One of those things was the release of PyTorch library in version 1. Model class API. If you don't know about VAE, go through the following links. The following are code examples for showing how to use torch. pytorch的主要概念. But you can choose other function and optimizer. Return the cross-entropy between an approximating distribution and a true distribution. Each training epoch includes a forward propagation, which yields some training hypothesis for training source sentences; then cross_entropy calculates loss for this hypothesis and loss. Cross Entropy Loss. Adversarial Variational Bayes in Pytorch¶ In the previous post, we implemented a Variational Autoencoder, and pointed out a few problems. The discovered approach helps to train both convolutional and dense deep sparsified models without significant loss of quality. Both loss and adversarial loss are backpropagated for the total loss. If the language model assigns a probability of 0. The architecture of the classsifier the neural network is almost the same as for regression one, except for the last layer. In this post, we go through an example from Natural Language Processing, in which we learn how to load text data and perform Named Entity Recognition (NER) tagging for each token. >>> PyTorch Tutorials Name: Process input through the network 3. Through our experiments we also compare and analyze the performance of our 2D and 3D models, both which achieve near state-of-the-art accuracy scores in terms of. PyTorch Loss-Input Confusion (Cheatsheet) torch. - zllrunning/SiameseX. But we also define 'adversarial loss' which is a loss based on F(X + e). When we defined the loss and optimization functions for our CNN, we used the torch. there is something I don't understand in the PyTorch implementation of Cross Entropy Loss. Pytorch with Google Colab. is_available() else "cpu") #Check whether a GPU is present. KLDivLoss: a Kullback-Leibler divergence loss. The full code is available in my github repo: link. Train our feed-forward network. I also defined a binary cross entropy loss and Adam optimizer to be used for the computation of loss and weight updates during training. 0006459923297370551 dcba. The transposed convolution operator multiplies each input value element-wise by a learnable kernel, and sums over the outputs from all input feature planes. In PyTorch, we use torch. class: center, middle, title-slide count: false # Regressions, Classification and PyTorch Basics. By using the cross-entropy loss we can find the difference between the predicted probability distribution and actual probability distribution to compute the loss of the network. The maximization of. α(alpha): balances focal loss, yields slightly improved accuracy over the non-α-balanced form. In the pasted setup, we have 20 latent variables representing 28×20=560 input pixels of the original image. Both of these losses compute the cross-entropy between the prediction of the network and the given ground truth. We could also use. Autoencoders can encode an input image to a latent vector and decode it, but they can't generate novel images. The MRNet is a convolutional neural network that takes as input an MRI scan and outputs a classification prediction, namely an ACL tear probability. Backward propagation for the optimization of the model (or weights) is performed (Notice that we set optimizer to zero grad. Although its usage in Pytorch in unclear as much open source implementations and examples are not. CrossEntropyLoss(). 사용되는 torch 함수들의 사용법은 여기에서 확인할 수 있다. Here we'll try to respect the paper by using the SGD optimizer and a momentum of 0. Pytorch_example : another complete pytorch example for Is a function connecting an input to an output Depends on (a lot of) parameters Cross-entropy loss (d. This summarizes some important APIs for the neural networks. device("cuda:0" if torch. During training, the loss function at the outputs is the Binary Cross Entropy. com/course/ud730. You can vote up the examples you like or vote down the ones you don't like. there is something I don't understand in the PyTorch implementation of Cross Entropy Loss. Training of D proceeds using the loss function of D. Since VAE is based in a probabilistic interpretation, the reconstruction loss used is the cross-entropy loss mentioned earlier. create a tensor y where all the values are 0. by Matthew Baas. His focus is making mixed-precision and multi-GPU training in PyTorch fast, numerically stable, and easy to use. I then created a class for the simple MLP model and defined the layers such that we can specify any number and size of hidden layers. 