Training Neural Networks with Implicit Variance.

We present a novel method to train predictive Gaussian distributions p(z|x) for regression problems with neural networks. ... While most approaches either ignore or explicitly model the variance as another response variable, it is trained implicitly in our case. ... To compare plain neural networks (NN), density networks (DN), networks trained with fast dropout (FD) and implicit variance networks (IVN), we constructed a setting which is far from tailored towards neural ...

doi:10.1007/978-3-642-42042-9_17 fatcat:bjggng4xgvgtvnsumdrtoto6iy

Derivation of a class of training algorithms. IEEE Transact. Neural Networks 1, 1229-1232. Martinetz, T., and Schulten, K. 1991. A ‘neural gas’ network learns topologies. Proc. ICANN-91, 397-402. ... In general, the cost of an implicit coordinate depends on the ratio between its variance (over all the different bumps) and the accuracy with which it must be communicated. ...

neural networks. ... It turns out that the presence of recurrent intra-layer connections within a one-layer implicit recurrent network enhances the performance of neural networks considerably: A single-layer implicit recurrent ... Our work indicates that with the use of implicit recurrent neural networks, it is also possible to increase the computational power of neural networks. ...

arXiv:2010.10564v1 fatcat:grnryhkxajgtvnypomchbcinmm

,” is implicit in much of the work about neural networks. ... The fundamental limitations resulting from the bias-variance dilemma apply to all nonparametric inference methods, including neural networks. ...

We term this as implicit saliency in deep neural networks. We calculate this implicit saliency using expectancy-mismatch hypothesis in an unsupervised fashion. ... Based on We introduce the background for the pre-trained deep neural networks in Section 2. In Section 3, we detail the proposed method to extract implicit saliency. ... To set expectancy, we use neural networks. ...

arXiv:2008.01874v1 fatcat:5d4ke26ofrculbsi54tj3257hi

During testing, we use a deterministic network with a new activation function to encode the average effect of dropping activations randomly. ... The experimental results on CIFAR-10, CIFAR-100, SVHN, EMNIST, and ImageNet show that Drop-Activation generally improves the performance of popular neural network architectures for the image classification ... Supercomputing Center (NSCC) Singapore [1] and High-Performance Computing (HPC) of the National University of Singapore for providing computational resources, and the support of NVIDIA Corporation with ...

arXiv:1811.05850v5 fatcat:smj77ifkcjbhpigzznmas52v3m

Multiple Versions

We present neural radiance fields (NeRF) with templates, dubbed Template-NeRF, for modeling appearance and geometry and generating dense shape correspondences simultaneously among objects of the same category ... We demonstrate the results and applications on both synthetic and real-world data with competitive results compared with other methods based on 3D information. ... Related Work Implicit Neural Representations and Rendering. ...

arXiv:2111.04237v1 fatcat:sulvlx4y6vfntnyi5pur5nhvxq

Open Access

IPs are therefore highly flexible implicit priors over functions, with examples including data simulators, Bayesian neural networks and non-linear transformations of stochastic processes. ... Experiments show that VIPs return better uncertainty estimates and lower errors over existing inference methods for challenging models such as Bayesian neural networks, and Gaussian processes. ... We also train VIP with neural sampler prior (VIP-NS), as defined in section 2. All neural networks use a 10-10-1 structure with two hidden layers of size 10. ...

arXiv:1806.02390v2 fatcat:t3yn25i3frff3plo7mjbgfnd4u

Multiple Versions

We demonstrate our scheme on different applications: (i) neural ODEs with the implicit Euler method, and (ii) system identification in model predictive control. ... These functions are parametrized by a set of learnable weights and may optionally depend on some input; making them perfectly suitable as a learnable layer in a neural network. ... Related Work Recurrent backpropagation (RBP) [Pineda, 1988 , Almeida, 1990 ] is the first training method for a specific type of implicit neural networks, i.e. infinitely deep recurrent neural networks ...

