Sophia Sanborn
@naturecomputes
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Theory, neural networks, neurotechnology @ | Organizer @neur_reps | Prev: @geometric_intel @berkeley_ai @redwood_neuro @intelai @harvard
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Joined March 2018
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In this new paper, led by
@giovannimarchet
, we present a unique theoretical result that provides guarantees for the concrete representational structure expected to emerge in a learning system
Glad to announce our new preprint with C. Hillar, D. Kragic, and
@naturecomputes
!
We show via group theory how Fourier features emerge in invariant neural networks -- a step towards a mathematical understanding of representational universality. 🧵1/n
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This figure summarizes the landscape of topological neural network architectures on hypergraphs, simplicial, cellular, & combinatorial complexes in a unified graphical notation. Check out our paper and full repository of TNN equations for more ✨
Topological Deep Learning is an immensely powerful and fast emerging field. Our new literature review is out and here’s why I’m very excited about it🧵1/5
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Bispectral Neural Networks go to
#ICLR2023
!
In this work, we present a new neural network architecture capable of learning unknown groups purely from the symmetries implicit in data
—with
@cashewmake2
, Bruno Olshausen, and Christopher Hillar
1/17
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🎉 If you're interested in working on understanding visual representations in deep networks through the lens of symmetry & geometry, the
@geometric_intel
lab is recruiting!
📣 The Geometric Intelligence lab receives a 1.2M$ NSF Grant to work on Lie Group Representation Learning for Vision
Lead by lab members Christian Shewmake and Sophia Sanborn, the grant will support research on vision models that incorporate hierarchical learnable symmetries
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Our workshop on Symmetry and Geometry in Neural Representations has been accepted to
@NeurIPSConf
2022!
We've put together a lineup of incredible speakers and panelists from 🧠 neuroscience, 🤖 geometric deep learning, and 🌐 geometric statistics.
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If you find this interesting, check out our ICLR 2023 paper, in which we demonstrate that you can *learn* group-Fourier transforms by learning to be invariant to transformations in data:
Representation theory defines a Fourier transform on groups. Finite commutative groups correspond to the classical discrete Fourier transform.
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Seeking: Creative and ambitious computational neuroscience / ML PhDs interested in building next-generation brain-computer interfaces. My team at is hiring research scientists. Reach out at sophias
@science
.xyz for more info.
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About a month ago, I joined to work on fundamental problems in neural coding & build next-generation high-dimensional brain computer interfaces. The team is amazing and gives new meaning to the term "full-stack"
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Looking forward to presenting our work at
@NeurIPSConf
in December!
Here we use the triple correlation on groups to define a group-invariant layer for group-equivariant networks that improves both accuracy and robustness. Stay tuned for the camera-ready release!
w/
@ninamiolane
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On this episode of the
@twimlai
podcast, I talk about some of my favorite topics - universality, compression, group theory - and how mathematics reveals principles of neural representation that transcend substrate
Today we’re joined by Sophia Sanborn (
@naturecomputes
) from
@UCSB
to discuss the universality between neural representations and deep neural networks along with her
#ICLR2023
paper on Bispectral Neural Networks.
🎧🎥 Check out the full episode at
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🦠🤖 Bio/ML grad students: The bio team at is seeking summer interns with background in ML/computer vision and interest in biomedical applications. See more details below & DM if interested 👇
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The phenomenon of universality is a fascinating one:
Why do certain features consistently emerge across different neural networks (incl. the brain!) trained on different datasets?
In our forthcoming paper, we provide one answer, grounded in group representation theory
Glad to share that our paper titled 'Harmonics of Learning' got accepted at the Conference on Learning Theory (COLT 2024)!
This is a joint work with C. Hillar, D. Kragic and S. Sanborn (
@naturecomputes
)
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Thrilled to receive this honor. Thank you
@pimsmath
and
@SimonsFdn
!
