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Mar 11

What's the Magic Word? A Control Theory of LLM Prompting

Prompt engineering is crucial for deploying LLMs but is poorly understood mathematically. We formalize LLM systems as a class of discrete stochastic dynamical systems to explore prompt engineering through the lens of control theory. We investigate the reachable set of output token sequences R_y(mathbf x_0) for which there exists a control input sequence mathbf u for each mathbf y in R_y(mathbf x_0) that steers the LLM to output mathbf y from initial state sequence mathbf x_0. We offer analytic analysis on the limitations on the controllability of self-attention in terms of reachable set, where we prove an upper bound on the reachable set of outputs R_y(mathbf x_0) as a function of the singular values of the parameter matrices. We present complementary empirical analysis on the controllability of a panel of LLMs, including Falcon-7b, Llama-7b, and Falcon-40b. Our results demonstrate a lower bound on the reachable set of outputs R_y(mathbf x_0) w.r.t. initial state sequences mathbf x_0 sampled from the Wikitext dataset. We find that the correct next Wikitext token following sequence mathbf x_0 is reachable over 97% of the time with prompts of kleq 10 tokens. We also establish that the top 75 most likely next tokens, as estimated by the LLM itself, are reachable at least 85% of the time with prompts of kleq 10 tokens. Intriguingly, short prompt sequences can dramatically alter the likelihood of specific outputs, even making the least likely tokens become the most likely ones. This control-centric analysis of LLMs demonstrates the significant and poorly understood role of input sequences in steering output probabilities, offering a foundational perspective for enhancing language model system capabilities.

Towards General Computer Control: A Multimodal Agent for Red Dead Redemption II as a Case Study

Despite the success in specific tasks and scenarios, existing foundation agents, empowered by large models (LMs) and advanced tools, still cannot generalize to different scenarios, mainly due to dramatic differences in the observations and actions across scenarios. In this work, we propose the General Computer Control (GCC) setting: building foundation agents that can master any computer task by taking only screen images (and possibly audio) of the computer as input, and producing keyboard and mouse operations as output, similar to human-computer interaction. The main challenges of achieving GCC are: 1) the multimodal observations for decision-making, 2) the requirements of accurate control of keyboard and mouse, 3) the need for long-term memory and reasoning, and 4) the abilities of efficient exploration and self-improvement. To target GCC, we introduce Cradle, an agent framework with six main modules, including: 1) information gathering to extract multi-modality information, 2) self-reflection to rethink past experiences, 3) task inference to choose the best next task, 4) skill curation for generating and updating relevant skills for given tasks, 5) action planning to generate specific operations for keyboard and mouse control, and 6) memory for storage and retrieval of past experiences and known skills. To demonstrate the capabilities of generalization and self-improvement of Cradle, we deploy it in the complex AAA game Red Dead Redemption II, serving as a preliminary attempt towards GCC with a challenging target. To our best knowledge, our work is the first to enable LMM-based agents to follow the main storyline and finish real missions in complex AAA games, with minimal reliance on prior knowledge or resources. The project website is at https://baai-agents.github.io/Cradle/.

An Interdisciplinary Comparison of Sequence Modeling Methods for Next-Element Prediction

Data of sequential nature arise in many application domains in forms of, e.g. textual data, DNA sequences, and software execution traces. Different research disciplines have developed methods to learn sequence models from such datasets: (i) in the machine learning field methods such as (hidden) Markov models and recurrent neural networks have been developed and successfully applied to a wide-range of tasks, (ii) in process mining process discovery techniques aim to generate human-interpretable descriptive models, and (iii) in the grammar inference field the focus is on finding descriptive models in the form of formal grammars. Despite their different focuses, these fields share a common goal - learning a model that accurately describes the behavior in the underlying data. Those sequence models are generative, i.e, they can predict what elements are likely to occur after a given unfinished sequence. So far, these fields have developed mainly in isolation from each other and no comparison exists. This paper presents an interdisciplinary experimental evaluation that compares sequence modeling techniques on the task of next-element prediction on four real-life sequence datasets. The results indicate that machine learning techniques that generally have no aim at interpretability in terms of accuracy outperform techniques from the process mining and grammar inference fields that aim to yield interpretable models.