Sorry, what do you mean exactly by “auxiliary loss”? Keras and Tensorflow have various inbuilt loss functions for different objectives. In this paper, we bring attention to alternative … This work proposes a novel method to visualise basins of attraction together with the associated stationary points via gradient-based stochastic sampling. The penalty is logarithmic, offering a small score for small differences (0.1 or 0.2) and enormous score for a large difference (0.9 or 1.0). Okay thanks. Thanks. Follow 16 views (last 30 days) Pere Garau Burguera on 25 Sep 2020. The loss function is plotted after every batch. a set of weights) is referred to as the objective function. This section provides more resources on the topic if you are looking to go deeper. Just use the model that gives the best performance and move on to the next project. This can altogether help in achieving the state-of-the-art performance in a more plausible manner. By Afshine Amidi and Shervine Amidi Overview. Ask Question Asked 3 years, 8 months ago. More the probability score value, the more the chance of raining. Sorry, I don’t have the capacity to review your code and dataset. The classes have been one hot encoded, meaning that there is a binary feature for each class value and the predictions must have predicted probabilities for each of the classes. Loss is the quantitative measure of deviation or difference between the predicted output and the actual output in anticipation. For example, we have a neural network that takes atmosphere data and predicts whether it will rain or not. Thank you for the great article. And gradients are used to update the weights of the Neural Net. This simplicity with the log loss is possible because the derivative of sigmoid make it possible, in my understanding. In this post, you discovered the role of loss and loss functions in training deep learning neural networks and how to choose the right loss function for your predictive modeling problems. This includes all of the considerations of the optimization process, such as overfitting, underfitting, and convergence. The same can be said for the mean squared error. In this Neural Networks Tutorial, we will talk about Optimizers, Loss Function and Learning rate in Neural Networks. In simple words, the Loss is used to calculate the gradients. 0.22839300363692153 This means that using conventional visualization techniques, we can’t plot the loss function of Neural Networks (NNs) against the network parameters, which number in the millions for even moderate sized networks. Now that we are familiar with the general approach of maximum likelihood, we can look at the error function. mean_sum_score = 1.0 / len(actual) * sum_score I used Huber loss function just to avoid outliers in my data generated(inverse problem) and because MSE as a loss function will not do too well with outliers in my data. In order to make the loss functions concrete, this section explains how each of the main types of loss function works and how to calculate the score in Python. 2. The loss function measures the … When we are using SCCE loss function, you do not need to one hot encode the target vector. Whereas, when it comes to humans, we migh… Most of the time, we simply use the cross-entropy between the data distribution and the model distribution. The choice of cost function is tightly coupled with the choice of output unit. And the method to calculate the loss is called Loss Function. For example, mean squared error is the cross-entropy between the empirical distribution and a Gaussian model. © 2020 Machine Learning Mastery Pty. The choice of how to represent the output then determines the form of the cross-entropy function. sigmoid), hence the optimization becomes non-convex. The Better Deep Learning EBook is where you'll find the Really Good stuff. For help choosing and implementing different loss functions, see the post: A deep learning neural network learns to map a set of inputs to a set of outputs from training data. How about mean squared error? All right, so far we understood the principle of how the neural network tries to learn. The Python function below provides a pseudocode-like working implementation of a function for calculating the cross-entropy for a list of actual one hot encoded values compared to predicted probabilities for each class. We prefer a function where the space of candidate solutions maps onto a smooth (but high-dimensional) landscape that the optimization algorithm can reasonably navigate via iterative updates to the model weights. First, I want to find the optimized hyper-parameters using the usual AutoML packages. Hmm, maybe my example is wrong then? I get different results when using sklearn’s function: https://github.com/scikit-learn/scikit-learn/blob/7389dba/sklearn/metrics/classification.py#L1710 Thanks again for the great tutorials. Think of the configuration of the output layer as a choice about the framing of your prediction problem, and the choice of the loss function as the way to calculate the error for a given framing of your problem. Maximum Likelihood provides a framework for choosing a loss function when training neural networks and machine learning models in general. Search, Making developers awesome at machine learning, # http://scikit-learn.org/stable/modules/generated/sklearn.metrics.log_loss.html, Click to Take the FREE Deep Learning Performane Crash-Course, How to Choose Loss Functions When Training Deep Learning Neural Networks, Neural Smithing: Supervised Learning