Truncated back-propagation improves hyperparameter tuning and meta learning efficiency.
problem Computational challenges in evaluating exact gradients for high-dimensional bilevel optimization problems.
method Use truncated back-propagation to approximate gradients for the lower-level problem.
result Optimization with few-step back-propagation approximations often performs comparably to exact gradients, but with less memory and computation.
In this paper, we revisit the recurrent back-propagation (RBP) algorithm, discuss the conditions under which it applies as well as how to satisfy them in deep neural networks. We show that RBP can be unstable and propose two variants based on conjugate gradient on the normal equations (CG-RBP) and Neumann series (Neuma…
New method optimizes weights and quantizers in ternary neural networks.
problem Reducing model size and computational cost in deep neural networks.
method Simultaneous optimization of weights and quantizers using truncated Gaussian approximation.
result 3.9-2.16% accuracy loss in ImageNet classification tasks.
A new method distills datasets more efficiently and effectively.
problem Achieving competitive performance on test data with a small synthetic dataset.
method Tackles dataset distillation as a bilevel optimization problem, introduces RaT-BPTT to stabilize gradients and speed up optimization.
result Establishes new state-of-the-art performance across various benchmarks.
This paper proposes an alternating back-propagation algorithm for learning the generator network model. The model is a non-linear generalization of factor analysis. In this model, the mapping from the continuous latent factors to the observed signal is parametrized by a convolutional neural network. The alternating bac…
Learning long-term dependencies in extended temporal sequences requires credit assignment to events far back in the past. The most common method for training recurrent neural networks, back-propagation through time (BPTT), requires credit information to be propagated backwards through every single step of the forward c…
The back-propagation algorithm is the cornerstone of deep learning. Despite its importance, few variations of the algorithm have been attempted. This work presents an approach to discover new variations of the back-propagation equation. We use a domain specific lan- guage to describe update equations as a list of primi…
As traditional neural network consumes a significant amount of computing resources during back propagation, \citet{Sun2017mePropSB} propose a simple yet effective technique to alleviate this problem. In this technique, only a small subset of the full gradients are computed to update the model parameters. In this paper …
The back-propagation algorithm is widely used for learning in artificial neural networks. A challenge in machine learning is to create models that generalize to new data samples not seen in the training data. Recently, a common flaw in several machine learning algorithms was discovered: small perturbations added to the…
Proposes a semi-implicit back propagation method for neural networks.
problem Challenges in training neural networks, especially gradient vanishing and small step sizes.
method Proposes a semi-implicit back propagation method using error back propagation and proximal methods.
result The proposed method leads to better performance in terms of loss decreasing and training/validation accuracy compared to SGD and ProxBP.
Deep networks trained with Hebbian updates perform similarly to back-propagation on image datasets.
problem Training deep networks with realistic asymmetric connections and updates.
method Use Hebbian updates with separate feedforward and feedback weights, and local rule for updates.
result Similar performance to back-propagation achieved with Hebbian updates on challenging image datasets.
The paper introduces various gradient descent algorithms for training deep learning models.
problem Training deep neural networks is challenging due to their complexity.
method Gradient descent and its variants are discussed for optimizing deep learning models.
result Gradient descent and its variants improve the training performance of deep learning models.
The study learns neural update rules by remembering past experiences.
problem Developing efficient online learning rules for neural networks.
method Representing neurons with vectors, using meta-neural networks for updates, and training for remembering past experiences.
result The approach reveals insights into learning rules and could be used for complex tasks like episodic memory.
The problem of an arbitrary truncated Levy flight description using the method of cumulant approach has been solved. The set of cumulants of the truncated Levy distribution given the assumption of arbitrary truncation has been found. The influence of truncation shape on the truncated Levy flight properties in the Gauss…
NoProp learns neural networks without full back-propagation or forward-propagation.
problem Learning hierarchical representations in neural networks.
method NoProp independently learns each block to denoise a noisy target using local targets and back-propagation within the block.
result NoProp is a viable learning algorithm that is easy to use and computationally efficient.
Artificial neural networks are most commonly trained with the back-propagation algorithm, where the gradient for learning is provided by back-propagating the error, layer by layer, from the output layer to the hidden layers. A recently discovered method called feedback-alignment shows that the weights used for propagat…
Truncated CauchyNMF robustly learns subspaces from noisy data.
problem Outliers in non-negative matrix factorization (NMF) cause failure.
method Proposes Truncated CauchyNMF loss to handle outliers.
result Theoretical analysis and experimental validation show Truncated CauchyNMF's robustness.