Meet Sophia
@naturecomputes
from our lab🤩
Sophia studies fascinating geometric properties of neural representations
@neur_reps
@ucsbcs
She was just awarded the prestigious PIMS-Simons fellowship for her outstanding research in mathematical sciences!🏆
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In a new paper led by
@hopfbifurcator
, we bring the power of Riemannian geometry to the problem of neural decoding 🌐🧠
To appear at the
@CVPR
@TAGinDS
workshop: Quantifying Local Extrinsic Curvature in Neural Manifolds
With co-authors
@manusmad
,
@kdaoduc
, &
@ninamiolane
The brain🧠uses a distributed code - where variables are represented by the activity of a large number of neurons - to store information about the outside world. In this sense, our brains compute *morphisms* (structure-preserving maps) from the physical environment and ... 1/6
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This year's
@icmlconf
will host the 2nd annual Topology, Algebra, and Geometry in ML Workshop 🌐
Stay tuned for our call for papers 📄
Can't wait to bring the TAG community to Hawaii 🌴
Co-organized w
@emerson_tegan
@HenryKvinge
@Pseudomanifold
@ninamiolane
@tdoster
@TAGinDS
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Our latest pre-print develops a method for automating interpretability research in vision models 🤖👁️
Our method is grounded in human perceptual judgments, but is fully scalable 👥
Preprint alert: Superposition in CNNs and Brains
Context: Recent work on LLMs showed how sparse coding can recover interpretable representations in transformers
@AnthropicAI
TL;DR: Concurrently, we have been doing similar analyses in vision models and brains.
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Curious about how Riemannian geometry and VAEs can be used to understand neural population codes? Check out our latest pre-print, lead by Francisco Acosta (
@hopfbifurcator
), with myself,
@kdaoduc
,
@manusmad
, and
@ninamiolane
Check out my first (!) first-author preprint, with
@naturecomputes
,
@kdaoduc
,
@manusmad
, and
@ninamiolane
:
We propose a method for calculating the curvature of neural manifolds, using deep generative models and Riemannian geometry.
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A very interesting and prescient quote from Mikhail Gromov in
@doristsao
's
@neur_reps
talk on constructing visual representations through local diffeomorphisms
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Great opportunities in the
@geometric_intel
lab for researchers interested in the intersection of geometry, topology, deep learning, and neuroscience
I am recruiting postdocs for 2024!😃
3 fellowships available:
🌐Geometric and Topological Deep Learning
🧠Foundation Models for Neuroscience
⚕️AI for Women’s Brain Health.
Interested? Apply here!
This is how our campus looks like in the winter🌴😜
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Are there principles of representation learning that transcend model architecture and substrate?
Looking forward to discussing this and more in the new 🔵
@unireps
@NeurIPSConf
workshop 🔴
We're excited to announce the first edition of 🔵🔴 UniReps: the Workshop on Unifying Representations in Neural Models! 🧠
To be held at
@NeurIPSConf
2023!
SUBMISSION DEADLINE: 4 October
Check out our Call for Papers, lineup of speakers and schedule at:
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@CimesaLjubica
I highly recommend Principles of Neural Design by Sterling & Laughlin: a beautiful book that reverse engineers the structure of neural systems from the physical / environmental constraints faced by organisms
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Looking forward to a day of dynamic presentations and conversations with the NeurReps community. Join us on December 16th in Ballroom A/B
NeurReps is this Saturday Dec 16 in Ballroom A/B at
@NeurIPSConf
!
Come out for an exciting program of talks, posters, and discussions at the intersection of deep learning, higher mathematics, and computational neuroscience
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Interested in getting into topological deep learning? Check out the TDL Coding Challenge at
#ICML2023
hosted by
@TAGinDS
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🧐 Getting into Topological Deep Learning?
👩💻 Try PyT, a new and comprehensive platform for deep learning on topological domains
🪢 Built on top of PyTorch, PyT libraries standardize diverse models and common operations into a single unifying framework
Start building your topological neural networks today with
#PyT
.