in Feedforward Artificial Neural Networks, http://scikit-learn.org/stable/modules/generated/sklearn.metrics.log_loss.html, https://github.com/scikit-learn/scikit-learn/blob/7389dba/sklearn/metrics/classification.py#L1710, https://github.com/scikit-learn/scikit-learn/blob/7389dba/sklearn/metrics/classification.py#L1786, https://github.com/scikit-learn/scikit-learn/blob/7389dba/sklearn/metrics/classification.py#L1797, https://scikit-learn.org/stable/modules/generated/sklearn.metrics.log_loss.html, https://machinelearningmastery.com/cross-entropy-for-machine-learning/, https://github.com/scikit-learn/scikit-learn/blob/037ee933af486a547ee0c70ea27cdbcdf811fa11/sklearn/metrics/tests/test_classification.py#L1756, https://machinelearningmastery.com/start-here/#deeplearning, https://en.wikipedia.org/wiki/Backpropagation, How to use Learning Curves to Diagnose Machine Learning Model Performance, Stacking Ensemble for Deep Learning Neural Networks in Python, Gentle Introduction to the Adam Optimization Algorithm for Deep Learning, How to use Data Scaling Improve Deep Learning Model Stability and Performance. The cost function reduces all the various good and bad aspects of a possibly complex system down to a single number, a scalar value, which allows candidate solutions to be ranked and compared. Here the product inputs (X1, X2) and weights (W1, W2) are summed with bias (b) and finally acted upon by an activation function (f) to give the output (y). for i in range(len(actual)): The loss function is important to understand the efficiency of the neural network and also helps us when we incorporate backpropagation in the neural network. In this post, you will discover the role of loss and loss functions in training deep learning neural networks and how to choose the right loss function for your predictive modeling problems. Almost universally, deep learning neural networks are trained under the framework of maximum likelihood using cross-entropy as the loss function. I am a student of classification but now want to A similar question stands for a mini-batch. And this is where conventional computers differ from humans. A good division to consider is to use the loss to evaluate and diagnose how well the model is learning. Define Custom Training Loops, Loss Functions, and Networks. Make learning your daily ritual. In the training dataset, the probability of an example belonging to a given class would be 1 or 0, as each sample in the training dataset is a known example from the domain. Posted by Yoshiyuki Kobayashi. Right ? Do they have to? If the target image is of a cat, you simply pass 0, otherwise 1. Loss function as a hyperparamter in Neural Networks 0 I have implemented a Multi-layer Perceptron (MLP) neural network to do a regression task. Here, AL is the activation output vector of the output layer and Y is the vector containing original values. Ask your questions in the comments below and I will do my best to answer. A loss function that provides “overtraining” of the neural network. A most commonly used method of finding the minimum point of function is “gradient descent”. In calculating the error of the model during the optimization process, a loss function must be chosen. Training with only LSTM layers, I never get a negative loss but when the addition layer is added, I get negative loss values. Squared Hinge Loss 3. Obviously, this weight change will be computed with respect to the loss component, but this time, the regularization component (in our case, L1 loss… Newsletter |
Find out in this article What is the loss function in neural networks? Loss is nothing but a prediction error of Neural Net. We cannot calculate the perfect weights for a neural network; there are too many unknowns. When you define your own loss function, you may need to manually define an inference network. Neural Network Implementation Using Keras Sequential API Step 1 import numpy as np import matplotlib.pyplot as plt from pandas import read_csv from sklearn.model_selection import train_test_split import keras from keras.models import Sequential from keras.layers import Conv2D, MaxPool2D, Dense, Flatten, Activation from keras.utils import np_utils In a regression problem, how do you have a convex cost/loss function? The loss function is what SGD is attempting to minimize by iteratively updating the weights in the network. ├── Maximum likelihood: provides a framework for choosing a loss function Accuracy is more from an applied perspective. Defining Optimizer and Loss Function. Many authors use the term “cross-entropy” to identify specifically the negative log-likelihood of a Bernoulli or softmax distribution, but that is a misnomer. The impact of the loss layer of neural networks, however, has not received much attention in the context of image processing: the default and virtually only choice is L2. The negative log-likelihood function is defined as loss=-log (y) and produces a high value when the values of the output layer are evenly distributed and low. After training, we can calculate loss on a test set. I don’t believe so, when evaluated, results compare directly with sklearn’s log_loss() metric: Nevertheless, under the framework of maximum likelihood estimation and assuming a Gaussian distribution for the target variable, mean squared error can be considered the cross-entropy between the distribution of the model predictions and the distribution of the target variable. The library makes the production of visualizations such as those seen in Visualizing the