arXiv research

Improves dialogue response model interpretability using attention and regularization.

The paper explores how AI systems use information geometry to encode semantic structure.

We introduce self-dual manifolds and show that they can be used to encode mirror symmetry for affine-Kähler manifolds and for elliptic curves. Their geometric properties, especially the link with special lagrangian fibrations and the existence of a transformation similar to the Fourier-Mukai functor, suggest that this …

New construction of self-dual black holes using quadrics.

This paper constructs Koszul duals for Heegaard Floer Dehn surgery formulas.

The local kinematic formulas on complex space forms induce the structure of a commutative algebra on the space $\mathrm{Curv}^{\mathrm{U}(n)*}$ of dual unitarily invariant curvature measures. Building on the recent results from integral geometry in complex space forms, we describe this algebra structure explicitly as a…

C-VAE improves VAE by resolving prior issues and generating better samples.

The Nonlinear autoregressive exogenous (NARX) model, which predicts the current value of a time series based upon its previous values as well as the current and past values of multiple driving (exogenous) series, has been studied for decades. Despite the fact that various NARX models have been developed, few of them ca…

We propose a new architecture called Memory-Augmented Encoder-Solver (MAES) that enables transfer learning to solve complex working memory tasks adapted from cognitive psychology. It uses dual recurrent neural network controllers, inside the encoder and solver, respectively, that interface with a shared memory module a…

A new deep learning framework selects representative samples for unsupervised learning.

We prove that higher moment maps on area measures of a euclidean vector space are injective, while the kernel of the centroid map equals the image of the first variation map. Based on this, we introduce the space of smooth dual area measures on a finite-dimensional euclidean vector space and prove that it admits a natu…

Machine-assisted treatment recommendations hold a promise to reduce physician time and decision errors. We formulate the task as a sequence-to-sequence prediction model that takes the entire time-ordered medical history as input, and predicts a sequence of future clinical procedures and medications. It is built on the …

Free differential algebras (FDA's) provide an algebraic setting for field theories with antisymmetric tensors. The "presentation" of FDA's generalizes the Cartan-Maurer equations of ordinary Lie algebras, by incorporating p-form potentials. An extended Lie derivative along antisymmetric tensor fields can be defined, an…

How to generate human like response is one of the most challenging tasks for artificial intelligence. In a real application, after reading the same post different people might write responses with positive or negative sentiment according to their own experiences and attitudes. To simulate this procedure, we propose a s…

Graph representation learning embeds nodes in large graphs as low-dimensional vectors and is of great benefit to many downstream applications. Most embedding frameworks, however, are inherently transductive and unable to generalize to unseen nodes or learn representations across different graphs. Although inductive app…

We introduce Primal-Dual Wasserstein GAN, a new learning algorithm for building latent variable models of the data distribution based on the primal and the dual formulations of the optimal transport (OT) problem. We utilize the primal formulation to learn a flexible inference mechanism and to create an optimal approxim…

One of the core tasks in multi-view learning is to capture relations among views. For sequential data, the relations not only span across views, but also extend throughout the view length to form long-term intra-view and inter-view interactions. In this paper, we present a new memory augmented neural network model that…

GPs with neural network dual kernels improve reinforcement learning performance.

Graph convolutional networks (GCNs) have shown the powerful ability in text structure representation and effectively facilitate the task of text classification. However, challenges still exist in adapting GCN on learning discriminative features from texts due to the main issue of graph variants incurred by the textual …

We consider sphere bundles P and P' of totally null planes of maximal dimension and opposite self-duality over a 4-dimensional manifold equipped with a Weyl or Riemannian geometry. The fibre product PP' of P and P' is found to be appropriate for the encoding of both the selfdual and the Einstein-Weyl equations for the …

Unified MTL framework for heterogeneous data integrates shared and task-specific encoders.

Paper tackles class-incremental time series classification with dual-stream feature extraction.

Proposes a secure communication method independent of eavesdropper's decoder.