#TopoModelX
#TopoNetX
#TopoEmbedX
@ninamiolane
@PaulRosenPHD
@tolga_birdal
@HajijMustafa
@mathildepapillo
@naturecomputes
@ghadazamzmi
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Check out the proceedings of the 2022 NeurIPS Workshop on Symmetry and Geometry in Neural Representations, now online with PMLR ✨
@NeurIPSConf
@neur_reps
The proceedings of the 2022 NeurReps Workshop are now online!
PMLR Volume 197: NeurIPS Workshop on Symmetry and Geometry in Neural Representations features 21 fantastic papers from our contributing authors
View online here:
@NeurIPSConf
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We're getting started this morning in ten minutes ✨
See you soon!
NeurReps is starting today Dec 16th at 8.55 am in ballrooms A/B!
Join us for a lively day of talks, panel and posters discussing symmetry and geometry in neural representations 🧠🤖
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Harmonic analysis
The common musical intervals have special relationships to each other in terms of their wavelengths:
Octave - 1/2
Fifth - 1/3
Fourth - 1/4
Discovered by Pythagorus in 500 BC
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A fantastic resource for those interested in manifold learning for neural population codes 🧠
We're also happy to share our 'tutorial on generative models', which
@marineschimel
,
@davindi09
and I generated for this workshop:
It consists of three notebooks giving an overview of some of the models discussed in the workshop!
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At NeurIPS this week. Come find me at the following places:
- Thu Poster Session 5 10:45:
#1016
on Invariance in G-CNNs
- Fri
@unireps
Workshop 9:00 - 9:30: Talk on Symmetry & Universality
- Sat
@neur_reps
Workshop 11:30 - 12:00: Moderating the panel / organizing all day ✨
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Check out our work featured in
@patrickmineault
's excellent NeuroAI paper roundup: polysemanticity & mechanistic interpretability in deep vision models & the visual cortex, led by
@klindt_david
👁️🧠
It's new post day 🎉 Could a neuroscientist understand an ANN? I cover recent work in mechanistic interpretability at
@AnthropicAI
led by
@ch402
and at UCSB with
@naturecomputes
@ninamiolane
@KlindtDavid
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@IntuitMachine
Nice paper from Rodola and colleagues! You might find our recent paper on symmetry and universality interesting:
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Beautiful real-world application of hypergraph neural networks!
I always questioned when do you really **need** hypergraph GNNs?
For modelling biological interactions beyond pairs, such as gene expression: HYFA processes gene expression values for patients collected from multiple organs.
Paper:
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⏰ Just two weeks to the deadline for the ICML Workshop on Topology, Algebra, and Geometry in ML!
🗓️ Deadline: May 8 AOE
🔗 Click here for submission instructions and more details
🧑🏫 We look forward to seeing your work!
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I'm at
@NeurIPSConf
all week and looking to meet as many new people as possible
If you're interested in the intersection of geometry, deep learning, and neuroscience, let's chat
Shoot me a DM or come by our NeurReps Workshop on Saturday ✨
@neur_reps
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(give rise to symmetries in learning systems - biological or artificial)
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We think this provides theoretical backing for the emergence of Fourier features / irreps in the nice recent papers by
@NeelNanda5
,
@bilalchughtai_
, et al in the context of learning modular arithmetic / group composition:
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New preprint with
@_cgcorrea
and colleagues on planning as sampling from an "action grammar"
Human behavior is hierarchically structured. But what determines *which* hierarchies people use? In a preprint, we run an experiment where people create programs that correspond to hierarchies, finding that people prefer structures with more reuse.
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@patrickmineault
For those interested in the intersection of neuroscience, ML, and geometry/topology, check out our repo awesome-neural-geometry 🧠🌐
Check out ✨awesome-neural-geometry✨ - a curated selection of resources and research for those wishing to dive into this interdisciplinary area.
