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BEGIN:VEVENT
SUMMARY:Tom Oliver (Nottingham)
DTSTART;VALUE=DATE-TIME:20210929T120000Z
DTEND;VALUE=DATE-TIME:20210929T130000Z
DTSTAMP;VALUE=DATE-TIME:20240522T213119Z
UID:CompAlg/1
DESCRIPTION:Title:
Supervised learning of arithmetic invariants\nby Tom Oliver (Nottingha
m) as part of Machine Learning Seminar\n\n\nAbstract\nWe explore the utili
ty of standard supervised learning algorithms for a range of classificatio
n problems in number theory. In particular\, we will consider class number
s of real quadratic fields\, ranks of elliptic curves over Q\, and endomor
phism types for genus 2 curves over Q. Each case is motivated by its appea
rance in an open conjecture. Throughout the basic strategy is the same: we
vectorize the underlying objects via the coefficients of their L-function
s.\n
LOCATION:https://researchseminars.org/talk/CompAlg/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexei Vernitski (Essex)
DTSTART;VALUE=DATE-TIME:20220701T130000Z
DTEND;VALUE=DATE-TIME:20220701T140000Z
DTSTAMP;VALUE=DATE-TIME:20240522T213119Z
UID:CompAlg/2
DESCRIPTION:Title:
Using machine learning to solve mathematical problems and to search for ex
amples and counterexamples in pure maths research\nby Alexei Vernitski
(Essex) as part of Machine Learning Seminar\n\n\nAbstract\nOur recent res
earch can be generally described as applying state-of-the-art technologies
of machine learning to suitable mathematical problems. As to machine lear
ning\, we use both reinforcement learning and supervised learning (underpi
nned by deep learning). As to mathematical problems\, we mostly concentrat
e on knot theory\, for two reasons\; firstly\, we have a positive experien
ce of applying another kind of artificial intelligence (automated reasonin
g) to knot theory\; secondly\, examples and counter-examples in knot theor
y are finite and\, typically\, not very large\, so they are convenient for
the computer to work with.\n\nHere are some successful examples of our re
cent work\, which I plan to talk about.\n\n1. Some recent studies used mac
hine learning to untangle knots using Reidemeister moves\, but they do not
describe in detail how they implemented untangling on the computer. We in
vested effort into implementing untangling in one clearly defined scenario
\, and were successful\, and made our computer code publicly available.\n2
. We found counterexamples showing that some recent publications claiming
to give new descriptions of realisable Gauss diagrams contain an error. We
trained several machine learning agents to recognise realisable Gauss dia
grams and noticed that they fail to recognise correctly the same counterex
amples which human mathematicians failed to spot.\n3. One problem related
to (and "almost" equivalent to) recognising the trivial knot is colouring
the knot diagram by elements of algebraic structures called quandles (I wi
ll define them). We considered\, for some types of knot diagrams (includin
g petal diagrams)\, how supervised learning copes with this problem.\n
LOCATION:https://researchseminars.org/talk/CompAlg/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anindita Maiti (Northeastern University)
DTSTART;VALUE=DATE-TIME:20220912T140000Z
DTEND;VALUE=DATE-TIME:20220912T150000Z
DTSTAMP;VALUE=DATE-TIME:20240522T213119Z
UID:CompAlg/3
DESCRIPTION:Title:
Non-perturbative Non-Lagrangian Neural Network Field Theories\nby Anin
dita Maiti (Northeastern University) as part of Machine Learning Seminar\n
\n\nAbstract\nEnsembles of Neural Network (NN) output functions describe f
ield theories. The Neural Network Field Theories become free i.e. Gaussian
in the limit of infinite width and independent parameter distributions\,
due to Central Limit Theorem (CLT). Interaction terms i.e. non-Gaussianiti
es in these field theories arise due to violations of CLT at finite width
and / or correlated parameter distributions. In general\, non-Gaussianitie
s render Neural Network Field Theories as non-perturbative and non-Lagrang
ian. In this talk\, I will describe methods to study non-perturbative non-
Lagrangian field theories in Neural Networks\, via a dual framework over p
arameter distributions. This duality lets us study correlation functions a
nd symmetries of NN field theories in the absence of an action\; further t
he partition function can be approximated as a series sum over connected c
orrelation functions. Thus\, Neural Networks allow us to study non-perturb
ative non-Lagrangian field theories through their architectures\, and can
be beneficial to both Machine Learning and physics.\n
LOCATION:https://researchseminars.org/talk/CompAlg/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manolis Tsakiris (Chinese Academy of Sciences)
DTSTART;VALUE=DATE-TIME:20230208T100000Z
DTEND;VALUE=DATE-TIME:20230208T110000Z
DTSTAMP;VALUE=DATE-TIME:20240522T213119Z
UID:CompAlg/4
DESCRIPTION:Title:
Unlabelled Principal Component Analysis\nby Manolis Tsakiris (Chinese
Academy of Sciences) as part of Machine Learning Seminar\n\n\nAbstract\nTh
is talk will consider the problem of recovering a matrix of bounded rank f
rom a corrupted version of it\, where the corruption consists of an unknow
n permutation of the matrix entries. Exploiting the theory of Groebner bas
es for determinantal ideals\, recovery theorems will be given. For a speci
al instance of the problem\, an algorithmic pipeline will be demonstrated\
, which employs methods for robust principal component analysis with respe
ct to outliers and methods for linear regression without correspondences.\
n
LOCATION:https://researchseminars.org/talk/CompAlg/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guido Montufar (UCLA)
DTSTART;VALUE=DATE-TIME:20230222T160000Z
DTEND;VALUE=DATE-TIME:20230222T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T213119Z
UID:CompAlg/5
DESCRIPTION:Title:
Geometry and convergence of natural policy gradient methods\nby Guido
Montufar (UCLA) as part of Machine Learning Seminar\n\n\nAbstract\nWe stud
y the convergence of several natural policy gradient (NPG) methods in infi
nite-horizon discounted Markov decision processes with regular policy para
metrizations. For a variety of NPGs and reward functions we show that the
trajectories in state-action space are solutions of gradient flows with re
spect to Hessian geometries\, based on which we obtain global convergence
guarantees and convergence rates. In particular\, we show linear convergen
ce for unregularized and regularized NPG flows with the metrics proposed b
y Kakade and Morimura and co-authors by observing that these arise from th
e Hessian geometries of conditional entropy and entropy respectively. Furt
her\, we obtain sublinear convergence rates for Hessian geometries arising
from other convex functions like log-barriers. Finally\, we interpret the
discrete-time NPG methods with regularized rewards as inexact Newton meth
ods if the NPG is defined with respect to the Hessian geometry of the regu
larizer. This yields local quadratic convergence rates of these methods fo
r step size equal to the penalization strength. This is work with Johannes
Müller.\n
LOCATION:https://researchseminars.org/talk/CompAlg/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kathlén Kohn (KTH)
DTSTART;VALUE=DATE-TIME:20230215T100000Z
DTEND;VALUE=DATE-TIME:20230215T110000Z
DTSTAMP;VALUE=DATE-TIME:20240522T213119Z
UID:CompAlg/6
DESCRIPTION:Title:
The Geometry of Linear Convolutional Networks\nby Kathlén Kohn (KTH)
as part of Machine Learning Seminar\n\n\nAbstract\nWe discuss linear convo
lutional neural networks (LCNs) and their critical points. We observe that
the function space (i.e.\, the set of functions represented by LCNs) can
be identified with polynomials that admit certain factorizations\, and we
use this perspective to describe the impact of the network’s architectur
e on the geometry of the function space. For instance\, for LCNs with one-
dimensional convolutions having stride one and arbitrary filter sizes\, we
provide a full description of the boundary of the function space. We furt
her study the optimization of an objective function over such LCNs: We cha
racterize the relations between critical points in function space and in p
arameter space and show that there do exist spurious critical points. We c
ompute an upper bound on the number of critical points in function space u
sing Euclidean distance degrees and describe dynamical invariants for grad
ient descent. This talk is based on joint work with Thomas Merkh\, Guido M
ontúfar\, and Matthew Trager.\n
LOCATION:https://researchseminars.org/talk/CompAlg/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nick Vannieuwenhoven (KU Leuven)
DTSTART;VALUE=DATE-TIME:20230308T100000Z
DTEND;VALUE=DATE-TIME:20230308T110000Z
DTSTAMP;VALUE=DATE-TIME:20240522T213119Z
UID:CompAlg/7
DESCRIPTION:Title:
Group-invariant tensor train networks for supervised learning\nby Nick
Vannieuwenhoven (KU Leuven) as part of Machine Learning Seminar\n\n\nAbst
ract\nInvariance under selected transformations has recently proven to be
a powerful inductive bias in several machine learning models. One class of
such models are tensor train networks. In this talk\, we impose invarianc
e relations on tensor train networks. We introduce a new numerical algorit
hm to construct a basis of tensors that are invariant under the action of
normal matrix representations of an arbitrary discrete group. This method
can be up to several orders of magnitude faster than previous approaches.
The group-invariant tensors are then combined into a group-invariant tenso
r train network\, which can be used as a supervised machine learning model
. We applied this model to a protein binding classification problem\, taki
ng into account problem-specific invariances\, and obtained prediction acc
uracy in line with state-of-the-art invariant deep learning approaches. Th
is is joint work with Brent Sprangers.\n
LOCATION:https://researchseminars.org/talk/CompAlg/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yang-Hui He (LIMS)
DTSTART;VALUE=DATE-TIME:20230405T090000Z
DTEND;VALUE=DATE-TIME:20230405T100000Z
DTSTAMP;VALUE=DATE-TIME:20240522T213119Z
UID:CompAlg/8
DESCRIPTION:Title:
Universes as Bigdata: Physics\, Geometry and Machine-Learning\nby Yang
-Hui He (LIMS) as part of Machine Learning Seminar\n\n\nAbstract\nThe sear
ch for the Theory of Everything has led to superstring theory\, which then
led physics\, first to algebraic/differential geometry/topology\, and the
n to computational geometry\, and now to data science. With a concrete pla
yground of the geometric landscape\, accumulated by the collaboration of p
hysicists\, mathematicians and computer scientists over the last 4 decades
\, we show how the latest techniques in machine-learning can help explore
problems of interest to theoretical physics and to pure mathematics. At th
e core of our programme is the question: how can AI help us with mathemati
cs?\n
LOCATION:https://researchseminars.org/talk/CompAlg/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julia Lindberg (UT Austin)
DTSTART;VALUE=DATE-TIME:20230315T150000Z
DTEND;VALUE=DATE-TIME:20230315T160000Z
DTSTAMP;VALUE=DATE-TIME:20240522T213119Z
UID:CompAlg/9
DESCRIPTION:Title:
Estimating Gaussian mixtures using sparse polynomial moment systems\nb
y Julia Lindberg (UT Austin) as part of Machine Learning Seminar\n\n\nAbst
ract\nThe method of moments is a statistical technique for density estimat
ion that solves a system of moment equations to estimate the parameters of
an unknown distribution. A fundamental question critical to understanding
identifiability asks how many moment equations are needed to get finitely
many solutions and how many solutions there are. We answer this question
for classes of Gaussian mixture models using the tools of polyhedral geome
try. Using these results\, we present a homotopy method to perform paramet
er recovery\, and therefore density estimation\, for high dimensional Gaus
sian mixture models. The number of paths tracked in our method scales line
arly in the dimension.\n
LOCATION:https://researchseminars.org/talk/CompAlg/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eduardo Paluzo-Hidalgo (Seville)
DTSTART;VALUE=DATE-TIME:20230329T140000Z
DTEND;VALUE=DATE-TIME:20230329T150000Z
DTSTAMP;VALUE=DATE-TIME:20240522T213119Z
UID:CompAlg/10
DESCRIPTION:Title: An introduction to Simplicial-map Neural Networks\nby Eduardo Paluzo-
Hidalgo (Seville) as part of Machine Learning Seminar\n\n\nAbstract\nIn a
recently accepted project RexasiPro\, we deal with a critical environment
where trustworthy is decisive. One of our approaches are simplicial-map ne
ural networks (SMNNs) which are explicitly defined using simplicial maps b
etween triangulations of the input and output spaces. Its combinatorial de
finition lets us prove and guarantee several nice properties following tru
stworthy AI principles. In "Two-hidden-layer feed-forward networks are uni
versal approximators: A constructive approach"\, the first definition of S
MNNs was given and its universal approximator property was proved. Later\,
in "Simplicial-Map Neural Networks Robust to Adversarial Examples"\, its
robustness against adversarial examples was described.\n
LOCATION:https://researchseminars.org/talk/CompAlg/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Patrizio Frosini (Bologna)
DTSTART;VALUE=DATE-TIME:20230322T100000Z
DTEND;VALUE=DATE-TIME:20230322T110000Z
DTSTAMP;VALUE=DATE-TIME:20240522T213119Z
UID:CompAlg/11
DESCRIPTION:Title: Some recent results on the theory of GENEOs and its application to Machin
e Learning\nby Patrizio Frosini (Bologna) as part of Machine Learning
Seminar\n\n\nAbstract\nGroup equivariant non-expansive operators (GENEOs)
have been introduced a few years ago as mathematical tools for approximati
ng data observers when data are represented by real-valued or vector-value
d functions. The use of these operators is based on the assumption that th
e interpretation of data depends on the geometric properties of the observ
ers. In this talk we will illustrate some recent results in the theory of
GENEOs\, showing how these operators can make available a new approach to
topological data analysis and geometric deep learning.\n
LOCATION:https://researchseminars.org/talk/CompAlg/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christoph Hertrich (LSE)
DTSTART;VALUE=DATE-TIME:20230419T150000Z
DTEND;VALUE=DATE-TIME:20230419T160000Z
DTSTAMP;VALUE=DATE-TIME:20240522T213119Z
UID:CompAlg/12
DESCRIPTION:Title: Understanding Neural Network Expressivity via Polyhedral Geometry\nby
Christoph Hertrich (LSE) as part of Machine Learning Seminar\n\n\nAbstrac
t\nNeural networks with rectified linear unit (ReLU) activations are one o
f the standard models in modern machine learning. Despite their practical
importance\, fundamental theoretical questions concerning ReLU networks re
main open until today. For instance\, what is the precise set of (piecewis
e linear) functions exactly representable by ReLU networks with a given de
pth? Even the special case asking for the number of layers to compute a fu
nction as simple as $\\max\\{0\, x_1\, x_2\, x_3\, x_4\\}$ has not been so
lved yet. In this talk we will explore the relevant background to understa
nd this question and report about recent progress using tropical and polyh
edral geometry as well as a computer-aided approach based on mixed-integer
programming. This is based on joint works with Amitabh Basu\, Marco Di Su
mma\, and Martin Skutella (NeurIPS 2021)\, as well as Christian Haase and
Georg Loho (ICLR 2023).\n
LOCATION:https://researchseminars.org/talk/CompAlg/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vasco Portilheiro (UCL)
DTSTART;VALUE=DATE-TIME:20230412T150000Z
DTEND;VALUE=DATE-TIME:20230412T160000Z
DTSTAMP;VALUE=DATE-TIME:20240522T213119Z
UID:CompAlg/13
DESCRIPTION:Title: Barriers to Learning Symmetries\nby Vasco Portilheiro (UCL) as part o
f Machine Learning Seminar\n\n\nAbstract\nGiven the success of equivariant
models\, there has been increasing interest in models which can learn a s
ymmetry from data\, rather than it being imposed a priori. We present work
which formalizes a tradeoff between (a) the simultaneous learnability of
symmetries and equivariant functions\, and (b) universal approximation of
equivariant functions. The work is motivated by an experiment which modifi
es the Equivariant Multilayer Perceptron (EMLP) of Finzi et al. (2021) in
an attempt to learn a group together with an equivariant function. Additio
nally\, the tradeoff is shown to not exist for group-convolutional network
s.\n
LOCATION:https://researchseminars.org/talk/CompAlg/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bastian Rieck (Munich)
DTSTART;VALUE=DATE-TIME:20230426T090000Z
DTEND;VALUE=DATE-TIME:20230426T100000Z
DTSTAMP;VALUE=DATE-TIME:20240522T213119Z
UID:CompAlg/14
DESCRIPTION:Title: Curvature for Graph Learning\nby Bastian Rieck (Munich) as part of Ma
chine Learning Seminar\n\n\nAbstract\nCurvature bridges geometry and topol
ogy\, using local information to derive global statements. While well-know
n in a differential topology context\, it was recently extended to the dom
ain of graphs. In fact\, graphs give rise to various notions of curvature\
, which differ in expressive power and purpose. We will give a brief overv
iew of curvature in graphs\, define some relevant concepts\, and show thei
r utility for data science and machine learning applications. In particula
r\, we shall discuss two applications: first\, the use of curvature to dis
tinguish between different models for synthesising new graphs from some un
known distribution\; second\, a novel framework for defining curvature for
hypergraphs\, whose structural properties require a more generic setting.
We will also describe new applications that are specifically geared towar
ds a treatment by curvature\, thus underlining the utility of this concept
for data science.\n
LOCATION:https://researchseminars.org/talk/CompAlg/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Taejin Paik (Seoul National University)
DTSTART;VALUE=DATE-TIME:20230524T090000Z
DTEND;VALUE=DATE-TIME:20230524T100000Z
DTSTAMP;VALUE=DATE-TIME:20240522T213119Z
UID:CompAlg/15
DESCRIPTION:Title: Isometry-Invariant and Subdivision-Invariant Representations of Embedded
Simplicial Complexes\nby Taejin Paik (Seoul National University) as pa
rt of Machine Learning Seminar\n\n\nAbstract\nGeometric objects such as me
shes and graphs are commonly used in various applications\, but analyzing
them can be challenging due to their complex structures. Traditional appro
aches may not be robust to transformations like subdivision or isometry\,
leading to inconsistent results. Here is a novel approach to address these
limitations by using only topological and geometric data to analyze simpl
icial complexes in a subdivision-invariant and isometry-invariant way. Thi
s approach involves using a graph neural network to create an $O(3)$-equiv
ariant operator and the Euler curve transform to generate sufficient stati
stics that describe the properties of the object.\n
LOCATION:https://researchseminars.org/talk/CompAlg/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Platt (KCL)
DTSTART;VALUE=DATE-TIME:20230503T090000Z
DTEND;VALUE=DATE-TIME:20230503T100000Z
DTSTAMP;VALUE=DATE-TIME:20240522T213119Z
UID:CompAlg/16
DESCRIPTION:Title: Group invariant machine learning by fundamental domain projections\nb
y Daniel Platt (KCL) as part of Machine Learning Seminar\n\n\nAbstract\nIn
many applications one wants to learn a function that is invariant under a
group action. For example\, classifying images of digits\, no matter how
they are rotated. There exist many approaches in the literature to do this
. I will mention two approaches that are very useful in many applications\
, but struggle if the group is big or acts in a complicated way. I will th
en explain our approach which does not have these two problems. The approa
ch works by finding some "canonical representative" of each input element.
In the example of images of digits\, one may rotate the digit so that the
brightest quarter is in the top-left\, which would define a "canonical re
presentative". In the general case\, one has to define what that means. Ou
r approach is useful if the group is big\, and I will present experiments
on the Complete Intersection Calabi-Yau and Kreuzer-Skarke datasets to sho
w this. Our approach is useless if the group is small\, and the case of ro
tated images of digits is an example of this. This is joint work with Benj
amin Aslan and David Sheard.\n
LOCATION:https://researchseminars.org/talk/CompAlg/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vasco Brattka (Bundeswehr München)
DTSTART;VALUE=DATE-TIME:20230614T090000Z
DTEND;VALUE=DATE-TIME:20230614T100000Z
DTSTAMP;VALUE=DATE-TIME:20240522T213119Z
UID:CompAlg/17
DESCRIPTION:Title: On the Complexity of Computing Gödel Numbers\nby Vasco Brattka (Bund
eswehr München) as part of Machine Learning Seminar\n\n\nAbstract\nGiven
a computable sequence of natural numbers\, it is a natural task to find a
Gödel number of a program that generates this sequence. It is easy to see
that this problem is neither continuous nor computable. In algorithmic le
arning theory this problem is well studied from several perspectives and o
ne question studied there is for which sequences this problem is at least
learnable in the limit. Here we study the problem on all computable sequen
ces and we classify the Weihrauch complexity of it. For this purpose we ca
n\, among other methods\, utilize the amalgamation technique known from le
arning theory. As a benchmark for the classification we use closed and com
pact choice problems and their jumps on natural numbers\, and we argue tha
t these problems correspond to induction and boundedness principles\, as t
hey are known from the Kirby-Paris hierarchy in reverse mathematics. We pr
ovide a topological as well as a computability-theoretic classification\,
which reveal some significant differences.\n
LOCATION:https://researchseminars.org/talk/CompAlg/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Edward Pearce-Crump (Imperial)
DTSTART;VALUE=DATE-TIME:20230621T090000Z
DTEND;VALUE=DATE-TIME:20230621T100000Z
DTSTAMP;VALUE=DATE-TIME:20240522T213119Z
UID:CompAlg/18
DESCRIPTION:Title: Exploring group equivariant neural networks using set partition diagrams<
/a>\nby Edward Pearce-Crump (Imperial) as part of Machine Learning Seminar
\n\n\nAbstract\nWhat do jellyfish and an 11th century Japanese novel have
to do with neural networks? In recent years\, much attention has been give
n to developing neural network architectures that can efficiently learn fr
om data with underlying symmetries. These architectures ensure that the le
arned functions maintain a certain geometric property called group equivar
iance\, which determines how the output changes based on a change to the i
nput under the action of a symmetry group. In this talk\, we will describe
a number of new group equivariant neural network architectures that are b
uilt using tensor power spaces of $\\mathbb{R}^n$ as their layers. We will
show that the learnable\, linear functions between these layers can be ch
aracterised by certain subsets of set partition diagrams. This talk will b
e based on several papers that are to appear in ICML 2023.\n
LOCATION:https://researchseminars.org/talk/CompAlg/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alvaro Torras Casas (Cardiff)
DTSTART;VALUE=DATE-TIME:20230531T090000Z
DTEND;VALUE=DATE-TIME:20230531T100000Z
DTSTAMP;VALUE=DATE-TIME:20240522T213119Z
UID:CompAlg/19
DESCRIPTION:Title: Dataset comparison using persistent homology morphisms\nby Alvaro Tor
ras Casas (Cardiff) as part of Machine Learning Seminar\n\n\nAbstract\nPer
sistent homology summarizes geometrical information of data by means of a
barcode. Given a pair of datasets\, $X$ and $Y$\, one might obtain their r
espective barcodes $B(X)$ and $B(Y)$. Thanks to stability results\, if $X$
and $Y$ are similar enough one deduces that the barcodes $B(X)$ and $B(Y)
$ are also close enough\; however\, the converse is not true in general. I
n this talk we consider the case when there is a known relation between $X
$ and $Y$ encoded by a morphism between persistence modules. For example\,
this is the case when $Y$ is a finite subset of euclidean space and $X$ i
s a sample taken from $Y$. As in linear algebra\, a morphism between persi
stence modules is understood by a choice of a pair of bases together with
the associated matrix. I will explain how to use this matrix to get barcod
es for images\, kernels and cokernels. Additionally\, I will explain how t
o compute an induced block function that relates the barcodes $B(X)$ and $
B(Y)$. I will finish the talk revising some applications of this theory as
well as future research directions.\n
LOCATION:https://researchseminars.org/talk/CompAlg/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Gebhart (Minnesota)
DTSTART;VALUE=DATE-TIME:20230705T150000Z
DTEND;VALUE=DATE-TIME:20230705T160000Z
DTSTAMP;VALUE=DATE-TIME:20240522T213119Z
UID:CompAlg/20
DESCRIPTION:Title: Specifying Local Constraints in Representation Learning with Cellular She
aves\nby Thomas Gebhart (Minnesota) as part of Machine Learning Semina
r\n\n\nAbstract\nMany machine learning algorithms constrain their learned
representations by imparting inductive biases based on local smoothness as
sumptions. While these constraints are often natural and effective\, there
are situations in which their simplicity is mis-aligned with the represen
tation structure required by the task\, leading to a lack of expressivity
and pathological behaviors like representational oversmoothing or inconsis
tency. Without a broader theoretical framework for reasoning about local r
epresentational constraints\, it is difficult to conceptualize and move be
yond such representational misalignments. In this talk\, we will see that
cellular sheaf theory offers an ideal algebro-topological framework for bo
th reasoning about and implementing machine learning models on data which
are subject to such local-to-global constraints over a topological space.
