Study finds Deep Taylor Decomposition is unreliable for explaining neural networks.
problem Reliability of Deep Taylor Decomposition for explaining neural networks.
method Investigated the theoretical foundations of Deep Taylor Decomposition (DTD) and found it under-constrained.
result DTD is unreliable because its theoretical foundations are under-constrained and roots do not align with input.
The Adomian decomposition method is shown to be equivalent to the Taylor series approach.
problem Incorrectly perceived complexity of the Adomian decomposition method.
method Demonstrates the Adomian decomposition method as equivalent to the Taylor series approach.
result The Adomian decomposition method is simpler and more straightforward.
A common machine learning task is to discriminate between normal and anomalous data points. In practice, it is not always sufficient to reach high accuracy at this task, one also would like to understand why a given data point has been predicted in a certain way. We present a new principled approach for one-class SVMs …
Nonlinear methods such as Deep Neural Networks (DNNs) are the gold standard for various challenging machine learning problems, e.g., image classification, natural language processing or human action recognition. Although these methods perform impressively well, they have a significant disadvantage, the lack of transpar…
In this article we will analyse how to compute the contribution of each input value to its aggregate output in some nonlinear models. Regression and classification applications, together with related algorithms for deep neural networks are presented. The proposed approach merges two methods currently present in the lit…
Developed Taylor series for muscle-finger system analysis.
problem Understanding the complex relationship between muscle activity and finger movement.
method Used Dendrite Net to develop Taylor series and construct relation spectrum.
result Found muscle synergy and coupling in hand movement.
Current techniques for explainable AI have been applied with some success to image processing. The recent rise of research in video processing has called for similar work n deconstructing and explaining spatio-temporal models. While many techniques are designed for 2D convolutional models, others are inherently applica…
Taylorized training improves neural network training at finite width.
problem Understanding and improving neural network training at finite width.
method Training the k-th order Taylor expansion of the neural network at initialization.
result Taylorized training agrees with full neural network training better as k increases and can significantly close the performance gap.
Understanding neural networks is becoming increasingly important. Over the last few years different types of visualisation and explanation methods have been proposed. However, none of them explicitly considered the behaviour in the presence of noise and distracting elements. In this work, we will show how noise and dis…
New sampling scheme improves ML accuracy in physics simulations.
problem Improving accuracy of ML models in physics simulations.
method Taylor-based data sampling scheme for DNNs.
result Reduces error in DNN solutions of ODE systems.
Unified framework for analyzing machine learning model attributions.
problem Lack of a general and theoretical framework for understanding attribution methods.
method Proposes a Taylor attribution framework to unify and analyze seven mainstream attribution methods.
result Established three principles for good attribution and empirically validated the Taylor reformulations.
TEAM uses Taylor expansion to generate adversarial examples.
problem Vulnerability of deep neural networks to adversarial examples.
method Approximates DNN output using Taylor expansion and optimizes with Lagrange multiplier method.
result Improves robustness of DNNs through adversarial training.
SOAR improves deep networks' robustness against adversarial examples.
problem Improving deep neural networks' robustness against adversarial examples.
method Formulated adversarial robustness problem under robust optimization framework, approximated loss function using second-order Taylor series expansion.
result SOAR significantly improves robustness of networks against adversarial perturbations.
New insights on pruning deep networks by preserving function locality.
problem Designing effective pruning methods for deep neural networks.
method Revisited loss modeling using first and second order Taylor expansions, emphasizing locality.
result Both first and second order Taylor expansions can achieve similar performance in pruning.
Proposes a Taylor framework to unify and analyze attribution methods.
problem Lack of a unified guideline for feature contribution assignment in machine learning models.
method Introduces a Taylor attribution framework to model the attribution problem and reformulates fourteen mainstream methods.
result Empirically validates the Taylor reformulations and reveals a positive correlation between performance and principles followed.
Paper presents a new backward deep BSDE method for solving nonlinear FBSDE problems.
problem Nonlinear Forward Backward Stochastic Differential Equations (FBSDE) with terminal conditions.
method Backward deep BSDE method applied to FBSDE with nonlinear generators and random initial conditions.
result Derives exact and Taylor-based approximations for time-stepping nonlinear BSDEs.
