arXiv research

Sharp lower bound on GHHs' representation power of CPWL functions.

Graph Neural Networks outperform the Weisfeiler-Lehman algorithm in representation power.

INNs can approximate diverse functions despite layer restrictions.

Extended quantum state result for gl_n weight systems.

We present a layered Boltzmann machine (BM) that can better exploit the advantages of a distributed representation. It is widely believed that deep BMs (DBMs) have far greater representational power than its shallow counterpart, restricted Boltzmann machines (RBMs). However, this expectation on the supremacy of DBMs ov…

Graph Neural Networks (GNNs) are an effective framework for representation learning of graphs. GNNs follow a neighborhood aggregation scheme, where the representation vector of a node is computed by recursively aggregating and transforming representation vectors of its neighboring nodes. Many GNN variants have been pro…

The paper explores mapping class group quotients by Dehn twists and their representations.

Study shows limits of certain normalizing flows in higher dimensions.

Unified data representation learning improves non-parametric two-sample testing.

This paper gives a connection between well chosen reductions of the Links-Gould invariants of oriented links and powers of the Alexander-Conway polynomial. We prove these formulas by showing the representations of the braid groups we derive the specialized Links-Gould polynomials from can be seen as exterior powers of …

In the context of stochastic volatility models, we study representation formulas in terms of expectations for the power series' coefficients associated to the call price-function. As in a recent paper by Antonelli and Scarlatti the expansion is done w.r.t. the correlation between the noises driving the underlying asset…

This work generalizes graph neural networks (GNNs) beyond those based on the Weisfeiler-Lehman (WL) algorithm, graph Laplacians, and diffusions. Our approach, denoted Relational Pooling (RP), draws from the theory of finite partial exchangeability to provide a framework with maximal representation power for graphs. RP …

Unified representation of density-power-based divergences simplifies estimation to M-estimation.

Bi-directional LSTMs are a powerful tool for text representation. On the other hand, they have been shown to suffer various limitations due to their sequential nature. We investigate an alternative LSTM structure for encoding text, which consists of a parallel state for each word. Recurrent steps are used to perform lo…

New method tests conditional independence using spectral representations.

MMD-B-Fair learns fair representations by minimizing MMD test power.

We use Nathanson's $g$-adic representation of integers to relate metric properties of Cayley graphs of the integers with respect to various infinite generating sets $S$ to problems in additive number theory. If $S$ consists of all powers of a fixed integer $g$, we find explicit formulas for the smallest positive intege…

Study forward investment performance in semimartingale markets with stochastic factors.

Modified group captures braid dynamics, revealing Burau kernel.

Graph neural networks (GNNs) are a powerful tool to learn representations on graphs by iteratively aggregating features from node neighbourhoods. Many variant models have been proposed, but there is limited understanding on both how to compare different architectures and how to construct GNNs systematically. Here, we p…

Graph neural networks improve topology control of power grids.

Learning disentangled representation from any unlabelled data is a non-trivial problem. In this paper we propose Information Maximising Autoencoder (InfoAE) where the encoder learns powerful disentangled representation through maximizing the mutual information between the representation and given information in an unsu…

We give criteria for real, complex and quaternionic representations to define s-representations, focusing on exceptional Lie algebras defined by spin representations. As applications, we obtain the classification of complex representations whose second exterior power is irreducible or has an irreducible summand of co-d…

To deepen our understanding of graph neural networks, we investigate the representation power of Graph Convolutional Networks (GCN) through the looking glass of graph moments, a key property of graph topology encoding path of various lengths. We find that GCNs are rather restrictive in learning graph moments. Without c…

Study on kernels of SO(3) WRT representations for surfaces of genus g≥3.

Latent representations are the essence of deep generative models and determine their usefulness and power. For latent representations to be useful as generative concept representations, their latent space must support latent space interpolation, attribute vectors and concept vectors, among other things. We investigate …

The beta-Bernoulli process provides a Bayesian nonparametric prior for models involving collections of binary-valued features. A draw from the beta process yields an infinite collection of probabilities in the unit interval, and a draw from the Bernoulli process turns these into binary-valued features. Recent work has …

Chemical representations derived from deep learning are emerging as a powerful tool in areas such as drug discovery and materials innovation. Currently, this methodology has three major limitations - the cost of representation generation, risk of inherited bias, and the requirement for large amounts of data. We propose…

There is general consensus that learning representations is useful for a variety of reasons, e.g. efficient use of labeled data (semi-supervised learning), transfer learning and understanding hidden structure of data. Popular techniques for representation learning include clustering, manifold learning, kernel-learning,…

Value functions struggle to represent transition dynamics, impacting statistical efficiency.

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…

UNTIE learns representations of coupled categorical data.

Defines complexity measure for neural networks and feature representations, revealing scaling patterns.

Instantly interprets black-box models using additive models.

DE improves GNNs by distinguishing graph substructures, enhancing accuracy.

Bayesian method models multivalued power data from wind farms.

Topo-MLP learns network representations without message passing.

We present state sums for quantum link invariants arising from the representation theory of $U_q(\mathfrak{gl}_{N|M})$. We investigate the case of the $N$-th exterior power of the standard representation of $U_q(\mathfrak{gl}_{N|1})$ and explicit the relation with Kashaev invariants.

This work improves independence tests for high-dimensional data.

Study genus-three Torelli maps and their fixed point sets in representation varieties.

Proposes GAAE for high-fidelity audio generation and representation learning.

Study compares different levels of supervision for training graph embeddings in wireless networks.

We construct an explicit categorification of the action of tangles on tensor powers of the fundamental representation of quantum sl(2).

GNNs learn graph representations, with new theory on their power and limitations.

We define a family of the braid group representations via the action of the $R$-matrix (of the quasitriangular extension) of the restricted quantum $\mathfrak{sl}(2)$ on a tensor power of a simple projective module. This family is an extension of the Lawrence representation specialized at roots of unity. Although the c…

The paper computes characteristic classes for Lie group representations.

We provide analytical tools for pricing power options with exotic features (capped or log payoffs, gap options ...) in the framework of exponential Lévy models driven by one-sided stable or tempered stable processes. Pricing formulas take the form of fast converging series of powers of the log-forward moneyness and of …

We consider infinite dimensional port-Hamiltonian systems. Based on a power balance relation we introduce the port-Hamiltonian system representation where we pay attention to two different scenarios, namely the non-differential operator case and the differential operator case regarding the structural mapping, the dissi…