We will introduce cellular sheaves from a categorical perspective\, observ
ing the relationship between their definition as a limit object and the co
nsistency objectives underlying representation learning. We will then turn
to a discussion of sheaf (co)homology as a semi-computable tool for imple
menting these categorical concepts. Finally\, we will observe two practica
l applications of these ideas in the form of sheaf neural networks\, a gen
eralization of graph neural networks for processing sheaf-valued signals\;
and knowledge sheaves\, a sheaf-theoretic reformulation of knowledge grap
h embedding.\n
LOCATION:https://researchseminars.org/talk/CompAlg/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Challenger Mishra (Cambridge)
DTSTART;VALUE=DATE-TIME:20230712T090000Z
DTEND;VALUE=DATE-TIME:20230712T100000Z
DTSTAMP;VALUE=DATE-TIME:20240522T213119Z
UID:CompAlg/21
DESCRIPTION:Title: Mathematical conjecture generation and Machine Intelligence\nby Chall
enger Mishra (Cambridge) as part of Machine Learning Seminar\n\n\nAbstract
\nConjectures hold a special status in mathematics. Good conjectures epito
mise milestones in mathematical discovery\, and have historically inspired
new mathematics and shaped progress in theoretical physics. Hilbert’s l
ist of 23 problems and André Weil’s conjectures oversaw major developme
nts in mathematics for decades. Crafting conjectures can often be understo
od as a problem in pattern recognition\, for which Machine Learning (ML) i
s tailor-made. In this talk\, I will propose a framework that allows a pri
ncipled study of a space of mathematical conjectures. Using this framework
and exploiting domain knowledge and machine learning\, we generate a numb
er of conjectures in number theory and group theory. I will present eviden
ce in support of some of the resulting conjectures and present a new theor
em. I will lay out a vision for this endeavour\, and conclude by posing so
me general questions about the pipeline.\n
LOCATION:https://researchseminars.org/talk/CompAlg/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Le Quoc Tung (ENS Lyon)
DTSTART;VALUE=DATE-TIME:20230726T090000Z
DTEND;VALUE=DATE-TIME:20230726T100000Z
DTSTAMP;VALUE=DATE-TIME:20240522T213119Z
UID:CompAlg/22
DESCRIPTION:Title: Algorithmic and theoretical aspects of sparse deep neural networks\nb
y Le Quoc Tung (ENS Lyon) as part of Machine Learning Seminar\n\n\nAbstrac
t\nSparse deep neural networks offer a compelling practical opportunity to
reduce the cost of training\, inference and storage\, which are growing e
xponentially in the state of the art of deep learning. In this presentatio
n\, we will introduce an approach to study sparse deep neural networks thr
ough the lens of another related problem: sparse matrix factorization\, i.
e.\, the problem of approximating a (dense) matrix by the product of (mult
iple) sparse factors. In particular\, we identify and investigate in detai
l some theoretical and algorithmic aspects of a variant of sparse matrix f
actorization named fixed support matrix factorization (FSMF) in which the
set of non-zero entries of sparse factors are known. Several fundamental q
uestions of sparse deep neural networks such as the existence of optimal s
olutions of the training problem or topological properties of its function
space can be addressed using the results of (FSMF). In addition\, by appl
ying the results of (FSMF)\, we also study butterfly parametrization\, an
approach that consists of replacing (large) weight matrices with the produ
cts of extremely sparse and structured ones in sparse deep neural networks
.\n
LOCATION:https://researchseminars.org/talk/CompAlg/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Honglu Fan (Geneva)
DTSTART;VALUE=DATE-TIME:20230802T090000Z
DTEND;VALUE=DATE-TIME:20230802T100000Z
DTSTAMP;VALUE=DATE-TIME:20240522T213119Z
UID:CompAlg/23
DESCRIPTION:Title: Local uniformization\, Hilbert scheme of points and reinforcement learnin
g\nby Honglu Fan (Geneva) as part of Machine Learning Seminar\n\n\nAbs
tract\nIn this talk\, I will give a brief tour about how local uniformizat
ion\, the Hilbert scheme of points\, and reinforcement learning come toget
her in a joint work (arXiv:2307.00252 [cs.LG]) with Gergely Berczi and Min
gcong Zeng.\n
LOCATION:https://researchseminars.org/talk/CompAlg/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charlotte Aten (Denver)
DTSTART;VALUE=DATE-TIME:20230906T140000Z
DTEND;VALUE=DATE-TIME:20230906T150000Z
DTSTAMP;VALUE=DATE-TIME:20240522T213119Z
UID:CompAlg/24
DESCRIPTION:Title: Discrete neural nets and polymorphic learning\nby Charlotte Aten (Den
ver) as part of Machine Learning Seminar\n\n\nAbstract\nClassical neural n
etwork learning techniques have primarily been focused on optimization in
a continuous setting. Early results in the area showed that many activatio
n functions could be used to build neural nets that represent any function
\, but of course this also allows for overfitting. In an effort to amelior
ate this deficiency\, one seeks to reduce the search space of possible fun
ctions to a special class which preserves some relevant structure. I will
propose a solution to this problem of a quite general nature\, which is to
use polymorphisms of a relevant discrete relational structure as activati
on functions. I will give some concrete examples of this\, then hint that
this specific case is actually of broader applicability than one might gue
ss.\n
LOCATION:https://researchseminars.org/talk/CompAlg/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Felix Schremmer (Hong Kong)
DTSTART;VALUE=DATE-TIME:20231018T090000Z
DTEND;VALUE=DATE-TIME:20231018T100000Z
DTSTAMP;VALUE=DATE-TIME:20240522T213119Z
UID:CompAlg/25
DESCRIPTION:Title: Machine learning assisted exploration for affine Deligne-Lusztig varietie
s\nby Felix Schremmer (Hong Kong) as part of Machine Learning Seminar\
n\n\nAbstract\nIn this interdisciplinary study\, we describe a procedure t
o assist and accelerate research in pure mathematics by using machine lear
ning. We study affine Deligne-Lusztig varieties\, certain geometric object
s related to a number of mathematical questions\, by carefully developing
a number of machine learning models. This iterated pipeline yields well in
terpretable and highly accurate models\, thus producing strongly supported
mathematical conjectures. We explain how this method could have dramatica
lly accelerated the research in the past. A completely new mathematical th
eorem\, found by our ML-assisted method and proved using the classical mat
hematical tools of the field\, concludes this study. This is joint work wi
th Bin Dong\, Pengfei Jin\, Xuhua He and Qingchao Yu.\n
LOCATION:https://researchseminars.org/talk/CompAlg/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bruno Gavranović (Strathclyde)
DTSTART;VALUE=DATE-TIME:20230920T090000Z
DTEND;VALUE=DATE-TIME:20230920T100000Z
DTSTAMP;VALUE=DATE-TIME:20240522T213119Z
UID:CompAlg/26
DESCRIPTION:Title: Fundamental Components of Deep Learning: A category-theoretic approach\nby Bruno Gavranović (Strathclyde) as part of Machine Learning Seminar\
n\n\nAbstract\nDeep learning\, despite its remarkable achievements\, is st
ill a young field. Like the early stages of many scientific disciplines\,
it is permeated by ad-hoc design decisions. From the intricacies of the im
plementation of backpropagation\, through new and poorly understood phenom
ena such as double descent\, scaling laws or in-context learning\, to a gr
owing zoo of neural network architectures - there are few unifying princip
les in deep learning\, and no uniform and compositional mathematical found
ation. In this talk I'll present a novel perspective on deep learning by u
tilising the mathematical framework of category theory. I'll identify two
main conceptual components of neural networks\, report on progress made th
roughout last years by the research community in formalising them\, and sh
ow how they've been used to describe backpropagation\, architectures\, and
supervised learning in general\, shedding a new light on the existing fie
ld.\n
LOCATION:https://researchseminars.org/talk/CompAlg/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rahul Sarkar (Stanford)
DTSTART;VALUE=DATE-TIME:20230927T140000Z
DTEND;VALUE=DATE-TIME:20230927T150000Z
DTSTAMP;VALUE=DATE-TIME:20240522T213119Z
UID:CompAlg/27
DESCRIPTION:Title: A framework for generating inequality conjectures\nby Rahul Sarkar (S
tanford) as part of Machine Learning Seminar\n\n\nAbstract\nIn this talk\,
I'll present some recent and ongoing work\, where we propose a systematic
approach to finding abstract patterns in mathematical data\, in order to
generate conjectures about mathematical inequalities. We focus on strict i
nequalities of type $f < g$ and associate them with a Banach manifold. We
develop a structural understanding of this conjecture space by studying li
near automorphisms of this manifold. Next\, we propose an algorithmic pipe
line to generate novel conjecture. As proof of concept\, we give a toy alg
orithm to generate conjectures about the prime counting function and diame
ters of Cayley graphs of non-abelian simple groups. Some of these conjectu
res were proved while others remain unproven.\n
LOCATION:https://researchseminars.org/talk/CompAlg/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martina Scolamiero (KTH)
DTSTART;VALUE=DATE-TIME:20231108T100000Z
DTEND;VALUE=DATE-TIME:20231108T110000Z
DTSTAMP;VALUE=DATE-TIME:20240522T213119Z
UID:CompAlg/28
DESCRIPTION:Title: Machine Learning with Topological Data Analysis features\nby Martina
Scolamiero (KTH) as part of Machine Learning Seminar\n\n\nAbstract\nIn Top
ological Data Analysis\, Persistent Homology has been widely used to extra
ct features from data. Such features are then used for clustering\, visual
ization and classification. In this talk I will describe how we define Lip
schitz continuous persistence features starting from pseudo metrics to com
pare topological representations of data. Special emphasis will be on the
variety of different features that can be constructed in this way and how
they can be used in machine learning pipelines. Joint work with the TDA gr
oup at KTH.\n
LOCATION:https://researchseminars.org/talk/CompAlg/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Agnese Barbensi (Queensland)
DTSTART;VALUE=DATE-TIME:20231122T100000Z
DTEND;VALUE=DATE-TIME:20231122T110000Z
DTSTAMP;VALUE=DATE-TIME:20240522T213119Z
UID:CompAlg/29
DESCRIPTION:Title: Persistent homology\, hypergraphs and geometric cycle matching\nby Ag
nese Barbensi (Queensland) as part of Machine Learning Seminar\n\n\nAbstra
ct\nTopological data analysis has been demonstrated to be a powerful tool
to describe topological signatures in real-life data\, and to extract comp
lex patterns arising in natural systems. An important challenge in topolog
ical data analysis is to find robust ways of computing and analysing persi
