A neural network with a single hidden layer can't represent certain multivariable functions.
problem Representing certain multivariable functions with a neural network having only one hidden layer.
method Developed a continuum version of a one-hidden-layer neural network with ReLU activation, and proved constraints on its parameters and second derivative.
result Existence of a smooth binary function that cannot be precisely represented by any such neural network.
RBM models reveal how hidden unit tail behavior affects pattern reconstruction.
problem Understanding how the tail behavior of hidden units in RBMs influences pattern reconstruction.
method Identified an effective energy function for RBMs and studied its local minima.
result The ability to reconstruct patterns depends on the tail behavior of the hidden unit prior distribution.
Study shows most hyperbolic knot complements lack hidden symmetries.
problem Proving most knot complements lack hidden symmetries.
method Using rational functions on varieties associated to a link.
result Most knot complements lack hidden symmetries.
New findings on hidden symmetries in ReLU networks.
problem Understanding the redundancy and symmetries in ReLU network parameter space.
method Analyzing parameter settings and function classes for various network architectures.
result For certain network architectures, there are no hidden symmetries.
This paper extends depth separation results to piece-wise oscillatory functions.
problem Approximating functions with piece-wise oscillatory structure using neural networks.
method Extends existing results to piece-wise oscillatory functions using proof strategy from (Eldan and Shamir, 2016).
result Approximation by one-hidden-layer networks holds at a poly(d) rate for functions with constant domain radius and oscillation rate.
RBMs model binary interactions with hidden node activation effects.
problem Understanding how RBM hidden node activation affects binary variable distributions.
method Investigated RBM marginal distributions with different hidden node activation functions.
result Found exact expressions for RBM marginals as interacting binary variables.
New methods for estimating causal effects in hidden variable DAGs.
problem Estimating causal effects in models with hidden variables.
method Influence function based estimators for causal effects in hidden variable DAGs.
result Achieves semiparametric efficiency bounds for identifiable effects.
Kolmogorov neural networks can represent various types of functions.
problem Representing different types of functions with neural networks.
method Continuous, discontinuous bounded or unbounded activation functions in a two hidden layer model.
result Kolmogorov neural networks can represent continuous, discontinuous bounded and all unbounded multivariate functions.
A novel RNN model with shuffled hidden states.
problem Improving recurrent neural network performance.
method Permuting hidden states and applying learned functions.
result Competitive results compared to literature baselines.
Revisits the connection between neural networks and the Kolmogorov-Arnold theorem.
problem Explains the limitations of using the Kolmogorov-Arnold theorem to explain neural networks with multiple hidden layers.
method Derives modifications of the Kolmogorov-Arnold representation that transfer smoothness properties to the outer function and can be well approximated by ReLU networks.
result Shows that a deep neural network with most layers approximating the interior function is a more natural interpretation of the Kolmogorov-Arnold representation.
CONE evaluates treatment assignment functions using networked observational data to mitigate hidden confounding bias.
problem Evaluate treatment assignment functions using networked observational data with hidden confounders.
method CONE framework that learns partial representations of latent confounders and combines them for counterfactual evaluation.
result Network information mitigates hidden confounding bias in counterfactual evaluation.
Universal MLPs with a single hidden layer can learn any function.
problem Learning on various data structures like sequences, images, sets, and graphs.
method Using group theory, the paper proves the universality of a broad class of equivariant MLPs with a single hidden layer.
result Having a hidden layer on which the group acts regularly is sufficient for universal equivariance (invariance).
George Cybenko's landmark 1989 paper showed that there exists a feedforward neural network, with exactly one hidden layer (and a finite number of neurons), that can arbitrarily approximate a given continuous function f on the unit hypercube. The paper did not address how to find the weight/parameters of such a networ…
Direct approach for handling contextual bandits with latent state dynamics.
problem Handling contextual bandits with latent state dynamics, especially when rewards depend on posterior probabilities of hidden states.
method Direct reduction to standard linear contextual bandits, extended analysis of HMM parameters, periodic update of reward-model parameters.
result Periodic update of reward-model parameters allows handling complex dependencies in hidden states.
