Conditional Probability Formula for Autoregressive Models using Softmax
In autoregressive models, the conditional probability of the next token , given an input and the preceding tokens , is often calculated using the softmax function. This is expressed as: Here, represents the unnormalized score (or logit) for the token . The probability is obtained by exponentiating this score and normalizing it by the sum of exponentiated scores of all candidate tokens within a specific vocabulary subset .
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Ch.5 Inference - Foundations of Large Language Models
Foundations of Large Language Models
Foundations of Large Language Models Course
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Conditional Probability Formula for Autoregressive Models using Softmax
A language model is predicting the next word in a sequence. After processing the context, it has assigned the following unnormalized scores to a set of four candidate words: 'mat' (score=6.0), 'rug' (score=3.0), 'floor' (score=0.5), and 'chair' (score=0.5). To convert these scores into a valid probability distribution over this set, what is the final probability assigned to the word 'mat'?
A language model is evaluating three candidate tokens (A, B, C) to follow a given context. Initially, their scores are: Token A = 4, Token B = 4, Token C = 2. If the score for Token C is increased to 12, while the scores for Token A and Token B remain unchanged, how does this affect the normalized probabilities of Token A and Token B?
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Conditional Probability Formula for Autoregressive Models using Softmax
A neural network's final layer produces the raw output scores (logits)
[2.0, 1.0, 0.1]for three possible classes. To convert these scores into class probabilities, a function is applied that first exponentiates each score and then normalizes these new values by dividing each by their sum. What is the resulting probability distribution? (Values are rounded to three decimal places).A function is used to convert a vector of raw, unnormalized scores
z = [z_1, z_2, ..., z_K]into a probability distribution. This function operates by first applying the standard exponential function to each score and then normalizing these new values by dividing each by their sum. If a constant valueCis added to every score in the input vectorz, resulting in a new vectorz' = [z_1+C, z_2+C, ..., z_K+C], how will the resulting output probability distribution be affected?Consider two input vectors of raw scores (logits) for a 3-class classification problem: Vector A =
[1, 2, 3]and Vector B =[1, 5, 10]. Both vectors are passed through a function that exponentiates each score and then normalizes the results by dividing by their sum. How will the resulting probability distribution for Vector B compare to the one for Vector A?You’re reviewing an internal evaluation script tha...
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An autoregressive model is generating a sequence and has computed the following unnormalized scores (logits) for three candidate next tokens: Token A (3.0), Token B (1.0), and Token C (0.0). If a constant value of 10.0 is added to each of these three logits before the final probability normalization step, how will the resulting conditional probabilities for the tokens be affected?
An autoregressive language model calculates unnormalized scores (logits) for a set of candidate next tokens. These scores are then transformed into a probability distribution. What is the primary reason for applying an exponential function to each logit before the final normalization step?