> Here’s a thought experiment: suppose that a mathematician solved a major problem by having a long exchange with an LLM in which the mathematician played a useful guiding role but the LLM did all the technical work and had the main ideas. Would we regard that as a major achievement of the mathematician? I don’t think we would.
This is a cultural choice. It makes sense that in the mathematics culture we currently have, this is alien. But already, other fields, and many individuals, would disagree and say that the human did have a major achievement here.
As long as human-AI collaborations are producing the best results, there is meaningful contribution by the humans, and people that are deeper experts and skilled LLM whisperers should be able to make outsized contributions. The real shoe drops when pure AI beats humans and human-AI collaboration.
Great summary. The fact that the auto encoding task is not grounded in thoughts, and their initial training on guessed internal thoughts, raise serious concerns on faithfulness. Feels like they might get better results by just training a supervised model on activations and "internal thoughts" measured by some different behavioral way.
Diffusion and flow matching models generate samples by iterative denoising. Iterative denoising means passing input to the neural network, running a forward pass, and taking the output back as input and rerunning the neural network. Often you do this 100 times, which is slow and expensive.
Flow maps / consistency models / shortcut models instead try to learn to compress this iterative work into 1 forward pass. This makes inference 100x faster as you'd only need to run the neural net forward pass once. Beyond speeding up inference, there are other advanced benefits to this, such as improved ability to perform inference-time steering.
Mathematically, learning a flow map corresponds to learning to solve an ordinary differential equation, i.e., learning the time integral of the velocity field. This mathematical foundation provides the basis for various training objectives for learning flow maps, which involve self-referential identities or identities such as the transport equation, which are discussed in the blog post.
Hope that helps! I'm an ML researcher currently researching flow maps.
The Jacobian is first derivatives, but for a function mapping N to M dimensions. It's the first derivative of every output wrt every input, so it will be an N x M matrix.
The gradient is a special case of the Jacobian for functions mapping N to 1 dimension, such as loss functions. The gradient is an N x 1 vector.
That's really interesting. What if they RAG search related videos from the prompt, and condition on that to generate? That might explain fidelity like this
'From my experience playing a few games on it against decently strong opponents has been that at high levels it becomes "Chess, but it's much much easier to checkmate, and 2~3 times a game some time travel shenanigans happen."
The main reason for that is time traveling and dimension hoping come at a tempo disadvantage. When you create a new timeline, you make 1 move, but give your opponent 2 moves. You used your turn in the present, and created a new board where it's their turn in the past.
Any time travel or dimension hops need to be worth twice as much, minimum, as a normal move to even consider making them.
It does have more depth than normal chess, but it's not infinity deep. I still love it. My biggest concern with high level chess matches is that many, many games end in draws. It feels like it's impossible to a draw a gam e in 5D chess' [0]