New method amplifies hidden structure in complex networks.
problem Difficulty in uncovering hidden structure in complex networks.
method Iterative weakening of dominant structure through randomization.
result Theoretical support for the effectiveness of structure amplification.
Neural networks can approximate any continuous function with a single hidden layer.
problem Approximating any continuous function using neural networks.
method Direct algebraic proof and explicit quantification of hidden units required.
result Explicit bounds on the number of hidden units needed for approximation.
New algorithm reduces sample complexity for learning CNNs.
problem Learning one-hidden-layer CNNs with various activation functions.
method Approximate gradient descent algorithm for training CNNs.
result Sample complexity matches information-theoretic lower bound for linear activation functions.
NoMoPy models noise as HMM/FHMM in Python.
problem Modeling noise in data.
method Approximate and exact EM algorithms, cross-validation, confidence region estimation.
result Validated on example problems.
New estimators for causal effects in DAGs with hidden variables, addressing computational and statistical challenges.
problem Estimating causal effects in DAGs with hidden variables beyond traditional criteria.
method Introduces novel one-step corrected plug-in and targeted minimum loss-based estimators for causal effects in DAGs with hidden variables.
result Root-n consistent causal effect estimates with desirable statistical properties.
Recent results in nonparametric regression show that deep learning, i.e., neural network estimates with many hidden layers, are able to circumvent the so-called curse of dimensionality in case that suitable restrictions on the structure of the regression function hold. One key feature of the neural networks used in the…
Recurrent networks learn beliefs from history in partially observable environments.
problem Learning optimal policies in partially observable environments.
method Trained recurrent neural networks to approximate value functions, measuring mutual information between hidden states and beliefs.
result Recurrent networks' hidden states correlate with beliefs of relevant state variables, improving expected return.
Language models based on deep neural networks and traditional stochastic modelling have become both highly functional and effective in recent times. In this work, a general survey into the two types of language modelling is conducted. We investigate the effectiveness of the Hidden Markov Model (HMM), and the Long Short…
The paper introduces FMCI and hybrid decoding for hidden Markov models.
problem Computing distributions and decoding hidden state sequences in HMMs.
method Finite Markov chain imbedding (FMCI) and hybrid decoding.
result Hybrid decoding improves performance over traditional methods.
It is well known that Artificial Neural Networks are universal approximators. The classical result proves that, given a continuous function on a compact set on an n-dimensional space, then there exists a one-hidden-layer feedforward network which approximates the function. Such result proves the existence, but it does …
In recent years, spectral clustering has become a standard method for data analysis used in a broad range of applications. In this paper we propose a new class of algorithms for multiway spectral clustering based on optimization of a certain "contrast function" over the unit sphere. These algorithms, partly inspired by…
We develop a new approach to learn the parameters of regression models with hidden variables. In a nutshell, we estimate the gradient of the regression function at a set of random points, and cluster the estimated gradients. The centers of the clusters are used as estimates for the parameters of hidden units. We justif…
B-Learner provides bounds on CATE under hidden confounding risks.
problem Estimating CATE in the presence of hidden confounding.
method Adapting bounds on average treatment effect to conditional distributional treatment effects.
result B-Learner offers valid, sharp, efficient, and quasi-oracle bounds on CATE.
Neural networks with random hidden nodes have gained increasing interest from researchers and practical applications. This is due to their unique features such as very fast training and universal approximation property. In these networks the weights and biases of hidden nodes determining the nonlinear feature mapping a…
We prove a negative result for the approximation of functions defined on compact subsets of Rd (where d≥2) using feedforward neural networks with one hidden layer and arbitrary continuous activation function. In a nutshell, this result claims the existence of target functions that are as difficult to…
We use the score function for causal discovery, tackling challenges with hidden variables.
problem Causal discovery from observational data with hidden variables.
method Fine-tuning identifiability results, establishing conditions for inferring causal relations from the score, proposing a flexible algorithm.
result Empirical validation of the proposed algorithm for causal discovery on linear, nonlinear, and latent variable models.
