AutoCross automatically generates feature interactions for tabular data.
problem Capturing interactions among categorical features in tabular data.
method Beam search in a tree-structured space, successive mini-batch gradient descent, multi-granularity discretization.
result Significantly enhances performance of linear and deep models.
GACAN combines multi-granularity time series for traffic forecasting.
problem High dynamics and complex spatial-temporal dependency of road networks in traffic forecasting.
method Graph Attention-Convolution-Attention Networks (GACAN) with Att-Conv-Att (ACA) block.
result GACAN outperforms state-of-the-art baselines in traffic forecasting.
The clustering ensemble technique aims to combine multiple clusterings into a probably better and more robust clustering and has been receiving an increasing attention in recent years. There are mainly two aspects of limitations in the existing clustering ensemble approaches. Firstly, many approaches lack the ability t…
Develops MgCSL for discovering causal structures in high-dimensional data.
problem Discovering causal relationships from high-dimensional data with complex interplay of variables.
method MgCSL uses sparse auto-encoders for coarse-graining and multi-layer perceptrons for detailed analysis, introducing simplified acyclicity constraints.
result MgCSL outperforms existing methods and finds explainable causal connections in fMRI datasets.
SGQuant reduces GNN memory usage without significant accuracy loss.
problem High memory consumption in GNNs limits their applicability on memory-constrained devices.
method Proposes a specialized GNN quantization scheme (SGQuant) with a quantization algorithm, fine-tuning scheme, and multi-granularity strategy.
result SGQuant reduces GNN memory footprint from 4.25x to 31.9x with minimal accuracy loss.
Nested learning improves model performance on multi-granular tasks.
problem Overconfident models and lack of fine-grained confidence in predictions.
method Introducing nested learning with a sequence of nested feature embeddings and explicit combination of outputs.
result Nested learning outperforms standard end-to-end training on various datasets.
In regression problems, the use of TSK fuzzy systems is widely extended due to the precision of the obtained models. Moreover, the use of simple linear TSK models is a good choice in many real problems due to the easy understanding of the relationship between the output and input variables. In this paper we present FRU…
Deep learning (DL) defines a new data-driven programming paradigm that constructs the internal system logic of a crafted neuron network through a set of training data. We have seen wide adoption of DL in many safety-critical scenarios. However, a plethora of studies have shown that the state-of-the-art DL systems suffe…
ATMSeer improves AutoML by making it more transparent and controllable.
problem Users distrust automatic AutoML results and increase search budgets.
method Interactive visualization tool to refine search space and analyze results.
result ATMSeer enhances efficiency and user trust in AutoML.
Conditional Random Fields (CRFs) are undirected graphical models, a special case of which correspond to conditionally-trained finite state machines. A key advantage of these models is their great flexibility to include a wide array of overlapping, multi-granularity, non-independent features of the input. In face of thi…
Aspect-level sentiment classification (ASC) aims at identifying sentiment polarities towards aspects in a sentence, where the aspect can behave as a general Aspect Category (AC) or a specific Aspect Term (AT). However, due to the especially expensive and labor-intensive labeling, existing public corpora in AT-level are…
Paper tackles many-class few-shot learning with class hierarchy, improving accuracy.
problem Many-class few-shot learning problem in practical applications.
method Leverages class hierarchy to train a coarse-to-fine classifier using memory-augmented hierarchical-classification network (MahiNet).
result MahiNet outperforms state-of-the-art models on MCFS problems in both supervised and meta-learning settings.
New discrete models for constant mean curvature surfaces and tori.
problem Creating discrete models for constant mean curvature surfaces and tori.
method Integrable theory of discrete polarised curves and Darboux transforms.
result Closed-form discrete parametrisations of discrete isothermic cylinders, discrete constant mean curvature cylinders, and discrete isothermic tori.
Simple constructions of semi-discrete and discrete surfaces using Jacobi elliptic functions.
problem Constructing semi-discrete and discrete surfaces explicitly.
method Using Jacobi elliptic functions and τ-functions.
result Explicit constructions and periodicities of semi-discrete and discrete surfaces.
The study classifies singularities in discrete improper affine spheres.
problem Classifying singularities in discrete improper affine spheres.
method Analysis of discrete improper affine spheres based on asymptotic nets, distinguishing singular edges and vertices.
result First step in classifying singularities of discrete nets.
