BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Andrea Bertozzi (UCLA)
DTSTART:20200423T183000Z
DTEND:20200423T193000Z
DTSTAMP:20260404T110824Z
UID:OneWorldMINDS/1
DESCRIPTION:Title: Epidemic modeling – basics and challenges\nby Andrea Be
rtozzi (UCLA) as part of One World MINDS seminar\n\n\nAbstract\nI will rev
iew basics of epidemic modeling including eponential growth\, compartmenta
l models and self-exciting point process models. I will illustrate how su
ch models have been used in the past for previous pandemics and what the c
hallenges are for forecasting the current COVID-19 pandemic. I will show
some examples of fitting of data to US states and what one can do with tho
se results. Overall\, model prediction has a degree of uncertainty especi
ally with early time data and with many unknowns.\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldMINDS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Strohmer (UC Davis)
DTSTART:20200430T183000Z
DTEND:20200430T193000Z
DTSTAMP:20260404T110824Z
UID:OneWorldMINDS/2
DESCRIPTION:Title: Pandemics\, Privacy\, and Paradoxes - Why We need a new parad
igm for data science and AI\nby Thomas Strohmer (UC Davis) as part of
One World MINDS seminar\n\n\nAbstract\nPioneered by giant internet corpora
tions and powered by machine learning\, a new economic system is emerging
that pushes for relentless data capture and analysis\, usually without use
rs' consent. Surveillance capitalism pursues the exploitation and control
of human nature\, thereby threatening our social fabric. To counter these
developments\, we need to rethink the role of data science and artificial
intelligence. We must urgently develop a new paradigm of what data is. Thi
s urgency is aggravated by the current pandemic\, which amplifies fundamen
tal paradoxes underlying data science and AI. I will argue that the key li
es in understanding the trialectic nature of data\, the careful balance of
which will be key to tackling the aforementioned disturbing developments\
, while still reaping the benefits of data science and AI. Based on this t
rialectic nature\, I will draw consequences for the role of mathematics in
data science and indicate how mathematicians can directly contribute to a
more just digital revolution.\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldMINDS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Gilbert (University of Michigan)
DTSTART:20200507T183000Z
DTEND:20200507T193000Z
DTSTAMP:20260404T110824Z
UID:OneWorldMINDS/3
DESCRIPTION:Title: Metric representations: Algorithms and geometry\nby Anna
Gilbert (University of Michigan) as part of One World MINDS seminar\n\n\nA
bstract\nGiven a set of distances amongst points\, determining what metric
representation is most “consistent” with the input distances or the m
etric that best captures the relevant geometric features of the data is a
key step in many machine learning algorithms. In this talk\, we focus on 3
specific metric constrained problems\, a class of optimization problems w
ith metric constraints: metric nearness (Brickell et al. (2008))\, weighte
d correlation clustering on general graphs (Bansal et al. (2004))\, and me
tric learning (Bellet et al. (2013)\; Davis et al. (2007)).\n\nBecause of
the large number of constraints in these problems\, however\, these and ot
her researchers have been forced to restrict either the kinds of metrics l
earned or the size of the problem that can be solved. We provide an algori
thm\, PROJECT AND FORGET\, that uses Bregman projections with cutting plan
es\, to solve metric constrained problems with many (possibly exponentiall
y) inequality constraints. We also prove that our algorithm converges to t
he global optimal solution. Additionally\, we show that the optimality err
or decays asymptotically at an exponential rate. We show that using our me
thod we can solve large problem instances of three types of metric constra
ined problems\, out-performing all state of the art methods with respect t
o CPU times and problem sizes.\n\nFinally\, we discuss the adaptation of P
ROJECT AND FORGET to specific types of metric constraints\, namely tree an
d hyperbolic metrics.\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldMINDS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilya Razenshteyn (Microsoft Research)
DTSTART:20200514T183000Z
DTEND:20200514T193000Z
DTSTAMP:20260404T110824Z
UID:OneWorldMINDS/4
DESCRIPTION:Title: Scalable Nearest Neighbor Search for Optimal Transport\nb
y Ilya Razenshteyn (Microsoft Research) as part of One World MINDS seminar
\n\n\nAbstract\nThe Optimal Transport (aka Wasserstein) distance is an inc
reasingly popular similarity measure for structured data domains\, such as
images or text documents. This raises the necessity for fast nearest neig
