I do machine learning and computer vision research, where I work with geometric models of observed data. The research tend to follow two directions: use geometric constructions to design models, or model constraints on data using geometry. Check the publications for more specific examples, and don't hesitate to get in touch.
October 26, 2023. Alison defended her PhD today. Such a beautiful presentation! I'm really honored to have worked with such an amazing thinker. You will be missed! Great to have Frank, Michael and Mikkel on the committee; I can't imagine a better fit!
September 22, 2023. The yearly dice roll went fairly well this year with 4 papers accepted at NeurIPS.
September 22, 2023. This years GenU is over. What a ride! This is such an enjoyable meeting, and I am grateful that we get to host such marvelous people in Copenhagen.
September 13, 2023. I visited Frederik's group in Linköbing to give a talk. I got to see so much cool work from fellow Scandinavians!
September 12, 2023. Hanging out in Manchester airport after attending and lecturing at GPSS. Super cool event with some great talks and wonderful hallway chats (somewhat less exciting airport, though).
August 29, 2023. Hadi's work on geometric motion skills is now accepted at IJRR. This is a rather significant extension of our 2021 R:SS paper. Really cool stuff!
August 23, 2023. Jeppe's paper on the pitfalls of machine learning for tumor assessment is now available in the Journal of Pathology. This really represents years of work from Jeppe, and its amazing to see the work out there. These findings should reach actual patients in the not-so-distant future.
June 29, 2023. I had a lot of fun lecturing at the GeMSS summer school; so many engaging discussions about the wonders of differential geometry in generative modeling. What better way to start the summer holidays :-)
June 13, 2023. Super cool preprint from Federico, Pablo, myself and Georgios! We develop a Laplace approximation for Riemannian manifolds and show that if you apply this to the loss surface of a neural network you get a super well-behaved Bayesian neural net. Way more meaningful that the usual Laplace approximation.
June 12, 2023. Miguel defended his PhD thesis today. Fantastic show of pure excellence! Watching such a show makes me overly proud to have played even just a small role. My favorite question from the committee: Angry Birds?
June 9, 2023. I'm super excited to finally share a pre-print of the work of Pablo and Pol on understanding masked pre-training from a Bayesian perspective. We show that masked pre-training amounts to maximizing the marginal likelihood of the associated probabilistic model, which helps to explain the excellent generalization performance often seen with self-supervision. Hopefully, this paves the way for more self-supervision in Bayesian models.
Mar 27, 2023. A nice aspect of the Laplace approximation that we developed for the LAE is that is scaled linearly with output size. This allows us to scale to U-Nets and get segmentation uncertainty. Check out the latest work from Killian and Selma!
Mar 1, 2023. Cilie defended her PhD thesis. Wow, what a fantastic show! Very emotional for this proud supervisor. You sure will be missed Cilie!
Feb 20, 2023. I went to Sweden! I talked about representation geometries at Chalmers. Amazing discussions; it's beyond fantastic to have physical audiences again :-)
Feb 6, 2023. New preprint on Bayesian metric learning from Frederik, Marco and Silas. It's rather nice when being Bayesian actually improves on state-of-the-art predictive results, while yielding nicely calibrated uncertainty.
Jan 3, 2023. Can't imagine a better way to start the new year than to release Alison's wonderful work on the geometry of expectations of random manifolds. Spoiler alert: turns out that expected distances on random Riemannian manifolds do not give rise to Riemannian metrics -- it's all Finslerian!
Oct 23, 2022. I gave a Zoom talk at the IROS geometry tutorial. It was great fun, but I was really sad not to be physically present for such a cool event. Hopefully next time...
Sep 16, 2022. GenU is over for this year. What an amazing run of discussions. To me, GenU is the most fun meeting to attend in machine learning research as it is one of the few places where there is the room for fruitful discussions.
Sep 15, 2022. Two papers accepted for NeurIPS this year. The first is our Laplacian Autoencoder, which (among other things) show how to do Laplace approximation on image models (making segmentation, etc, possible). The second is a new training technique for Gaussian Process latent variable models. This is way more practical than inducing points. I'll share a pre-print of that real-soon-now.
Sep 8, 2022. Pola did an overwhelming fanstic job defending her thesis today. I can't help but cry a bit. Both because I'll miss her, but also because I'm proud to have been part of the journey that formed such an excellent thinker.