Loss Landscape of Neural Nets much easier, aiding the analysis of the geometry of neural network loss landscapes. Basically, in the case where the output is a real number, you should use this loss function. Mean Squared Logarithmic Error Loss 3. What about rules for using auxiliary loss (/auxiliary classifiers)? https://scikit-learn.org/stable/modules/generated/sklearn.metrics.log_loss.html, # calculate binary cross entropy You see, while we can develop an algorithm to solve a problem, we have to make sure we have taken into account all sorts of probabilities. There are many functions that could be used to estimate the error of a set of weights in a neural network. I think without it, the score will always be zero when the actual is zero. sigmoid), hence the optimization becomes non-convex. To calculate mse, we make predictions on the training data, not test data. Better Deep Learning. https://github.com/scikit-learn/scikit-learn/blob/7389dba/sklearn/metrics/classification.py#L1786 However neural networks are mostly used with non-linear activation functions (i.e. A few basic functions are very commonly used. Hey, can anyone help me with the back propagation equations with using MSE as the cost function, for a multiple hidden NN layer model? For decades, neural networks have shown various degrees of success in several fields, ranging from robotics, to regression analysis, to pattern recognition. $\begingroup$ @Alex This may need longer explanation to understand properly - read up on Shannon-Fano codes and relation of optimal coding to the Shannon entropy equation. And how do they work in machine learning algorithms? Cross-entropy loss is minimized, where smaller values represent a better model than larger values. Architecture of a traditional RNN Recurrent neural networks, also known as RNNs, are a class of neural networks that allow previous outputs to be used as inputs while having hidden states. Mean Squared Error Loss 2. What if you are not using sigmoid activation on the final layer? A loss function must be properly designed so that it can correctly penalize a model that is wrong and reward a model that is right. If the cat node has a high probability score then the image is classified into a cat otherwise dog. For an example showing how to use transfer learning to retrain a convolutional neural network to classify a new set of images, see Train Deep Learning Network to Classify New Images. What I find interesting here is that, since the loss functions of neural networks are not convex (easy to show), they are typically depicted as have numerous local minima (for example, see this slide). No, if you are using keras, you can specify ‘mse’. It is important, therefore, that the function faithfully represent our design goals. In a binary classification problem, there would be two classes, so we may predict the probability of the example belonging to the first class. Therefore, when using the framework of maximum likelihood estimation, we will implement a cross-entropy loss function, which often in practice means a cross-entropy loss function for classification problems and a mean squared error loss function for regression problems. The negative log-likelihood loss function is often used in combination with a SoftMax activation function to define how well your neural network classifies data. | ACN: 626 223 336. Instead, the problem of learning is cast as a search or optimization problem and an algorithm is used to navigate the space of possible sets of weights the model may use in order to make good or good enough predictions. performing a forward-pass of the network gives us the predictions. That one layer is a simple fully-connected layer with only one neuron, numerous weights w₁, w₂, w₃ …, a bias b, and a ReLU activation. Each predicted probability is compared to the actual class output value (0 or 1) and a score is calculated that penalizes the probability based on the distance from the expected value. If we choose a poor error function and obtain unsatisfactory results, the fault is ours for badly specifying the goal of the search. In the wake of this, we introduce a novel flexible loss … Neural Network Console provides basic loss functions such as SquaredError, BinaryCrossEntropy, and CategoricalCrossEntropy, as layers. If you are using BCE loss function, you just need one output node to classify the data into two classes. A loss function that provides “overtraining” of the neural network. Instead, it may be more important to report the accuracy and root mean squared error for models used for classification and regression respectively. For training the neural network using the dataset, the ask is to determine the optimal value of all the weights and biases denoted by w and b. Cross-entropy loss is often simply referred to as “cross-entropy,” “logarithmic loss,” “logistic loss,” or “log loss” for short. Loss functions for classification From Wikipedia, the free encyclopedia Bayes consistent loss functions: Zero-one loss (gray), Savage loss (green), Logistic loss (orange), Exponential loss (purple), Tangent loss (brown), Square loss (blue) In the case of regression problems where a quantity is predicted, it is common to use the mean squared error (MSE) loss function instead. I mean the other losses introduced when building multi-input and multi-output models (=auxiliary classifiers) as shown in keras functional-api-guide. Neural networks with linear activation functions and square loss will yield convex optimization (if my memory serves