hbor search with respect to this distance\, a problem that poses a substan
tial computational bottleneck for various tasks on massive datasets. In th
is talk\, I will discuss fast tree-based approximation algorithms for sear
ching nearest neighbors with respect to the Wasserstein-1 distance. I will
start with describing a standard tree-based technique\, known as QuadTree
\, which has been previously shown to obtain good results. Then I'll intro
duce a variant of this algorithm\, called FlowTree\, and show that it achi
eves better accuracy\, both in theory and in practice. In particular\, the
accuracy of FlowTree is in line with previous high-accuracy methods\, whi
le its running time is much faster.\n\nThe talk is based on a joint work w
ith Arturs Backurs\, Yihe Dong\, Piotr Indyk and Tal Wagner. The paper can
be found at https://arxiv.org/abs/1910.04126 and the code -- at https://g
ithub.com/ilyaraz/ot_estimators\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldMINDS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Spielman (Yale)
DTSTART:20200521T183000Z
DTEND:20200521T193000Z
DTSTAMP:20260404T110824Z
UID:OneWorldMINDS/5
DESCRIPTION:Title: Balancing covariates in randomized experiments using the Gram
–Schmidt walk\nby Daniel Spielman (Yale) as part of One World MINDS
seminar\n\n\nAbstract\nIn randomized experiments\, such as a medical trial
s\, we randomly assign the treatment\, such as a drug or a placebo\, that
each experimental subject receives. Randomization can help us accurately e
stimate the difference in treatment effects with high probability. We also
know that we want the two groups to be similar: ideally the two groups wo
uld be similar in every statistic we can measure beforehand. Recent advanc
es in algorithmic discrepancy theory allow us to divide subjects into grou
ps with similar statistics.\n\nBy exploiting the recent Gram-Schmidt Walk
algorithm of Bansal\, Dadush\, Garg\, and Lovett\, we can obtain random as
signments of low discrepancy. These allow us to obtain more accurate estim
ates of treatment effects when the information we measure about the subjec
ts is predictive\, while also bounding the worst-case behavior when it is
not.\n\nWe will explain the experimental design problem we address\, the G
ram-Schmidt walk algorithm\, and the major ideas behind our analyses. This
is joint work with Chris Harshaw\, Fredrik Sävje\, and Peng Zhang.\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldMINDS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ronald Coifman (Yale)
DTSTART:20200528T183000Z
DTEND:20200528T193000Z
DTSTAMP:20260404T110824Z
UID:OneWorldMINDS/6
DESCRIPTION:Title: The Analytic Geometries of Data\nby Ronald Coifman (Yale)
as part of One World MINDS seminar\n\n\nAbstract\nWe will describe method
ologies to build data geometries designed to simultaneously analyze and pr
ocess data bases. The different geometries or affinity metrics arise natu
rally as we learn to contextualize and conceptualize. I.e\; relate data re
gions\, and data features (which we extend to data tensors). Moreover we
generate tensorial multiscale structures. \n\nWe will indicate connection
to analysis by deep nets and describe applications to modeling observatio
ns of dynamical systems\, from stochastic molecular dynamics to calcium im
aging of brain activity.\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldMINDS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Adcock (Simon Fraser University)
DTSTART:20200604T183000Z
DTEND:20200604T193000Z
DTSTAMP:20260404T110824Z
UID:OneWorldMINDS/7
DESCRIPTION:Title: The troublesome kernel: instabilities in deep learning for in
verse problems\nby Ben Adcock (Simon Fraser University) as part of One
World MINDS seminar\n\n\nAbstract\nDue to their stunning success in tradi
tional machine learning applications such as classification\, techniques b
ased on deep learning have recently begun to be actively investigated for
problems in computational science and engineering. One of the key areas at
the forefront of this trend is inverse problems\, and specifically\, inve
rse problems in imaging. The last few years have witnessed the emergence o
f many neural network-based algorithms for important imaging modalities su
ch as MRI and X-ray CT. These claim to achieve competitive\, and sometimes
even superior\, performance to current state-of-the-art techniques.\n\nHo
wever\, there is a problem. Techniques based on deep learning are typicall
y unstable. For example\, small perturbations in the data can lead to a my
riad of artefacts in the recovered images. Such artifacts can be hard to d
ismiss as obviously unphysical\, meaning that this phenomenon has potentia
lly serious consequences for the safe deployment of deep learning in pract