Modern convolutional networks, incorporating rectifiers and max-pooling, are neither smooth nor convex; standard guarantees therefore do not apply. Nevertheless, methods from convex optimization such as gradient descent and Adam are widely used as building blocks for deep learning algorithms. This paper provides the fi…
Deep networks are able to learn highly predictive models of video data. Due to video length, a common strategy is to train them on small video snippets. We apply the deep Taylor / LRP technique to understand the deep network's classification decisions, and identify a "border effect": a tendency of the classifier to loo…
SPIDER uses deep neural networks for streaming tensor factorization.
problem Lack of effective approach for deep tensor factorization of streaming data.
method Bayesian neural networks with spike-and-slab prior, Taylor expansions, moment matching, and EPI framework.
result Effective incremental updates for latent factors and NN weights.
New method finds better loss functions for neural nets.
problem Finding effective loss functions for deep neural networks.
method Optimizes multivariate Taylor polynomial parameterizations using CMA-ES.
result TaylorGLO finds loss functions that outperform existing methods.
Neural networks learn higher-order derivatives for physics problems.
problem Lack of higher-order derivatives in neural networks for theoretical physics.
method Graph-theoretical approach to assign diagrams to partial derivatives, iterative NN perturbation theory.
result NNs can learn higher-order derivatives, improving machine-learned approximations.
Kernelized Taylor diagram visualizes data populations with fewer assumptions.
problem Limitations of Taylor diagram in capturing non-linear relationships and sensitivity to outliers.
method Proposes a kernelized version of the Taylor diagram that uses maximum mean discrepancy and kernel mean embedding.
result Kernelized Taylor diagram visualizes data populations with minimal assumptions of data distributions.
Attribution methods aim to explain a neural network's prediction by highlighting the most relevant image areas. A popular approach is to backpropagate (BP) a custom relevance score using modified rules, rather than the gradient. We analyze an extensive set of modified BP methods: Deep Taylor Decomposition, Layer-wise R…
Let M and N be smooth manifolds without boundary. Immersion theory suggests that an understanding of the space of smooth embeddings emb(M,N) should come from an analysis of the cofunctor V |--> emb(V,N) from the poset O of open subsets of M to spaces. We therefore abstract some of the properties of this cofunctor, and …
Taylor expansions improve reinforcement learning policies.
problem Improving reinforcement learning policy optimization.
method Taylor expansion policy optimization.
result Taylor expansions enhance performance of distributed algorithms.
Generative adversarial networks (GANs) are an exciting alternative to algorithms for solving density estimation problems---using data to assess how likely samples are to be drawn from the same distribution. Instead of explicitly computing these probabilities, GANs learn a generator that can match the given probabilisti…
NN2Poly converts deep neural networks into polynomial models for better understanding.
problem Improving neural network interpretability and theoretical understanding.
method Taylor expansion on activation functions, combinatorial properties, and polynomial coefficients calculation.
result NN2Poly accurately represents deep feed-forward neural networks as polynomial models.
Improved saliency maps for deep neural networks with reduced noise.
problem Noisy explanations in Integrated Gradients for deep neural networks.
method SmoothTaylor, adaptive noising, and SmoothGrad techniques.
result SmoothTaylor and adaptive noising generate better quality saliency maps.
TEAM generates more powerful adversarial examples for DNNs.
problem Vulnerability of DNNs to imperceptible adversarial examples.
method TEAM uses Taylor expansion and Lagrangian multiplier method to craft adversarial examples.
result TEAM generates adversarial examples with 100% attack success rate using smaller perturbations.
Enhances influence functions for deep models without costly Hessian inversion.
problem Challenges in computing Hessian matrix inverse for deep models.
method Substitutes Hessian inverse with identity matrix and extends applications.
result TracIn method performs well in measuring model utility and fairness.
DDD reformulated for sparse matrices, integrating trajectory and snapshot time series data.
problem Efficiently integrate trajectory and snapshot time series data.
method Reformulate DDD to use compact basis functions, reducing parameter scaling.
result Inference of sparse matrices reduces the number of parameters in DDD.