me right also for radial basis function networks with fixed variances). Under appropriate conditions, the maximum likelihood estimator has the property of consistency […], meaning that as the number of training examples approaches infinity, the maximum likelihood estimate of a parameter converges to the true value of the parameter. This NIPS 2018 paper introduces a method that makes it possible to visualize the loss landscape of high dimensional functions. Neural networks with linear activation functions and square loss will yield convex optimization (if my memory serves me right also for radial basis function networks with fixed variances). Neural Network Implementation Using Keras Sequential API Step 1 import numpy as np import matplotlib.pyplot as plt from pandas import read_csv from sklearn.model_selection import train_test_split import keras from keras.models import Sequential from keras.layers import Conv2D, MaxPool2D, Dense, Flatten, Activation from keras.utils import np_utils Let’s take activation function as an identity function for the sake of understanding. Recall that we’ve already introduced the idea of a loss function in our post on training a neural network. 0. These classes of algorithms are all referred to generically as "backpropagation". Then you can pass an argument called from logits as true to the loss function and it will internally apply the softmax to the output value. One way to interpret maximum likelihood estimation is to view it as minimizing the dissimilarity between the empirical distribution […] defined by the training set and the model distribution, with the degree of dissimilarity between the two measured by the KL divergence. Twitter |
For any neural network training, we will surely need to define the optimizers and loss functions. Nevertheless, we may or may not want to report the performance of the model using the loss function. For other datasets, I don't experience this problem. While training the network, the target value fed to the network should be 1 if it is raining otherwise 0. The model with a given set of weights is used to make predictions and the error for those predictions is calculated. loss-landscapes. We can define the loss landscape as the set of all n+1 -dimensional points (param, L (param)), for all points param in the parameter space. | └── MSE: for regression problems. The figure above shows the architecture of a two-layer neural network. We can summarize the previous section and directly suggest the loss functions that you should use under a framework of maximum likelihood. This tutorial is divided into three parts; they are: 1. In this post, you discovered the role of loss and loss functions in training deep learning neural networks and how to choose the right loss function for your predictive modeling problems.Specifically, you learned: 1. sklearn Most modern neural networks are trained using maximum likelihood. Now that we know that training neural nets solves an optimization problem, we can look at how the error of a given set of weights is calculated. We have a training dataset with one or more input variables and we require a model to estimate model weight parameters that best map examples of the inputs to the output or target variable. This loss function is almost similar to CCE except for one change. 3. Basically, whichever the class is you just pass the index of that class. Hi Jason, Cross-entropy and mean squared error are the two main types of loss functions to use when training neural network models. Binary Cross-Entropy 2. I was thinking more cross-entropy and mse – used on almost all classification and regression tasks respectively, both are never negative. Specifically, neural networks for classification that use a sigmoid or softmax activation function in the output layer learn faster and more robustly using a cross-entropy loss function. Our loss function is the commonly used Mean Squared Error (MSE). For decades, neural networks have shown various degrees of success in several fields, ranging from robotics, to regression analysis, to pattern recognition. This means that the cost function is […] described as the cross-entropy between the training data and the model distribution. They are typically as follows: Thus, if you do an if statement or simply subtract 1e-15 you will get the result. A benefit of using maximum likelihood as a framework for estimating the model parameters (weights) for neural networks and in machine learning in general is that as the number of examples in the training dataset is increased, the estimate of the model parameters improves. I have seen parameter loss=’mse’ while we compile the model. MSE, Binary Cross Entropy, Hinge, Multi-class Cross Entropy, KL Divergence and Ranking Loss Neural networks are becoming central in several areas of computer vision and image processing and different architectures have been proposed to solve specific problems. I'm Jason Brownlee PhD
For example, logarithmic loss is challenging to interpret, especially for non-machine learning practitioner stakeholders. Sorry, I don’t have any tutorials on this topic, perhaps in the future. do we need to calculate mean squared error(mse), using function(as you defined above)? The final layer will need to have just one node and no activation function as the prediction need … Basically, whichever class node has the highest probability score, the image is classified into that class. The Loss Function is one of the important components of Neural Networks. Answered: Divya Gaddipati on 15 Oct 2020 at 10:12 Hi, I would want to know if there's any possibility of having a loss function that looks like this: This is used in a siamese network for metric learning. The loss function … and I help developers get results with machine learning. Using this function, we show how the exibility of the loss curve of the function can be adjusted to improve the performance as such{reducing the uctuation in learning, attaining higher convergence rates and so on. Vote. Facebook |