July 2, 2022. We finally got around to releasing the preprint of our work on Laplacian approximations to Bayesian autoencoders. It's remarkable how many of the "minor" issues with VAEs that simply disappear once you go Bayesian. Amazing stuff! I can't wait to do geometry in these models!
June 16, 2022. The final version of Pola's probabilistic spatial transformer model is finally out (to appear at UAI). This is a really neat way to think about data augmentation and how we might learn it. Also it seems to consistently be better (easier to train) than the regular STN.
June 9, 2022. videnskab.dk (a Danish popular science outlet) has a piece about our latest Nature Communications paper on mapping the space of proteins (in Danish). Might be a fun read about the overarching ideas we are pursuing.
June 7, 2022. New preprint from Helene! We investigate the basic question of uniqueness of representations in autoencoder. That is, for a given decoder, does a given data point have a unique representation? The autoencoder is built on the assumption that this is always true, but math disagrees. Surprisingly, one can actually provide a very rich answer to this simple question. Super exciting!
June 2, 2022. It's official: I'm a gamer (even if I haven't played since the days of the tentacles)! Miguel's work on using geometry guide the creation of Mario levels using VAEs is now available on arxiv. This should correspond to the camera-ready that will appear at the Conference on Games. Really cool stuff -- makes me feel young again :-)
April 8, 2022. Finally! After a long stretch, our work on protein representations and their geometry is now out in Nature Communications. This is such an amazing showcase of geometry!
March 24, 2022. I gave a talk while home alone with the two kids. Ended up with a kid on each arm at the end of the talk. Achievement Unlocked!
March 18, 2022. Andri and I finally managed to write up his nice Msc thesis work on visualizing Riemannian data. Enjoy!
March 16, 2022. New pre-print from Hadi and friends. This is a really cool collection of niceties: geometry-controlled robots, variational autoencoders with change-of-variable induced likelihoods and more.
February 23, 2022. New preprint from Simon and friends. This neatly shows that you can use intrinsic calculations of the Cholesky decomposition to bound the true marginal likelihood of Gaussian processes. I love it when numerics and models, just go this nicely hand in hand!
February 16, 2022. We've released an exciting new dataset for place recognition (and other tasks if you are so inclined). Check out the corresponding paper. This is challenging stuff, so have fun! Personally, I'm really excited that this was made possible by the open data policy of the Danish government!
February 8, 2022. I'm out of isolation again and was able to go to the office today. This had the wonderful side-effect that I got to hang out with Georgios whom recently re-joined DTU as an assistant professor. Not only is it amazing that the department is investing in geometric machine learning, but even better, then this means I get to hang out with my old friend! Great to have you back, minion :-)
January 28, 2022. Wow, ICML deadline was not fun this year, as the entire family was down with COVID at the same time. Yikes. Fortunately, the lab is full of amazing people, so some great papers got shipped :-)
January 19, 2022. Both Federico's work on OOD detection, and our work on pulling back information geometry has been accepting to AISTATS. Papers will appear here soon...
January 19, 2022. Pierre and Eugene's work on training from pseudo-inputs are now on arXiv. This is a really neat trick for calibrating your VAE's uncertainty.
December 15, 2021. Jeppe defended his PhD today. I'm humbled to have been part of this, and I have great faith that this work will directly result in improved clinical practice. I'm so happy that I was talked into co-supervising Jeppe's MSc thesis many moons ago...
October 14, 2021. GenU is done for this year. What a fantastic show. Amazing speakers and even better discussions. Really good to meet in person after so long. So long and thanks for all the fish! (already looking forward to next year)
September 29, 2021. Cong's amazing work on energy-based models will appear at this years NeurIPS. We'll get a PDF online soon as it really is work worth sharing. Very exciting!
July 16, 2021. Humbling news: our paper at R:SS got the best student paper award. After years of working on random geometries it's really rewarding to see the theory being put to real use, and it's nice that others see value as well.
July 16, 2021. LogML is over. The organizers did a fantastic job, and I had great fun meeting the students in my team. Such a cool crowd!
June 25, 2021. I had fun speaking at DiffCVML about identifiability. Such a cool meeting!
June 18, 2021. Jeppe's work on sTIL scoring is out! This is the first time an algorithm adheres to TIL working group guidelines, and results so far are as good as one could hope for. I look forward to seeing Visiopharm put this into production :-)
May 11, 2021. It's official: I'm a roboticist :-) Hadi's paper on geometry for robot learning has been accepted for R:SS. Really awesome to see a robot arm flying around according to geodesics on learned random manifolds!
