arXiv research

Efficient Winograd convolution for INT8 networks using RNS.

Localization of unknown faults in industrial systems is a difficult task for data-driven diagnosis methods. The classification performance of many machine learning methods relies on the quality of training data. Unknown faults, for example faults not represented in training data, can be detected using, for example, ano…

Study on residual Monge-Ampère mass for symmetric plurisubharmonic functions.

Deep learning networks are approximated using dynamical systems theory.

Study on residual Monge-Ampère mass for symmetric plurisubharmonic functions.

We generalize Luck's Theorem to show that the L^2-Betti numbers of a residually amenable covering space are the limit of the L^2-Betti numbers of a sequence of amenable covering spaces. We show that any residually amenable covering space of a finite simplicial complex is of determinant class, and that the L^2 torsion i…

Residual flows are shown to approximate MMD well.

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…

Generalized ResNet learns unknown dynamical systems using neural networks.

We regard pre-trained residual networks (ResNets) as nonlinear systems and use linearization, a common method used in the qualitative analysis of nonlinear systems, to understand the behavior of the networks under small perturbations of the input images. We work with ResNet-56 and ResNet-110 trained on the CIFAR-10 dat…

The use of computational methods to evaluate aesthetics in photography has gained interest in recent years due to the popularization of convolutional neural networks and the availability of new annotated datasets. Most studies in this area have focused on designing models that do not take into account individual prefer…

STRIC detects anomalies in time series by analyzing residual signals.

Study on deep multi-head self-attention dynamics, proving homogenized limits under specific scalings.

REMAL: Residual Equilibrium Manifold Active Learning for Surrogate-Based Multidisciplinary Design Analysis

New method improves predictive systems with better theoretical guarantees.

Training deep recurrent neural network (RNN) architectures is complicated due to the increased network complexity. This disrupts the learning of higher order abstracts using deep RNN. In case of feed-forward networks training deep structures is simple and faster while learning long-term temporal information is not poss…

Deep residual networks can approximate any continuous function using control theory.

Unified framework detects change-points and estimates parameters in nonlinear systems with regime switching.

New method improves matrix completion accuracy, especially in noisy data.

Unified ODE model explains residual and non-residual networks.

This research improves asset life prediction by integrating deep learning with mixture distributions.

This article is about applications of linear algebra to knot theory. For example, for odd prime p, there is a rule (given in the article) for coloring the arcs of a knot or link diagram from the residues mod p. This is a knot invariant in the sense that if a diagram of the knot under study admits such a coloring, then …

Study excess logarithmic residues for foliations to bound invariant hypersurfaces and test log canonicity.

Improved real-time UAV terrain following with RVM-RLS filter.

New method predicts heat load in thermal grids using latent variables.

We introduce mod 3 triple Milnor invariants and triple cubic residue symbols for certain primes of the Eisenstein number field $\mathbb{Q}(\sqrt{-3})$, following the analogies between knots and primes. Our triple symbol generalizes both the cubic residue symbol and Rédei's triple symbol, and describes the decomposition…

New method for Sharpe ratio analysis in high dimensions using residual-based nodewise regression.

Residual generation helps diagnose engine faults using neural networks.

This paper proposes a deep speech enhancement method which exploits the high potential of residual connections in a wide neural network architecture, a topology known as Wide Residual Network. This is supported on single dimensional convolutions computed alongside the time domain, which is a powerful approach to proces…

In this paper, we introduce transformations of deep rectifier networks, enabling the conversion of deep rectifier networks into shallow rectifier networks. We subsequently prove that any rectifier net of any depth can be represented by a maximum of a number of functions that can be realized by a shallow network with a …

A new method suppresses echo more effectively with lower latency.

Researchers compute Wodzicki residue for pseudo-differential operators on compact Lie groups.

The covariance matrix is formulated in the framework of a linear multivariate ARCH process with long memory, where the natural cross product structure of the covariance is generalized by adding two linear terms with their respective parameter. The residuals of the linear ARCH process are computed using historical data …

Deep residual networks (ResNets) and their variants are widely used in many computer vision applications and natural language processing tasks. However, the theoretical principles for designing and training ResNets are still not fully understood. Recently, several points of view have emerged to try to interpret ResNet …

Residual neural networks don't help overcome sampling complexity issues.

CN-SBM clusters cancer samples and regions based on copy number variants.

This paper begins to explore the determinants of the topological properties of the international - trade network (ITN). We fit bilateral-trade flows using a standard gravity equation to build a "residual" ITN where trade-link weights are depurated from geographical distance, size, border effects, trade agreements, and …

Paper defines AI-specific loss reconstruction problem and introduces CER framework.

Deep adaptive sampling improves surrogate modeling for complex systems.

Unified framework for sampling and approximating high-dimensional energy landscapes.

The paper shows dense and residual sets of continuous maps with positive metric mean dimension.

We present a new physics informed neural network (PINN) algorithm for solving brittle fracture problems. While most of the PINN algorithms available in the literature minimize the residual of the governing partial differential equation, the proposed approach takes a different path by minimizing the variational energy o…

sFML learns stochastic dynamical systems from data.

ContinuousNet generalizes ResNets to continuous dynamical systems.

Study on profinite rigidity of direct products of free and surface groups.

RPPs improve deep learning models with soft equivariance constraints.

RDL-Net improves speech enhancement with fewer parameters and better performance.

In this thesis we study the topology and geometry of hyperkähler quotients, as well as some related non-compact Kähler quotients, from the point of view of Hamiltonian group actions. The main technical tool we employ is Morse theory with moment maps. We prove a Lojasiewicz inequality which permits the use of Morse theo…