsions and reciprocity.
For a compact 3-manifold N with non-empty boundary, Zickert gave a combinatorial formula for computing the volume and Chern-Simons invariant of a boundary parabolic representation π1(N)→PSL(2,C). In this paper, we introduce a notion of deformed Ptolemy varieties and extend the formula …
The paper proves properties of quantum representations and their Toledo invariants.
problem Proving properties of quantum representations and their Toledo invariants.
method Computing Toledo invariants for specific quantum representations and extending the concept to a series of cohomological invariants.
result The proof of properties of quantum representations and their Toledo invariants, including the computation of the R-matrix at first order. EC^2-VAE generates music analogies by disentangling pitch and rhythm representations.
problem Disentangling music representations for generating creative analogies.
method Explicitly-constrained variational autoencoder (EC^2-VAE) for disentangling pitch and rhythm representations.
result EC^2-VAE enables the generation of music analogies by borrowing representations from different pieces.
Algorithm simplifies computing knot invariants for weaving knots.
problem Computing the trace of Hecke algebra elements for knot invariants.
method Developed an algorithm and Mathematica program to compute Hecke algebra traces.
result Computed invariants for weaving knots and explored their topological/geometric relationships.