A software library for constructing and learning probabilistic models is presented. The library offers a set of building blocks from which a large variety of static and dynamic models can be built. These include hierarchical models for variances of other variables and many nonlinear models. The underlying variational B…
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48 results for “Building Blocks”
Knots of Constant Curvaturemath.GT
In this paper we show how to realize all knot (and link) types as C^{2} smooth curves of constant curvature. Our proof is constructive: we build the knots with copies of a fixed finite number of "building blocks" that are particular segments of helices and circles. We use these building blocks to construct all closed b…
Deep learning has shown promising results on many machine learning tasks but DL models are often complex networks with large number of neurons and layers, and recently, complex layer structures known as building blocks. Finding the best deep model requires a combination of finding both the right architecture and the co…
This paper provides a topological method to construct all simply-connected, spin, smooth -manifolds with torsion-free homology using simply-connected, smooth -manifolds as building blocks. We explicitly determine the invariants that classify these -manifolds from the intersection form and specific homology cla…
Study general hyperbolic gluings, proving quasi-arithmeticity of building blocks.
problem Proving quasi-arithmeticity of building blocks in hyperbolic gluings.
method Generalized gluings of hyperbolic orbifolds, proving quasi-arithmeticity.
result Building blocks of quasi-arithmetic gluings must also be quasi-arithmetic.
SiBBlInGS discovers interpretable building blocks across states in multi-way data.
problem Identifying interpretable units (Building Blocks) in multi-state, multi-way data.
method Graph-based dictionary learning approach for sparse BBs and temporal traces.
result Captures per-trial variability and state-specific vs. state-invariant components.
A geometric structure (FAP-structure), having both absolute parallelism and Finsler properties, is constructed. The building blocks of this structures are assumed to be functions of position and direction. A non-linear connection emerges naturally and is defined in terms of the building blocks of the structure. Two lin…
Building Bayesian Neural Networks with Blocks: On Structure, Interpretability and Uncertaintystat.ML
We provide simple schemes to build Bayesian Neural Networks (BNNs), block by block, inspired by a recent idea of computation skeletons. We show how by adjusting the types of blocks that are used within the computation skeleton, we can identify interesting relationships with Deep Gaussian Processes (DGPs), deep kernel l…
We introduce a method to construct -instantons over compact -manifolds arising as the twisted connected sum of a matching pair of building blocks [Kov03,KL11,CHNP12]. Our construction is based on gluing -instantons obtained from holomorphic bundles over the building blocks via the first named author's wo…
Researchers develop methods to construct Lagrangian cobordisms between Legendrian knots.
problem Understanding the relationship between Legendrian knots through Lagrangian cobordisms.
method Combinatorial and geometric methods, including Heegaard Floer Homology and contact surgery.
result Construction of nondecomposable Lagrangian cobordisms between Legendrian knots.
Learning Deep Representation Without Parameter Inference for Nonlinear Dimensionality Reductioncs.LG
Unsupervised deep learning is one of the most powerful representation learning techniques. Restricted Boltzman machine, sparse coding, regularized auto-encoders, and convolutional neural networks are pioneering building blocks of deep learning. In this paper, we propose a new building block -- distributed random models…
We describe rules for building 2d theories labeled by 4-manifolds. Using the proposed dictionary between building blocks of 4-manifolds and 2d N=(0,2) theories, we obtain a number of results, which include new 3d N=2 theories T[M_3] associated with rational homology spheres and new results for Vafa-Witten partition fun…
We study compact Riemannian manifolds for which the light between any pair of points is blocked by finitely many point shades. Compact flat Riemannian manifolds are known to have this finite blocking property. We conjecture that amongst compact Riemannian manifolds this finite blocking property characterizes the flat m…
Graph learning categorizes DeFi services into similar functionalities.
problem Identifying similar financial services in decentralized finance protocols.
method Graph representation learning (GRL) to categorize smart contract blocks into clusters.
result Purity of clustering reaches .888 in the best-case scenario.
R&D Strategy Documentq-fin.TR
We outline what we believe are the prerequisites and building-blocks for successfully devising trading models and other financial applications based on a complex systems perspective.
