Creativity Beyond the Manifold

This is a hypothesis and not an established result. To the most philosophical and technical, discovering mathematical laws for understanding and influencing the world seems like a plausible trajectory which can be used for better AI alignment, as encoding this mathematically can help in AI models better understanding human foundations, and values., to quote Richard Ngo's 'Towards a scale-free theory of intelligent agency' . I believe that this model of intelligence even if constructed will itself depends on representational assumptions that constrain the forms of intelligence it can describe. I want to make this as a position of my theory of intelligence which includes the current paradigm of intelligent LLM agents and also why the 'mathematical laws' theory will also be incomplete due to it's dependence on geometry. In this post I would like to clarify my position and also make arguments for a 'radical' heading, my contributions are hence as follows: creativity is often described as thinking out of box. Geometry restrict LLMs to explore and be creative. How current LLM agents can be made creative which might require the 'The Most Forbidden Technique'. Current LLMs and Latent Space The space of representations in LLMs which they form under optimisation helps them in forming sentences and gives them the ability to construct a conversation with great efficiency to the point that they can be extremely persuasive about their arguments, while much has been said about the latent space, and much research has been done on LLMs representations, neural geometry, this space is inherently a constraint to creativity, LLMs basic flow of constructing a sentence requires prefill and decoding as the two main steps, this way of constructing meaning or understanding meaning where every new words and any experience related to those words will be attracted to the manifold in the basin which seems most likely to hold the most similar representations while that can be extremely helpful in conversations and the vast ways in which LLMs can stastically produce coherent sentences, this geometrical space when optimised to predict the next word can only constrain the models into always constructing the sentence with respect to the past and the events of the past and their details, it cannot construct all-novel ideas. While some pushback is deserved here from people in light of recent events where GPT 5.6 being able to solve 100 year old problems, and various other events, discovery requires something much more than statistical correlations and the ability to manipulate language.Recent examples of LLMs making apparently novel mathematical discoveries provide an important challenge to the strongest version of this hypothesis. The question is whether such discoveries can be shown to require the construction of representations that were not reachable under the model's existing geometry. Why Geometry is a constraint to Intelligence? Let's took a look at an example. Let's say there is a prompt P talking about a concept/idea X, when the user prompts the model, the model does the following: a) The tokenizer T converts X into n tokens, which get converted to embeddings E mjx-container[jax="CHTML"] { line-height: 0; } mjx-container [space="1"] { margin-left: .111em; } mjx-container [space="2"] { margin-left: .167em; } mjx-container [space="3"] { margin-left: .222em; } mjx-container [space="4"] { margin-left: .278em; } mjx-container [space="5"] { margin-left: .333em; } mjx-container [rspace="1"] { margin-right: .111em; } mjx-container [rspace="2"] { margin-right: .167em; } mjx-container [rspace="3"] { margin-right: .222em; } mjx-container [rspace="4"] { margin-right: .278em; } mjx-container [rspace="5"] { margin-right: .333em; } mjx-container [size="s"] { font-size: 70.7%; } mjx-container [size="ss"] { font-size: 50%; } mjx-container [size="Tn"] { font-size: 60%; } mjx-container [size="sm"] { font-size: 85%; } mjx-container [size="lg"] { font-size: 120%; } mjx-container [size="Lg"] { font-size: 144%; } mjx-container [size="LG"] { font-size: 173%; } mjx-container [size="hg"] { font-size: 207%; } mjx-container [size="HG"] { font-size: 249%; } mjx-container [width="full"] { width: 100%; } mjx-box { display: inline-block; } mjx-block { display: block; } mjx-itable { display: inline-table; } mjx-row { display: table-row; } mjx-row > * { display: table-cell; } mjx-mtext { display: inline-block; } mjx-mstyle { display: inline-block; } mjx-merror { display: inline-block; color: red; background-color: yellow; } mjx-mphantom { visibility: hidden; } _::-webkit-full-page-media, _:future, :root mjx-container { will-change: opacity; } mjx-math { display: inline-block; text-align: left; line-height: 0; text-indent: 0; font-style: normal; font-weight: normal; font-size: 100%; font-size-adjust: none; letter-spacing: normal; border-collapse: