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BEGIN:VEVENT
SUMMARY:Tom Oliver (Nottingham)
DTSTART;VALUE=DATE-TIME:20210929T120000Z
DTEND;VALUE=DATE-TIME:20210929T130000Z
DTSTAMP;VALUE=DATE-TIME:20230331T101357Z
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:20230331T101357Z
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:20230331T101357Z
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:20230331T101357Z
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:20230331T101357Z
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:20230331T101357Z
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:20230331T101357Z
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:20230331T101357Z
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\nInteractive livestre
am: https://us06web.zoom.us/j/83280019752?pwd=b1ZSaVlZaEdXSVJDQTdzMU04dDZU
QT09\n\nAbstract\nThe search for the Theory of Everything has led to super
string theory\, which then led physics\, first to algebraic/differential g
eometry/topology\, and then to computational geometry\, and now to data sc
ience. With a concrete playground of the geometric landscape\, accumulated
by the collaboration of physicists\, mathematicians and computer scientis
ts 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 the core of our programme is the question: how can
AI help us with mathematics?\n
LOCATION:https://researchseminars.org/talk/CompAlg/8/
URL:https://us06web.zoom.us/j/83280019752?pwd=b1ZSaVlZaEdXSVJDQTdzMU04dDZU
QT09
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julia Lindberg (UT Austin)
DTSTART;VALUE=DATE-TIME:20230315T150000Z
DTEND;VALUE=DATE-TIME:20230315T160000Z
DTSTAMP;VALUE=DATE-TIME:20230331T101357Z
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:20230331T101357Z
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:20230331T101357Z
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:20230331T101357Z
UID:CompAlg/12
DESCRIPTION:Title: Understanding Neural Network Expressivity via Polyhedral Geometry\nby
Christoph Hertrich (LSE) as part of Machine Learning Seminar\n\nInteracti
ve livestream: https://us06web.zoom.us/j/88698656183?pwd=ZDcrWCtOREZBbTErT
lg0RlhnVTdBQT09\n\nAbstract\nNeural networks with rectified linear unit (R
eLU) activations are one of the standard models in modern machine learning
. Despite their practical importance\, fundamental theoretical questions c
oncerning ReLU networks remain open until today. For instance\, what is th
e precise set of (piecewise linear) functions exactly representable by ReL
U networks with a given depth? Even the special case asking for the number
of layers to compute a function as simple as $\\max\\{0\, x_1\, x_2\, x_3
\, x_4\\}$ has not been solved yet. In this talk we will explore the relev
ant background to understand this question and report about recent progres
s using tropical and polyhedral geometry as well as a computer-aided appro
ach based on mixed-integer programming. This is based on joint works with
Amitabh Basu\, Marco Di Summa\, and Martin Skutella (NeurIPS 2021)\, as we
ll as Christian Haase and Georg Loho (ICLR 2023).\n
LOCATION:https://researchseminars.org/talk/CompAlg/12/
URL:https://us06web.zoom.us/j/88698656183?pwd=ZDcrWCtOREZBbTErTlg0RlhnVTdB
QT09
END:VEVENT
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