New method for deep learning hierarchies like sequences and graphs.
problem Lack of formalism for dealing with hierarchical structures in deep learning.
method Express equivariant maps for hierarchies using combinations of building block symmetries.
result Demonstrates effectiveness on semantic segmentation of point-cloud data.
Investigates the fundamental components of attention mechanisms.
problem Understanding the building blocks of attention in deep learning.
method Classified and studied three key mechanisms: additive, multiplicative output, and synaptic attention.
result Additive activation attention is central in proofs of lower bounds.
This study ranks feature-block importance in multiblock neural networks.
problem Understanding feature contributions in multiblock neural networks.
method Three methods: composite, knock-in, and knock-out strategies.
result Each strategy has its merits for specific application scenarios.
Due to the success of residual networks (resnets) and related architectures, shortcut connections have quickly become standard tools for building convolutional neural networks. The explanations in the literature for the apparent effectiveness of shortcuts are varied and often contradictory. We hypothesize that shortcut…
Finding the best neural network architecture requires significant time, resources, and human expertise. These challenges are partially addressed by neural architecture search (NAS) which is able to find the best convolutional layer or cell that is then used as a building block for the network. However, once a good buil…
LieTransformer extends self-attention to Lie groups for improved deep learning tasks.
problem Improving deep learning performance through group equivariant self-attention.
method LieSelfAttention layers that are equivariant to arbitrary Lie groups and their discrete subgroups.
result Competitive experimental results on various tasks.
In this paper we provide a valuation formula for different classes of actuarial and financial contracts which depend on a general loss process, by using the Malliavin calculus. In analogy with the celebrated Black-Scholes formula, we aim at expressing the expected cash flow in terms of a building block. The former is r…
Big data sets must be carefully partitioned into statistically similar data subsets that can be used as representative samples for big data analysis tasks. In this paper, we propose the random sample partition (RSP) data model to represent a big data set as a set of non-overlapping data subsets, called RSP data blocks,…
Deep learning improves time series forecasting, outperforming other methods.
problem Improving time series forecasting accuracy.
method Deep learning models for time series prediction.
result Deep learning models consistently outperform other methods in forecasting competitions.
We propose unitary group convolutions (UGConvs), a building block for CNNs which compose a group convolution with unitary transforms in feature space to learn a richer set of representations than group convolution alone. UGConvs generalize two disparate ideas in CNN architecture, channel shuffling (i.e. ShuffleNet) and…
AANets balance stability and plasticity in CIL.
problem Stability-plasticity dilemma in class-incremental learning.
method Adaptive Aggregation Networks (AANets) with stable and plastic residual blocks.
result AANets improve performance on CIL benchmarks.
Constant Mean Curvature Hypersurfaces in the (n+1)-Sphere by Gluing Spherical Building Blocksmath.DG
The techniques developed by Butscher in arXiv:math/0703469 for constructing constant mean curvature (CMC) hypersurfaces in the (n+1)-sphere by gluing together spherical building blocks are generalized to handle less symmetric initial configurations. The outcome is that the approximately CMC hypersurface obtained by glu…
New taxonomy and improved solvers for discrete energy minimization.
problem Maximum-a-posteriori inference in discrete graphical models.
method Dual block-coordinate ascent rule, theoretical analysis, new solver variants.
result Improved state-of-the-art solver outperforming existing methods on all test instances.
The paper discovers the family of identically-derived Euclidean one-parameter even-dimensional differential linear operators with unique eigenproperties, which prove to be inherently related to the emergent characterizations of fundamental building blocks of embedded minimal surfaces and the Nitsche conjecture proof.
Paper finds sharpness differences in transformer blocks accelerating LLM training.
problem Understanding and accelerating large language model pre-training.
method Uncovering sharpness disparity across transformer blocks and proposing Blockwise Learning Rate.
result Blockwise Learning Rate strategy accelerates LLM pre-training with lower loss and speedup.
This note presents in a technical though hopefully pedagogical way the three most common forms of neural network architectures: Feedforward, Convolutional and Recurrent. For each network, their fundamental building blocks are detailed. The forward pass and the update rules for the backpropagation algorithm are then der…
Machine learning predicts Atlantic blocking using limited data.
problem Underestimation of blocking event duration in climate models.
method Transfer Learning and Explainable AI (SHAP analysis)
result High-pressure anomalies in specific regions contribute to blocking events.