Extends causal inference to hidden mediators with proxies.
problem Identifying causal effects with hidden mediators and error-prone proxies.
method Established causal hidden mediation analysis and hidden front-door criterion.
result Identification of population intervention indirect effect possible with hidden mediators.
We present a new mixture model-based discriminant analysis approach for functional data using a specific hidden process regression model. The approach allows for fitting flexible curve-models to each class of complex-shaped curves presenting regime changes. The model parameters are learned by maximizing the observed-da…
In this work, we propose the marginal structured SVM (MSSVM) for structured prediction with hidden variables. MSSVM properly accounts for the uncertainty of hidden variables, and can significantly outperform the previously proposed latent structured SVM (LSSVM; Yu & Joachims (2009)) and other state-of-art methods, espe…
In this work, a method of random parameters generation for randomized learning of a single-hidden-layer feedforward neural network is proposed. The method firstly, randomly selects the slope angles of the hidden neurons activation functions from an interval adjusted to the target function, then randomly rotates the act…
In this paper, we explore different ways to extend a recurrent neural network (RNN) to a \textit{deep} RNN. We start by arguing that the concept of depth in an RNN is not as clear as it is in feedforward neural networks. By carefully analyzing and understanding the architecture of an RNN, however, we find three points …
The paper analyzes identifiability in ODE systems with hidden confounders.
problem Identifiability of ODE systems with hidden confounders.
method Systematic analysis of identifiability in linear ODE systems with hidden confounders, considering both no causal relationships and causal dependencies.
result Comprehensive identifiability analysis of ODE systems with hidden confounders, including causal dependencies.
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 general Boltzmann machine with continuous visible and discrete integer valued hidden states is introduced. Under mild assumptions about the connection matrices, the probability density function of the visible units can be solved for analytically, yielding a novel parametric density function involving a ratio of Riema…
Three-hidden-layer neural networks can approximate Hölder continuous functions uniformly with exponential rate.
problem Approximating Hölder continuous functions with neural networks.
method Introduced Floor-Exponential-Step (FLES) networks with three hidden layers.
result Uniform approximation of Hölder continuous functions with an exponential rate.
Supervised training of neural networks for classification is typically performed with a global loss function. The loss function provides a gradient for the output layer, and this gradient is back-propagated to hidden layers to dictate an update direction for the weights. An alternative approach is to train the network …
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.
Regularized training of an autoencoder typically results in hidden unit biases that take on large negative values. We show that negative biases are a natural result of using a hidden layer whose responsibility is to both represent the input data and act as a selection mechanism that ensures sparsity of the representati…
New CFNN architecture approximates functions with machine accuracy.
problem Function approximation with high precision.
method Chebyshev Feature Neural Network (CFNN) with learnable frequencies.
result Achieves machine accuracy in function approximation.
New method accounts for hidden context in preference learning for RLHF models.
problem Incomplete data with hidden context affects RLHF model outcomes.
method Distributional Preference Learning (DPL) methods estimate hidden context distributions.
result DPL methods reduce RLHF vulnerabilities by accounting for hidden context.
New neural network models for functional data.
problem Handling non-linear functional data.
method Functional Direct Neural Network (FDNN) and Functional Basis Neural Network (FBNN) with gradient-based optimization.
result Demonstrated effectiveness in complex functional models.
New method for causal effect estimation with hidden confounders.
problem Estimating causal effects in the presence of hidden confounders.
method Singular value decomposition of a conditional expectation operator followed by saddle-point optimization.
result Our method outperforms existing methods on common benchmarks.
ReLU activations lead to smoother learning curves compared to sigmoidal activations in neural networks.
problem Comparing the performance of ReLU and sigmoidal activations in neural networks.
method Analytical computation of learning curves in shallow networks with different activation functions.
result ReLU networks exhibit continuous transitions in performance, while sigmoidal networks show discontinuous transitions.
Based on the tree architecture, the objective of this paper is to design deep neural networks with two or more hidden layers (called deep nets) for realization of radial functions so as to enable rotational invariance for near-optimal function approximation in an arbitrarily high dimensional Euclidian space. It is show…