This paper undertakes a study of the structure of the fibers of the Chevalley exponentiation maps $f_{(i_1,\dots ,i_d)}$. The fibers of these maps $f_{(i_1,\dots ,i_d)}$ encode the nonnegative real relations amongst exponentiated Chevalley generators. Our main theorems show that the fibers admit cell stratifications, t…

This paper proposes an embedding-based neural network for more accurate investment return prediction.

We study integrable non-degenerate Monge-Ampere equations of Hirota type in 4D and demonstrate that their symmetry algebras have a distinguished graded structure, uniquely determining the equations. This is used to deform these heavenly type equations into new integrable PDE of the second order with large symmetry pseu…

Capacity control, the bias/variance dilemma, and learning unknown functions from data, are all concerned with identifying effective and consistent fits of unknown geometric loci to random data points. A geometric locus is a curve or surface formed by points, all of which possess some uniform property. A geometric locus…

We uncover and highlight relations between the M-branes in M-theory and various topological invariants: the Hopf invariant over $\mathbb{Q}$, $\mathbb{Z}$ and $\mathbb{Z}_2$, the Kervaire invariant, the $f$-invariant, and the $ν$-invariant. This requires either a framing or a corner structure. The canonical framing pro…

New tensors reveal full curvature structure from Riemann tensor.

Unsupervised anomaly detection aims to identify anomalous samples from highly complex and unstructured data, which is pervasive in both fundamental research and industrial applications. However, most existing methods neglect the complex correlation among data samples, which is important for capturing normal patterns fr…

Introduces Legendre bundle for dually flat manifolds and quantum field theories.

Symplectic homology matches dual capacities for convex domains.

We discuss relations between quantum BPS invariants defined in terms of a product decomposition of certain series, and difference equations (quantum A-polynomials) that annihilate such series. We construct combinatorial models whose structure is encoded in the form of such difference equations, and whose generating fun…

Motivated by recent developments in the AdS/CFT correspondence, we provide several alternative bulk descriptions of an arbitrary Wilson loop operator in Chern-Simons theory. Wilson loop operators in Chern-Simons theory can be given a description in terms of a configuration of branes or alternatively anti-branes in the …

Dual-edge spatial Jacobian image graph for interpretable diabetic retinopathy grading

This paper studies the interplay between the N=2 gauge theories in three and four dimensions that have a geometric description in terms of twisted compactification of the six-dimensional (2,0) SCFT. Our main goal is to construct the three-dimensional domain walls associated to any three-dimensional cobordism. We find t…

Graph clustering, aiming to partition nodes of a graph into various groups via an unsupervised approach, is an attractive topic in recent years. To improve the representative ability, several graph auto-encoder (GAE) models, which are based on semi-supervised graph convolution networks (GCN), have been developed and th…

Four-dimensional quaternion-Kahler metrics, or equivalently self-dual Einstein spaces M, are known to be encoded locally into one real function h subject to Przanowski's Heavenly equation. We elucidate the relation between this description and the usual twistor description for quaternion-Kahler spaces. In particular, w…

Study presents a method to induce a generalized neural network from joint group invariant functions.

Systemic risk measures are crucial for the stability of financial markets, yet classical formulations fail to capture the complexity of market volatility. We propose a new framework for systemic risk measurement on the variable-exponent Bochner-Lebesgue space $L^{p(\cdot)}$, where the exponent $p(\cdot)$ is a random va…

CardiCat generates synthetic data for high-cardinality tabular datasets.

New DG method minimizes barycentric alignment and reconstruction loss.

iWGAN improves GANs by stabilizing training and preventing mode collapse.

Paper develops efficient estimator for Hawkes processes using representer theorem.

Study reveals LLM personas have two distinct components: frame-robust aggregated traits and frame-dependent geometric features.

engGNN combines external and generated graphs to improve disease classification and biomarker discovery.

Since the introduction of Generative Adversarial Networks (GANs) and Variational Autoencoders (VAE), the literature on generative modelling has witnessed an overwhelming resurgence. The impressive, yet elusive empirical performance of GANs has lead to the rise of many GAN-VAE hybrids, with the hopes of GAN level perfor…

Infinitesimal calculations link fundamental groups to Lie algebras.