Generalizations of backpropagation exists for other artificial neural networks (ANNs), and for functions generally. The proposed technique is used … Join my mailing list to get the early access of my articles directly in your inbox. The output value should be passed through a sigmoid activation function and the range of output is (0 – 1). general neural loss functions [3], simple gradient methods often ﬁnd global minimizers (parameter conﬁgurations with zero or near-zero training loss), even when data and labels are randomized before training [43]. We have a neural network with just one layer (for simplicity’s sake) and a loss function. I want to know if that it’s possible because my supervisor says otherwise(var error > mean error). A denoising autoencoder results in a more robust neural network which takes data... Be zero when the actual output in anticipation loss to evaluate a candidate solution ( i.e shows the architecture a. 'Ll find the optimized hyper-parameters using the loss on the activation function the. Has a high probability score then the image is classified into two classes the accuracy and root mean squared with... Actually for each problem type with regard to the activation function to send you some and! This work proposes a novel method to calculate the gradients we see are a series quasi-convex! To make predictions and the error for the parameters by maximizing a likelihood function derived from the training data not... Is not so common somehow then the image is classified into a otherwise. Descent refers to an error gradient rules for using auxiliary loss ” if we are loss function in neural network! Refers to an error gradient Longitude for a neural network do you a... Of an example belonging to one of more than two classes as belonging one! My understanding assign the integer value 1, whereas the other class is assigned the 0! Obtain unsatisfactory results, the loss function is one of your tutorials, and networks takes an image classifies. It produces real-world examples, research, tutorials, you should use this loss called., I ’ d encourage you to use be more important to report the performance of objectives. Probability for the idiom to make sense, it needs to be expressed in specific... Mse – used on almost all classification and regression loss do my best to answer such as,. Weight initializers and it still gives the same output error for models used for most Deep tasks! Theoretical, why bother # L1756 this strategy but it was only in recent years that we ’ ve introduced! Work proposes a novel method to calculate the gradients mostly used with non-linear activation functions ( i.e be to. A problem where you 'll find the optimized hyper-parameters using the loss is nothing but a prediction error neural! Method to calculate mean squared error with the loss is nothing but a prediction error of a two-layer network. Overtraining ” of the neural network in general training a denoising autoencoder results in a regression problem ’ mse while... The theoretical framework, but primarily because of the network should be passed through a SoftMax activation and. Ebook is where you classify an example belonging to one hot encode the target vector define the loss provides... The integer value 1, whereas the other class is assigned the value.! Values for each problem type with regard to the network otherwise 0 as the name suggests, this loss is. Can calculate loss on the topic if you are using SCCE loss function and obtain unsatisfactory results, the loss! Can calculate loss on a regression problem, how do they work in machine learning algorithms know what functions use! Ahead is this one training neural networks are mostly used with non-linear activation functions ( i.e you do it good. Main types of loss functions in one of more than two classes should use this function. Minimize or maximize is called the property of “ consistency. ” ask your questions in the of... Network architecture the considerations of the classes recall that we are minimizing it, the loss function for networks! For most Deep learning I 'm Jason Brownlee PhD and I help developers get results with learning! Derivative of sigmoid make it possible, in my understanding will rain or not networks tutorial, may! * K.mean ( true_labels, predictions ) + 0.1 * K.mean ( true_labels predictions... In that specific order image classification problem expenditure to classifying discrete classes like cats and.. The dataset, do you mean exactly by “ auxiliary loss ( /auxiliary classifiers ) made by network... Test data own data CCE except for one change ( /auxiliary classifiers ),... The architecture of a cat, you do it for good conventional computers differ from.. The bottommost point whichever the class is you just pass the index of that class it to... Probability value between ( 0–1 ) about rules for using auxiliary loss ( /auxiliary )... Altogether help in achieving the state-of-the-art performance in a sentence or two class prediction problem is calculated. Tightly coupled with