We link our favorite 📚 math books, 📜 blogposts, 👩🏫online lectures, 📄 papers, and 🧠 more.
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We're hoping to bring the 2nd edition of the
@neur_reps
workshop back to NeurIPS this year — Let us know what you want to see at NeurReps 2023 ✨
We are beginning to look towards
#NeurIPS2023
& we want to incorporate your ideas!
For the 2023 NeurReps Workshop:
🔣 What topics do you want to see?
👩🏫 Who do you want to hear from?
👥 Have ideas for interactive programming?
Leave comments & submit suggestions below 👇
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The deadline for NeurReps has been extended to October 4th AOE 🌟
We have two tracks: Extended Abstracts (4 pg, non-archival) and Proceedings (9 pg, published in PMLR)
Last year saw a fantastic batch of submissions. We look forward to seeing this year's creative work! 🧠
📢 Deadline extension
The NeurReps submission deadline has been extended to October 4th AOE.
If you're working in geometric deep learning, topological data analysis, applied geometry, computational neuroscience, or somewhere in the intersection, send us your work!
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✈️Amsterdam bound. Thrilled to be participating in the Geometry and Shape Analysis for Neuroscience Minisymposium at
#SIAMCSE23
this Monday. Please reach out if you are attending or in the area. Looking forward to great conversations
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Cayley tables contain all information about the structure of a finite group. Our work is the first to show that a group's Cayley table can be learned purely from observing transformations. This is an exciting result for machine learning and computational mathematics alike!
8/17
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Christian Shewmake (
@cashewmake2
) leads our last panel discussion on geometric and topological principles for representations in the brain with Bruno Olshausen,
@manusmad
,
@KrisTorpJensen
, and
@gkreiman
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In the
@neur_reps
slack community, we've been compiling our favorite resources on geometry for neuroscience and deep learning. Check it out on Github and contribute yours!
Check out ✨awesome-neural-geometry✨ - a curated selection of resources and research for those wishing to dive into this interdisciplinary area.
We link our favorite 📚 math books, 📜 blogposts, 👩🏫online lectures, 📄 papers, and 🧠 more.
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Our call for papers is out!
Seeking your latest work on GDL, geometric statistics, and geometric/topological methods for neuroscience.
Hope to see you in New Orleans 💫
📣 Announcing 📣
💥 The NeurIPS 2022 Workshop on Symmetry and Geometry in Neural Representations💥
(NeurReps 😉)
We're bringing a killer lineup to NeurIPS this year — spanning GDL, applied geometry, and neuroscience.
See our call for papers below 👇
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@rballeba
Stay tuned for a review paper surveying the landscape of topological deep learning architectures with my co-authors
@ninamiolane
@HajijMustafa
and lead author
@mathildepapillo
! We'll be posting it online next month.
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👩💻 Seeking reviewers with expertise in topology, algebra, and geometry for
#ICML2023
🌟 Sign up to help out below 👇
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The TAG-ML proceedings are now online. Check out this collection of excellent papers at the intersection of topology, algebra, geometry, and machine learning! 🌐
The proceedings volume of the 2nd Annual TAG-ML workshop
@icmlconf
is available now at
Thank you to all of the contributing authors and editors- it takes a village!
@neur_reps
@mathildepapillo
@ninamiolane
@Pseudomanifold
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This algebraic perspective offers a new lens on representation learning and deep learning theory, grounded in the mathematics of symmetry
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Symmetry has the potential to serve as an organizing principle for theories of neural coding, much like it did for 20th century physics. Thrilled to be a part of this exciting workshop organized by
@simoneazeglio
and
@ari_dibe
.
It's official!
@BernsteinNeuro
accepted our - with
@ari_dibe
- workshop proposal 🧠
In "Symmetry, Invariance and Neural Representations" we will explore the intimate relationship between the physical world and neural representations.
Join our speakers in this experience!