ice. In this talk\, I will first showcase the instability phenomenon empir
ically in a range of examples. I will then focus on its mathematical under
pinnings\, the consequences of these insights when it comes to potential r
emedies\, and the future possibilities for computing genuinely stable neur
al networks for inverse problems in imaging.\n\nThis is joint work with Ve
gard Antun\, Nina M. Gottschling\, Anders C. Hansen\, Clarice Poon\, and F
rancesco Renna\n\nPapers:\n\nhttps://www.pnas.org/content/early/2020/05/08
/1907377117\n\nhttps://arxiv.org/abs/2001.01258\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldMINDS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jelani Nelson (UC Berkeley)
DTSTART:20200611T183000Z
DTEND:20200611T193000Z
DTSTAMP:20260404T110824Z
UID:OneWorldMINDS/8
DESCRIPTION:Title: terminal dimensionality reduction in Euclidean space\nby
Jelani Nelson (UC Berkeley) as part of One World MINDS seminar\n\n\nAbstra
ct\nThe Johnson-Lindenstrauss lemma states that for any $X$ a subset of $R
^d$ with $|X| = n$ and for any epsilon\, there exists a map $f:X\\to R^m$
for $m = O(\\log n / \\epsilon^2)$ such that: for all $x \\in X$\, for all
$y \\in X$\, $(1-\\epsilon)|x - y|_2 \\le |f(x) - f(y)|_2 \\le (1+\\epsil
on)|x - y|_2$. We show that this statement can be strengthened. In particu
lar\, the above claim holds true even if "for all $y \\in X$" is replaced
with "for all $y \\in R^d$". Joint work with Shyam Narayanan.\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldMINDS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gitta Jutyniok (TU Berlin)
DTSTART:20200618T183000Z
DTEND:20200618T193000Z
DTSTAMP:20260404T110824Z
UID:OneWorldMINDS/9
DESCRIPTION:Title: Understanding Deep Neural Networks: From Generalization to In
terpretability\nby Gitta Jutyniok (TU Berlin) as part of One World MIN
DS seminar\n\n\nAbstract\nDeep neural networks have recently seen an impre
ssive comeback with applications both in the public sector and the science
s. However\, despite their outstanding success\, a comprehensive theoretic
al foundation of deep neural networks is still missing.\n\nFor deriving a
theoretical understanding of deep neural networks\, one main goal is to an
alyze their generalization ability\, i.e. their performance on unseen data
sets. In case of graph convolutional neural networks\, which are today he
avily used\, for instance\, for recommender systems\, already the generali
zation capability to signals on graphs unseen in the training set\, typica
lly coined transferability\, was not rigorously analyzed. In this talk\, w
e will prove that spectral graph convolutional neural networks are indeed
transferable\, thereby also debunking a common misconception about this ty
pe of graph convolutional neural networks.\n\nIf such theoretical approach
es fail or if one is just given a trained neural network without knowledge
of how it was trained\, interpretability approaches become necessary. Tho
se aim to "break open the black box" in the sense of identifying those fea
tures from the input\, which are most relevant for the observed output. Ai
ming to derive a theoretically founded approach to this problem\, we intro
duced a novel approach based on rate-distortion theory coined Rate-Distort
ion Explanation (RDE)\, which not only provides state-of-the-art explanati
ons\, but in addition allows first theoretical insights into the complexit
y of such problems. In this talk we will discuss this approach and show th
at it also gives a precise mathematical meaning to the previously vague te
rm of relevant parts of the input.\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldMINDS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Richard Baraniuk (Rice University)
DTSTART:20200625T183000Z
DTEND:20200625T193000Z
DTSTAMP:20260404T110824Z
UID:OneWorldMINDS/10
DESCRIPTION:Title: Affine spline insights into deep learning\nby Richard Ba
raniuk (Rice University) as part of One World MINDS seminar\n\n\nAbstract\
nWe build a rigorous bridge between deep networks (DNs) and approximation
theory via spline functions and operators. Our key result is that a large
class of DNs can be written as a composition of max-affine spline operator
s (MASOs)\, which provide a powerful portal through which to view and anal
yze their inner workings. For instance\, conditioned on the input signal\,
the output of a MASO DN can be written as a simple affine transformation
of the input. This implies that a DN constructs a set of signal-dependent\
, class-specific templates against which the signal is compared via a simp
le inner product\; we explore the links to the classical theory of optimal
classification via matched filters and the effects of data memorization.
