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Francisco Vargas — Projects to Supervise

Projects to Supervise

Learning to Learn by Denoising Diffusion Optimisers

Supervisors: Francisco Vargas, Neil D. Lawrence

The seminal paper Learning to Learn by Gradient Descent By Gradient Descent [1] explores learning optimisers (rather than using SGD or Adam) through an RNN architecture which models time steps as training steps and an RL based loss.

In this project we aim to achieve a similar product but rather than RNNs and RL we would like to explore the closely linked diffusion models [5,6] and stochastic control. In particular there is already theoretical work that motivates the use of these methodologies for global optimisation [2], what now remains is to explore it in practice.

We expect the student to lightly adapt the methods in [3,4] to the optimisation setting in [2] (This simply amounts to exploring low temperatures in the artificial target distribution induced by the loss function). Furthermore, exploring tasks in engineering as in [1] might require being creative about the inductive biases baked into the NN parametrisation that we are working with.

The nature of this project will be mostly ML-engineering and playing around / being creative about NN inductive biases. That said if the student is more mathematically/theory oriented we could explore extending the results in [2] (which apply to the method in [4] only) to the method in in [3] using the mixing rates in [7] and maybe comparing to things like [8] (last bit would be very bonus/extra type of thing).

As always the student should explore simple 1d and 2d toy optimisation examples to assess the validity of the method before moving onto real world examples.

[1] https://arxiv.org/pdf/1606.04474.pdf 

[2] https://arxiv.org/abs/2111.00402

[3] https://openreview.net/forum?id=8pvnfTAbu1f

[4] https://arxiv.org/abs/2111.15141

[5] https://arxiv.org/abs/2006.11239

[6] https://arxiv.org/abs/2006.11239

[7] https://arxiv.org/pdf/2209.11215.pdf

[8] https://arxiv.org/abs/1707.06618

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Protein Folding Explantions via Diffusion Bridge Score Matching

Supervisors: Neil D. Lawrence, Francisco Vargas, Pierre Thodoroff

Technical Title: Sampling Transition Paths Between Molecular Conformations Using Diffusion Bridges and Score Matching.

Recent advances in Schrodinger Bridges [1,2] have enabled to learn stochastic mappings between 2 probability distributions (p(x) and q(x)) such that the stochastic map (which is modelled by a diffusion / SDE) is regularised by some prior process (whether it be computational or physical).

This project seeks to explore these methodologies in particular the simpler case studied in [3] where both the source and the target distributions are modeled as point masses (dirac delta functions / measures). We seek to apply the approach in [3] to sampling physically meaningful transition paths between two protein configurations as done in [4]. Ideally, we would aim to start working with simple/toy proteins and then move on to larger scale tasks where one of the protein configurations is a flat amino-acid and proteins produced by alpha fold, the end product would be to generate a video which gives a physically plausible folding process for alphafold [5] predictions.

An example Timeline of the project could be:

  1. Get the codebase of [4] working and reproduce results on simple proteins.
  2. Extend the work in [3] to the underdampened version. (Francisco can help with this)
  3. Apply the extensions and adaptions of [3] to work on the simple proteins of [4] and compare to the method in [4].
  4. Consider enhancements / extensions, would a full Schrödinger bridge work better here?
  5. If time allowing, pick some of the most recently exciting discoveries from alphafold [5] that have a known potential and try and see if we can get it working.

Point 5. is an “if time allows” type of objective and I predict most the time will be spent in 3., successful completion of 3 could lead to a publication at a top venue whilst 5. could have a broader impact on the field.

Ideally a good background in the following could be very helpful for this project:

  1. Timeseries models (Kalman filters, AR processes, Gaussian processes).
  2. Introductory calculus (ODEs, Basic PDEs, limits).
  3. Probability Theory (Limit Theorems, Change of Variables, basic concentration inequalities e.g., Markov/Chebyshev)
  4. Variational Inference (MFVI, Amortised VI, Deep hierarchical latent variable models)


[1] https://arxiv.org/pdf/2106.01357.pdf
[2] https://arxiv.org/pdf/2106.02081.pdf
[3] https://arxiv.org/pdf/2207.02149.pdf
[4] https://arxiv.org/pdf/2111.07243.pdf
[5] https://alphafold.ebi.ac.uk/

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