Summary Auto-Regressive Next-Token Predictors A Theoretical Framework arxiv.org
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ARNPs like GPT-3 and GPT-4 simplify function learning by treating each token as both input and label, producing coherent responses and effectively generating text while investigating the trade-off between length complexity and other measures.
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Slide Presentation (10 slides)
Key Points
- Auto-Regressive Next-Token Predictors (ARNPs) are universal learners capable of solving complex tasks.
- ARNPs trained on the task of next-token prediction can approximate any function efficiently computed by a Turing machine.
- Linear ARNPs can compute any Turing computable function, demonstrating the power of linear models.
- Auto-regressive learning allows for supervision on intermediate steps in the computation process and enables the learner to compute non-linear functions.
- Length complexity, which measures the number of intermediate tokens required to approximate a target function, plays a crucial role in the performance of ARNPs.
- Experimental results show the effectiveness of simple next-token predictors in generating coherent text and solving arithmetic tasks.
- Chain-of-Thought (CoT) reasoning and scratchpad techniques enhance the performance of language models in logical reasoning and arithmetic tasks.
- Theoretical investigations into language models and transformers contribute to a better understanding of their capabilities and constraints.
Summaries
41 word summary
ARNPs like GPT-3 and GPT-4 generate coherent responses. They treat each token as both input and label, simplifying function learning. Next-token predictors are effective in generating text and solving arithmetic tasks. Research examines the trade-off between length complexity and other measures.
62 word summary
Auto-Regressive Next-Token Predictors (ARNPs) like GPT-3 and GPT-4 are powerful models that can generate coherent and contextually relevant responses. They simplify complex function learning by treating each token as both an input and a label. Experimental results show the effectiveness of next-token predictors in generating text and solving arithmetic tasks. Ongoing research explores the trade-off between length complexity and other complexity measures.
151 word summary
Auto-Regressive Next-Token Predictors (ARNPs) like GPT-3 and GPT-4 are powerful models that can generate coherent and contextually relevant responses. They can efficiently approximate any function computed by a Turing machine. Linear ARNPs can implement any target function. ARNPs simplify complex function learning by treating each token as both an input and a label, enabling the computation of non-linear functions. Length complexity, which measures the number of intermediate tokens needed to approximate a target function, is crucial for ARNP performance. Experimental results demonstrate the effectiveness of simple next-token predictors in generating coherent text and solving arithmetic tasks. Chain-of-Thought (CoT) reasoning and scratchpad techniques enhance language model performance. MLP-based architectures show promise as alternatives to transformers in language modeling tasks. Ongoing research explores the trade-off between length complexity and other complexity measures. The theoretical underpinnings of language models and transformers are relatively unexplored, but recent investigations shed light on their capabilities and constraints.
455 word summary
Auto-Regressive Next-Token Predictors (ARNPs) like GPT-3 and GPT-4 are powerful models that can solve complex tasks by generating coherent and contextually relevant responses. ARNPs trained on next-token prediction can efficiently approximate any function computed by a Turing machine. The length complexity, which measures the number of intermediate tokens needed to approximate a target function, is crucial for ARNP performance. Linear ARNPs can compute any Turing computable function, demonstrating that linear models can implement any target function.
Auto-regressive learning simplifies complex function learning by treating each token as both an input and a label. This enables the learner to compute non-linear functions, unlike classical supervised learning. However, there is a complexity trade-off with ARNPs. They require long sequences of tokens to detail the internal computations of the target, and length complexity quantifies the number of intermediate tokens necessary to learn a specific concept. Length complexity can be traded off with sample complexity or computational complexity for certain tasks.
Experimental results show that simple next-token predictors are effective. A linear next-token predictor trained on the TinyStories dataset generates plausible and grammatically sound stories. Additionally, a shallow Multi-Layer Perceptron (MLP) outperforms GPT-4 in multiplying two 4-digit numbers, achieving comparable results to Goat, a transformer trained for arithmetic tasks. These results highlight the power of next-token predictors in solving complex tasks.
Chain-of-Thought (CoT) reasoning and scratchpad techniques enhance language model performance in logical reasoning and arithmetic tasks. Theoretical investigations into CoT reasoning in auto-regressive models contribute to understanding their capabilities. The length complexity measure allows the study of how intermediate token sequences influence the difficulty of learning problems.
Language models for arithmetic tasks have gained interest, but they struggle with straightforward arithmetic operations. Structuring language models using an algorithmic pipeline can improve efficiency in arithmetic tasks. MLP-based architectures show promise as alternatives to transformers in language modeling tasks.