April 8, 2021. I gave a talk in Johan's group at KU Leuven. Some of the thoughest and most well-thoughout questions I have met in a while. I really enjoyed that (really wished it hadn't been virtual).
February 22, 2021. Nicki defended his thesis. What a show! I am so grateful that Nicki is sticking around for a while longer :-)
February 18, 2021. The lockdown has taken my time, resulting in no updates to this site. Fortunately, I work with people that manage to be productive even when I'm not, so a few updates are still in order. (1) One current and one former PhD student managed to produce a baby -- Yay, there's still hope for humanity :-) (2) Georgios' paper got accepted to AISTATS -- amazing! (3) I'm part of a newly funded research center on basic machine learning research in life science -- absolutely amazing. Consequently, new positions will be made available.
December 7, 2020. Nicki, myself and Wouter have a new paper out on how to reason about protein representations. The experiments showing links between Riemannian representations and evolutionary developments are still blowing my mind!
November 27, 2020. Martin defended his thesis. Overwhelming and emotional! A fantastic show from a fantastic thinker! Thankfully, I get to keep him for a little while longer. Thanks to Carl Henrik, Arno and Jes for "the attack" :-)
November 26, 2020. Frederik put out a new preprint on a Bayesian treatment of image retrieval. Super cool stuff with an elegant likelihood and priors that actually correspond to state-of-the-art engineering tricks. Nice!
June 15, 2020. Frederik and I wrote up some thoughts on the societal impact of proprietary maps (Google maps, etc) and they might end up increasing global inequality. This is based on the bias we observe in visual mapping. The English version is now online.
June 23, 2020. Martin and I released a preprint of what I think of as "Isomap with curvature". This is so cool!
June 15, 2020. Frederik and I wrote up some thoughts on the societal impact of proprietary maps (Google maps, etc) and they might end up increasing global inequality. This is based on the bias we observe in visual mapping. Anyway, the write-up is available (in Danish; sorry we're working on getting the English version out) at videnskab.dk.
June 8, 2020. A bunch of us are organizing an IROS workshop on the interplay of robotics and geometry. We don't know if it will be physical or virtual, but we know that it will be fun -- so do join us :-)
April 28, 2020. Pola put out a new preprint on learned data augmentation. In my book, this is the most elegant formulation of data augmentation available. Not only that, it's also easy to implement and actually works :-)
February 24, 2020. Frederik's CVPR paper is on the magic list of accepted papers. Amazing work; I look forward to sharing the camera ready!
February 24, 2020. Dimitris put out a new preprint on sensible priors for VAEs. In my view, this is an essential step needed to have well-defined models, which in turn will lead to interpretability, disentanglement, causal models, and much more. I'm so excited, and I just can't hide it!
January 10, 2020. Starting first of January, 2020, I have been upgraded to full professor here at DTU. I'm really excited that DTU decided to upgrade me while I am on parental leave; this very well summarize DTU as a working environment!
December 28, 2019. I am on parental leave until summer 2020. While I expect to read e-mail from time to time, I may not reply as fast as I otherwise would. If it's urgent, then say so explicitly in the e-mail subject.
December 19, 2019. Sitting in Helsinki airport on my way home from the Deep Structures workshop where I talked about the stuff only Bayes should do. Absolutely fantastic meeting, and a much needed change from NeurIPS.
December 13, 2019. Packing up and heading home from NeurIPS where Martin, Nicki and I presented two posters. Fun and exciting, but the meeting sure is getting crowded.
December 5, 2019. Martin, Nicki and myself wrote a short piece on the importance of uncertainty in AI for the Danish science communication platform 'Videnskab.dk'. If you read Danish, then you might enjoy this!
November 27, 2019. I visited the Geometry and Topologi group at Aarhus University to talk about random manifolds. Exciting discussions about 'reach' and related topics!
November 7, 2019. The camera-ready of our variance paper at NeurIPS is now online. Sweet stuff; enjoy!
November 7, 2019. Two new open positions (1 Phd; 1 postdoc). Read more here if you're interested.
September 26, 2019. Based on feedback collected along the way, I have now updated the manuscript of what only Bayes should do. Enjoy!