arXiv:2010.07078v2 fatcat:haa66iewtjaudb2g7nhm23otba

Multiple Versions

In our paper we compare these results with an alternative direct approach where the the mapping from market implied volatilities to model parameters is approximated by the neural network, without the need ... The paper should be understood as a technical comparison of neural network techniques and not as an methodically new Ansatz. ... For example for the Rough Bergomi model with piece-wise forward variance we use three hidden layers with 68, 49, and 30 neurons, which amount to 11274 calibration parameter of the neural network. ...

arXiv:2007.03494v1 fatcat:m6ocn3tvxvexrbtpr6nucskrm4

Without the necessity of pathwise gradients, our approach allows the design process to be achieved through a unified procedure with an approximate gradient for implicit models. ... However, the approach requires a sampling path to compute the pathwise gradient of the MI lower bound with respect to the design variables, and such a pathwise gradient is usually inaccessible for implicit ... Figure 1 shows the MI lower bound as a function of neural network training epochs. ...

arXiv:2103.08026v1 fatcat:jksb3ia75vfbdn3xakpvvqy2ma

Open Access

This paper derives the generalized extreme value (GEV) model with implicit availability/perception (IAP) of alternatives and proposes a variational autoencoder (VAE) approach for choice set generation ... and implicit perception of alternatives. ... network, and are the weights of the neural network, variance σ is a fixed hyperparameter, and ( | ) is bound from below at 0. ...

arXiv:2106.13319v1 fatcat:hg2kcd7isngwbc73w76qhvn46u

As far as we know, for the first time implicit variational inference is successfully applied to Bayesian neural networks, which shows promising results on both regression and classification tasks. ... However, existing methods on implicit posteriors still face challenges of noisy estimation and computational infeasibility when applied to models with high-dimensional latent variables. ... Thus, we can use an MMNN as g in the variational posterior for normal-size neural networks. In tasks with very small networks, we still use an MLP as g. ...

arXiv:1705.10119v3 fatcat:fjajtfw5urabpjbj45y3swjlnq

Multiple Versions

This suggests that there might not be a bias-variance tradeoff in neural networks with respect to network width, unlike was originally claimed by, e.g., Geman et al. (1992). ... However, recent empirical results with over-parameterized neural networks are marked by a striking absence of the classic U-shaped test error curve: test error keeps decreasing in wider networks. ... Visualization with regression on sinusoid We trained different width neural networks on a noisy sinusoidal distribution with 80 independent training examples. ...

arXiv:1810.08591v4 fatcat:w4pj2e3szrhvjpzbfmjel25lzy

Multiple Versions

Current methods for the interpretability of discriminative deep neural networks commonly rely on the model's input-gradients, i.e., the gradients of the output logits w.r.t. the inputs. ... Our experiments show that improving the alignment of the implicit density model with the data distribution enhances gradient structure and explanatory power while reducing this alignment has the opposite ... Score-Matching We propose to use the score-matching objective as a regularizer in neural network training to increase the alignment of the implicit density model to the ground truth, as shown in equation ...

arXiv:2006.09128v2 fatcat:ghtkibd3hbclfgoimsnqr2f75i

Open Access Multiple Versions

Training Neural Networks with Implicit Variance [chapter]

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Page 563 of Neural Computation Vol. 7, Issue 3 [page]

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Implicit recurrent networks: A novel approach to stationary input processing with recurrent neural networks in deep learning [article]

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Page 45 of Neural Computation Vol. 4, Issue 1 [page]

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Implicit Saliency in Deep Neural Networks [article]

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Drop-Activation: Implicit Parameter Reduction and Harmonic Regularization [article]

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Template NeRF: Towards Modeling Dense Shape Correspondences from Category-Specific Object Images [article]

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Variational Implicit Processes [article]

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Differentiable Implicit Layers [article]

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Volatility model calibration with neural networks a comparison between direct and indirect methods [article]

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A Scalable Gradient-Free Method for Bayesian Experimental Design with Implicit Models [article]

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A variational autoencoder approach for choice set generation and implicit perception of alternatives in choice modeling [article]

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Kernel Implicit Variational Inference [article]

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A Modern Take on the Bias-Variance Tradeoff in Neural Networks [article]

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Rethinking the Role of Gradient-Based Attribution Methods for Model Interpretability [article]

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