100%| | 100000/100000 [12:16<00:00, 135. class ConvTranspose3d (_ConvTransposeMixin, _ConvNd): r """Applies a 3D transposed convolution operator over an input image composed of several input planes. This is precisely how the loss is implemented for graph-based deep learning frameworks such as PyTorch and TensorFlow. We use a cross entropy loss, with momentum based SGD optimisation algorithm. Cross Entropy Loss. The following are code examples for showing how to use torch. losses = tf. BCEWithLogitsLoss. backward # backpropagation, compute gradients optimizer. The authors also noted that there would be class imbalances for the colour values. It consists of two loss functions: 1) cross-entropy loss for classification, which learned by labeled source samples; 2) triplet loss for similarity learning, which imposes camera invariance and domain connectedness to the model and learned through labeled source samples, unlabeled target samples and cameras style transferred samples. Now let's have a look at a Pytorch implementation below. I am the founder of MathInf GmbH, where we help your business with PyTorch training and AI modelling. One of those things was the release of PyTorch library in version 1. Here's a simple example of how to calculate Cross Entropy Loss. However, for this chapter, let's implement the loss function ourselves:. In this post, we go through an example from Natural Language Processing, in which we learn how to load text data and perform Named Entity Recognition (NER) tagging for each token. e is defined as dF(X)/dX multiplied by some constant. That means it’s time to derive some gradients! ⚠️ The following section assumes a basic knowledge of multivariable calculus. device("cuda:0" if torch. Derspite the name, since there is no notion of a training set or minibatches here, this is not actually stochastic gradient descent, but just gradient descent. Softmax loss and cross-entropy loss terms are used interchangeably in industry. Implementing a logistic regression model using PyTorch; the input data has the shape (m_examples, Implement the computation of the binary cross-entropy loss. We use a cross entropy loss, with momentum based SGD optimisation algorithm. Variational Dropout Sparsifies NN (Pytorch) Make your neural network 300 times faster! Pytorch implementation of Variational Dropout Sparsifies Deep Neural Networks (arxiv:1701. package Array; /** * 旋转数组的最小数字 * 把一个数组最开始的若干个元素搬到数组的末尾,我们称之为数组的旋转。. Tell me more about Cross Entropy Loss. We also used a smooth factor of 1 for backpropagation. Since this is a regression problem, we use a loss function called sum of squared. Introduction to TensorFlow and PyTorch Kendall Chuang and David Clark February 16, 2017 2. These scenarios cover input sequences of fixed and variable length as well as the loss functions CTC and cross entropy. In PyTorch, we use torch. BCELoss: a binary cross entropy loss, torch. 4], during the second try [0. data # 要把 h_state 重新包装一下才能放入下一个 iteration, 不然会报错 loss = loss_func (prediction, y) # cross entropy loss optimizer. Which loss function should you use to train your machine learning model? The huber loss? Cross entropy loss? How about mean squared error? If all of those seem confusing, this video will help. BCELoss, binary cross entropy criterion. I've implemented an analog of weighted_cross_entropy_with_logits in my current project. a handle that can be used to remove the added hook by calling handle. A Friendly Introduction to Cross-Entropy Loss. Introduces entropy, cross entropy, KL divergence, and discusses connections to likelihood. nll_loss (outputs, Variable (labels)) Note that we don't use the Cross Entropy loss function since the outputs are already the logarithms of the softmax, and that the labels must also be wrapped inside a Variable. Another step not shown is dropout, which we will apply after Softmax. In PyTorch, these refer to implementations that accept different input arguments (but compute the same thing). We then take the mean of the losses. In order to enforce this property a second term is added to the loss function in the form of a Kullback-Liebler (KL) divergence between the distribution created by the encoder and the prior distribution. But PyTorch treats them as outputs, that don't need to sum to 1, and need to be first converted into probabilities for which it uses the sigmoid function. This initialization is the default initialization in Pytorch , that means we don’t need to any code changes to implement this. In the pasted setup, we have 20 latent variables representing 28×20=560 input pixels of the original image. His focus is making mixed-precision and multi-GPU training in PyTorch fast, numerically stable, and easy to use. edu is a platform for academics to share research papers. Basic Models in TensorFlow CS 20SI: TensorFlow for Deep Learning Research Lecture 3 1/20/2017 1. Loss function. The overlap between classes was one of the key problems. We suppose you have had fundamental understanding of Anaconda Python, created Anaconda virtual environment (in my case, it's named condaenv), and had PyTorch installed successfully under this Anaconda virtual environment condaenv. Ok, enough discussion. For a quick understanding of Feedforward Neural Network, you can have a look at our previous article. PyTorch is a popular deep learning library released by Facebook’s AI Research lab. During last year (2018) a lot of great stuff happened in the field of Deep Learning. These steps include subtracting a mean pixel value and scaling the image. 