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.
Extends partitioned local depth concept with probabilistic considerations.
BN refines local partition geometry in piecewise-affine networks during training.
Optimized parallel algorithms for identifying strong ties in data.
Online PaLD extends PaLD for semi-supervised online applications.
Generates infinite-depth hierarchical clusters from few examples.
In distributed machine learning, data is dispatched to multiple machines for processing. Motivated by the fact that similar data points often belong to the same or similar classes, and more generally, classification rules of high accuracy tend to be "locally simple but globally complex" (Vapnik & Bottou 1993), we propo…
In deep learning, \textit{depth}, as well as \textit{nonlinearity}, create non-convex loss surfaces. Then, does depth alone create bad local minima? In this paper, we prove that without nonlinearity, depth alone does not create bad local minima, although it induces non-convex loss surface. Using this insight, we greatl…
Locally isoperimetric partitions minimize perimeter in space.
This work generalizes bounds on the number of linear regions in CPWL NNs.
Deep neural networks perform well on local tasks but struggle with global tasks.
The paper constructs Markov partitions for geodesic flow on hyperbolic surfaces.
MD-split+ creates locally valid prediction regions for complex data.
Deeper networks are better for local labels, but shallower for global labels.
Paper corrects GIRP algorithm to ensure isotonic models.
In this paper, we analyze the effects of depth and width on the quality of local minima, without strong over-parameterization and simplification assumptions in the literature. Without any simplification assumption, for deep nonlinear neural networks with the squared loss, we theoretically show that the quality of local…
We introduce a new family of deep neural network models. Instead of specifying a discrete sequence of hidden layers, we parameterize the derivative of the hidden state using a neural network. The output of the network is computed using a black-box differential equation solver. These continuous-depth models have constan…
We address representational challenges in normalizing flows, particularly depth and conditioning issues.
Piecewise linear activations create many spurious local minima in neural networks.
A new algorithm, Regular Tree Search, tackles non-convex simulation optimization problems.
Chern-Simons theory on a closed contact three-manifold is studied when the Lie group for gauge transformations is compact, connected and abelian. A rigorous definition of an abelian Chern-Simons partition function is derived using the Faddeev-Popov gauge fixing method. A symplectic abelian Chern-Simons partition functi…
We study the localization of a cluster of activated vertices in a graph, from adaptively designed compressive measurements. We propose a hierarchical partitioning of the graph that groups the activated vertices into few partitions, so that a top-down sensing procedure can identify these partitions, and hence the activa…
Minimal partitions with minimal perimeter found in metric spaces.
New methods improve prediction performance and reduce computation time in boosting and random forest models.
This paper presents a new approach for Gaussian process (GP) regression for large datasets. The approach involves partitioning the regression input domain into multiple local regions with a different local GP model fitted in each region. Unlike existing local partitioned GP approaches, we introduce a technique for patc…
Space partitions of underlie a vast and important class of fast nearest neighbor search (NNS) algorithms. Inspired by recent theoretical work on NNS for general metric spaces [Andoni, Naor, Nikolov, Razenshteyn, Waingarten STOC 2018, FOCS 2018], we develop a new framework for building space partitions re…
LA-MCTS learns search space partition for black-box optimization using Monte Carlo Tree Search.
Localized transfer learning improves nonparametric regression performance.
In this paper, we prove that depth with nonlinearity creates no bad local minima in a type of arbitrarily deep ResNets with arbitrary nonlinear activation functions, in the sense that the values of all local minima are no worse than the global minimum value of corresponding classical machine-learning models, and are gu…
DCTN uses tensor networks for image classification, achieving state-of-the-art results.
Traditionally, an artificial neural network (ANN) is trained slowly by a gradient descent algorithm such as the backpropagation algorithm since a large number of hyperparameters of the ANN need to be fine-tuned with many training epochs. To highly speed up training, we created a novel shallow 4-layer ANN called "Pairwi…
Study reveals how Fisher information changes with network depth, finding it grows linearly.
We present a new way of constructing an ensemble classifier, named the Guided Random Forest (GRAF) in the sequel. GRAF extends the idea of building oblique decision trees with localized partitioning to obtain a global partitioning. We show that global partitioning bridges the gap between decision trees and boosting alg…
Develops an MS-inspired algorithm for regression mode finding and space partitioning.
A common divide-and-conquer approach for Bayesian computation with big data is to partition the data, perform local inference for each piece separately, and combine the results to obtain a global posterior approximation. While being conceptually and computationally appealing, this method involves the problematic need t…
Minimal networks minimize length and mass in certain configurations.
ParK efficiently solves kernel ridge regression for large datasets.
A novel non-supervised method detects anomalies in multivariate time series.
Hyperkahler quotients by non-free actions are typically highly singular, but are remarkably still partitioned into smooth hyperkahler manifolds. We show that these partitions are topological stratifications, in a strong sense. We also endow the quotients with global Poisson structures which induce the hyperkahler struc…
New approach predicts generalization of deep neural networks in proportional-width regime.
Recently, locality sensitive hashing (LSH) was shown to be effective for MIPS and several algorithms including -ALSH, Sign-ALSH and Simple-LSH have been proposed. In this paper, we introduce the norm-range partition technique, which partitions the original dataset into sub-datasets containing items with similar 2-…
Region-specific linear models are widely used in practical applications because of their non-linear but highly interpretable model representations. One of the key challenges in their use is non-convexity in simultaneous optimization of regions and region-specific models. This paper proposes novel convex region-specific…
Definition of the partition function of U(1) gauge theory is extended to a class of four-manifolds containing all compact spaces and certain asymptotically locally flat (ALF) ones including the multi-Taub--NUT spaces. The partition function is calculated via zeta-function regularization with special attention to its mo…
LDP speeds up causal discovery by partitioning, improving VAS recall and runtime.
We present graph partition neural networks (GPNN), an extension of graph neural networks (GNNs) able to handle extremely large graphs. GPNNs alternate between locally propagating information between nodes in small subgraphs and globally propagating information between the subgraphs. To efficiently partition graphs, we …
In this paper, we investigate a divide and conquer approach to Kernel Ridge Regression (KRR). Given n samples, the division step involves separating the points based on some underlying disjoint partition of the input space (possibly via clustering), and then computing a KRR estimate for each partition. The conquering s…
Enhances POU-Nets with probabilistic noise model for efficient spatial data clustering.
Study on optimal partitions and nodal solutions for the Yamabe equation.
New findings show learning deeper neural networks is hard even with Gaussian inputs and non-degenerate weights.