How can Kneser-Ney Smoothing be integrated into a neural language model?

I found a paper titled Multimodal representation: Kneser-Ney Smoothing/Skip-Gram based neural language model. I am curious about how the Kneser-Ney Smoothing technique can be integrated into a feed-forward neural language model with one linear hidden layer and a softmax activation. What is the purpose of the Kneser-Ney in such a neural network, and how can it be used for learning the conditional probability for the next word?

A pretrained model for mathematical equations characters detection

I am working on a project to convert equations to LaTeX code. After segmenting out the characters, I got stuck on the detection part and was looking for some pre-trained model that could detect characters of the equation for later conversion to LaTeX. Is there any such pre-trained model available on the internet that could be used in Python to identify characters. If not then can somebody share some source to find a dataset to train such kind of model in Keras? I was able to find one on GitHub but It doesn’t detect symbols accurately.

How to deside what model should be picket for security operation center, design and implimentation?

To pick the right model for design and implement a Security Operation Center, it should pick a most suitable model that is for the business, that could be capable to be tailored.

What are the differences, between Best practices, standards, and frameworks in SOC design?

Significance of model in arithmetic coding

I am trying to understand the concept of arithmetic coding, i understand how the range is subdivided after each character is read from the string. But i am unable to understand why using a more accurate model compresses the string. Whether the model is static/adaptive either way the number of characters in the compressed string would be the same. What am i missing?

How to model opposed rolls in Anydice?

I’ve seen there are quite a lot of brilliant people on this board answering questions about Anydice. I am hoping somebody will be kind enough to answer this one too.

I want to use anydice to figure out the probability of success with opposing dice rolls. For example, 1d6+1d8 (test roll) vs 1d10+1d4 (challenge roll). The challenge roll determines the target number. If the test roll meets or exceeds the challenge roll, the attempt succeeds.

How do I set that up in Anydice?

Automaton-based model checking on finite traces

I want to check whether a formula in finite LTL is valid on a finite, linear trace.

For infite traces I would create a Kripke structure of the trace and a B├╝chi automaton for the negated formula, and check if the intersection is empty. Would this also work with a finite trace and formula in FLTL? I already tried adding another atomic proposition “alive” to the Kripke structure and automaton (like here But how could I do it without this additional atomic proposition?

How do you calculate the training error and validation error of a linear regression model?

I have a linear regression model that I’ve implemented using Gradient Descent and my cost function is a Mean Squared Error function. I’ve split my full dataset into three datasets, a training set, a validation set, and a testing set. I am not sure how to calculate the training error and validation error (and the difference between the two).

Is the training error the Residual Sum of Squares error calculated using the training dataset? Is the validation error the Residual Sum of Squares error calculated using the validation dataset? What is the test set for exactly (I’ve learned the model using the training set, from the textbooks I’ve read I think this is the set to use to learn the model)?

Any help in clearing up these points is much appreciated.

How to model diffusion through a membrane?

This is a follow-up on How to handle discontinuity in diffusion coefficient?

Consider diffusion of $ u(t,x)$ on the domain $ x \in [0,2]$ with some simple boundary conditions such as $ u(0) = 2, u(1) = 1$ .

Our domain is split into two parts: $ [0,1)$ on the left and $ (1,2]$ on the right, with different diffusion coefficients, e.g. $ D^\text{left} = 1, D^\text{right} = 3$ .

The diffusion equation is: $ $ \partial_t u = \partial_x (D \partial_x u) $ $

So far, this is the summary of the linked question.

This time we also have a membrane at $ x=1$ , imposing the following condition on the fluxes at $ x=1$ : $ $ D^\text{left} \partial_x u^\text{left} = D^\text{right} \partial_x u^\text{right} = d^\text{membrane} (u^\text{right} – u^\text{left}) $ $

What is the cleanest way to model this with NDSolve? Is there a way to preserve the sharp conditions at $ x=1$ ? Perhaps one approximation that could be used is to consider a membrane of finite thickness, having a very high diffusion coefficient of its own. However, this is really a hack. Is it possible to solve the equation on the two half-domains “separately” and couple the boundary conditions at $ x=1$ ?