New method builds hyperbolic spheres with controlled holonomy.
problem Creating hyperbolic spheres with specific holonomy properties.
method Gluing simple building blocks to form hyperbolic cone spheres.
result Any Deroin-Tholozan representation can be realized as cone sphere holonomy.
In this paper we construct an infinite family of homotopically rigid spaces. These examples are then used as building blocks to forge highly connected rational spaces with prescribed finite group of self-homotopy equivalences. They are also exploited to provide highly connected inflexible and strongly chiral manifolds.
Spectral algorithms solve optimal community detection and related problems.
problem Optimal detection of community structures and related substructures.
method Spectral algorithms applied to various planted substructures.
result Spectral algorithms achieve optimal performance for a wide range of planted substructures.
The ability to decompose scenes in terms of abstract building blocks is crucial for general intelligence. Where those basic building blocks share meaningful properties, interactions and other regularities across scenes, such decompositions can simplify reasoning and facilitate imagination of novel scenarios. In particu…
Graph generation techniques are increasingly being adopted for drug discovery. Previous graph generation approaches have utilized relatively small molecular building blocks such as atoms or simple cycles, limiting their effectiveness to smaller molecules. Indeed, as we demonstrate, their performance degrades significan…
New method identifies latent variables with sparse perturbations.
problem Identifying latent variables with minimal supervision.
method Weakly supervised representation learning with sparse perturbations.
result Identification of latent variables up to specified blocks.
We give the characterization of Arnol'd-Mather type for stable singular Legendre immersions. The most important building block of the theory is providing a module structure on the space of infinitesimal integral deformations by means of the notion of natural liftings of differential systems and of contact Hamiltonian v…
Study of psc metrics via block diffeomorphisms and cubical sets.
problem Understanding the concordance of psc metrics.
method Constructing cubical sets and using block Dirac operators.
result Construction of a cubical Kan set and comparison map.
Large-scale L1-regularized loss minimization problems arise in high-dimensional applications such as compressed sensing and high-dimensional supervised learning, including classification and regression problems. High-performance algorithms and implementations are critical to efficiently solving these problems. Building…
Recent advances in deep learning motivate the use of deep neural networks in Internet-of-Things (IoT) applications. These networks are modelled after signal processing in the human brain, thereby leading to significant advantages at perceptual tasks such as vision and speech recognition. IoT applications, however, ofte…
New kernels from neural networks show better performance than traditional methods.
problem Improving neural network performance on small datasets.
method Developed algebraic operations to create compositional kernels from neural network architectures.
result Compositional kernels achieve higher accuracy than neural tangent kernels and neural networks on small datasets.
Orthogonium offers unified, efficient layers for robust deep learning.
problem Fragmented and computationally demanding implementations of orthogonal and 1-Lipschitz layers.
method Unified, efficient PyTorch library providing orthogonal and 1-Lipschitz layers.
result Reduced overhead and standardized tools for robust experimentation.
Study on neuron dynamics for XOR classification with zero-margin.
problem Understanding neural network training dynamics in zero-margin classification problems.
method Analysis of Gaussian XOR problem, focusing on neuron block dynamics and generalization without margin assumptions.
result Neurons cluster into four directions and block-level signals evolve coherently, essential for reliable prediction in the Gaussian setting.
mlr3mbo is a modular R toolbox for Bayesian optimization.
problem Efficiently solving optimization problems with multiple objectives and constraints.
method Bayesian optimization with support for multi-objective, multi-point proposals, parallelization, and custom algorithms.
result mlr3mbo performs competitively with state-of-the-art optimizers and robustly handles various optimization regimes.
We introduce the simulation tool SABCEMM (Simulator for Agent-Based Computational Economic Market Models) for agent-based computational economic market (ABCEM) models. Our simulation tool is implemented in C++ and we can easily run ABCEM models with several million agents. The object-oriented software design enables th…
Recently it has become popular to learn sparse Gaussian graphical models (GGMs) by imposing l1 or group l1,2 penalties on the elements of the precision matrix. Thispenalized likelihood approach results in a tractable convex optimization problem. In this paper, we reinterpret these results as performing MAP estimation u…