To construct flexible nonlinear predictive distributions, the paper introduces a family of softplus function based regression models that convolve, stack, or combine both operations by convolving countably infinite stacked gamma distributions, whose scales depend on the covariates. Generalizing logistic regression that…
On-device research index
arXiv research
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.
168,742 papers · 148 categories
Trend · papers per month
48 results for “softplus function”
In this paper, we prove that a shallow neural network with a monotone sigmoid, ReLU, ELU, Softplus, or LeakyReLU activation function can arbitrarily well approximate any L^p(p>=2) integrable functions defined on R*[0,1]^n. We also prove that a shallow neural network with a sigmoid, ReLU, ELU, Softplus, or LeakyReLU act…
We introduce a novel uncertainty estimation for classification tasks for Bayesian convolutional neural networks with variational inference. By normalizing the output of a Softplus function in the final layer, we estimate aleatoric and epistemic uncertainty in a coherent manner. The intractable posterior probability dis…
Deep networks can approximate various activation functions with modest adjustments.
problem Expressive power of deep neural networks with diverse activation functions.
method Approximation of any activation function in set A by ReLU networks with specific scaling factors.
result Approximation of any activation function in a specific subset of A by ReLU networks with (1,1) scaling factors.
Improved variational inference for logistic regression and classification.
problem Intractability of Evidence Lower Bound in variational logistic regression.
method Introducing a new bound for the expectation of softplus function, applied to variational logistic regression and Gaussian process classification.
result The new bound results in a tighter posterior and faster computation compared to Monte-Carlo methods.
To model categorical response variables given their covariates, we propose a permuted and augmented stick-breaking (paSB) construction that one-to-one maps the observed categories to randomly permuted latent sticks. This new construction transforms multinomial regression into regression analysis of stick-specific binar…
SGD converges globally to logistic loss minima for two-layer nets.
problem Global convergence of SGD for logistic loss on two-layer neural nets.
method Demonstrates existence of Frobenius norm regularized logistic loss functions as Villani functions, proving convergence and exponential rate.
result SGD converges globally to the global minima of appropriately regularized logistic empirical risk of depth 2 nets.
A new method lifts training of input-convex neural networks to avoid dead weights and plateaued loss.
problem Training input-convex neural networks with non-negative weights.
method Introduces a hypernetwork that emits non-negative weights from a summary of the input batch, adding stochasticity to soften the loss landscape.
result The lift method achieves lower test loss than projected gradient descent and direct softplus reparametrization.
We study the sample complexity of learning one-hidden-layer convolutional neural networks (CNNs) with non-overlapping filters. We propose a novel algorithm called approximate gradient descent for training CNNs, and show that, with high probability, the proposed algorithm with random initialization grants a linear conve…
AGGLIO optimizes non-convex functions with local convexity guarantees.
problem Optimizing non-convex functions with local convexity.
method Stage-wise, graduated optimization technique for locally convex functions.
result Global convergence to the global optimum for non-convex and locally convex objectives.
Filtering out unrealistic images from trained generative adversarial networks (GANs) has attracted considerable attention recently. Two density ratio based subsampling methods---Discriminator Rejection Sampling (DRS) and Metropolis-Hastings GAN (MH-GAN)---were recently proposed, and their effectiveness in improving GAN…
Global convergence of SGD proven for two-layer neural nets with regularization.
problem Proving global convergence of SGD for two-layer neural nets.
method Regularized empirical risk, SGD iterates, Villani functions.
result Global convergence of SGD for a special class of initializations.
We propose , a novel self-regularized non-monotonic activation function which can be mathematically defined as: . As activation functions play a crucial role in the performance and training dynamics in neural networks, we validated experimentally on several well-known benchmarks…
This research improves neural network performance with adaptive activation functions in sparse data settings.
problem Limited data availability in scientific and engineering problems.
method Investigation of two types of adaptive activation functions with individual trainable parameters.
result Adaptive activation functions, especially with individual trainable parameters, enhance prediction accuracy and confidence in sparse data settings.
Quantized neural networks can represent all fixed-point functions under certain conditions.
problem Expressive power of quantized neural networks under fixed-point arithmetic.
method Analyzing necessary and sufficient conditions for quantized networks to represent all fixed-point functions.
result Various popular activation functions satisfy the sufficient condition for representing all fixed-point functions.
SAD Neural Networks: Divergent Gradient Flows and Asymptotic Optimality via o-minimal Structurescs.LG
Gradient flows of neural networks converge to optimal values or diverge, with thresholds and asymptotic behaviors.
problem Understanding the convergence and divergence of gradient flows in neural networks.
method Analysis of gradient flows on loss landscapes of neural networks using o-minimal structures.
result Gradient flows either converge to optimal values or diverge to infinity, with thresholds and asymptotic behaviors.
