Analyze the junior engineer's hypothesis. Is their reasoning correct for how standard generative language models compute the score for an output sequence? Explain why or why not.

Google

In common implementations of Large Language Models (LLMs), the log-probability of the input sequence does not need to be computed. Instead, the model directly computes the conditional log-probability of the output sequence given the input. This is done by summing the log-probabilities of each individual output token. The formula is:

$$ \log \Pr(\mathbf{y}|\mathbf{x}) = \sum_{i=1}^{n} \log \Pr(y_i|\mathbf{x},\mathbf{y}_{<i}) $$

In this notation, $$[\mathbf{x},\mathbf{y}_{<i}]$$ represents the context used for predicting the token $$y_i$$. Furthermore, the expression $$\Pr(y_i|\mathbf{x},\mathbf{y}_{<i})$$ is a common literature shorthand used to denote $$\Pr(y_i|[\mathbf{x},\mathbf{y}_{<i}])$$.

Direct Computation of Output Sequence Log-Probability in LLMs

In text generation, candidate sequences are evaluated based on their log-probability. Given an input `x`, the quality of a potential output sequence `y` (composed of tokens `y1...yi`) is measured by `log Pr(y|x)`. Using log-probabilities is a standard practice because it simplifies computation; the joint probability of a sequence, which is a product of conditional probabilities, becomes a sum of log-probabilities. This conversion is more numerically stable and computationally easier to manage.

Sequence Evaluation using Log-Probability

An engineer is using a generative language model to decide which of two possible sentences is a more likely completion for the input prompt 'Once upon a time,'. The model can compute various log-probability scores. To select the better completion, which of the following scores should the engineer compare for each candidate sentence?

Debugging a Language Model's Output Score

A developer is using a large language model to evaluate the quality of a generated sentence (the output) in response to a user's prompt (the input). The developer's colleague suggests that to get a complete score, they must calculate both the log-probability of the input and the log-probability of the output. Explain why this suggestion is incorrect for this specific task and what the model actually needs to compute.

Rationale for Log-Probability Calculation in Generative Models

The fundamental computational task of an autoregressive language model is to model the conditional probability of the next token given the preceding context, `Pr(y_i|x, y_{<i})`. A key requirement for practical implementation is that this computation must be performed in an efficient manner.

Core Computational Task in Autoregressive Generation

The process of computing the log-probability of an output sequence given an input, $$\log \Pr(\mathbf{y}|\mathbf{x})$$, in a Transformer language model involves several sequential operations. First, the input $$\mathbf{x}$$ and output $$\mathbf{y}$$ are concatenated. For each position $$i'$$, the corresponding token embedding is processed through a stack of Transformer layers, where self-attention networks update the KV cache and compute attention outputs. If the position corresponds to a generated token, the model utilizes a Softmax layer to determine the token's prediction probability. Finally, the total log-probability is calculated by summing these individual token log-probabilities over the entire generated sequence.

Learn Before

Related