Going further\, we propose a simple penalty term that can be added to the
cost function of any DN learning algorithm to force the templates to be or
thogonal with each other\; this leads to significantly improved classifica
tion performance and reduced overfitting with no change to the DN architec
ture. The spline partition of the input signal space that is implicitly in
duced by a MASO directly links DNs to the theory of vector quantization (V
Q) and K-means clustering\, which opens up new geometric avenue to study h
ow DNs organize signals in a hierarchical fashion. To validate the utility
of the VQ interpretation\, we develop and validate a new distance metric
for signals and images that quantifies the difference between their VQ enc
odings.\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldMINDS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stéphane Malla (École Normale Supérieure)
DTSTART:20200702T183000Z
DTEND:20200702T193000Z
DTSTAMP:20260404T110824Z
UID:OneWorldMINDS/11
DESCRIPTION:Title: Beyond sparsity: Non-linear harmonic analysis with phase for
deep networks\nby Stéphane Malla (École Normale Supérieure) as par
t of One World MINDS seminar\n\n\nAbstract\nUnderstanding the properties o
f deep neural networks is not just about applying standard harmonic analys
is tools with a bit of optimization. It is shaking our understanding of no
n-linear harmonic analysis and opening new horizons. By considering comple
x image generation and classification problems of different complexities\,
I will show that sparsity is not always the answer and phase plays an imp
ortant role to capture important structures including symmetries within mu
ltiscale representations. This talk will raise more questions than answers
.\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldMINDS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Holger Rauhut (RWTH Aachen University)
DTSTART:20200709T183000Z
DTEND:20200709T193000Z
DTSTAMP:20260404T110824Z
UID:OneWorldMINDS/12
DESCRIPTION:Title: Convergence of gradient flows for learning deep linear neura
l networks\nby Holger Rauhut (RWTH Aachen University) as part of One W
orld MINDS seminar\n\n\nAbstract\nLearning neural networks amounts to mini
mizing a loss function over given training data. Often gradient descent al
gorithms are used for this task\, but their convergence properties are not
yet well-understood. In order to make progress we consider the simplified
setting of linear networks optimized via gradient flows. We show that suc
h gradient flow defined with respect to the layers (factors) can be reinte
rpreted as a Riemannian gradient flow on the manifold of rank-$r$ matrices
in certain cases. The gradient flow always converges to a critical point
of the underlying loss functional and\, for almost all initializations\, i
t converges to a global minimum on the manifold of rank-$k$ matrices for s
ome $k$.\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldMINDS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Caroline Uhler (MIT)
DTSTART:20200716T183000Z
DTEND:20200716T193000Z
DTSTAMP:20260404T110824Z
UID:OneWorldMINDS/13
DESCRIPTION:Title: Multi-domain data integration: from observations to mechanis
tic insights\nby Caroline Uhler (MIT) as part of One World MINDS semin
ar\n\n\nAbstract\nMassive data collection holds the promise of a better un
derstanding of complex phenomena and ultimately\, of better decisions. An
exciting opportunity in this regard stems from the growing availability of
perturbation / intervention data (manufacturing\, advertisement\, educati
on\, genomics\, etc.). In order to obtain mechanistic insights from such d
ata\, a major challenge is the integration of different data modalities (v
ideo\, audio\, interventional\, observational\, etc.). Using genomics and
in particular the problem of identifying drugs for the repurposing against
COVID-19 as an example\, I will first discuss our recent work on coupling
autoencoders in the latent space to integrate and translate between data
of very different modalities such as sequencing and imaging. I will then p
resent a framework for integrating observational and interventional data f
or causal structure discovery and characterize the causal relationships th
at are identifiable from such data. We end by a theoretical analysis of au
toencoders linking overparameterization to memorization. In particular\, I
will characterize the implicit bias of overparameterized autoencoders and
show that such networks trained using standard optimization methods imple
ment associative memory. Collectively\, our results have major implication