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Fantastic and fascinating new work from the
@atolias
lab. I've been wanting to this experiment run like this since the original Circuits thread by
@ch402
et al 👏
Does the concept of cortical columns extend to higher-level primate cortex?
Using
#DeepLearning
& physiology, we found that V4 neurons cluster in columns & form functional groups
Led by
@KonstantinWille
@kelli_restivo
w/
@sinzlab
@kfrankelab
@alxecker
🧵
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@patrickmineault
If you're interested: we applied a similar approach to both deep image models and data from the visual cortex and found some interesting results, in line with the concept of "mixed selectivity" / "polysemanticity"
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Our results offer an explanation for the emergence of certain universal features across both artificial and biological learning systems, including the localized Fourier features common to vision models and the visual cortex
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📄 Paper:
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An exciting program on geometry and dynamics in the brain put together by
@adelardalan
,
@tafazolisina
, and
@timbuschman
. Looking forward to discussing these topics with everyone in Mont Tremblant 🍁
📣 COSYNE’23 Workshop Announcement 📣
📐+🧠 Dynamic geometrical transformations: Language of flexible brain computations
🕰 March 14, 2023, Mont Tremblant, Quebec, Canada
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Our theoretical investigations were originally motivated by the highly consistent and precise phenomena we observed in Bispectral Neural Networks, which reliably learn the irreps of unknown groups from observations of transformed data
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Our goal is to bring together researchers in these fields to illuminate geometric principles for neural representations across both biological and artificial systems -- with special focus on invariant and equivariant representations and neural manifolds.
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Very cool new work on learning symmetry groups from data ✨
How can we learn equivariant neural networks, where the group actions are interpretable and completely learnable from data?
Happy to share our preprint with Karim Helwani and Demba Ba: (1/n)
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Join us on Slack to take part in a growing community at the intersection of applied mathematics, deep learning, and neuroscience 🌐🤖🧠
Last year, we started a Slack workspace to build community at the intersection of math, deep learning, + neuroscience. Today we are ~900 members strong 🦾
We have some exciting new plans in the works, including seminars, tutorials, + hackathons
Join us online to take part! 🔗👇
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Another exciting paper on symmetry discovery. Great to see more attention on this problem!
How can
#GenerativeAI
help scientists discover symmetry from data? Check out our
#ICML2023
paper on ``Generative Adversarial Symmetry Discovery''.
Paper:
Code:
(1/3)
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The model makes use of some of my favorite mathematics—harmonic analysis, group representation theory, and an object called the *bispectrum*—to simultaneously learn a group-equivariant and -invariant map
2/17
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Despite the simplicity of Bispectral Networks, their mathematical foundations give them power💥
We're excited about their potential as a computational primitive for robust invariant representation learning.
To dive deeper, check out our paper:
15/17
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The latest set from my DJ project with Mils if you need some hard beats to study / do math to
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The future of BCI goes far beyond traditional control. I'm thrilled to join the team and build out this new paradigm. Reach out if you're interested in getting involved -
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🟰 Equations:
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Now is an incredible time to work on neurotechnology, leveraging the inherent synergy between the brain's representations of the world & the rich sensory-semantic representations derived by large-scale artificial neural networks
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While powerful, Group-Equivariant CNNs require knowing and building in the relevant groups by hand. In this paper, we present a method for *learning* the groups that structure the data by learning to collapse image orbits
5/17
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In NYC for the week. Reach out if you want to meet up 🗽
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@CimesaLjubica
One thing I appreciate greatly is that they start from single-celled organisms that have no neurons at all. An individual cell exhibits an immense amount of intelligence & I think the field would do well to release our fixation on the brain as the locus of intelligent computation
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This simple objective combined with mathematical constraints permits the model to learn the irreducible representations of the group. That is, the model learns to perform a Fourier transform on an unknown group. The result is a learned equivariant layer
6/17
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The bispectrum, by contrast, is a *complete* invariant. This means that it only removes variations due to group actions on the domain, preserving all signal structure
11/17
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Reviewers needed for the Topology Algebra and Geometry in Pattern Recognition Applications workshop
@CVPR
! Fill out the Google form below if you are able to help out 👇🙏
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And be sure to check out our poster at
#ICLR2023
: Wednesday May 3rd 11:30AM to 1:30PM in MH 1-2-3-4
#90
I was not able to make it in person, but
@Yubei_Chen
has transported the poster across the globe 🗺️🙏
16/17
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Thrilled to have contributed to this work! Loihi 2 allows engineers to program custom neuron models, facilitating the design of all sorts of exotic spiking neural networks.
