A useful mental model for an LLM is a giant matrix where each row is a possible prompt and columns represent next-token probabilities. This matrix is impossibly large but also extremely sparse, as most token combinations are gibberish. The LLM's job is to efficiently compress and approximate this matrix.

MIT research reveals that large language models develop "spurious correlations" by associating sentence patterns with topics. This cognitive shortcut causes them to give domain-appropriate answers to nonsensical queries if the grammatical structure is familiar, bypassing logical analysis of the actual words.

Contrary to the view that in-context learning is a distinct process from training, Karpathy speculates it might be an emergent form of gradient descent happening within the model's layers. He cites papers showing that transformers can learn to perform linear regression in-context, with internal mechanics that mimic an optimization loop.

Early Wittgenstein's "logical space of possibilities" mirrors how LLM embeddings map words into a high-dimensional space. Late Wittgenstein's "language games" explain their core function: next-token prediction and learning through interactive feedback (RLHF), where meaning is derived from use and context.

A common misconception is that Transformers are sequential models like RNNs. Fundamentally, they are permutation-equivariant and operate on sets of tokens. Sequence information is artificially injected via positional embeddings, making the architecture inherently flexible for non-linear data like 3D scenes or graphs.

The core transformer architecture is permutation-equivariant and operates on sets of tokens, not ordered sequences. Sequentiality is an add-on via positional embeddings, making transformers naturally suited for non-linear data structures like 3D worlds, a concept many practitioners overlook.

We can now prove that LLMs are not just correlating tokens but are developing sophisticated internal world models. Techniques like sparse autoencoders untangle the network's dense activations, revealing distinct, manipulable concepts like "Golden Gate Bridge." This conclusively demonstrates a deeper, conceptual understanding within the models.

The 2017 introduction of "transformers" revolutionized AI. Instead of being trained on the specific meaning of each word, models began learning the contextual relationships between words. This allowed AI to predict the next word in a sequence without needing a formal dictionary, leading to more generalist capabilities.

Contrary to common perception shaped by their use in language, Transformers are not inherently sequential. Their core architecture operates on sets of tokens, with sequence information only injected via positional embeddings. This makes them powerful for non-sequential data like 3D objects or other unordered collections.