Dirk L.
@Dirque_L
Followers
1,141
Following
381
Media
516
Statuses
4,504
Does and teaches applied mathematics. (he/him, er/ihn)
Joined September 2016
Don't wanna be here?
Send us removal request.
Explore trending content on Musk Viewer
Black
• 1988658 Tweets
La OEA
• 839008 Tweets
NABJ
• 564075 Tweets
Petro
• 370585 Tweets
Flamengo
• 248438 Tweets
Hugo
• 101019 Tweets
Jamaican
• 69347 Tweets
Corinthians
• 65774 Tweets
Abel
• 47958 Tweets
gremio
• 38123 Tweets
Wesley
• 32854 Tweets
Renato
• 30312 Tweets
無課金おじさん
• 29935 Tweets
Saint Dr MSG
• 27637 Tweets
#AEWDynamite
• 27218 Tweets
Rony
• 26913 Tweets
Luiz Araújo
• 22890 Tweets
Rojas
• 22628 Tweets
Amad
• 21814 Tweets
#MHA430
• 21747 Tweets
Paiva
• 20071 Tweets
Nkunku
• 16514 Tweets
O Vasco
• 16110 Tweets
Lavia
• 16061 Tweets
Gerson
• 14389 Tweets
Vegetti
• 14167 Tweets
Cavani
• 12961 Tweets
Veiga
• 12798 Tweets
Reinaldo
• 11930 Tweets
Yuri Alberto
• 10713 Tweets
Raniele
• 10185 Tweets
I invented a math joke:
Why does matrix multiplication work from home?
Because it doesn't commute.
29
242
2K
So simple, yet effective!
Just learned: Adding randomness before quantization helps! One-bit quantization of X is sign(X). If |X|≤c then it's better to store sign(X+Y) where Y is uniformly distributed on [-c,c]!
Why? We still have
E[X] = E[c*sign(X+Y)]
1/n
9
28
338
6
54
538
Just learned: Adding randomness before quantization helps! One-bit quantization of X is sign(X). If |X|≤c then it's better to store sign(X+Y) where Y is uniformly distributed on [-c,c]!
Why? We still have
E[X] = E[c*sign(X+Y)]
1/n
9
28
338
I also had to do one…
5
27
213
This book draft "Large-Scale Convex Optimization via Monotone Operators" by Ernest Ryu and Wotao Yin is awesome!
The "scaled relative graph" framework allows for a beautiful and totally graphical analysis of methods for monotone inclusions!
1
33
143
It is completely irrelevant if one should know what PAC stands for or not. Always define acronyms. Always. It's not about now - it's about producing literature that can be understood indefinitely.
8
3
122
This is quite amazing: It works sind 5*sqrt(2) is very close to 7. More precisely: (5*sqrt(2))² = 50 = 49+1 = 7².
Are there other possibilities? Turn out there are infinitely many of them!
1/n
1
9
80
The book is out! Visit or
to get you a copy of Mathematical Image Processing by Kristian Bredies and myself.
1
12
76
Germany's math undergrad curricula often contain a course "complex analysis". When I ask colleagues why, they never answer "because it is so useful". Why is it still there and how should we replace it? My modest proposal:
Just change from 𝐜𝐨𝐦𝐩𝐥𝐞𝐱 to 𝐜𝐨𝐧𝐯𝐞𝐱! 1/10
15
5
77
Als "Arbeitgeber" von Postdocs sage ich: Es ist zum Verzweifeln.
Mit genügend Drittmitteln lassen sich zwar immer noch halbwegs annehmbare Bedingungen für Postdocs schaffen, es wird aber nichts leichter oder gar besser.
Das Bundeskabinett hat heute die Reform des
#WissZeitVG
beschlossen. Damit verbessern wir die Arbeitsbedingungen für
#Wissenschaftlerinnen
und
#Wissenschaftler
. 🎓
Alle Details sind hier nachzulesen:
283
38
84
6
5
65
This obituary for Jean Bourgain by Terry Tao is another must-read for every mathematician.
0
23
61
@TonyTheLion2500
Purely mathematical: The product of the variance of a function and the variance of its Fourier transform has a positive universal lower bound.
