Question:

question 1 only IN STEP 1 GIVE THE INTRODUCTION OF THE CONCEPT AND GIVE ANSWER FOR EACH PART OF THE QUESTION IN EACH DIFFERENT STEP WITH CLEAR EXPLANATION AND IN THE FINAL STEP GIVE THE WHOLE FINAL ANSWER IN JUST VERY FEW SENTENCES AND MOREOVER I NEED COMPLETE AND CLEAR ANSWER at last explain what we did in each step in just few sentence1 Problem Introduction A large language model (LLM) is trained on massive amounts of data and can process natural language instructions and generate texts. Given the extensive applications of LLMs in real-world scenarios, understanding their limitations and potential risks is crucial. LLMs could exhibit bias towards certain demographic groups, which may be related to gender, race, and age. In this project, we aim to develop a debiasing method for a simplified LLM. 2 Problem Description An LLM is a generative model that outputs only one word (or token) at each step. We make the following assumptions. Assumptions: 1. The vocabulary set only consists of two words, which are M and F. That is, at each step, the generative model can only output M or F. One can treat M as male and F as female, so in this simple example, we are studying only binary gender bias. 2. Assume the LLM is a biased model, at each generation step, regardless of the texts already generated, it will always output M with a fixed probability of 2 and F with a fixed probability of 1. This is a strong assumption, as LLMs originally should be given the context to output the probability. 3. Assume we have the following debasing strategy. At each generation step, we can directly adjust the probability distribution. For example, at step 1, we can alter the probability by ay, the probability of generating M becomes 4 — ay and the probability of generating F becomes § + a;. (a) Note that the sum of the probabilities should always be 1. (b) —% < ay < 2 because probability should be between 0 and 1. 4. However, we cannot adjust the probability too much. We have the cost when adjusting probability by a1. Formally, we define the cost as the total variation between the previous probability distribution and the adjusted probability distribution, which is |a;|. We have a budget of B for the total cost.