100%| | 100000/100000 [12:16<00:00, 135. BCEWithLogitsLoss. For ground truth, it will have class 111. Loss Function and Learning Rate Scheduler. BCELoss torch. In my case, I wanted to understand VAEs from the perspective of a PyTorch implementation. Our learning rate is decayed by a factor of 0. Compute the loss function in PyTorch. BCEWithLogitsLoss, or # Bernoulli loss, namely negative log Bernoulli probability nn. nn ,而另一部分则来自于 torch. They are extracted from open source Python projects. 写在前面这篇文章的重点不在于讲解FR的各种Loss,因为知乎上已经有很多,搜一下就好,本文主要提供了各种Loss的Pytorch实现以及Mnist的可视化实验,一方面让大家借助代码更深刻地理解Loss的设计,另一方面直观的比…. The following are code examples for showing how to use torch. softmax_cross_entropy_with_logits(self. 100%| | 100000/100000 [12:16<00:00, 135. Now that we have a loss, we’ll train our RNN using gradient descent to minimize loss. device = torch. This video is part of the Udacity course "Deep Learning". To calculate the loss we first define the criterion then pass in the output of our network and correct labels. I settled on using binary cross entropy combined with DICE loss. nn to build layers. We introduce a new dice loss function, and compare its performance with traditional cross entropy loss and combined cross entropy-dice loss. Cross entropy is more advanced than mean squared error, the induction of cross entropy comes from maximum likelihood estimation in statistics. The complete code is in Chapter16/04_cheetah_ga. step() uses the gradient to adjust model parameters and. Xavier(Glorot) Initialization: Works better with sigmoid activations. The hook should not modify its arguments, but it can optionally return a new gradient with respect to input that will be used in place of grad_input in subsequent computations. Conditional Variational Autoencoder (VAE) in Pytorch 6 minute read This post is for the intuition of Conditional Variational Autoencoder(VAE) implementation in pytorch. We will then combine this dice loss with the cross entropy to get our total loss function that you can find in the _criterion method from nn. MNIST is used as the dataset. We told pytorch we would need them when we typed requires_grad=True. cross_entropy(). Now we need to define loss function and optimizer. This is Part Two of a three part series on Convolutional Neural Networks. Cross Entropy vs MSE. Entropy is also used in certain Bayesian methods in machine learning, but these won’t be discussed here. Pytorch has two options for BCE loss. Post navigation. Three different configurations of GANs are investigated and compared with e. mnist import input_data # Cross entropy loss. We will use cross entropy loss because this is classification task and SGD is good baseline, you can also try another one. in the library specific format, i. >>> PyTorch Tutorials Name: Process input through the network 3. softmax? Here log is for computing cross entropy. SRGANをpytorchで実装してみました。上段が元画像、中段がbilinear補完したもの、下段が生成結果です。 ipynbのコードをgithubにあげました SRGANとは SRGANはDeepLearningを用いた超解像のアルゴリズムです。 超解像とはその名の通り. ndarray / Tensor library Tensors are similar to numpy's ndarrays, with the addition being that Tensors can also be used on a GPU to accelerate computing. It is now time to consider the commonly used cross entropy loss function. Loss is checked according to the criterion set above (cross entropy loss). Cross entropy is, at its core, a way of measuring the “distance” between two probability distributions P and Q. criterion—the loss function. Note: when using the categorical_crossentropy loss, your targets should be in categorical format (e. BCEWithLogitsLoss, or # Bernoulli loss, namely negative log Bernoulli probability nn. Post navigation. If the prediction is a hard threshold to 0 and 1, it is difficult to back propagate the dice loss. device = torch. zero_grad # clear gradients for this training step loss. For ground truth, it will have class 111. The discovered approach helps to train both convolutional and dense deep sparsified models without significant loss of quality. PyTorch 확장하기 (Cross-Entropy loss)과 모멘텀(momentum) 값을 갖는 SGD를 사용합니다. The grad_input and grad_output may be tuples if the module has multiple inputs or outputs. Compute the loss function in PyTorch. Total span extraction loss is the sum of a Cross-Entropy for the start and end positions. His focus is making mixed-precision and multi-GPU training in PyTorch fast, numerically