A neural network derived from first principles using MaxEnt.
problem Developing a neural network from first principles.
method Derived a neural network using the principle of Maximum Entropy, with linear dimension-reducing transformations and conditional mean estimators.
result Unified theoretical justification for activation functions like sigmoid, softplus, and relu.
Minimum width for ReLU networks on compact domain is exactly max{d_x, d_y, 2}
problem Characterizing the minimum width for ReLU networks to approximate functions on compact domains
method Analyzing the minimum width for approximation of functions from to using ReLU-like activation functions
result The minimum width for approximation on a compact domain is exactly max{d_x, d_y, 2} for ReLU-like activation functions
Using back-propagation and its variants to train deep networks is often problematic for new users. Issues such as exploding gradients, vanishing gradients, and high sensitivity to weight initialization strategies often make networks difficult to train, especially when users are experimenting with new architectures. Her…
Adaptive gradient methods (AGMs) have become popular in optimizing the nonconvex problems in deep learning area. We revisit AGMs and identify that the adaptive learning rate (A-LR) used by AGMs varies significantly across the dimensions of the problem over epochs (i.e., anisotropic scale), which may lead to issues in c…
We develop embeddings for nonlinear subspaces preserving vector norms.
problem Preserving vector norms in nonlinear subspaces.
method Low-distortion embeddings for subspaces under nonlinear transformations.
result First low-distortion embeddings for a wide class of nonlinear functions.
Imitation learning is a control design paradigm that seeks to learn a control policy reproducing demonstrations from expert agents. By substituting expert demonstrations for optimal behaviours, the same paradigm leads to the design of control policies closely approximating the optimal state-feedback. This approach requ…
Lower bound proves ridgeless regression performs poorly near interpolation threshold.
problem Proving performance of ridgeless regression near interpolation threshold.
method Distribution-independent lower bound for mean squared error in noisy ridgeless linear regression.
result Lower bound implies ridgeless regression performs poorly near interpolation threshold.
This paper proposes a continuous timing strategy for growth vs. defensive style allocation.
problem Dynamic allocation of growth and defensive ETF baskets using macro-market timing signals.
method Continuous smooth score combining multiple factors, mapped to G/D weights, smoothed with EWMA.
result Continuous style timing strategy outperforms static benchmarks in risk-adjusted returns.
IGNIS: A Robust Neural Network Framework for Constrained Parameter Estimation in Archimedean Copulasstat.ML
IGNIS uses neural networks to estimate copula parameters robustly.
problem Pathological properties of Archimedean copulas make traditional estimators brittle.
method Unified neural estimation framework with multi-input architecture and softplus output layer.
result Accurate and stable estimates for real-world datasets.
Efficient Subsampling of Realistic Images From GANs Conditional on a Class or a Continuous Variablecs.CV
This work introduces an efficient method to sample high-quality images from conditional GANs.
problem Efficient subsampling of images from conditional GANs (cGANs) is challenging.
method Developed a novel conditional density ratio estimation method (cDRE-F-cSP) and rejection sampling scheme (cDR-RS).
result cDR-RS outperforms state-of-the-art methods in both effectiveness and efficiency.
New neural network models for complex functional data analysis.
problem Complex relations between functional predictors and responses.
method Function-on-Function regression models using neural networks with continuous hidden layers.
result Demonstrated power and flexibility in handling complex functional models.
Distance function to a finite set is a topological Morse function.
problem Characterizing the topological Morse function of a finite set.
method Analyzing the distance function to a finite set in \(\mathbb{R}^n\).
result Distance function is a topological Morse function, with precise critical points and indices.
Introduces new weighted floating functions and affine surface areas.
problem Developing new mathematical concepts for convex bodies.
method Introducing weighted floating functions and weighted functional affine surface areas.
result New relations to traditional and classical affine surface areas.
Develops methods for selecting and estimating smooth functional coefficients in high-dimensional multivariate functional data.
problem Functional predictor selection and estimation of smooth functional coefficients in high-dimensional multivariate functional data.
method Functional group-sparse regression methods in a generic Hilbert space of infinite dimension.
result Consistency of estimation and selection (oracle property) under infinite-dimensional Hilbert spaces.
Neural networks can approximate functionals on RKHS with error bounds.
problem Approximating functionals on RKHS using neural networks.
method Interpolating orthogonal projections in RKHS using point evaluations.
result Explicit error bounds for various kernels (inverse multiquadric, Gaussian, Sobolev).
FFBO optimizes functions as inputs and outputs, improving on existing BO methods.
problem Optimizing functions as both inputs and outputs in complex systems.
method Function-on-function Gaussian process (FFGP) model with a separable operator-valued kernel, scalar upper confidence bound (UCB) acquisition function, and scalable functional gradient ascent algorithm (FGA).
result FFBO outperforms existing methods in synthetic and real-world data.