September 6, 2019. Returned from some hectic days at DALI, where I gave two talks (on operational representation learning and the stuff only Bayes should do) and presented a poster. To add to the excitements, I had a baby strapped to my chest most of the time :-)
August 22, 2019. New preprint online. Here David provide rather tight approximation bounds on the expected length of a curve on a random manifold. Pretty exciting stuff as it justifies an approximation we keep on using :-)
August 13, 2019. Talked about operational representation learning at the DTU+DIKU Summer School on Generative Models. Good fun!
July 15, 2019.
I got sick and tired of typing
plt.plot(x.detach().cpu().numpy(), y.detach().cpu().numpy(), color="green"),
so I put together a little
pyplot wrapper that converts
torch tensors automatically to numpy arrays. Here's
the code; let me know if you have smarter ways of getting the same result!
April 3, 2019. Just returned from a great Villum meeting on equality, diversity and inclusiveness in science. Having a four year old daughter creates a bit of a ticking clock for me on this topic... scary!
January 31, 2019. Today is Georgios's last day as a PhD student. Excellent thesis submitted. Very emotional! Good luck m'boy -- you will be missed!
January 2, 2019. Returned to the office after an offline-holiday to see two papers accepted at AISTATS. Yay! Excellent work by Georgios and Anton. I'll post the camera-ready papers when they're ready :-)
October 24, 2018. The ERC just posted a short video interview with me on the key issues of ML. The actual interview was repeatedly interupted by people shaking cow bells (that's a Davos thing); hopefully, you can't see that in the final take :-)
October 8, 2018. Last week I had a one-week-intern from 9th grade in the lab; made him solve linear regression with grid search. Interesting reminder that people who are not familiar with derivatives would never think of minimizing sum-of-squares (he naturally arrived at sum-of-absolute-values)...
September 24, 2018. I am back from the "Summer Davos" meeting in the World Economic Forum. Quite intense. I think the research community could learn quite a lot on how to structure a meeting to focus on "discussion" rather than "presentation". More on this later...
August 24, 2018. I talked about data augmentation and CPAB at our machine learning summer school. Enter the dragon...
July 14, 2018. The second installment of GiMLi is now over. What a fantastic show -- thanks to all involved in making this happen!
June 21, 2018. Nicki and I presented the diffeomorphic spatial transformer network at CVPR. Excellent discussions; much fun!
June 14, 2018. New preprint online (it's NIPS formatted, but hasn't been submitted) on why uncertainty quantification is essential for manifold/representation learning. That's at least the case, when you approach the problem from a differential geometric viewpoint, but I expect that the underlying message is generally true.
June 4, 2018. I put up a short note on the non-central Nakagami distribution as I couldn't find information on this distribution elsewhere.
May 14, 2018. It seems I was nominated for teacher-of-the-year award. Thanks to whoever nominated me :-)
March 24, 2018. I have uploaded the camera-ready of our work on diffeomorphic statial transformer nets. If you don't need the flexibility of CPAB, then at least take the matrix exponential of your affine transformation matrix.
February 19, 2018. Nicki's paper on spatial transformer nets appears to be on the magic list of accepted CVPR papers -- yay! I'll link to the PDF once we have finished the camera-ready version.
January 26, 2018. I talked about the geometry of latent variable models (random Riemannian metrics to the rescue!) at the Oberwolfach workshop on Statistics for Data with Geometric Structure (check link for a picture of me and Agnes).
November 10, 2017. Machine Learning & Molecules is over for now -- what an amazing ride! Thanks to all 16 amazing speakers and to the Bard for final disruptions!
November 1, 2017. Some of our latest results on deep generative models are now on arXiv. Lovely to see how geometry vastly improves the usefulness of latent variable models.
August 30, 2017. Lectured on metric learning at our yearly machine learning summer school. Always fun when people realize that metric learning is "easier" (for a suitable definition of "easy") in infinite dimensions...
March 2, 2017. Yesterday was my first day as an associate professor here at CogSys. Yesterday I was also home sick with a delightful fever; I sure hope there's no link between these event...
December 21, 2016. The Villum Foundation has awarded me a Young Investigator grant. Absolutely amazing, and very humbling! As a consequence, I have several open positions at both PhD and post doc levels.
August 23, 2016. Had fun lecturing about metric learning at the Advanced Topics in ML summer school. Always fun when the audience almost cries out for a Riemannian approach...
August 12, 2016. Our work on locally adaptive normal distributions has been accepted for NIPS 2016. This is a wonderfully simple way to build well-behaved nonparametric models. I'll link to the camera-ready version when it's finished.