stable, and easy to use. 3 is number of color channel per slice. Since this is a regression problem, we use a loss function called sum of squared. To calculate the loss we first define the criterion then pass in the output of our network and correct labels. autograd module will calculate their gradients automatically, starting from D_loss. The layers of Caffe, Pytorch and Tensorflow than use a Cross-Entropy loss without an embedded activation function are: Caffe: Multinomial Logistic Loss Layer. Note: this post is also available as Colab notebook here. So predicting a probability of. inputは確率分布だから,総和は1になる. torch. Pretrained PyTorch Resnet models for anime images using the Danbooru2018 dataset. This is a case from the Keras multi-class tutorial. Introduction to TensorFlow and PyTorch Kendall Chuang and David Clark February 16, 2017 2. Torch定义了七种CPU tensor类型和八种GPU tensor类型:. Technically, there is no term as such Softmax loss. Softmax loss and cross-entropy loss terms are used interchangeably in industry. CrossEntropyLoss时,输入的input和target分别应为多少?. Following on from the previous post that bridged the gap between VI and VAEs, in this post, I implement a VAE (heavily based on the Pytorch example script!). Entropy is also used in certain Bayesian methods in machine learning, but these won’t be discussed here. Building an LSTM with PyTorch Cross Entropy Loss. CrossEntropyLosstorch. Now, as we can see above, the loss doesn't seem to go down very much even after training for 1000 epochs. The idea behind the loss function doesn't change, but now since our labels are one-hot encoded, we write down the loss (slightly) differently: This is pretty similar to. Dealing with Pad Tokens in Sequence Models: Loss Masking and PyTorch's Packed Sequence One challenge that we encounter in models that generate sequences is that our targets have different lengths. softmax_cross_entropy. We use a cross entropy loss, with momentum based SGD optimisation algorithm. PyTorchとともにscikit-learnの関数もいろいろ活用するのでインポート。 # hyperparameters input_size = 4 num_classes = 3 num_epochs = 10000 learning_rate = 0. The goal of our machine learning models is to minimize this value. By using the cross-entropy loss we can find the difference between the predicted probability distribution and actual probability distribution to compute the loss of the network. It is now time to consider the commonly used cross entropy loss function. Classification and Loss Evaluation - Softmax and Cross Entropy Loss Lets dig a little deep into how we convert the output of our CNN into probability - Softmax; and the loss measure to guide our optimization - Cross Entropy. Introduction to TensorFlow and PyTorch Kendall Chuang and David Clark February 16, 2017 2. Cross Entropy Loss. CrossEntropyLoss时,输入的input和target分别应为多少?. The networks are optimised using a contrastive loss function(we will get to the exact function). In PyTorch, these refer to implementations that accept different input arguments (but compute the same thing). GitHub Gist: instantly share code, notes, and snippets. This is summarized below. BCELoss, binary cross entropy criterion. Both of these losses compute the cross-entropy between the prediction of the network and the given ground truth. Optimization : So , to improve the accuracy we will backpropagate the network and optimize the loss using optimization techniques such as RMSprop, Mini Batch. Technically, there is no term as such Softmax loss. 사용되는 torch 함수들의 사용법은 여기에서 확인할 수 있다. This time it uses sigmoid activation function, which limits the output to [0,1]. To perform a Logistic Regression in PyTorch you need 3 things: Labels(targets) encoded as 0 or 1; Sigmoid activation on last layer, so the num of outputs will be 1; Binary Cross Entropy as Loss function. Entropy is also used in certain Bayesian methods in machine learning, but these won’t be discussed here. BCEWithLogitsLoss. We will use the same optimiser, but for the loss function we now choose binary cross entropy, which is more suitable for classification problem. But PyTorch treats them as outputs, that don’t need to sum to 1, and need to be first converted into probabilities for which it uses the sigmoid function. This video is part of the Udacity course "Deep Learning". Let’s see what this looks like in practice. Although its usage in Pytorch in unclear as much open source implementations and examples are not. PyTorch Loss-Input Confusion (Cheatsheet) torch. calculate_loss( ) is used to calculate loss – loss_positive: co-occurrences appeared in the corpus. This is because in pytorch, the gradients are accumulated and we need to set gradients to zero to calculate the loss). So predicting a probability of. Loss function. One of those things was the release of PyTorch library in version 1. Loss is checked according to the criterion set above (cross entropy