Welcome to ShortScience.org! |

- ShortScience.org is a platform for post-publication discussion aiming to improve accessibility and reproducibility of research ideas.
- The website has 1584 public summaries, mostly in machine learning, written by the community and organized by paper, conference, and year.
- Reading summaries of papers is useful to obtain the perspective and insight of another reader, why they liked or disliked it, and their attempt to demystify complicated sections.
- Also, writing summaries is a good exercise to understand the content of a paper because you are forced to challenge your assumptions when explaining it.
- Finally, you can keep up to date with the flood of research by reading the latest summaries on our Twitter and Facebook pages.

Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift

Ioffe, Sergey and Szegedy, Christian

International Conference on Machine Learning - 2015 via Local Bibsonomy

Keywords: dblp

Ioffe, Sergey and Szegedy, Christian

International Conference on Machine Learning - 2015 via Local Bibsonomy

Keywords: dblp

[link]
The main contribution of this paper is introducing a new transformation that the authors call Batch Normalization (BN). The need for BN comes from the fact that during the training of deep neural networks (DNNs) the distribution of each layer’s input change. This phenomenon is called internal covariate shift (ICS). #### What is BN? Normalize each (scalar) feature independently with respect to the mean and variance of the mini batch. Scale and shift the normalized values with two new parameters (per activation) that will be learned. The BN consists of making normalization part of the model architecture. #### What do we gain? According to the author, the use of BN provides a great speed up in the training of DNNs. In particular, the gains are greater when it is combined with higher learning rates. In addition, BN works as a regularizer for the model which allows to use less dropout or less L2 normalization. Furthermore, since the distribution of the inputs is normalized, it also allows to use sigmoids as activation functions without the saturation problem. #### What follows? This seems to be specially promising for training recurrent neural networks (RNNs). The vanishing and exploding gradient problems \cite{journals/tnn/BengioSF94} have their origin in the iteration of transformation that scale up or down the activations in certain directions (eigenvectors). It seems that this regularization would be specially useful in this context since this would allow the gradient to flow more easily. When we unroll the RNNs, we usually have ultra deep networks. #### Like * Simple idea that seems to improve training. * Makes training faster. * Simple to implement. Probably. * You can be less careful with initialization. #### Dislike * Does not work with stochastic gradient descent (minibatch size = 1). * This could reduce the parallelism of the algorithm since now all the examples in a mini batch are tied. * Results on ensemble of networks for ImageNet makes it harder to evaluate the relevance of BN by itself. (Although they do mention the performance of a single model). |

Cutting out the Middle-Man: Training and Evaluating Energy-Based Models without Sampling

Grathwohl, Will and Wang, Kuan-Chieh and Jacobsen, Jorn-Henrik and Duvenaud, David and Zemel, Richard

- 2020 via Local Bibsonomy

Keywords: bayesian, generative-models, energy-models, uncertainty

Grathwohl, Will and Wang, Kuan-Chieh and Jacobsen, Jorn-Henrik and Duvenaud, David and Zemel, Richard