June 26, 2016. GIMLI is over. We had an amazing set of speakers, but equally important we also had an amazing set of attendees. Great discussions!
June 16, 2016. It seems I was given an Outstanding Reviewer Award from the ICML 2016 program committee -- thanks!
June 10, 2016. Sofie, myself, and Lars get our work on modeling forward models for EEG source reconstruction accepted at NeuroImage. Sometimes I'm amazed at how far you can get just using PCA... I'll link to the paper as soon as possible.
May 23, 2016. Aasa and I have an "Open Problems" paper at this years COLT posing problems around the probability of seeing a positive definite kernel matrix over geodesic spaces. Quite an intriguing problem; do think about it :-)
May 2, 2016. I finally put the final version of the augmentation paper online. This really is a fun example of how diffeomorphisms can be of great use in machine learning. Hope to see you for the talk at AISTATS!
February 5, 2016. I use Sozi (the extension) together with Inkscape for creating slides. Sometimes it can be helpful to have a PDF version of the slides rather than viewing the SVG file in your browser. I've hacked together a naive script for making this conversion -- it may be helpful to you as well.
January 12, 2016. The PAMI version of the Grassmann Average paper is now online. More theory, more experiments, more pictures. Fun stuff!
December 28, 2015. Our paper on learning data augmentation schemes has been accepted at AISTATS. If you just can't wait for the talk, you can enjoy the arXiv version, which essentially match the submitted paper. I'll link to the camera-ready once it's done.
November 9, 2015. My PAMI paper on generalizing the classic principal curves to Riemannian manifolds is now online. It's remarkable how well such a simple well-known algorithm works compared to standard Riemannian models.
October 13, 2015. Our paper on learning data augmentation schemes is now available online. This is a great example of why everybody should care about diffeomorphisms!
September 18, 2015. Our ICCV 2015 paper on simple and efficient representations of diffeomorphisms is now online. I'm very excited that diffeomorphisms can be so simple to work with -- this is really a big change compared to standard representations!
June 17, 2015. I'll be on paternity leave until January 2016, so my response time might be suboptimal in the mean time. If you really want a reply from me, and you don't get one, just keep trying :-)
April 21, 2015. Presented some of the tractography work at the Probabilistic Numerics for Differential Equations workshop at Warwick -- very entertaining interactions on the role of uncertainty in computations.
April 13, 2015. We're currently on our way back from DALI 2015; An extremely exciting small-scale meeting consisting of nothing but awesome talks and discussions.
November 4, 2014. Did you ever feel like designing a Gaussian kernel on a Riemannian manifold using the intrinsic metric? Or perhaps on a more general metric space? If so, you will want to tread lightly as this is generally not possible; check out our recent work on this if you're curious!
October 3, 2014. I just noticed that my Youtube channel has gotten more than one thousand views. Wow -- thanks for watching!
September 17, 2014. Michael and Niklas presented our poster at MICCAI 2014 on using probabilistic numerics in tractography. There was a rather large interest in understanding the hidden uncertainties in the numerical algorithms we tend to take for granted -- wonderful!
September 12, 2014. Gave a talk on Grassmann Averages work at the Dept. of Biomedical Engineering at the City College of New York. Impressive work going on at Lucas's lab.
August 28, 2014. Lectured the morning session of the Advanced Topics in Machine Learning summer school at DTU -- a rather fun interactive coding session on Geometric Statistics.
August 21, 2014. Attended the Roundtable on Probabilistic Numerics in Tubingen -- it seems the community is beginning to form!
August 7, 2014. The poster teaser video for our MICCAI 2014 paper is now online -- check it out!
August 7, 2014. My talk at CVPR 2014 on Grassmann Averages is now available at techtalks.tv -- enjoy!
July 2, 2014. Posted a blog entry about choices of subspace metrics for the Grassmann Average subspace estimator. Summary: for Gaussian data most metrics gives the first principal component as the subspace average.
June 24, 2014. Presented the poster for Model Transport: Towards Scalable Transfer Learning on manifolds with Michael at CVPR 2014. Much fun!
May 30, 2014. The paper Metrics for Probabilistic Geometries has been accepted at UAI 2014. It's all about distributions of manifolds in the form of random Riemannian metrics -- very exciting first steps!
April 14, 2014. The paper Probabilistic shortest path tractography in DTI using Gaussian Process ODE solvers has been accepted at MICCAI 2014. This is a cool case-study for probabilistic numerics.