loss). cross_entropy (input, target, loss based on max-entropy, between input `x` (a 2D mini-batch `Tensor`) and pytorch - 张量和动态神经网络在. • This paper utilizes GAN for data augmentation to improve speech recognition under noise conditions. Is limited to multi-class classification. Classification and Loss Evaluation - Softmax and Cross Entropy Loss Lets dig a little deep into how we convert the output of our CNN into probability - Softmax; and the loss measure to guide our optimization - Cross Entropy. Given a training dataset (x,y), we want to identify a function f Θ such that the predictions ŷ = f Θ (x) over the training dataset are as accurate as possible, and a Loss Function L(y,ŷ) - write the criterion that the optimal value of Θ must satisfy:. The joint s. Now let's have a look at a Pytorch implementation below. Loss Function : To find the loss on the Validation Set , we use triplet loss function , contrastive loss, regularized cross entropy etc to find out the loss and calculate the accuracy. See next Binary Cross-Entropy Loss section for more details. Now, Some loss functions can compute per-sample losses in a mini-batch. We will then combine this dice loss with the cross entropy to get our total loss function that you can find in the _criterion method from nn. # loss function (categorical cross-entropy) criterion = nn. Train our feed-forward network. Classification in PyTorch because information flows forward from the input through the hidden layers to the output. 001 as defined in the hyper parameter above. That happens at the very least in the final loss. Classification and Loss Evaluation - Softmax and Cross Entropy Loss Lets dig a little deep into how we convert the output of our CNN into probability - Softmax; and the loss measure to guide our optimization - Cross Entropy. Cross Entropy Loss. Each training epoch includes a forward propagation, which yields some training hypothesis for training source sentences; then cross_entropy calculates loss for this hypothesis and loss. Variational Autoencoder¶. Want a longer explanation? Read the Cross-Entropy Loss section of my introduction to Convolutional Neural Networks (CNNs). KLDivLoss torch. reduce - Variable holding a str which determines whether to reduce the shape of the input. Since this is a regression problem, we use a loss function called sum of squared. A simple and powerful regularization technique for neural networks and deep learning models is dropout. if you have 10 classes, the target for each sample should be a 10-dimensional vector that is all-zeros except for a 1 at the index corresponding to the class of the sample). This post should be quick as it is just a port of the previous Keras code. pytorch 的Cross Entropy Loss 输入怎么填? 以识别一个四位数的验证码为例,批次取为100,标签用one_hot 表示,则标签的size为[100,4,10],input也为[100,4,10],请问loss用torch. BCEWithLogitsLoss. I settled on using binary cross entropy combined with DICE loss. computervision) submitted 4 hours ago by obsezer This repo aims to cover Pytorch details, Pytorch example implementations, Pytorch sample codes, running Pytorch codes with Google Colab (with K80 GPU/CPU) in a nutshell. nn to build layers. For example if the probabilities are supposed to be [0. functional (常缩写为 F )。. zero_grad # clear gradients for this training step loss. 2 but you are getting 2. Among the various deep. It provides a wide range of algorithms for deep learning, and uses the scripting language LuaJIT, and an underlying C implementation. I also defined a binary cross entropy loss and Adam optimizer to be used for the computation of loss and weight updates during training. CrossEntropyLoss() object which computes the softmax followed by the cross entropy. Let's supposed that we're now interested in applying the cross-entropy loss to multiple (> 2) classes. TL;DR version: Pad sentences, make all the same length, pack_padded_sequence, run through LSTM, use pad_packed_sequence, flatten all outputs and label, mask out padded outputs, calculate cross-entropy. Three different configurations of GANs are investigated and compared with e. The loss function also equally weights errors in large boxes and small boxes. 12 for class 1 (car) and 4. Whilst we’ve been otherwise occupied – investigating hyperparameter tuning, weight decay and batch norm – our entry for training CIFAR10 to 94% test accuracy has slipped five (!) places on the DAWNBench leaderboard: The top six entries all use 9-layer ResNets which are cousins – or twins – of the network […]. 8 for class 2 (frog). Cross Entropy Loss, also referred to as Log Loss, outputs a probability value between 0 and 1 that increases as the probability of the predicted label diverges from the actual label. As we start with random values, our learnable parameters, w and b, will result in y_pred, which will not be anywhere close to the actual y. This was limiting to users. I started with the VAE example on the PyTorch github, adding explanatory comments and Python type annotations as I was working my way through it. In my case, I wanted to understand VAEs from the perspective of a PyTorch implementation. 