The theoretical underpinnings of language models and transformers are relatively unexplored. Early investigations show that transformers can emulate any Turing machine, and recent work demonstrates that transformers can simulate automata using few layers. The inductive biases of self-attention have been studied, showing that bounded-norm transformer networks can represent sparse functions with logarithmically scaling sample complexity. Language models trained with CoT can efficiently learn arbitrary Turing machines.
In conclusion, auto-regressive next-token predictors are universal learners that can efficiently approximate any function computed by a Turing machine. The power of language models lies in the auto-regressive training scheme rather than a specific architectural choice. Length complexity is crucial in the learning process, and ongoing research explores its trade-off with other complexity measures. Experimental results show the effectiveness of simple next-token predictors in generating coherent text and solving arithmetic tasks. Theoretical investigations contribute to understanding the capabilities and constraints of language models and transformers.
642 word summary
Auto-Regressive Next-Token Predictors (ARNPs) are universal learners capable of solving complex tasks. These models, such as GPT-3 and GPT-4, are trained on large amounts of text data and learn to generate coherent and contextually relevant responses. Despite their simplicity, ARNPs trained on the task of next-token prediction can approximate any function efficiently computed by a Turing machine. The length complexity, which measures the number of intermediate tokens required to approximate a target function, plays a crucial role in the performance of ARNPs. Linear ARNPs, where the next-token probability is a linear function of the input sequence, can compute any Turing computable function. This theoretical result demonstrates that linear models can implement practically any target function of interest.
In supervised learning, the learner only has access to the input sequence and the target label, making it difficult to learn complex functions. However, in auto-regressive learning, the learner treats each token as both an input and a label, allowing for supervision on intermediate steps in the computation process. This significantly simplifies the learning task and enables the learner to compute non-linear functions. The power of auto-regressive learning is not possible in classical supervised learning.
While ARNPs have the capacity to generate proficient learners, there is a trade-off in terms of complexity. One significant expense is the requirement for long sequences of tokens detailing the internal computations of the target. This prompts the introduction of length complexity as a measure of learning complexity, which quantifies the quantity of intermediate tokens necessary for the model to learn a particular concept class. Length complexity can be traded off with sample complexity or computational complexity when learning certain tasks.
Experimental results demonstrate the effectiveness of simple next-token predictors. A linear next-token predictor trained on the TinyStories dataset generates plausible and grammatically sound stories. Additionally, a shallow Multi-Layer Perceptron (MLP) outperforms GPT-4 in the task of multiplying two 4-digit numbers, achieving comparable results to Goat, a 7B-parameter transformer trained for arithmetic tasks. These results highlight the power of next-token predictors and their ability to solve complex tasks.
Chain-of-Thought (CoT) reasoning and scratchpad techniques have been shown to enhance the performance of language models in logical reasoning and arithmetic tasks. Theoretical investigations into CoT reasoning in auto-regressive models contribute to a better understanding of their capabilities. The length complexity measure allows for the study of the influence of intermediate token sequences on the difficulty of learning problems.
Language models for arithmetic tasks have gained significant interest. While these models have demonstrated promising capacity for solving mathematical problems, they often encounter difficulties in executing straightforward arithmetic operations. Structuring language models to perform calculations using an algorithmic pipeline can enhance their efficiency in arithmetic tasks. MLP-based architectures have shown promise as alternatives to transformers in language modeling tasks.
The theoretical underpinnings of language models and transformers remain relatively unexplored. Early investigations have established the universality of transformers and their ability to emulate any Turing machine. Recent work has demonstrated that transformers can simulate automata using few layers. The inductive biases of self-attention have been studied, showing that bounded-norm transformer networks can represent sparse functions with logarithmically scaling sample complexity. The ability of language models to learn computationally challenging problems using CoT has been explored, demonstrating that arbitrary Turing machines can be efficiently learned by language models trained with CoT.
In conclusion, auto-regressive next-token predictors are universal learners capable of approximating any function efficiently computed by a Turing machine. The power of language models can be attributed to the auto-regressive training scheme and not necessarily to a specific architectural choice. Length complexity plays a crucial role in the learning process, and its trade-off with other complexity measures is an area of ongoing research. Experimental results demonstrate the effectiveness of simple next-token predictors in generating coherent text and solving arithmetic tasks. Theoretical investigations contribute to a better understanding of the capabilities and constraints of