Rob Cornish
@rob_cornish
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Incoming Assistant Professor, CCDS @ Nanyang Technological University. Currently a Research fellow @ Oxford Statistics Department.
Joined April 2019
I still have positions available for a January 2026 intake - get in touch ASAP! Later intakes are also possible (please get in touch to discuss). For more information, and details on how to apply, please see:
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We develop methodology with precise guarantees under minimal assumptions, with large-scale safety-critical applications in mind. We also develop better tools for describing and reasoning about AI systems, using category theory, programming languages theory, and proof assistants.
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My lab works on AI safety and robustness across a variety of topics, including - Generative modelling - Geometric deep learning - Causal inference - Uncertainty quantification
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I'm looking for talented and ambitious PhD students to join me at Nanyang Technological University Singapore to work on safe and robust AI systems! Full scholarships covering tuition and a stipend are available, and are open to local and international students alike.
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We finally have the strong law of large numbers in Markov categories. https://t.co/0zBxYXzscE
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You can also find an extended abstract of my longer Markov categories paper here:
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If this is of interest to you, here is a recent talk that @PaoloPMath and I gave for a class at MIT:
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This meta-strategy of using category theory to simplify complex reasoning appears useful much more generally, and I think the days of category theory for machine learning are just getting started.
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Using Markov categories, this earlier paper explained all previous work on symmetrisation as instances of a single common principle (sec 5 of https://t.co/7xlUGQMOZI). It also extended this to methodology suited for *stochastic* models, which our ICLR paper applied to diffusions.
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The underlying theory we use here comes from https://t.co/7xlUGQMhaa, which studied the problem of symmetrisation using *Markov categories*. Markov categories allow for reasoning about probability in a conceptual, diagrammatic way, while also maintaining full mathematical rigour.
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A meta-point of this paper is that category theory has utility for reasoning about current problems of interest in mainstream machine learning. The theory is predictive, not just descriptive. 🧵(1/6)
In our new paper (accepted at ICLR!), we propose the first framework for constructing equivariant diffusion models via symmetrisation This allows us to ensure E(3)-equivariance with just highly scalable standard architectures such as Diffusion Transformers, instead of EGNNs, for
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In our new paper (accepted at ICLR!), we propose the first framework for constructing equivariant diffusion models via symmetrisation This allows us to ensure E(3)-equivariance with just highly scalable standard architectures such as Diffusion Transformers, instead of EGNNs, for
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Extended @neur_reps abstract of my full paper on neural network symmetrisation in Markov categories: https://t.co/AZCb5wAA4n See for an overview of the story in terms of deterministic functions and Markov kernels rather than general Markov categories.
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Here's a lecture at MIT on Markov categories, symmetries, and generative AI, by Rob Cornish and myself. https://t.co/KbJGNnSZXb
#touchdesigner #streamdiffusion #bananas
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A very clever application of Markov categories to equivariance in neural networks, by Rob Cornish. https://t.co/V0HIVvd3u5
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Relaxing Bijectivity Constraints with Continuously Indexed Normalising Flows with @rob_cornish, A. Caterini and @GeorgeDeligian9: https://t.co/JR7l1hjQAi Major revision of our previous work: we show pathologies of NFs for complex topologies and introduce methodology addressing it
arxiv.org
We show that normalising flows become pathological when used to model targets whose supports have complicated topologies. In this scenario, we prove that a flow must become arbitrarily numerically...
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