Efficiently estimate Boolean product distribution parameters from truncated samples.
problem Estimating parameters of Boolean product distributions from truncated samples.
method Introducing fatness of truncation set, using membership queries, and adapting Stochastic Gradient Descent.
result Efficiently learn Boolean product distributions from truncated samples with small sample complexity.
In the paper "On Truncated Variation of Brownian Motion with Drift" (Bull. Pol. Acad. Sci. Math. 56 (2008), no.4, 267 - 281) we defined truncated variation of Brownian motion with drift, Wt=Bt+μt,t≥0, where (Bt) is a standard Brownian motion. Truncated variation differs from regular variation by neglect…
Optimal algorithm learns Gaussian under halfspace truncation with minimal samples.
problem Learning a Gaussian distribution truncated to an unknown halfspace.
method Efficient algorithm using n=ildeO(d2/ε2) samples and runtime dominated by empirical covariance matrix computation. result Optimal sample and time complexity bounds for learning a Gaussian under halfspace truncation.
New method for constructing truncated vine copulas.
problem High-dimensional parameter space in vine copulas.
method Propose a new score and algorithm for constructing truncated vines.
result New algorithms exploit conditional independences.
Paper proposes approximate Stein classes for efficient truncated density estimation.
problem Difficulties in estimating truncated density models due to intractable normalising constants and boundary conditions.
method Adapts score matching to solve the problem, introduces approximate Stein classes and a novel discrepancy measure, TKSD.
result TKSD does not require a fixed weighting function and can be evaluated using only boundary samples, leading to improved accuracy.
Paper defines new risk measures for elliptical distributions.
problem Risk measurement for elliptical distributions.
method DTM, DTS, DTK definitions and formula derivation for specific distributions.
result Explicit formulas for DTE, DTV, DTS, and DTK for various distributions.
Paper uses AI to predict stock market volatility with neural networks and genetic algorithms.
problem Traditional methods for predicting stock market volatility have high errors.
method Back-propagation neural network and genetic algorithm integrated model.
result The model predicts future volatility with low errors and high accuracy.
Paper proposes a method to estimate truncated density models using Score Matching.
problem Estimating parameters of truncated probability densities.
method Score Matching with a novel weight function derived from Stein discrepancy.
result The proposed method minimizes a weighted Fisher divergence and corrects outlier-trimming bias.
New DP framework using data truncation for efficient estimation.
problem Differential privacy in unbounded data support.
method Data truncation, exponential family distributions, maximum likelihood estimation, DP stochastic gradient descent.
result Near-optimal sample complexity for Gaussian mean and covariance estimation.
Unified framework for mean testing under truncation bias.
problem High-dimensional mean testing under arbitrary truncation.
method Characterizes fundamental limits and develops a simple second-order test.
result Unified framework connects finite-moment, sub-Gaussian, and median-regular structural regimes.
Defines a calculus for integrating Moreau envelopes in differentiable programming.
problem Lack of a mathematical framework for applying Moreau envelopes to deep networks and machine learning systems.
method Develops a compositional calculus adapted to Moreau envelopes and integrates it into differentiable programming.
result Integrates Moreau envelopes into differentiable programming, enabling new gradient back-propagation methods.
A new backprop method reduces memory usage for deep neural networks.
problem Memory-intensive backpropagation in deep neural networks.
method Uses approximations of activations in buffers to reduce memory usage.
result Performance close to exact training with 4-bit precision activations.
Score matching method improves density estimation for truncated data on manifolds.
problem Density estimation for truncated data on manifolds with intractable normalising constant.
method Truncated score matching extended to Riemannian manifolds with boundary.
result Score matching estimator approximates true parameter values with low error.
The paper provides estimates for flows on Riemannian manifolds using truncated expansions.
problem Quantifying the relationship between flows on Riemannian manifolds and their truncated logarithms.
method Using truncated versions of the Magnus and Baker-Cambel-Hausdorff-Dynkin expansions.
result Quantitative estimates between flows and their truncated logarithms.