2
3
58
@DrLutzBoehm
Ich grübele jetzt schon länger, was "zwei Punkte haben immer den maximal möglichen Abstand" bedeuten soll. Hilfe!
10
0
57
More and more people realize that training neural networks is essentially the same as fitting parameters in ODEs
These older papers on fitting a few parameters in ODEs are pretty interesting:
[2007] Parameter estimation for differential equations
[2009] On Identifiability of Nonlinear ODE Models and Applications in Viral Dynamics
1
9
50
1
16
51
I had my inaugural lecture yesterday at
@unibremen
!
I talked about Ax=b and treated: What if
… we only have a single row of A at the same time?
… we only have a black-box function x → Ax (and maybe also y→ V T y with V T ≈ AT)?
… we want to have min φ(x) s.t. Ax=b?
1
1
52
Teaching the Jordan normal form in German is fun: You teach the Hauptvektorkettenbasisbestimmungsverfahren…
5
3
52
Who had the stupid idea to use "orthogonal matrix" and "orthonormal matrix" to mean the same thing?
6
4
50
New preprint 📄 "Linearly convergent adjoint free solution of least squares problems by random descent" by Felix Schneppe,
@ltondji
and myself
In this paper we revisited an old problem: What if you want to minimize ||Av-b||² 𝗕𝗨𝗧 1/10
5
8
47
Goodbye
@tuBraunschweig
! Today is the day I move out of my office. Thanks for the great time I had!
Will be on campus regularly for the next few months still, though.
9
0
43
@TaliaRinger
In my experience that's not exactly how it works, at least not everywhere in math. There are enough referees for "top journals" who judge harshly based on what they deem to be of interest or use. "Almost top" journals are more relaxed.
1
0
44
@Anthony_Bonato
The correct answer would have been "Nothing - it means absolutely nothing."
(It is used to indicate which one is the integration variable, though.)
4
0
40
Q: What is the simplest nonlinear function?
Of course, it's a matter of opinion.
People in ML, please answer too!
34
1
37
The purpose of the white boxes and the end of a proof? To check it off once you checked it!
1
0
36
I had to cancel my trip to trip to the
@CIRM
workshop "Optimization for Machine Learning" this week. My talk would have been today so I thought I twitter the message. Thread on "Extensions of the randomized Kaczmarz method: sparsity and mismatched adjoints"
Ping
@salmonjsph
2
9
36
@LongFormMath
Let x stand for the set of real numbers and consider the function i(f) = f² from x to x.
2
0
35
Cyclically monotone maps are subgradients by the fundamental theorem of calculus
1
9
35
Yesterday I attended a PhD defense where the student stuttered. The stutter was severe and at times it was hard for me to follow. I got very much distracted by the stutter.
End of the story: It was an excellent defense and the student graduated with distinction!
2
0
34
Neat!
One of these papers where you think "Nobody did this before? Why didn't I think of this?"
New optimization paper alert! "Directional Smoothness and Gradient Methods: Convergence and Adaptivity". We develop new sub-optimality bounds for gradient descent that depend on the local smoothness (curvature) along the optimization path.
2
31
146
0
3
32
“Most of the time it doesn’t work out. As pretty much every single graduate student in mathematics can attest, [..] you probably spend two-thirds of your time getting stuck and banging your head against a wall.” Encouraging quote, especially from this guy!
2
4
32
@thegautamkamath
Wrong question. Every paper should define *all* acronyms used. Basic rule of scientific writing.
3
0
31
@TaliaRinger
This can get more extreme:
German title drop-down menus. Including the rarely-seen-in-the-wild "Dr. Dr. Dr." option.
21
31
233
0
1
29
New preprint "A Bregman-Kaczmarz method for nonlinear systems of equations" with
@gowerrobert
and Maximilian Winkler on the arxiv:
What's it about? 🧵 1/5
1
2
29
Reminds me of the Seven C's of Analysis:
Convergence, completeness, closedness, compactness, continuity, connectedness, and convexity.
(From Kenneth Lange's book "Optimization".)
Six D's at the core of machine learning: Discrepancies, deviations, dissimilarities, divergences, distances, and diversities!