- 2020 via Local Bibsonomy

Keywords: bayesian, generative-models, energy-models, uncertainty

[link]
The authors introduce a new, sampling-free method for training and evaluating energy-based models (aka EBMs, aka unnormalized density models). There are two broad approches for training EBMs. Sampling-based approaches like contrastive divergence try to estimate the likelihood with MCMC, but can be biased if the chain is not sufficiently long. The speed of training also greatly depends on the sampling parameters. Other approches, like score matching, avoid sampling by solving a surrogate objective that approximates the likelihood. However, using a surrogate objective also introduces bias in the solution. In any case, comparing goodness of fit of different models is challenging, regardless of how the models were trained. The authors introduce a measure of probability distance between distributions $p$ and $q$ called the Learned Stein Discrepancy ($LSD$): $$ LSD(f_{\phi}, p, q) = \mathbb{E}_{p(x)} [\nabla_x \log q(x)^T f_{\phi}(x) + Tr(\nabla_x f_{\phi} (x)) $$ This measure is derived from the Stein Discrepancy $SD(p,q)$. Note that like the $SD$, the $LSD$ is 0 iff $p = q$. Typically, $p$ is the data distribution and $q$ is the learned approximate distribution (an EBM), although this doesn't have to be the case. Note also that this objective only requires a differentiable unnormalized distribution $\tilde{q}$, and does not require MCMC sampling or computation of the normalizing constant $Z$, since $\nabla_x \log q(x) = \nabla_x \log \tilde{q}(x) - \nabla_x \log Z = \nabla_x \log \tilde{q}(x)$. $f_\phi$ is known as the critic function, and minimizing the $LSD$ with respect to $\phi$ (i.e. with gradient descent) over a bounded space of functions $\mathcal{F}$ can approximate the $SD$ over that space. The authors choose to define the function space $\mathcal{F} = \{ f: \mathbb{E}_{p(x)} [f(x)^Tf(x)] < \infty \}$, which is convenient because it can be optimized by introducing a simple L2 regularizer on the critic's output: $\mathcal{R}_\lambda (f_\phi) = \lambda \mathbb{E}_{p(x)} [f_\phi(x)^T f_\phi(x)]$. Since the trace of a matrix is expensive to backpropagate through, the authors use a single-sample Monte Carlo estimate $Tr(\nabla_x f_\phi(x)) \approx \mathbb{E}_{\mathbb{N}(\epsilon|0,1)} [\epsilon^T \nabla_x f_\phi(x) \epsilon] $, which is more efficient since $\epsilon^T \nabla_x f_\phi(x)$ is a vector-Jacobian product. The overall objective is thus the following: $$ \text{arg} \max_\phi \mathbb{E}_{p(x)} [\nabla_x \log q(x)^T f_{\phi}(x) + \mathbb{E}_{\epsilon} [\epsilon^T \nabla_x f_{\phi} (x) \epsilon)] - \lambda f_\phi(x)^T f_\phi(x)] $$ It is possible to compare two different EBMs $q_1$ and $q_2$ by optimizing the above objective for two different critic parameters $\phi_1$ and $\phi_2$, using the training and validation data for critic optimization (then evaluating on the held-out test set). Note that when computing the $LSD$ on the test set, the exact trace can be computed instead of the Monte Carlo approximation to reduce variance, since gradients are no longer required. The model that is closer to 0 has achieved a better fit. Similarly, a hypothesis test using the $LSD$ can be used to test if $p = q$ for the data distribution $p$ and model distribution $q$. The authors then show how EBM parameters $\theta$ can actually be optimized by gradient descent on the $LSD$ objective, in a minimax problem that is similar to the problem of optimizing a generative adversarial network (GAN). For given $\theta$, you first optimize the critic $f_\phi$ w.r.t. $\phi$ to try to get the $LSD(f_\phi, p, q_\theta)$ close to its theoretical optimum with the current $q_\theta$, then you take a single gradient step $\nabla_\theta LSD$ to minimize the $LSD$. They show some experiments that indicates that this works pretty well. One thing that was not clear to me when reading this paper is whether the $LSD(f_\phi,p,q)$ should be minimized or maximized with respect to $\phi$ to get it close to the true $SD(p,q)$. Although it it possible for $LSD$ to be above or below 0 for a given choice of $q$ and $f_\phi$, the problem can always be formulated as minimization by simply changing the sign of $f_\phi$ at the beginning such that the $LSD$ is positive (or as maximization by making it negative). |

Understanding deep learning requires rethinking generalization

Chiyuan Zhang and Samy Bengio and Moritz Hardt and Benjamin Recht and Oriol Vinyals

arXiv e-Print archive - 2016 via Local arXiv

Keywords: cs.LG

**First published:** 2016/11/10 (7 years ago)

**Abstract:** Despite their massive size, successful deep artificial neural networks can
exhibit a remarkably small difference between training and test performance.
Conventional wisdom attributes small generalization error either to properties
of the model family, or to the regularization techniques used during training.
Through extensive systematic experiments, we show how these traditional
approaches fail to explain why large neural networks generalize well in
practice. Specifically, our experiments establish that state-of-the-art
convolutional networks for image classification trained with stochastic
gradient methods easily fit a random labeling of the training data. This
phenomenon is qualitatively unaffected by explicit regularization, and occurs
even if we replace the true images by completely unstructured random noise. We
corroborate these experimental findings with a theoretical construction showing
that simple depth two neural networks already have perfect finite sample
expressivity as soon as the number of parameters exceeds the number of data
points as it usually does in practice.
We interpret our experimental findings by comparison with traditional models.
more
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Chiyuan Zhang and Samy Bengio and Moritz Hardt and Benjamin Recht and Oriol Vinyals

