In machine learning, loss functions help models determine how wrong it is and improve itself based on that wrongness. They are mathematical functions that quantify the difference between predicted and actual values in a machine learning model, but this isn’t all they do. The measure of error f...
In particular, we have the monotonicity formula where is the “energy” where in the last line we use the antisymmetrisation identity Among other things, this shows that as one goes backwards in time, the entropy decreases, and so no collisions can occur to the past, only in the futu...
Binary cross entropy formula Binary cross entropy loss function w.r.t to p value (source) From the calculations above, we can make the following observations: When the true label t is 1, the cross-entropy loss approaches 0 as the predicted probability p approaches 1 and When the true label...
Considering advantages of deep learning methods, a classifier based on CNN (Convolutional Neural Network) is designed with a new loss function based on Havrda-Charvat entropy which is a parametrical generalization of the Shannon entropy. We propose to use this formula to get a better hold on ...
Considering the residual connection, the formula of deep learning is the same as the construction formula of reversible computing theory. When solving problems by reversible computing, it will inevitably involve the problem of deep nesting of multiple models, just like the multi-layer neural netw...
In the special case when the vector 𝑦∈(0,1)𝐾 is calculated based on the vector 𝑥∈ℝ𝐾 according to the formula 𝑦𝑖=𝑆𝑜𝑓𝑡𝑀𝑎𝑥(𝑥)𝑖=𝑒𝑥𝑖/∑𝑘𝑒𝑥𝑘, the gradient of 𝐶𝐸 with respect to x has a particularly simple resultant formula...
The Shannon entropy, S, which is applicable only to probability measures, is expressed within DST by the formula S(m)=−∑x∈Xm({x})log2m({x}) This functional, which forms the basis for classical information theory, has been proven in numerous ways to be the only sensible measure of...
Substitute the result into the calculation formula (1) of information entropy and the information entropy \(H({\varvec{\beta}})\) can be obtained. Formula (2) is used to calculate conditional entropy \(H({\varvec{\beta}}|{\boldsymbol{\alpha }}_{{\varvec{i}}}\)) of each ...
To reduce the loss values to a scalar, the function then reduces the element-wise loss using the formula loss=1N∑jmjwjlossj, whereNis the normalization factor,mjis the mask value for elementj, andwjis the weight value for elementj. ...
Taking the absolute value of the partial derivative of the target output fc (hardness and phase in this work) with respect to the inputs xi (fraction of components in this work), the formula is expressed as(5)Sicx=∂fcx∂xi 3. Results and analysis In this work, the latent space ...