Our aim in this paper is to provide a theory of discrete Riemann surfaces based on quadrilateral cellular decompositions of Riemann surfaces together with their complex structure encoded by complex weights. Previous work, in particular of Mercat, mainly focused on real weights corresponding to quadrilateral cells havin…
Operational guide to discrete exterior calculus on cubic cells.
problem Applying calculus on discrete manifolds.
method Defining discrete exterior calculus on cubic cells for discrete manifolds.
result Gauss and Stokes theorems are recovered on the discrete torus.
We introduce the discrete Einstein metrics as critical points of discrete energy on triangulated 3-manifolds, and study them by discrete curvature flow of second (fourth) order. We also study the convergence of the discrete curvature flow. Discrete curvature flow of second order is an analogue of smooth Ricci flow.
New method solves discrete mKdV equation from curve motions.
problem Solving the discrete potential mKdV equation.
method Discrete Darboux transformation.
result Efficient route to discrete mKdV equation.
This paper explores geometric insights into discrete R-congruences and their envelopes.
problem Understanding the ambiguity in discrete R-congruences and their envelopes.
method Analyzes discrete R-congruences that are enveloped by specific types of surfaces and maps.
result Discovers a 2-parameter family of discrete enveloping surfaces for discrete R-congruences.
Permutability of surface transforms yields discrete analogs.
problem Discretization of smooth surfaces with specific properties.
method Permutability of transforms of smooth surfaces.
result Discrete surfaces with discrete analogs of original properties.
New representations for discrete surfaces derived from dual transforms.
problem Constructing discrete surfaces in differential geometry.
method Using Ω-dual transform and lightlike Gauss maps in Laguerre geometry. result All discrete linear Weingarten surfaces arise via Weierstrass-type representations.
In this paper, we consider the discrete deformation of the discrete space curves with constant torsion described by the discrete mKdV or the discrete sine-Gordon equations, and show that it is formulated as the torsion-preserving equidistant deformation on the osculating plane which satisfies the isoperimetric conditio…
Study on discrete surfaces with constant principal curvature for nanocarbon applications.
problem Understanding discrete geometry properties of nanocarbon materials.
method Developed discrete surface theory on 3-ary oriented trees, defined discrete principal directions, constructed examples of discrete CPC surfaces.
result Construction of discrete constant principal curvature surfaces, including discrete CPC tori.
We construct explicit solutions to continuous motion of discrete plane curves described by a semi-discrete potential modified KdV equation. Explicit formulas in terms the τ function are presented. Bäcklund transformations of the discrete curves are also discussed. We finally consider the continuous limit of discrete …
The paper introduces discrete Dirac structures for mechanics, simplifying dynamics.
problem Formulating discrete mechanics with constraints.
method Developed (±)-discrete Dirac structures and induced Dirac structures. result Discrete Lagrange--Dirac systems are equivalent to (±)-discrete Lagrange--d'Alembert equations. New method linearizes Darboux transformations of discrete curves.
problem Linearizing Darboux transformations of discrete curves.
method Expressing Darboux transformations as parallel sections of discrete connections in quaternionic formalism.
result Closed-form discrete parametrisations of all Darboux transforms and bicycle correspondences.
We obtain a unified theory of discrete minimal surfaces based on discrete holomorphic quadratic differentials via a Weierstrass representation. Our discrete holomorphic quadratic differential are invariant under Möbius transformations. They can be obtained from discrete harmonic functions in the sense of the cotangent …
Paper proposes a new generative model for discrete distributions using flows on submanifolds.
problem Discretization issues and complex statistical dependencies in discrete data.
method Continuous normalizing flows on factorizing discrete measures, geodesic flow matching.
result Efficient training and broad applicability demonstrated through experiments.
In this paper, we introduce a parameterized discrete curvature (α-curvature) for piecewise linear metrics on polyhedral surfaces, which is a generalization of the classical discrete curvature. A discrete uniformization theorem is established for the parameterized discrete curvature, which generalizes the discrete uni…
Formula derived for discrete improper affine spheres.
problem Constructing discrete improper affine spheres.
method Loop group factorizations and Birkhoff decomposition.
result Representation formula for discrete indefinite affine spheres.