Biological neurons learn tensor decompositions of higher-order correlations using nonlinear Hebbian plasticity.
problem Learning higher-order correlations in biological neurons.
method Introduce and study generalized nonlinear Hebbian learning rules.
result Neurons can learn tensor eigenvectors of higher-order input correlation tensors.
New samplers reduce NFEs for diffusion models.
problem High NFEs in diffusion models.
method Quasi-Taylor samplers based on ideal derivatives.
result Reduced NFEs for image synthesis.
In the present paper, a decomposition formula for the call price due to Alòs is transformed into a Taylor type formula containing an infinite series with stochastic terms. The new decomposition may be considered as an alternative to the decomposition of the call price found in a recent paper of Alòs, Gatheral and Radoi…
The first aperiodic monotiling, introduced by Taylor, was based on a trapezoidal prototile equipped with 14 distinct decorations. A presentation of the closely related Taylor-Socolar aperiodic monotiling is based on a hexagonal prototile equipped with 7 decorations. This paper gives decoration-free algebraic descriptio…
The paper is concerned with non-linear Gaussian filtering and smoothing in continuous-discrete state-space models, where the dynamic model is formulated as an Itô stochastic differential equation (SDE), and the measurements are obtained at discrete time instants. We propose novel Taylor moment expansion (TME) Gaussian …
New method improves neural network performance by focusing on steep function regions.
problem Improving neural network performance by focusing on steep function regions.
method Variance Based Samples Weighting (VBSW) using labels local variance to weight training points.
result Significantly increases the performances of neural networks for various tasks.
New approximations for Asian basket spread options using stochastic Taylor expansions.
problem Pricing Asian basket spread options under the Black-Scholes model.
method Stochastic Taylor expansion applied to a log-normal proxy model.
result Highly accurate approximations for Asian and spread options, without numerical integration.
FFCP improves FCP's speed without sacrificing accuracy.
problem Inefficient feature transformation in FCP.
method Introduces FFCP using Taylor expansion for faster computation.
result FFCP achieves a 50x speedup with comparable accuracy.
Develops state-space deep Gaussian processes for irregular signals.
problem Solving deep Gaussian process regression problems for irregular signals/functions.
method Represent DGPs as SDEs, solve using state-space filtering and smoothing methods.
result Rich class of priors compatible with irregular signals/functions.
Paper develops a new algorithm to find shortest paths on surfaces.
problem Finding shortest paths on surfaces with defined metrics.
method Uses Taylor expansion of exponential map for numerical computation.
result Developed a new algorithm to find geodesics efficiently.
TaylorPODA uses Taylor expansions to improve feature attributions for opaque models.
problem Lack of systematic framework for quantifying feature contributions in opaque models.
method Taylor expansion framework with postulates (precision, federation, zero-discrepancy, adaptation).
result TaylorPODA achieves competitive results and provides principled explanations.
The paper explores tensor decompositions in deep learning models.
problem Compressing parameter space and creating richer representations.
method Tensor decompositions applied to deep learning models.
result Tensor methods can yield richer adaptive representations of complex data.
Article presents QR and LQ decomposition algorithms for various matrix sizes and ranks.
problem Solving least squares problems in machine learning and computer vision.
method Developed novel matrix backpropagation algorithms for QR and LQ decompositions of different matrix sizes and ranks.
result Numerical stability and computational efficiency of the proposed methods.
Proves a special case of the Gaussian kinematic formula using large sphere limits.
problem Proving a special case of the Gaussian kinematic formula.
method Viewing the GKF as the limit of spherical kinematic formulas for large dimension spheres.
result Proves a special case of the Gaussian kinematic formula.
We introduce Taylor expansions that do not require the differentiability. We also provide new solutions to partial differential equations. We apply our methods to finance.
An expanding literature articulates the view that Taylor rules are helpful in predicting exchange rates. In a changing world however, Taylor rule parameters may be subject to structural instabilities, for example during the Global Financial Crisis. This paper forecasts exchange rates using such Taylor rules with Time V…
In this work we consider the Taylor expansion of the exponential map of a submanifold immersed in R^n up to order three, in order to introduce the concepts of lateral and frontal deviation. We compute the directions of extreme lateral and frontal deviation for surfaces in R^3. Also we compute, by using the Taylor expan…