s for planning and learning from interventions in various application doma
ins.\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldMINDS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tamara Kolda (Sandia National Laboratories)
DTSTART:20200723T183000Z
DTEND:20200723T193000Z
DTSTAMP:20260404T110824Z
UID:OneWorldMINDS/14
DESCRIPTION:Title: Practical Leverage-Based Sampling for Low-Rank Tensor Decomp
osition\nby Tamara Kolda (Sandia National Laboratories) as part of One
World MINDS seminar\n\n\nAbstract\nConventional algorithms for finding lo
w-rank canonical polyadic (CP) tensor decompositions are unwieldy for larg
e sparse tensors. The CP decomposition can be computed by solving a sequen
ce of overdetermined least problems with special Khatri-Rao structure. In
this work\, we present an application of randomized algorithms to fitting
the CP decomposition of sparse tensors\, solving a significantly smaller s
ampled least squares problem at each iteration with probabilistic guarante
es on the approximation errors. Prior work has shown that sketching is eff
ective in the dense case\, but the prior approach cannot be applied to the
sparse case because a fast Johnson-Lindenstrauss transform (e.g.\, using
a fast Fourier transform) must be applied in each mode\, causing the spars
e tensor to become dense. Instead\, we perform sketching through leverage
score sampling\, crucially relying on the fact that the structure of the K
hatri-Rao product allows sampling from overestimates of the leverage score
s without forming the full product or the corresponding probabilities. Nai
ve application of leverage score sampling is ineffective because we often
have cases where a few scores are quite large\, so we propose a novel hybr
id of deterministic and random leverage-score sampling which consistently
yields improved fits. Numerical results on real-world large-scale tensors
show the method is significantly faster than competing methods without sac
rificing accuracy. This is joint work with Brett Larsen\, Stanford Univers
ity.\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldMINDS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mary Wootters (Stanford University)
DTSTART:20200730T183000Z
DTEND:20200730T193000Z
DTSTAMP:20260404T110824Z
UID:OneWorldMINDS/15
DESCRIPTION:by Mary Wootters (Stanford University) as part of One World MI
NDS seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldMINDS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tselil Schramm (MIT)
DTSTART:20200806T183000Z
DTEND:20200806T193000Z
DTSTAMP:20260404T110824Z
UID:OneWorldMINDS/16
DESCRIPTION:Title: Reconciling Statistical Queries and the Low Degree Likelihoo
d Ratio\nby Tselil Schramm (MIT) as part of One World MINDS seminar\n\
n\nAbstract\nIn many high-dimensional statistics problems\, we observe inf
ormation-computation tradeoffs: given access to more data\, statistical es
timation and inference tasks require fewer computational resources. Though
this phenomenon is ubiquitous\, we lack rigorous evidence that it is inhe
rent. In the current day\, to prove that a statistical estimation task is
computationally intractable\, researchers must prove lower bounds against
each type of algorithm\, one by one\, resulting in a "proliferation of low
er bounds". We scientists dream of a more general theory which unifies the
se lower bounds and explains computational intractability in an algorithm-
independent way.\n\nIn this talk\, I will make one small step towards real
izing this dream. I will demonstrate general conditions under which two po
pular frameworks yield the same information-computation tradeoffs for high
-dimensional hypothesis testing: the first being statistical queries in th
e "SDA" framework\, and the second being hypothesis testing with low-degre
e hypothesis tests\, also known as the low-degree-likelihood ratio. Our eq
uivalence theorems capture numerous well-studied high-dimensional learning
problems: sparse PCA\, tensor PCA\, community detection\, planted clique\
, and more.\n\nBased on joint work with Matthew Brennan\, Guy Bresler\, Sa
muel B. Hopkins and Jerry Li.\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldMINDS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dustin Mixon (Ohio State)
DTSTART:20200813T183000Z
DTEND:20200813T193000Z
DTSTAMP:20260404T110824Z
UID:OneWorldMINDS/17
DESCRIPTION:Title: Ingredients matter: Quick and easy recipes for estimating cl
usters\, manifolds\, and epidemics\nby Dustin Mixon (Ohio State) as pa
rt of One World MINDS seminar\n\n\nAbstract\nData science resembles the cu
linary arts in the sense that better ingredients allow for better results.
