RT @drmichaellevin: I'm constantly irritated that I don't have time to read the torrent of cool papers coming faster and faster from amazin….

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RT @TacoCohen: Nobody wants to hear it, but working on data is more impactful than working on methods or architectures.

RT @EmilevanKrieken: We propose Neurosymbolic Diffusion Models! We find diffusion is especially compelling for neurosymbolic approaches, co….

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RT @alfcnz: Scaling continuous latent variable models as probabilistic integral circuits @tetraduzione @gengala13

RT @tetraduzione: Less than two weeks to submit your papers on:. 📈 #lowrank adapters and #factorizations.🧊 #tensor networks.🔌 probabilistic….

RT @tetraduzione: factorizing a tensor with infinite dimensions⁉️.yes that's possible‼️. and this gives you tractable inference, and the si….

This is joint work with amazing collaborators @cassiopc, @tetraduzione, and @equaeghe.Check out the paper.📜(preprint).📜(neurips). and code.🖥️

In extensive distribution estimation benchmarks, QPCs materialized from PICs with functional sharing systematically outperform standard PCs commonly learned via EM or Adam/SGD.

In practice, PICs with functional sharing (green), unlike those w/o (orange), need the same resources as PCs (blue), and up to 99% less params!.We plot the param num. for PCs (K is layer size), and for PICs (M is MLP size): PICs with sharing hit 5M params, while the others 2B!

Materializing QPCs is expensive when function evaluation is costly, so we propose neural functional sharing: We parameterize all integral units at the same depth with a multi-headed MLP. We show this for 4 bivariate functions, that we discretize to what we call CP folded layer.

Zooming-in the QPC materialization, we show how the above function f4 can be discretized via numerical quadrature and used to parameterize a Tucker layer. The two gaussian blocks are just vectors, which get multiplied via an outer product that is then matrix-multiplied by \tildeW

We propose a pipeline that from arbitrary variable decompositions (1) builds DAG-shaped PICs (2), that we train by materializing them as tensorized circuits (aka tensor networks) called Quadrature-PCs (QPCs) (3), which we also fold to allow fast inference (4).

In previous work, to keep training feasible, we only built tree-shaped PICs with simple univariate dependencies among latents. How can we build more intricate structures and allow for multivariate latent relationships while providing scalable training?.

Background: PICs are symbolic computational graphs over positive functions, and allow to build and represent continuous hierarchical mixtures. They are an extension of probabilistic circuits (PCs), as they use a new type of computation unit: the integral unit.

I’ll be attending #NeurIPS2024, where I’ll present our spotlight: Scaling Continuous Latent Variable Models as Probabilistic Integral Circuits (PICs). TL;DR: We learn continuous hierarchical mixtures as DAG-shaped PICs, and scale them using neural functional sharing techniques.

Lorenzo & team are really pushing the boundaries of tractable models, check out this banger!.