“We are trying to establish a new flexible and versatile, general purpose intelligent computing chip,” says Mike Davies,
@Intel
’s
#Neuromorphic
Computing Director. Read about Intel’s neuromorphic research journey and the Loihi-2 chip in
@ScienceMagazine
.
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Euclidean rythyms
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⌛️ One week to the TAG-ML Deadline for
#ICML2023
🍩 Get in your work on topology, algebra, and geometry in machine learning!
🎯 Deadline: May 8th AOE
👉
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📄 New pub! Here --->
Mini-thread below 🧵
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Can't think of anyone more deserving. Congrats to our lab leader! 🏆💥
Honored to be named Hellman Fellow!
Esp grateful to extraordinary lab members
@mathildepapillo
@AdeleMyersPhD
@hopfbifurcator
@BongjinKoo
@naturecomputes
@klindt_david
@cashewmake2
who made it happen!
👉We create cutting-edge AI to reveal the geometries of intelligent life🌐🍩
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Deadline extended to Friday! 😌 Time to put on those finishing touches.
📢 Last call for papers 📢
NEW DEADLINE: Friday Oct 6 23:59 AoE
We are giving authors until the end of the week to submit their work
Get all the info you need to submit here! 👇
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Keep an eye out for our speaker lineup, call for papers, and other updates. We are so excited to build community in this interdisciplinary space 🌟
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We especially appreciate folks with background in geometry/topology, dynamical systems, and/or mechanistic interpretability research
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Groups are mathematical objects that describe many of the transformations that show up in natural data, such as shifts, rotations, reflections, and many more
3/17
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As a consequence, Bispectral Neural Networks are both invariant and robust. We demonstrate this in experiments in which we attempt to generate model "metamers"—inputs that yield the same model representation but do not look the same
12/17
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Since I couldn't make it to the conference, please reach out if you're interested in chatting: sanborn
@berkeley
.edu 📨
17/17
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Had fun making generative suminagashi last night with
@eangolden
and
@FluintArt
. Awesome project.
Fluint Series B has it's own language of generative logic for cut and paint paths. You will get to play with that code in live sessions. Here is a simple but beautiful example we made last night ⚫️⚪️⚫️
Watch the full length version (17 minutes) here:
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I'll be joining for the
@geomstats
hackathon. Hope to see some of you in Paris!
📢We are pleased to announce the beginning of the thematic trimester "Geometry and Statistics in Data Sciences” (GESDA) to be held at
#IHP
(05/09 - 09/12/2022)
👉Full programme on
#scientificprogramme
#geometry
#statistics
#datascience
#Maths
#gesdaihp
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The structure of our model is remarkably simple: It's comprised of a single linear layer that parameterizes a Fourier transform on an unknown group, followed by a bispectral layer that computes invariant coefficients from the first. Note: the weights are random to start
14/17
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Many operations are invariant. The max of an image is the same if the image is rotated. However, it's *also* the same if the pixels are randomly permuted. Most invariant maps are degenerate in this way—they lose signal structure & throw the baby out with the bathwater 🛁
10/17
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Looking forward to speaking in the Mathematics of Neuroscience Symposium on the beautiful island of Crete this summer! 🌊☀️🇬🇷
The call for talk/poster submissions is now open, check it out below 👇
#ICNAAM2022
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