Exploring the Boundaries of Language Models and the Philosophy of Ludwig Wittgenstein
I came across two things that sparked a train of thought that I wanted to explore:
1. This tweet
2. This lecture
Interpolating Ideas in Billion-Dimensional Spaces
In the realm of artificial intelligence, particularly with large language models (LLMs), there's a burgeoning discussion about the extent of these models' capabilities. A thought-provoking tweet recently suggested that perhaps all LLMs can do is interpolate, yet this might be more profound than it sounds, given our limited understanding of what interpolation means within the context of billion-dimensional concept spaces.
Interpolation, in mathematical terms, involves estimating within the range of a discrete set of known data points. When applied to LLMs like OpenAI's GPT models, interpolation could imply that these models generate responses based on a vast but finite set of training data, without truly 'understanding' or 'creating' anything new. Instead, they navigate through an immensely complex space of pre-existing human-generated text, finding pathways between points in ways that can seem surprisingly intuitive or creative.
The tweet challenges us to reconsider what we deem as creative or novel. If an LLM operates within the "convex hull" of existing ideas (a mathematical concept describing the smallest convex set that contains all the points), does this mean all conceivable ideas are just recombinations of existing knowledge? This is a humbling perspective, suggesting that human creativity itself might fundamentally be a process of navigating and recombining known concepts in novel ways.
Wittgenstein and the Limits of Language
This view aligns intriguingly with the philosophical inquiries of Ludwig Wittgenstein, particularly his later work focused on the philosophy of language. Wittgenstein argued that the limits of our language are the limits of our world, proposing that meaning derives from use within specific life forms or language-games. This suggests that understanding and innovation are bound by the contexts in which language is used, and thus, inherently limited by the constructs available within those contexts.
From Wittgenstein's perspective, every idea is inherently bound by the language used to express and think about it. Thus, if LLMs are operating within the confines of human language, their ability to generate 'new' ideas is inherently constrained by the language in which they were trained. They are, in a sense, playing an immense game of language, following rules derived from the data they were fed.
In conclusion, as we delve deeper into the capabilities of language models and their philosophical implications, we find ourselves confronting fundamental questions about the nature of creativity, understanding, and the very structure of human knowledge.