We consider three instances of this phenomenon. First\, we estimate clust
ers in graphs\, and we find that more signal allows for faster estimation.
Here\, "signal" refers to having more edges within planted communities th
an across communities. Next\, in the context of manifolds\, we find that a
n informative prior allows for estimates of lower error. In particular\, w
e apply the prior that the unknown manifold enjoys a large\, unknown symme
try group. Finally\, we consider the problem of estimating parameters in e
pidemiological models\, where we find that a certain diversity of data all
ows one to design estimation algorithms with provable guarantees. In this
case\, data diversity refers to certain combinatorial features of the soci
al network. Joint work with Jameson Cahill\, Charles Clum\, Hans Parshall\
, and Kaiying Xie.\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldMINDS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Helmut Bölcskei (ETH Zürich)
DTSTART:20200820T183000Z
DTEND:20200820T193000Z
DTSTAMP:20260404T110824Z
UID:OneWorldMINDS/18
DESCRIPTION:Title: Fundamental limits of learning in deep neural networks\n
by Helmut Bölcskei (ETH Zürich) as part of One World MINDS seminar\n\n\n
Abstract\nWe develop a theory that allows to characterize the fundamental
limits of learning in deep neural networks. Concretely\, we consider Kolmo
gorov-optimal approximation through deep neural networks with the guiding
theme being a relation between the epsilon-entropy of the hypothesis class
to be learned and the complexity of the approximating network in terms of
connectivity and memory requirements for storing the network topology and
the quantized weights and biases. The theory we develop educes remarkable
universality properties of deep networks. Specifically\, deep networks ca
n Kolmogorov-optimally learn essentially any hypothesis class. In addition
\, we find that deep networks provide exponential approximation accuracy
—i.e.\, the approximation error decays exponentially in the number of no
n-zero weights in the network—of widely different functions including th
e multiplication operation\, polynomials\, sinusoidal functions\, general
smooth functions\, and even one-dimensional oscillatory textures and fract
al functions such as the Weierstrass function\, both of which do not have
any known methods achieving exponential approximation accuracy. We also sh
ow that in the approximation of sufficiently smooth functions finite-width
deep networks require strictly smaller connectivity than finite-depth wid
e networks. We conclude with an outlook on the further role our theory cou
ld play.\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldMINDS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nir Sochen (University of Tel Aviv)
DTSTART:20200827T183000Z
DTEND:20200827T193000Z
DTSTAMP:20260404T110824Z
UID:OneWorldMINDS/19
DESCRIPTION:by Nir Sochen (University of Tel Aviv) as part of One World MI
NDS seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldMINDS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Potts (TU Chemnitz)
DTSTART:20200903T183000Z
DTEND:20200903T193000Z
DTSTAMP:20260404T110824Z
UID:OneWorldMINDS/20
DESCRIPTION:by Daniel Potts (TU Chemnitz) as part of One World MINDS semin
ar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldMINDS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rima Alifari (September 10: Rima Alifari ()
DTSTART:20200910T183000Z
DTEND:20200910T193000Z
DTSTAMP:20260404T110824Z
UID:OneWorldMINDS/21
DESCRIPTION:by Rima Alifari (September 10: Rima Alifari () as part of One
World MINDS seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/OneWorldMINDS/21/
END:VEVENT
END:VCALENDAR