Chirped sinosoids and interferometric phase plots are functions that are not periodic, but are the composition of a smooth function and a periodic function. These functions functions factor into a pair of maps: from their domain to a circle, and from a circle to their codomain. One can easily imagine replacing the circ…
The Fridman function is bounded by the injectivity radius for certain hyperbolic manifolds.
problem Bounding the Fridman function for hyperbolic manifolds.
method Analyzing the relationship between the Fridman function and the injectivity radius function.
result The Fridman function is bounded above by the injectivity radius function for certain hyperbolic manifolds.
Nuisance Function Tuning and Sample Splitting for Optimally Estimating a Doubly Robust Functionalmath.ST
Optimally estimates a functional using nuisance function tuning and sample splitting.
problem Estimating optimal rates for a doubly robust functional.
method Combines nuisance function tuning and sample splitting strategies.
result Shows optimal rates of convergence for various estimators.
The paper extends mixability theory to function-valued forecasts, proving various loss functions are mixable.
problem Efficient aggregation of functional and probabilistic forecasts in online prediction games.
method Adapting mixable and exponentially concave loss functions to function-valued forecasts.
result Various loss functions used for probabilistic forecasting are mixable (exp-concave).
The paper proves isoparametric functions on Finsler space forms under specific conditions.
problem Understanding isoparametric functions in Finsler space forms.
method Proving transnormal functions as isoparametric functions and constructing global and local isoparametric functions using the distance function.
result Generalization of Theorem B to Finsler space forms.
Paper introduces a nonparametric functional graphical model for random functions.
problem Estimating probabilistic conditional independence in functional graphical models.
method Functional sufficient dimension reduction to relax Gaussian or copula Gaussian assumptions.
result Enhances estimation accuracy and retains probabilistic conditional independence.
Robustifies elicitable functionals to handle small distribution misspecifications.
problem Determining uniquely optimal forecasts under distributional misspecification.
method Integrates statistical robustness into elicitable functionals using Kullback-Leibler divergence.
result Robust elicitable functionals admit unique solutions at the boundary of uncertainty regions.
The paper characterizes strong Hamel functions using symmetries and proves their preservation properties.
problem Characterizing strong Hamel functions and their symmetries in Finsler spaces.
method Analyzing geodesic spray, strong dual symmetries, and strong dynamical symmetries.
result Strong Hamel functions can be characterized in terms of strong dual symmetries and strong dynamical symmetries.
Study biharmonic functions on vector bundles with spherical symmetry.
problem Investigate biharmonic functions on vector bundles with spherically symmetric metrics.
method Analyze vertical lifts and radial functions of functions on vector bundle manifolds.
result Construct an infinite two-parameter family of proper biharmonic functions.
Two new methods improve forecasting of functional time series data.
problem Forecasting of functional time-dependent data.
method Functional Singular Spectrum Analysis (FSFA) based forecasting methods.
result Our methods outperform existing algorithms for periodic stochastic processes.
This paper introduces the concept of functional current as a mathematical framework to represent and treat functional shapes, i.e. sub-manifold supported signals. It is motivated by the growing occurrence, in medical imaging and computational anatomy, of what can be described as geometrico-functional data, that is a da…
Study stabilizers of smooth functions on surfaces, focusing on Morse-Bott functions.
problem Understanding the homotopy type of stabilizers of smooth functions on surfaces.
method Analyzing the homotopy properties of stabilizers for a specific class of smooth functions.
result The homotopy type of the connected component of the identity map of the stabilizer is completely described for Morse-Bott functions.
The paper connects convex functions to p-subharmonic functions and proves their equivalence.
problem Understanding the relationship between convex functions and p-subharmonic functions.
method Average principle, variational methods, and PDE techniques.
result Convex functions on R^n are p-subharmonic for every p > 1.
A new deep neural network tackles nonlinear functional regression with improved dimensionality reduction.
problem Nonlinear functional regression in infinite-dimensional functional data analysis.
method Functional deep neural network with adaptive kernel embedding and projection steps.
result Explicit rates of approximating nonlinear smooth functionals are derived, and the network is shown to be effective in both simulated and real datasets.
New model for network analysis using functional data.
problem Existing network models treat nodes as functions, but this paper introduces functional edges.
method Transform adjacency matrix into functional adjacency tensor, apply Tucker decomposition, regularize basis matrices, and solve tensor completion problem.
result The model effectively captures community structure and handles irregular functional edge data.
The study finds a special type of smooth function on connected sums of manifolds.
problem Finding smooth functions that are Morse on preimages of non-extrema values.
method Investigates internally Morse (I-Morse) and neat with respect to Reeb graph (N-Reeb) functions.
result Constructs an IN-Morse-Reeb function on a connected sum of given manifolds.