A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Explicit computation of Kontsevich weights for symplectic Poisson structures.
New framework for dense weighted networks with community-specific patterns.
New methods train neural networks without changing weights, achieving similar or higher performance.
We show that deep networks can be trained using Hebbian updates yielding similar performance to ordinary back-propagation on challenging image datasets. To overcome the unrealistic symmetry in connections between layers, implicit in back-propagation, the feedback weights are separate from the feedforward weights. The f…
Graded bundles are a particularly nice class of graded manifolds and represent a natural generalisation of vector bundles. By exploiting the formalism of supermanifolds to describe Lie algebroids we define the notion of a weighted -connection on a graded bundle. In a natural sense weighted -connections are adapte…
Proves non-positivity of Hirzebruch form on stable weights and connects to flat logarithmic connections.
In this paper we study sectional curvature bounds for Riemannian manifolds with density from the perspective of a weighted torsion free connection introduced recently by the last two authors. We develop two new tools for studying weighted sectional curvature bounds: a new weighted Rauch comparison theorem and a modifie…
This paper is concerned with the sparsification of the input-hidden weights of ELM (Extreme Learning Machine). For ordinary feedforward neural networks, the sparsification is usually done by introducing certain regularization technique into the learning process of the network. But this strategy can not be applied for E…
Proposes neuron alignment to optimize mode connectivity in neural networks.
In this work, we extend the SchNet architecture by using weighted skip connections to assemble the final representation. This enables us to study the relative importance of each interaction block for property prediction. We demonstrate on both the QM9 and MD17 dataset that their relative weighting depends strongly on t…
A new kernel measures brain network similarities, improving disease classification.
Paper proves a sharp weighted Isoperimetric inequality for substatic manifolds.
Connections between nodes of fully connected neural networks are usually represented by weight matrices. In this article, functional transfer matrices are introduced as alternatives to the weight matrices: Instead of using real weights, a functional transfer matrix uses real functions with trainable parameters to repre…
New algorithm detects communities in weighted networks, improving on binary ones.
New bounds for convex clustering under graph connectivity.
Normal forms and moduli stacks for flat connections on complex manifolds.
We prove structure theorems for complete manifolds satisfying both the Ricci curvature lower bound and the weighted Poincaré inequality. In the process, a sharp decay estimate for the minimal positive Green's function is obtained. This estimate only depends on the weight function of the Poincaré inequality, and yields …
A model explains credit assignment in deep learning networks.
We prove several results about chordal graphs and weighted chordal graphs by focusing on exposed edges. These are edges that are properly contained in a single maximal complete subgraph. This leads to a characterization of chordal graphs via deletions of a sequence of exposed edges from a complete graph. Most interesti…
We show that the Teukolsky connection, which defines generalized wave operators governing the behavior of massless fields on Einstein spacetimes of Petrov type D, has its origin in a distinguished conformally and GHP covariant connection on the conformal structure of the spacetime. The conformal class has a (metric com…
A method of simultaneously optimizing both the structure of neural networks and the connection weights in a single training loop can reduce the enormous computational cost of neural architecture search. We focus on the probabilistic model-based dynamic neural network structure optimization that considers the probabilit…
New method connects neural networks to diagrammatic algebra.
We show that the skip-gram formulation of word2vec trained with negative sampling is equivalent to a weighted logistic PCA. This connection allows us to better understand the objective, compare it to other word embedding methods, and extend it to higher dimensional models.
Functional connections in the brain are frequently represented by weighted networks, with nodes representing locations in the brain, and edges representing the strength of connectivity between these locations. One challenge in analyzing such data is that inference at the individual edge level is not particularly biolog…
The paper finds upper bounds for eigenvalues of a weighted Laplacian.
New loss function connects learning rate and momentum.
This work is a continuation of the former paper in which principal bundles are given by compact spin toric manifolds and compact connected semisimple Lie groups. In this paper, ambient manifolds are assumed to be compact toric manifolds and Lie groups are compact connected. The main result is that locally smooth manifo…
New duality found linking neural network weights and activities for better generalization.
Study connects weighted isoperimetric problems to nonlocal elliptic operator extensions.
Study preserves metrics with positive Bakry-Émry Ricci curvature via surgery.
Currents on cusped hyperbolic surfaces have a denseness property similar to compact surfaces.
Real-world machine learning applications often have complex test metrics, and may have training and test data that are not identically distributed. Motivated by known connections between complex test metrics and cost-weighted learning, we propose addressing these issues by using a weighted loss function with a standard…
A new model clusters network nodes based on relative edge weights.
Recent work on mode connectivity in the loss landscape of deep neural networks has demonstrated that the locus of (sub-)optimal weight vectors lies on continuous paths. In this work, we train a neural network that serves as a hypernetwork, mapping a latent vector into high-performance (low-loss) weight vectors, general…
The paper computes characteristic classes for Lie group representations.
We present a Bayesian formulation of weighted stochastic block models that can be used to infer the large-scale modular structure of weighted networks, including their hierarchical organization. Our method is nonparametric, and thus does not require the prior knowledge of the number of groups or other dimensions of the…
We show that from an even degree symplectic NQ-manifold, whose homological vector field Q preserves the symplectic form, one can construct a weight system for tri-valent graphs with values in the Q-cohomology ring, satisfying the IHX relation. Likewise, given a representation of the homological vector field, one can co…
Motivated by a remark and a question of Nicholas Katz, we characterize the tangent space of the space of Fuchsian equations with given generic exponents inside the corresponding moduli space of logarithmic connections: we construct a weight 1 Hodge structure on the tangent space of the moduli of logarithmic connections…
The paper generalizes a Steklov eigenvalue inequality for substatic triples under non-negative Ricci curvature.
On a manifold with a projective connection we canonically assign a second order differential operator acting on the algebra of all densities to any tensor density of fixed weight . In particular, this implies that on any projectively connected manifold, a `bracket' (symmetric biderivation) on the algebra of…
Bayesian priors for neural networks are improved by incorporating weight correlations and tail behavior.
SGD and weight decay encourage neural networks to learn low-rank weight matrices.
The paper connects neural collapse and low-rank bias in networks with L2 regularization.
Study shapes of 3D bounded domains using Morse height functions and Reeb graphs.
Gradient descent with random weights in linear regression analyzed for various noise types.
The study connects minimal and maximal surfaces in 3D and 3-L space.
Residual connections significantly boost the performance of deep neural networks. However, there are few theoretical results that address the influence of residuals on the hypothesis complexity and the generalization ability of deep neural networks. This paper studies the influence of residual connections on the hypoth…
Low-rank structure emerges in neural networks during learning.