在使用Pytorch时经常碰见这些函数cross_entropy,CrossEntropyLoss, log_softmax, softmax。 看得我头大,所以整理本文以备日后查阅。 首先要知道上面提到的这些函数一部分是来自于 torch. Instantiating The Cross entropy loss. As we can see in the figure, center+ cross-entropy loss performs better clustering than just cross-entropy loss and they both perform better than the model just pre-trained on Imagenet. After running cell, links for authentication are appereared, click and copy the token pass for that session. We also need to define a loss function, e. Posted by kyuhyoung on March 13, 2018 in PyTorch ← Intrinsic camera parameters for resized images set of a chessboard Preventing MobaXTerm SSH session from freezing →. Pytorch Manual F. 이번 글에서는 Pytorch의 Tensor를 사용하는 간단한 방법에 대하여 알아보겠습니다. VAE blog; VAE blog; I have written a blog post on simple. CrossEntropyLoss(). 先の数式解釈で 0に近い方がよい、1に近い方がよいと言っていたのを正解ラベルとのBCELoss(Binary Cross Entropy Loss)で置き換えているのがポイント; GANはDiscriminatorのパラメータ更新とGeneratorのパラメータ更新を順番に繰り返す. The full code is available in my github repo: link. When γ = 0, focal loss is equivalent to categorical cross-entropy, and as γ is increased the effect of the modulating factor is likewise increased (γ = 2 works best in experiments). Through our experiments we also compare and analyze the performance of our 2D and 3D models, both which achieve near state-of-the-art accuracy scores in terms of. binary_cross_entropy_with_logits takes logits as inputs. Adversarial Variational Bayes in Pytorch¶ In the previous post, we implemented a Variational Autoencoder, and pointed out a few problems. Here we are passing the loss function to train_ as an argument. reduce_mean(losses) [/py] Here, tf. I also defined a binary cross entropy loss and Adam optimizer to be used for the computation of loss and weight updates during training. Dealing with Pad Tokens in Sequence Models: Loss Masking and PyTorch's Packed Sequence One challenge that we encounter in models that generate sequences is that our targets have different lengths. 使用 PyTorch 进行图像风格转换 对抗性示例生成 使用 ONNX 将模型从 PyTorch 传输到 Caffe2 和移动端 >>> loss = F. You can notice that we feed into optimizer model parameters we want to optimize (we don’t need to feed in all if we don’t want to) and define learning rate. Loss scaling involves multiplying the loss by a scale factor before computing gradients, and then dividing the resulting gradients by the same scale again to re-normalize them. I am the founder of MathInf GmbH, where we help your business with PyTorch training and AI modelling. Input should be a sequence pair Total span extraction loss is the sum of a Cross-Entropy for the start and end positions. We can get richer representations by altering the number of units in the intermediate layers. In our case we don't need such thing so we will just use cross entropy without any weight map. as PackedSequence in PyTorch, as sequence_length parameter of dynamic_rnn in TensorFlow and as a mask in Lasagne. KLDivLoss torch. Then for a batch of size N, out is a PyTorch Variable of dimension NxC that is obtained by passing an input batch through the model. The input into the network are integer indexes of words, based on a map. Cross Entropy loss. Training of G proceeds using the loss function of G. The objective of the siamese architecture is not to classify input images, but to differentiate between them. The following are code examples for showing how to use torch. Both loss and adversarial loss are backpropagated for the total loss. Module 층을 차례로 쌓아서 신경망을 구축할 때 사용합니다. Lernapparat. They are extracted from open source Python projects. I then created a class for the simple MLP model and defined the layers such that we can specify any number and size of hidden layers. Hi Is it smart to use the cross entropy loss function when the activation function used is Relu and is unbounded? The input is the MNIST data, so binary. As you observed. It is now time to consider the commonly used cross entropy loss function. Now let's have a look at a Pytorch implementation below. Current methods to interpret deep learning models by generating saliency maps generally rely on two key assumptions. Cross-entropy as a loss function is used to learn the probability distribution of the data. This is because in pytorch, the gradients are accumulated and we need to set gradients to zero to calculate the loss). During training, the loss function at the outputs is the Binary Cross Entropy. Tell me more about Cross Entropy Loss. softmax_cross_entropy_with_logits is a convenience function that calculates the cross-entropy loss for each class, given our scores and the correct input labels.