Notice: This page requires JavaScript to function properly.
Please enable JavaScript in your browser settings or update your browser.Lernen Multi-class Cross-Entropy and the Softmax Connection | Classification Loss Functions
Understanding Loss Functions in Machine Learning

bookMulti-class Cross-Entropy and the Softmax Connection

The multi-class cross-entropy loss is a fundamental tool for training classifiers when there are more than two possible classes. Its formula is:

LCE(y,p^)=−∑kyklog⁡p^kL_{CE}(y, \hat{p}) = -\sum_{k} y_k \log \hat{p}_k

where yky_k is the true distribution for class kk (typically 1 for the correct class and 0 otherwise), and p^k\hat{p}_k is the predicted probability for class kk, usually produced by applying the softmax function to the model's raw outputs.

Note
Note

Cross-entropy quantifies the difference between true and predicted class distributions. It measures how well the predicted probabilities match the actual class labels, assigning a higher loss when the model is confident but wrong.

The softmax transformation is critical in multi-class classification. It converts a vector of raw output scores (logits) from a model into a probability distribution over classes, ensuring that all predicted probabilities p^k\hat{p}_k are between 0 and 1 and sum to 1. This is defined as:

p^k=exp⁡(zk)∑jexp⁡(zj)\hat{p}_k = \frac{\exp(z_k)}{\sum_{j} \exp(z_j)}

where zkz_k is the raw score for class kk. Softmax and cross-entropy are paired because softmax outputs interpretable probabilities, and cross-entropy penalizes the model based on how far these probabilities are from the true class distribution. When the model assigns a high probability to the wrong class, the loss increases sharply, guiding the model to improve its predictions.

question mark

Which statement best describes the role of softmax in multi-class classification and the way cross-entropy penalizes predictions?

Select the correct answer

War alles klar?

Wie können wir es verbessern?

Danke für Ihr Feedback!

Abschnitt 3. Kapitel 2

Fragen Sie AI

expand

Fragen Sie AI

ChatGPT

Fragen Sie alles oder probieren Sie eine der vorgeschlagenen Fragen, um unser Gespräch zu beginnen

Awesome!

Completion rate improved to 6.67

bookMulti-class Cross-Entropy and the Softmax Connection

Swipe um das Menü anzuzeigen

The multi-class cross-entropy loss is a fundamental tool for training classifiers when there are more than two possible classes. Its formula is:

LCE(y,p^)=−∑kyklog⁡p^kL_{CE}(y, \hat{p}) = -\sum_{k} y_k \log \hat{p}_k

where yky_k is the true distribution for class kk (typically 1 for the correct class and 0 otherwise), and p^k\hat{p}_k is the predicted probability for class kk, usually produced by applying the softmax function to the model's raw outputs.

Note
Note

Cross-entropy quantifies the difference between true and predicted class distributions. It measures how well the predicted probabilities match the actual class labels, assigning a higher loss when the model is confident but wrong.

The softmax transformation is critical in multi-class classification. It converts a vector of raw output scores (logits) from a model into a probability distribution over classes, ensuring that all predicted probabilities p^k\hat{p}_k are between 0 and 1 and sum to 1. This is defined as:

p^k=exp⁡(zk)∑jexp⁡(zj)\hat{p}_k = \frac{\exp(z_k)}{\sum_{j} \exp(z_j)}

where zkz_k is the raw score for class kk. Softmax and cross-entropy are paired because softmax outputs interpretable probabilities, and cross-entropy penalizes the model based on how far these probabilities are from the true class distribution. When the model assigns a high probability to the wrong class, the loss increases sharply, guiding the model to improve its predictions.

question mark

Which statement best describes the role of softmax in multi-class classification and the way cross-entropy penalizes predictions?

Select the correct answer

War alles klar?

Wie können wir es verbessern?

Danke für Ihr Feedback!

Abschnitt 3. Kapitel 2
some-alt