arXiv e-Print archive - 2016 via Local arXiv

Keywords: cs.LG

[link]
This paper deals with the question what / how exactly CNNs learn, considering the fact that they usually have more trainable parameters than data points on which they are trained. When the authors write "deep neural networks", they are talking about Inception V3, AlexNet and MLPs. ## Key contributions * Deep neural networks easily fit random labels (achieving a training error of 0 and a test error which is just randomly guessing labels as expected). $\Rightarrow$Those architectures can simply brute-force memorize the training data. * Deep neural networks fit random images (e.g. Gaussian noise) with 0 training error. The authors conclude that VC-dimension / Rademacher complexity, and uniform stability are bad explanations for generalization capabilities of neural networks * The authors give a construction for a 2-layer network with $p = 2n+d$ parameters - where $n$ is the number of samples and $d$ is the dimension of each sample - which can easily fit any labeling. (Finite sample expressivity). See section 4. ## What I learned * Any measure $m$ of the generalization capability of classifiers $H$ should take the percentage of corrupted labels ($p_c \in [0, 1]$, where $p_c =0$ is a perfect labeling and $p_c=1$ is totally random) into account: If $p_c = 1$, then $m()$ should be 0, too, as it is impossible to learn something meaningful with totally random labels. * We seem to have built models which work well on image data in general, but not "natural" / meaningful images as we thought. ## Funny > deep neural nets remain mysterious for many reasons > Note that this is not exactly simple as the kernel matrix requires 30GB to store in memory. Nonetheless, this system can be solved in under 3 minutes in on a commodity workstation with 24 cores and 256 GB of RAM with a conventional LAPACK call. ## See also * [Deep Nets Don't Learn Via Memorization](https://openreview.net/pdf?id=rJv6ZgHYg) |

Automatic chemical design using a data-driven continuous representation of molecules

Gómez-Bombarelli, Rafael and Duvenaud, David and Hernández-Lobato, José Miguel and Aguilera-Iparraguirre, Jorge and Hirzel, Timothy D. and Adams, Ryan P. and Aspuru-Guzik, Alán

arXiv e-Print archive - 2016 via Local Bibsonomy

Keywords: dblp

Gómez-Bombarelli, Rafael and Duvenaud, David and Hernández-Lobato, José Miguel and Aguilera-Iparraguirre, Jorge and Hirzel, Timothy D. and Adams, Ryan P. and Aspuru-Guzik, Alán