4
7
27
0
7
27
@TonyTheLion2500
I find the view from signal processing most intuitive: A signal that is localized in time cannot be well localized in frequency and vice versa. Put differently, if you want to build a signal that is localized in time you need to use arbitrarily large frequencies.
0
1
28
This is a remarkable fact. Especially since the definition of "convex" only needs a linear structure but no topology whatsoever. As a consequence, the statement is true for any topology! (Hint: Change of topology changes both the notion of continuity and interior.)
A convex function is continuous on the interior of its domain.
0
14
59
2
4
26
Was trying to figure out if "stepsize" or "step size" is more common. Checked just to learn that it contains "step size" seven times and "stepsize" six times… 🤔
5
0
26
Fun problem: How to sample from {1,…m} uniformly if you only have a fair coin?
Follow-up: Which method needs the lowest number of coin tosses on average? 1/4
2
1
26
Funny read:
"We denote the standard basis vectors by e_i, i.e., e_i consists of…"
1
0
27
Jannis Marquardt,
@emanuele_naldi
and me just uploaded the paper "The Degenerate Variable Metric Proximal Point Algorithm and Adaptive Stepsizes for Primal-Dual Douglas-Rachford" to the arxiv (). The convergence of DR still seems mysterious the me and… 1/2
1
2
27

Yesterday I uploaded the preprint "Adaptive Bregman-Kaczmarz: An Approach to Solve Linear Inverse Problems with Independent Noise Exactly" (with
@ltondji
and
@Idriss_Tondji
) to the arxiv. Here is a 
1/7
3
8
26
Well, I may not have won the Lehrleo from
@tuBraunschweig
this year but at least my teaching evaluation says
"Herr Lorenz ist ein Ehrenmann"
💪
(Sorry, no translation possible, I guess.)
2
2
24
The history of CT is quite amazing. This "algebraic reconstruction technique" is a reinvention of the Kaczmarz method from 1931 and it is still under intense research these days! (Btw. the method "just" solves a linear system of eqs.)
The first CT scan of a patient's brain was taken on this day in 1971.
The images from these scans took over 2 hours to be processed by algebraic reconstruction techniques on a large computer.
24
696
3K
0
2
25
Look who appeared as associate editor of the
@TheSIAMNews
SIAM Journal on Imaging Sciences!
Quite exited to see the other side of the business soon!
2
0
24
Recently I uploaded the paper "Learning Variational Models with Unrolling and Bilevel Optimization" (together with
@gusgustav85
, Niklas Breustedt and
@timodewolff
). What's that about? Find out in a… 🧵
1/7
1
2
25
@rnielikki
@memecrashes
Thanks! Without canceling the + it was just plain wronge because canceling out of sums is clearly not valid.
0
0
23
@francoisfleuret
For me the SVD finally provided good intuition: A linear map is rotation, axis scaling and another rotation. The inverse is "inverse rotation, inverse scaling, and inverse rotation". The transpose inverts the scaling but not the scaling
3
0
22
Off to a half-day long train ride to the DIPOpt workshop on deep learning inverse problems and optimization in Lyon! 🤞
1
1
24
Hey, math tweeps! I am looking for a convergence proof for projected SGD for a minimization problem of the form
minᵤ 𝔼ₓ[F(u,x)] s.t. u∈ C
with convex C. Does such a proof exist already?
(Algo is: sample x, do gradient step u − τ∇ᵤF(u,x) and project result onto C.)
5
4
23
We've got
@paperswithcode
and
@arxiv
(even partnered up) which is great, but why don't we have "papers with videos" yet? There are tons of recordings of talks but they're hard to find when you found the paper...
#AcademicTwitter
#mathtwitter
0
2
24
Has surprising properties when used for regression with noisy samples: Seems to converge to true function (in some Sobolev norm) when number of samples go to infty (but constant noise level). Anyone knows a proof?
Shepard interpolation is a surprisingly simple multi-dimensional interpolation method. It uses singular radial basis functions inversely proportional to the distances to the samples. Nearest neighbor interpolation is the limit case.
1
74
407
1
6
24
We are hiring an assistant prof in statistical learning and information theory! Please retweet and forward to potential candidates.
Any questions directly to me!