stent generators\, and to match significant topological signals across dis
tinct systems. In this talk\, I will present some recent work dealing with
these problems. Our method is based on an interpretation of persistent ho
mology summaries with network theoretical tools\, combined with statistica
l and optimal transport techniques.\n
LOCATION:https://researchseminars.org/talk/CompAlg/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kyu-Hwan Lee (Connecticut)
DTSTART;VALUE=DATE-TIME:20231206T150000Z
DTEND;VALUE=DATE-TIME:20231206T160000Z
DTSTAMP;VALUE=DATE-TIME:20240522T213119Z
UID:CompAlg/30
DESCRIPTION:Title: Data-scientific study of Kronecker coefficients\nby Kyu-Hwan Lee (Con
necticut) as part of Machine Learning Seminar\n\n\nAbstract\nThe Kronecker
coefficients are the decomposition multiplicities of the tensor product o
f two irreducible representations of the symmetric group. Unlike the Littl
ewood--Richardson coefficients\, which are the analogues for the general l
inear group\, there is no known combinatorial description of the Kronecker
coefficients\, and it is an NP-hard problem to decide whether a given Kro
necker coefficient is zero or not. In this talk\, we take a data-scientifi
c approach to study whether Kronecker coefficients are zero or not. We sho
w that standard machine-learning classifiers may be trained to predict whe
ther a given Kronecker coefficient is zero or not. Motivated by principal
component analysis and kernel methods\, we also define loadings of partiti
ons and use them to describe a sufficient condition for Kronecker coeffici
ents to be nonzero.\n
LOCATION:https://researchseminars.org/talk/CompAlg/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shailesh Lal (BIMSA)
DTSTART;VALUE=DATE-TIME:20240320T100000Z
DTEND;VALUE=DATE-TIME:20240320T110000Z
DTSTAMP;VALUE=DATE-TIME:20240522T213119Z
UID:CompAlg/31
DESCRIPTION:Title: Neural Network solvers for the Yang-Baxter Equation\nby Shailesh Lal
(BIMSA) as part of Machine Learning Seminar\n\n\nAbstract\nWe develop a no
vel neural network architecture that learns solutions to the Yang Baxter e
quation for R matrices of difference form. This method already enables us
to learn all solution classes of the 2d Yang Baxter equation. We propose a
nd test paradigms for exploring the landscape of Yang Baxter equation solu
tion space aided by these methods. Further\, we shall also comment on the
application of these methods to generating new solutions of the Yang Baxte
r equation. The talk is based on joint work with Suvajit Majumder and Evge
ny Sobko available in part in arXiv:2304.07247.\n
LOCATION:https://researchseminars.org/talk/CompAlg/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniele Angella (Università di Firenze)
DTSTART;VALUE=DATE-TIME:20240313T100000Z
DTEND;VALUE=DATE-TIME:20240313T110000Z
DTSTAMP;VALUE=DATE-TIME:20240522T213119Z
UID:CompAlg/32
DESCRIPTION:Title: Constructing and Machine Learning Calabi-Yau Five-Folds\nby Daniele A
ngella (Università di Firenze) as part of Machine Learning Seminar\n\n\nA
bstract\nThe significance of Calabi-Yau manifolds transcends both Complex
Geometry and String Theory. One possible approach to constructing Calabi-Y
au manifolds involves intersecting hypersurfaces within the product of pro
jective spaces\, defined by polynomials of a specific degree. We show a me
thod to construct all possible complete intersections Calabi-Yau ﬁve-fol
ds within a product of four or less complex projective spaces\, with up to
four constraints. This results in a comprehensive set of 27\,068 distinct
spaces. For approximately half of these constructions\, excluding the pro
duct spaces\, we can compute the cohomological data\, yielding 2\,375 dist
inct Hodge diamonds. We present distributions of the invariants and engage
in a comparative analysis with their lower-dimensional counterparts. Supe
rvised machine learning techniques are applied to the cohomological data.
The Hodge number $h^{1\,1}$ can be learnt with high efficiency\; however\,
accuracy diminishes for other Hodge numbers due to the extensive ranges o
f potential values. The talk is a joint collaboration with Rashid Alawadhi
\, Andrea Leonardo\, and Tancredi Schettini Gherardini.\n
LOCATION:https://researchseminars.org/talk/CompAlg/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ellie Heyes (City\, University of London)
DTSTART;VALUE=DATE-TIME:20240417T090000Z
DTEND;VALUE=DATE-TIME:20240417T100000Z
DTSTAMP;VALUE=DATE-TIME:20240522T213119Z
UID:CompAlg/33
DESCRIPTION:Title: Generating Calabi–Yau Manifolds with Machine Learning\nby Ellie Hey
es (City\, University of London) as part of Machine Learning Seminar\n\n\n
Abstract\nCalabi–Yau n-folds can be obtained as hypersurfaces in toric v
arieties built from (n+1)-dimensional reflexive polytopes. Calabi–Yau 3-
folds are of particular interest in string theory as they reduce 10-dimens
ional superstring theory to 4-dimensional quantum field theories with N=1
supersymmetry. We generate Calabi–Yau 3-folds by generating 4-dimensiona
l reflexive polytopes and their triangulations using genetic algorithms an
d reinforcement learning respectively. We show how\, by modifying the fitn
ess function of the genetic algorithm\, one can generate Calabi–Yau mani
folds with specific properties that give rise to certain string models of
particular interest.\n
LOCATION:https://researchseminars.org/talk/CompAlg/33/
END:VEVENT
END:VCALENDAR