We define discrete flat surfaces in hyperbolic 3-space from the perspective of discrete integrable systems and prove properties that justify the definition. We show how these surfaces correspond to previously defined discrete constant mean curvature 1 surfaces in hyperbolic 3-space, and we also describe discrete focal …
Discretization of curves is an ancient topic. Even discretization of curves with an eye toward differential geometry is over a century old. However there is no general theory or methodology in the literature, despite the ubiquitous use of discrete curves in mathematics and science. There are conflicting definitions of …
Study proposes Local Linear Encoding for better feature discretization.
problem Improving feature discretization for numeric data.
method Theoretical analysis and Local Linear Encoding (LLE) method.
result LLE outperforms conventional methods with fewer parameters.
Exact discrete mechanics for nonholonomic systems defined.
problem Discrete mechanics for nonholonomic systems.
method Constructing an exponential map and deriving exact discrete nonholonomic integrators.
result Reproduces continuous nonholonomic flow as discrete flow on constraint submanifold.
Paper generalizes discrete CMC surfaces and shows how they can be derived.
problem Defining and deriving discrete constant mean curvature surfaces.
method Using discrete isothermic surfaces and the additive rational Toda system.
result Discrete isothermic CMC surfaces can be derived from discrete holomorphic data.
Discrete differential geometry aims to develop discrete equivalents of the geometric notions and methods of classical differential geometry. In this survey we discuss the following two fundamental Discretization Principles: the transformation group principle (smooth geometric objects and their discretizations are invar…
Discrete flows extend normalizing flows to discrete data, improving various applications.
problem Applying normalizing flows to discrete data distributions.
method Developed discrete autoregressive and bipartite flows, showing their effectiveness on various discrete data tasks.
result Discrete autoregressive flows outperform autoregressive baselines on synthetic discrete distributions and Potts models.
Discrete analogues of ellipsoids with preserved circular cross sections.
problem Constructing discrete analogues of ellipsoids with preserved geometric properties.
method A novel discretization procedure to create discrete analogues of ellipsoids composed of planar quadrilaterals.
result Discrete analogues of ellipsoids have preserved circular cross sections and can be deformed.
Connections on principal bundles play a fundamental role in expressing the equations of motion for mechanical systems with symmetry in an intrinsic fashion. A discrete theory of connections on principal bundles is constructed by introducing the discrete analogue of the Atiyah sequence, with a connection corresponding t…
Plane triangulations remain rigid under discrete conformal changes.
problem Rigidity of acute triangulations under discrete conformal changes.
method Maximum principles, discrete Liouville theorem, extremal lengths, Euclidean to hyperbolic discrete conformality.
result Uniformly acute triangulations are rigid under Luo's discrete conformal change.
Study integrable discretizations of cyclic systems with circular coordinate lines.
problem Integrable discretizations of 3D cyclic systems with circular coordinate lines.
method Investigate circle congruences and flat connections in the context of discrete cyclic systems.
result Characterization of circle congruences and existence of certain flat connections.
Survey on discrete minimal surfaces and their properties.
problem Discretizing minimal surfaces in Euclidean space.
method Polyhedral surfaces with parallel face offsets and circle patterns.
result All simply connected discrete minimal surfaces can be constructed from circle patterns.
In this paper, we develop several related finite dimensional variational principles for discrete optimal transport (DOT), Minkowski type problems for convex polytopes and discrete Monge-Ampere equation (DMAE). A link between the discrete optimal transport, discrete Monge-Ampere equation and the power diagram in computa…
Study on discrete Gaussian curvature for polyhedral surfaces.
problem Discretization of Gaussian curvature for polyhedral surfaces.
method Generalization of discrete conformal equivalence to define discrete Gaussian curvature and classify polyhedral surfaces.
result Existence of polyhedral surfaces with constant discrete Gaussian curvature in every discrete conformal class.
Geometric approach uses Bäcklund transformations to create integrable discrete analogs of surface nets.
problem Creating integrable discrete analogs of surface nets and conjugate nets.
method Interpreting classical differential geometry results through Bäcklund transformations and applying permutability properties.
result Integrable discrete analogs of asymptotic and conjugate nets are constructed.
Unified discrete diffusion for categorical data simplifies training and sampling.
problem Training and sampling in discrete diffusion models for categorical data.
method Mathematical simplifications and elegant unification of discrete-time and continuous-time discrete diffusion.
result Unified Simplified Discrete Denoising Diffusion (USD3) outperforms SOTA baselines.
Study discretizes Dirac and port-Hamiltonian systems using manifolds.
problem Discretization of Dirac and port-Hamiltonian systems.
method Retraction and discretization maps on manifolds for Dirac structures, applied to port-Hamiltonian systems.
result Numerical integrators for port-Hamiltonian systems derived from discretization techniques.