0
25
23
Did you ever use unrolling for training of a variational model? Wonder why it worked (or didn't as expected)? Come to MS79 at
#SIAMMDS22
in Palm 3 tomorrow at 9:30a (6:30p CEST) organized by
@moskitos_bite
and myself!
(Part 2 will be on Thursday, same time, same place.)
1
3
23
Did I see correctly, that
@gabrielpeyre
just secured his *third* ERC grant!? Well done, congrats!
0
0
23
Induction as dominoes or as an engine - which one do you prefer?
(Credit: Left - myself, right, "Discrete Mathematics" by Biggs)
4
0
21
MFO in Oberwolfach has this amazing library and these bookshelves where they display some new books. Somehow they always manage to present quite many books I am eager to read. Here are some in a 🧵
2
3
22
Tfw
@gabrielpeyre
links to your blog instead of Wikipedia or a paper
😲🤩
Oldies but goldies: P. L. Lions and B. Mercier, Splitting Algorithms for the Sum of Two Nonlinear Operators, 1979. Douglas-Rachford algorithm (dual of ADMM) minimizes the sum of two convex functions. Typical convergence pattern is spiralling.
0
23
116
1
0
21
@docmilanfar
Would make much more sense to call lse(z) the softmax, and σ(z) the softargmax (because the former approximates the max and the latter the argmax…), but that battle is lost…
0
0
21
Oh, that's me!
The paper I talked about is
btw. Got great questions and remarks!
Day 2 in DIPOpt starts with a great talk by
@Dirque_L
analyzing unrolled vs bilevel optimization
0
0
8
1
1
21
If you attend the
@TheSIAMNews
Imaging conference next week and are interested in monotone inclusions, TV reg and such, don't miss our minisymposium "Challenges in Nonsmooth Convex Optimization and Monotone Inclusions Problems"!
(btw, timezome is UTC-4)
0
3
19
I can't remember a time at which I found such an illustration in a math book helpful.
(It's from Luenberger's "Optimization by vector space methods" which is awsome. But this illustration… 🙄
5
1
20
In our star-wars-themed lecture on May 4th I asked the students to submit memes in our chat. They delivered big time! A few more there 👇
1
3
20
I used to gaslight myself into thinking that I can't do probability…
0
0
20
Takeaway from this rundown of software for scientific computing: If
@matlab
is the BMW sedan of scientific computing, then
@ThePSF
(Python) is the Ford pickup, and
@JuliaLanguage
is Tesla.
Feels about right.
3
56
125
1
6
20
Optimal transport is the new math of deep learning, and deep learning is practically all of artificial intelligence these days, and artificial intelligence in the new electricity according to
@AndrewYNg
I conclude that optimal transport is an electrifying field!
0
2
20
Nice article about the great Ingrid Daubechies:
0
11
19
A few days ago I upload the paper "Chambolle-Pock's Primal-Dual Method with Mismatched Adjoint" together with Felix Schneppe. We wanted to know what happens to CP when the computation of the adjoint is not exact.
2
1
19
I was reading the paper "Proximal methods for point source location" and found myself looking for the "like"-button 🤦
On a second thought: arXiv should really implement something like that…
1
1
19
I don't care the slightest bit about tau, but wanted to add that ]a,b[ is the only way to write open intervals. (a,b) is either the ordered pair or (if you are evil) the inner product.
5
0
19
Student shows up for an oral exam and brings his own chalk 😲
It's Hagoromo 🤯
2
0
19
A data science master costs between 30.000 and 100.000!? Not at
@tuBraunschweig
! Our international Master of Data Science starts this fall and you just pay standard admission (< €400 per semester). Apply until July 15!
0
3
19
Yess. Remove it.
Also remove every appearance of "very" in your scientific writing.
Paper writing tip:
You can remove "note that" without replacement in 99% of cases.
Thank you.
12
6
77
2
0
19
Hilda Geiringer - another great figure of applied math I haven't heard of until today!
1
11
18
@sp_monte_carlo
Gradient descent has two upgrades: Conjugate gradients and Nesterov acceleration.
1
0
19
Our master program Data Science starts in a few weeks! It's the first program at
@tuBraunschweig
that's fully taught in englisch - looking forward to welcoming the first students!
0
4
18