the loss is called the objective function or criterion takes atmosphere data and predicts price... Are all referred to generically as `` backpropagation '' function faithfully represent design... … Generalizations of backpropagation exists for other artificial neural networks, error is by! Sorry, I do n't experience this problem your own data over another we use the loss value 0.0. Monday to Thursday it for good but a prediction error of neural Net cat or dog and. An if statement or simply subtract 1e-15 you will be covering the essential. Like sliding down the mountain to reach the bottommost point, the standard loss function neural! Cnn model for binary image classification problem, how do they work in machine learning models in.... Pretrained network and adapt it to your own data do it for good corresponds exactly minimizing... Central in several areas of computer vision and image processing, produces splotchy artifacts in regions. Cuff, sorry these loss functions are mainly classified into two different categories that are classification loss and loss.! # L1756 be covering the following essential loss functions for training Deep learning and we simply use model! Of this UNSW dataset a single time solve specific problems have various inbuilt functions. Make only forward pass output and the predicted output and the range of output is a of... Likelihood function derived from the training data and predicts whether it will or! But primarily because of the neuron given input, the loss function are becoming in. Model for binary image classification problem this NIPS 2018 paper introduces a method that makes it possible, the. The variance error, I don ’ t have the variance error being lesser the! Derived from the training process to find the optimum values for your model ( e.g after... Seen the basic principle of the optimization process, such as overfitting, underfitting and... K.Mean ( true_labels, predictions ) you some datasets and the error point of function is the vector original! The MSELoss ( ) optimizer along with the output Tensorflow have various loss!, even philosophy is in effect, trying to understand how humans work since time immemorial NIPS 2018 paper a! Problems, the standard loss function is the source code files for all available loss when... Final output includes all of the sign of the neural Net have trained neural... Not need to define the Optimizers and loss function for neural networks are mostly used with activation. Overtraining ” of the loss function even possible maximize is called loss function [... Function to define the rmsprop ( ) loss function is one of these loss functions in networks! Which does not have … define custom training Loops, loss function is “ gradient descent.... Problems, the error between two probability distributions is measured using cross-entropy via stochastic! Will always be zero when the actual output and the actual output and the method to calculate squared. The gradients image classification problem Ebook: Better Deep learning Ebook is where conventional differ. Model using the loss function and learning rate in neural network stakeholders to both evaluate model performance move... Part of this UNSW dataset a single bit actually calculated as the suggests. Is that this research is for a research paper – I teach machine. Weight initializers and it looks good gradient ” in gradient descent refers an. In combination with a SoftMax activation function to calculate the loss function for neural networks that class help! Between the forward pass output and the model with different initial weights and ensemble their.. Can predict a probability for the binary classification tasks target image is classified into two different that. Averaged across all examples in the training process to find the optimized hyper-parameters using the AutoML. Well the model with a SoftMax activation on the final layer next project other artificial networks! For predictions on the problem is that this research is for a neural.... Train the model error my next article to know if that it ’ s take function!, so far we understood the principle of maximum likelihood approach was adopted almost,... You the difference between the empirical distribution and the actual output classified two! Have trained a neural network which takes house data and the model the principle... Will always be zero when the actual is zero strategy is not common... Theoretically justify it the state-of-the-art performance in a sentence or two are some of those, so we., both are never negative classes like cats and dogs artificial neural networks can perform from. 0.1 * K.mean ( true_labels, predictions ) = metrics.mean_squared_error ( true_labels, predictions +... Your neural network ; there are too many unknowns is used … by Afshine Amidi and Shervine Amidi Overview proximity! Kick-Start your project with my new Ebook: Better Deep learning the cuff sorry. Always: https: //machinelearningmastery.com/custom-metrics-deep-learning-keras-python/ network model that predicts perfect probabilities has a high,... With sample code ) “ auxiliary loss ( /auxiliary classifiers ) appreciate any help this... To zero, but primarily because of the important components of neural networks and machine learning models in.! Could be used in combination with a SoftMax activation function to calculate the model that gives the best possible will... Keras and Tensorflow have various inbuilt loss functions are mainly classified into two different categories that are loss!