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Autoregressive language modeling assigns probabilities to a token sequence through next-token distributions conditioned on preceding context.
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This objective supports training and generation, while predicting likely text alone does not establish the truth of its contents.
Language modeling concerns probabilities of text sequences. In an autoregressive formulation, each next-token distribution is conditioned on earlier tokens, and the probability of a specified prefix is the product of its conditional token probabilities. An illustrative two-token prefix has probability one-half for its first token and one-fifth for its second token given the first. Their joint prefix probability is one-tenth. This calculation concerns the stated prefix and does not add an unstated end-of-sequence event. N-gram models approximate context with a fixed short history and estimate continuation probabilities from counts. Without appropriate smoothing, unseen continuations can receive zero probability; smoothing can change that behavior, so novelty is not a guarantee that every n-gram system fails. Neural models use learned representations and can provide a different context-dependent distribution. Transformer decoder attention uses masking to prevent access to later target positions in the stated autoregressive training setup. The next-token training target is already present in the observed text, providing a self-supervised prediction task. During teacher-forced training, the prefix for a target comes from the observed training sequence. During autoregressive generation, selected output tokens are appended and used as context for later predictions. Those are different sources of context even when they use the same learned model. Cross-entropy or negative log-likelihood rewards assigning probability to the observed target tokens. Sampling settings then affect how a continuation is selected from model scores. Temperature rescales a distribution and nucleus sampling selects a probability-mass subset. Changes to selection can affect output variety without certifying factuality, safety, or useful reasoning.
Comparing next-token probabilities for a stated text prefix.
Studying an n-gram count model and its treatment of unseen continuations.
Training a causal model from target tokens already present in text sequences.
Examining how a sampling procedure chooses among predicted continuation tokens.
Language-model research can compare representations, objectives, data choices, and decoding procedures on identified tasks. A lower prediction loss can be useful evidence about the modeled text distribution, while application behavior needs additional assessment. Post-training, retrieval, and tool use introduce other components whose effects should be evaluated separately from the next-token objective. Reports should distinguish teacher-forced likelihood evaluation from sampled generation and explain which context was available. This makes it easier to interpret an observed improvement without treating statistical prediction as a proof of complete understanding or factual reliability.
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Autoregressive language modeling assigns probabilities to a token sequence through next-token distributions conditioned on preceding context. This objective supports training and generation, while predicting likely text alone does not establish the truth of its contents.
The formulation models conditional next-token probabilities for text sequences.
Short fixed histories restrict context, while smoothing affects how unseen events are assigned probability.
The text supplies prediction targets; this does not make collection or computation free.
Generation proceeds conditionally through a sequence; an implementation can limit the available context window.
The objective rewards probability assigned to the observed next-token targets under the stated training formulation.
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