What if we can use diffusion models to generate Laproscopic surgeries to train surgeons?

Problem

Asking dalle to just “generate a Laproscopic surgery” is not going to work. It will give you cartoons.

Approach

1. text problem formulation: “grasper grasp gallbladder”
2. encode text into latents
3. do diffusion with late fusion of latents

Data: Cholec T-45

Weighting

Scoring: Perception Prioritized Weighting + Prioritization for Signal-to-Noise

(Ho et al, 2020)

Text

“[subject] [verb] [object] [surgical phase]”

The dimension of a vector space is the length of any basis in the vector space. It is denoted as \(\dim V\).

additional information

See also finite-dimensional vector space and infinite-demensional vector space

dimension of subspace is smaller or equal to that of its parent

If we have a finite-dimensional \(V\) and a subspace thereof \(U\), then \(\dim U \leq \dim V\).

Firstly, the every subspace of a finite-dimensional vector space is a finite-dimensional vector space is itself a finite-dimensional vector space. Therefore, it has a finite dimension.

direct estimation of the probability of failure:

1. perform a rollout of the system
2. label the outcome as \(1\) if the trajectory is a failure, and \(0\) otherwise

this is just Direct Sampling.

From there, we can just go about estimating this using standard parameter estimation (i.e. using MLE estimation or Baysian estimation.)

maximum-likelihood estimation of failure distribution

\begin{equation} \hat{p}_{\text{fail}} = \frac{1}{m} \sum_{i=1}^{m} 1\qty {\tau_{i} \not \in \psi} = \frac{n}{m} \end{equation}

for \(n\) failures and \(m\) rollouts, where \(\tau \sim p\qty(\cdot)\).