arXiv e-Print archive - 2016 via Local Bibsonomy

Keywords: dblp

[link]
I'll admit that I found this paper a bit of a letdown to read, relative to expectations rooted in its high citation count, and my general excitement and interest to see how deep learning could be brought to bear on molecular design. But before a critique, let's first walk through the mechanics of how the authors' approach works. The method proposed is basically a very straightforward Variational Auto Encoder, or VAE. It takes in a textual SMILES string representation of a molecular structure, uses an encoder to map that into a continuous vector representation, a decoder to map the vector representation back into a a SMILES string, and an auxiliary predictor to predict properties of a molecule given the continuous representation. So, the training loss is a combination of the reconstruction loss (log probability of the true molecule under the distribution produced by the decoder) and the semi-supervised predictive loss. The hope with this model is that it would allow you to sample from a space of potential molecules by starting from an existing molecule, and then optimizing the the vector representation of that molecule to make it score higher on whatever property you want to optimize for. https://i.imgur.com/WzZsCOB.png The authors acknowledge that, in this setup, you're just producing a probability distribution over characters, and that the continuous vectors sampled from the latent space might not actually map to valid SMILES strings, and beyond that may well not correspond to chemically valid molecules. Empirically, they said that the proportion of valid generated molecules ranged between 1 and 70%. But they argue that it'd be too difficult to enforce those constraints, and instead just sample from the model and run the results through a hand-designed filter for molecular validity. In my view, this is the central weakness of the method proposed in this paper: that they seem to have not tackled the question of either chemical viability or even syntactic correctness of the produced molecules. I found it difficult to nail down from the paper what the ultimate percentage of valid molecules was from points in latent space that were off of the training . A table reports "percentage of 5000 randomly-selected latent points that decode to valid molecules after 1000 attempts," but I'm confused by what the 1000 attempts means here - does that mean we draw 1000 samples from the distribution given by the decoder, and see if *any* of those samples are valid? That would be a strange metric, if so, and perhaps it means something different, but it's hard to tell. https://i.imgur.com/9sy0MXB.png This paper made me really curious to see whether a GAN could do better in this space, since it would presumably be better at the task of incentivizing syntactic correctness of produced strings (given that any deviation from correctness could be signal for the discriminator), but it might also lead to issues around mode collapse, and when I last checked the literature, GANs on text data in particular were still not great. |

Not All Unlabeled Data are Equal: Learning to Weight Data in Semi-supervised Learning

Ren, Zhongzheng and Yeh, Raymond A. and Schwing, Alexander G.

- 2020 via Local Bibsonomy

Keywords: dataset, semi-supervised, machine-learning, data, 2020

Ren, Zhongzheng and Yeh, Raymond A. and Schwing, Alexander G.

- 2020 via Local Bibsonomy

Keywords: dataset, semi-supervised, machine-learning, data, 2020

[link]
This paper argues that, in semi-supervised learning, it's suboptimal to use the same weight for all examples (as happens implicitly, when the unsupervised component of the loss for each example is just added together directly. Instead, it tries to learn weights for each specific data example, through a meta-learning-esque process. The form of semi-supervised learning being discussed here is label-based consistency loss, where a labeled image is augmented and run through the current version of the model, and the model is optimized to try to induce the same loss for the augmented image as the unaugmented one. The premise of the authors argument for learning per-example weights is that, ideally, you would enforce consistency loss less on examples where a model was unconfident in its label prediction for an unlabeled example. As a way to solve this, the authors suggest learning a vector of parameters - one for each example in the dataset - where element i in the vector is a weight for element i of the dataset, in the summed-up unsupervised loss. They do this via a two-step process, where first they optimize the parameters of the network given the example weights, and then the optimize the example weights themselves. To optimize example weights, they calculate a gradient of those weights on the post-training validation loss, which requires backpropogating through the optimization process (to determine how different weights might have produced a different gradient, which might in turn have produced better validation loss). This requires calculating the inverse Hessian (second derivative matrix of the loss), which is, generally speaking, a quite costly operation for huge-parameter nets. To lessen this cost, they pretend that only the final layer of weights in the network are being optimized, and so only calculate the Hessian with respect to those weights. They also try to minimize cost by only updating the example weights for the examples that were used during the previous update step, since, presumably those were the only ones we have enough information to upweight or downweight. With this model, the authors achieve modest improvements - performance comparable to or within-error-bounds better than the current state of the art, FixMatch. Overall, I find this paper a little baffling. It's just a crazy amount of effort to throw into something that is a minor improvement. A few issues I have with the approach: - They don't seem to have benchmarked against the simpler baseline of some inverse of using Dropout-estimated uncertainty as the weight on examples, which would, presumably, more directly capture the property of "is my model unsure of its prediction on this unlabeled example" - If the presumed need for this is the lack of certainty of the model, that's a non-stationary problem that's going to change throughout the course of training, and so I'd worry that you're basically taking steps in the direction of a moving target - Despite using techniques rooted in meta-learning, it doesn't seem like this models learns anything generalizable - it's learning index-based weights on specific examples, which doesn't give it anything useful it can do with some new data point it finds that it wasn't specifically trained on Given that, I think I'd need to see a much stronger case for dramatic performance benefits for something like this to seem like it was worth the increase in complexity (not to mention computation, even with the optimized Hessian scheme) |

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