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.
The Brylinski beta function is extended for coaxial layers on submanifolds.
Study smoothings of singular intersections of ellipsoids.
Wright showed that, if a 1-ended simply connected locally compact ANR Y with pro-monomorphic fundamental group at infinity admits a proper Z-action, then that fundamental group at infinity can be represented by an inverse sequence of finitely generated free groups. Geoghegan and Guilbault strengthened that result, prov…
In 3-dimensional Lorentz-Minkowski space we determine the number of catenoids connecting two coaxial circles in parallel planes. This study is separated according to the types of circles and the causal character (spacelike and timelike) of the catenoid.
Method constructs harmonic immersions in R^3 using Enneper-type representation.
We construct a new family of high genus examples of free boundary minimal surfaces in the Euclidean unit 3-ball by desingularizing the intersection of a coaxial pair of a critical catenoid and an equatorial disk. The surfaces are constructed by singular perturbation methods and have three boundary components. They are …
We show that any complete, immersed self-expander to the inverse mean curvature flow, which has one end asymptotic to a cylinder, or has two ends asymptotic to two coaxial cylinders, must be rotationally symmetric.
In this article we give a criterion for the existence of a metric of curvature on a -sphere with conical singularities of prescribed angles and non-coaxial holonomy. Such a necessary and sufficient condition is expressed in terms of linear inequalities in $\vartheta_1,\dot…
Study smoothings of ellipsoid intersections with singularities.
Study proves existence and nonexistence for annular surfaces with specific curvature and boundary.
The idea of end-to-end learning of communication systems through neural network-based autoencoders has the shortcoming that it requires a differentiable channel model. We present in this paper a novel learning algorithm which alleviates this problem. The algorithm enables training of communication systems with an unkno…
This study examines geometric properties and offsets of slant timelike-ruled surfaces.
Study local features of decorated representation spaces for spherical surfaces.
The class of traveling wave solutions of the sine-Gordon equation is known to be in 1-1 correspondence with the class of (necessarily singular) pseudospherical surfaces in Euclidean space with screw-motion symmetry: the pseudospherical helicoids. We explicitly describe all pseudospherical helicoids in terms of elliptic…
The topology of the intersection of two real homogeneous coaxial quadrics was studied by the second author who showed that its intersection with the unit sphere is in most cases diffeomorphic to a connected sum of sphere products. Combining that approach with a recent one (due to Antony Bahri, Martin Bendersky, Fred Co…
3-layer NTK models generalize better than 2-layer models, especially with large input dimensions.
This paper presents two unsupervised learning layers (UL layers) for label-free video analysis: one for fully connected layers, and the other for convolutional ones. The proposed UL layers can play two roles: they can be the cost function layer for providing global training signal; meanwhile they can be added to any re…
Two-layer CNNs can overfit well if initialized correctly.
To infer a multilayer representation of high-dimensional count vectors, we propose the Poisson gamma belief network (PGBN) that factorizes each of its layers into the product of a connection weight matrix and the nonnegative real hidden units of the next layer. The PGBN's hidden layers are jointly trained with an upwar…
Proposes a fixed smooth convolutional layer to reduce checkerboard artifacts in CNNs.
Three-layer networks learn more complex features than two-layer networks.
To infer multilayer deep representations of high-dimensional discrete and nonnegative real vectors, we propose an augmentable gamma belief network (GBN) that factorizes each of its hidden layers into the product of a sparse connection weight matrix and the nonnegative real hidden units of the next layer. The GBN's hidd…
Study shows LLMs can remove half of layers without significant performance drop.
The AIBC is an Artificial Intelligence and blockchain technology based large-scale decentralized ecosystem that allows system-wide low-cost sharing of computing and storage resources. The AIBC consists of four layers: a fundamental layer, a resource layer, an application layer, and an ecosystem layer. The AIBC implemen…
We improve neural network explainability by bypassing batch normalization.
We address the problem of learning hierarchical deep neural network policies for reinforcement learning. In contrast to methods that explicitly restrict or cripple lower layers of a hierarchy to force them to use higher-level modulating signals, each layer in our framework is trained to directly solve the task, but acq…
Recent trends of incorporating attention mechanisms in vision have led researchers to reconsider the supremacy of convolutional layers as a primary building block. Beyond helping CNNs to handle long-range dependencies, Ramachandran et al. (2019) showed that attention can completely replace convolution and achieve state…
Proposes continuous convolution layers for flexible feature map resizing.
One-layer transformers can't solve induction heads task efficiently.
Unified framework LPCD optimizes quantization of complex submodules.
A new neural network model MDRBM improves noise-robustness in classification.
Many real-world complex systems across natural, social, and economical domains consist of manifold layers to form multiplex networks. The multiple network layers give rise to nonlinear effect for the emergent dynamics of systems. Especially, weak layers that can potentially play significant role in amplifying the vulne…
Residual Networks with convolutional layers are widely used in the field of machine learning. Since they effectively extract features from input data by stacking multiple layers, they can achieve high accuracy in many applications. However, the stacking of many layers raises their computation costs. To address this pro…
The study shows removing fully connected output layers improves efficiency without sacrificing performance.
Our work presents extensive empirical evidence that layer rotation, i.e. the evolution across training of the cosine distance between each layer's weight vector and its initialization, constitutes an impressively consistent indicator of generalization performance. In particular, larger cosine distances between final an…
Unified SVD compression fails in practical tasks, highlighting the importance of per layer activation reconstruction.
Introduces Causal Energy Minimization to understand Transformer layers.
A deep convolutional fuzzy system (DCFS) on a high-dimensional input space is a multi-layer connection of many low-dimensional fuzzy systems, where the input variables to the low-dimensional fuzzy systems are selected through a moving window across the input spaces of the layers. To design the DCFS based on input-outpu…
The rapid development of high-throughput technologies has enabled the generation of data from biological or disease processes that span multiple layers, like genomic, proteomic or metabolomic data, and further pertain to multiple sources, like disease subtypes or experimental conditions. In this work, we propose a gene…
FPGAs have become a popular choice for deploying deep learning architectures (DLA). There are many researchers that have explored the deployment and mapping of DLA on FPGA. However, there has been a growing need to do design-time hardware-software co-verification of these deployments. To the best of our knowledge this …
PLN-Nets with two linear layers and parallel LN achieve universal approximation.
Smectic liquid crystals are materials formed by stacking deformable, fluid layers. Though smectics prefer to have flat, uniformly-spaced layers, boundary conditions can impose curvature on the layers. Since the layer spacing and curvature are intertwined, the problem of finding minimal configurations for the layers bec…
Improved recommendation systems using multi-layer embeddings reduce model size while maintaining accuracy.
Inferencing with network data necessitates the mapping of its nodes into a vector space, where the relationships are preserved. However, with multi-layered networks, where multiple types of relationships exist for the same set of nodes, it is crucial to exploit the information shared between layers, in addition to the …
Batch-normalization (BN) layers are thought to be an integrally important layer type in today's state-of-the-art deep convolutional neural networks for computer vision tasks such as classification and detection. However, BN layers introduce complexity and computational overheads that are highly undesirable for training…
A method to analyze neural network performance by measuring layer saturation.
A new tensor-based layer reduces neural network dimensions without losing important features.
Graph embedding is an important approach for graph analysis tasks such as node classification and link prediction. The goal of graph embedding is to find a low dimensional representation of graph nodes that preserves the graph information. Recent methods like Graph Convolutional Network (GCN) try to consider node attri…