Algorithm estimates Gaussian parameters under unknown truncation sets.
problem Estimating Gaussian parameters when samples are truncated to unknown sets.
method Efficient algorithm for arbitrary unknown truncation sets, using Gaussian surface area as complexity measure.
result Algorithm works for large families of sets including intersections of halfspaces and general convex sets.
The method approximates stationary distributions of Markov models by truncating irrelevant states.
problem Computing the stationary distribution of complex Markov models is computationally challenging.
method A state-space lumping scheme that aggregates states in a grid structure, iteratively refining the state-space.
result The method provides a well-justified finite-state projection tailored to the stationary behavior of Markov models.
Paper tackles overestimation bias in continuous control, improving performance by 25%.
problem Overestimation bias in off-policy learning.
method Truncated Quantile Critics (TQC) combines distributional representation, truncation, and ensembling of critics.
result TQC outperforms state-of-the-art methods by 25% on the Humanoid environment.
A new method improves fitting neural data with spiking network models.
problem Fitting spiking network models to neural activity does not produce realistic data.
method Augment log-likelihood with dissimilarity terms measured by summary statistics and optimized via back-propagation.
result The new method generates more realistic neural activity statistics and improves network connectivity inference.
Paper learns dynamic generator models for video sequences.
problem Modeling spatial-temporal processes like dynamic textures and actions.
method Alternating back-propagation through time algorithm to learn latent state vectors and generator model.
result Trains realistic models for dynamic textures and actions.
We consider an appoximation of a catenoid constructed from "odd" truncated cones that maintains minimality in a certain sense. Thorough this procedure, we obtain a discrete curve approximating a catenary by exploiting the fact that it is the function that generates a catenoid. In this investigation, the theory of the G…
Estimates domain truncation error for option pricing PDEs.
problem Estimating error in option pricing models with domain truncation.
method Derives an estimate of domain truncation error for a multidimensional PDE system.
result Proposes a sharper error estimate for option pricing models.
We marry ideas from deep neural networks and approximate Bayesian inference to derive a generalised class of deep, directed generative models, endowed with a new algorithm for scalable inference and learning. Our algorithm introduces a recognition model to represent approximate posterior distributions, and that acts as…
Choppy optimizes ranked list truncation using Transformer architecture.
problem Optimal truncation of ranked search results to balance relevance and user cost.
method Assumption-free Transformer model optimizing user-defined IR metrics.
result Choppy improves upon recent state-of-the-art methods.
Paper proposes using truncated normal distribution for RRC model, improving detection of minority classes.
problem Improving weak classifiers in RRC models.
method Proposes using truncated normal distribution and soft confusion matrix for RRC model.
result Truncated-normal-based SCM algorithm outperforms beta distribution in discovering minority classes.
New COS method formula improves option pricing accuracy.
problem Determining the optimal truncation range for COS method.
method Derive new formula using Markov's inequality to ensure convergence.
result New formula leads to more accurate option pricing.
We solve for functions from their truncated Hilbert transforms using Chebyshev series.
problem Finding functions from their truncated Hilbert transforms.
method Express functions in Chebyshev series and numerically estimate coefficients.
result Numerical methods work well for extrapolating functions from truncated Hilbert transforms.
Adaptive TBPTT controls gradient bias in RNNs for faster convergence.
problem Choosing optimal truncation length in TBPTT for RNNs is difficult.
method Adaptive TBPTT converts lag selection to bias control, estimating optimal truncation length during training.
result Adaptive TBPTT improves convergence rate and computational efficiency in RNNs.
New method adapts without backprop, faster and better.
problem Efficient domain adaptation without source data.
method Computing class prototypes from pre-trained model.
result Significant accuracy improvements over pre-trained model.
Spectrally-truncated KRR outperforms full KRR for large data.
problem Computational intensity of KRR for large datasets.
method Spectrally truncating the kernel matrix to its largest r eigenvalues. result Spectrally-truncated KRR can outperform full KRR for all finite samples above a threshold.
The generalized correlation approach, which has been successfully used in statistical radio physics to describe non-Gaussian random processes, is proposed to describe stochastic financial processes. The generalized correlation approach has been used to describe a non-Gaussian random walk with independent, identically d…
Lower bound shows super-polynomial gap for estimating truncated Gaussian means.
problem Estimating mean of truncated Gaussian distribution with limited samples.
method Statistical Query (SQ) lower bounds for learning.
result Super-polynomial information-computation gap for the task.