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‎_bibliography/references.bib‎

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@inproceedings{jacobs2025mirror,
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title={Mirror, Mirror of the Flow: How Does Regularization Shape Implicit Bias?},
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author={Tom Jacobs and Chao Zhou and Rebekka Burkholz},
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booktitle={Forty-second International Conference on Machine Learning},
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year={2025},
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url={https://arxiv.org/abs/2504.12883},
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pdf={https://arxiv.org/pdf/2504.12883},
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img={mirror-mirror.jpg},
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abstract={Implicit bias plays an important role in explaining how overparameterized models generalize well. Explicit regularization like weight decay is often employed in addition to prevent overfitting. While both concepts have been studied separately, in practice, they often act in tandem. Understanding their interplay is key to controlling the shape and strength of implicit bias, as it can be modified by explicit regularization. To this end, we incorporate explicit regularization into the mirror flow framework and analyze its lasting effects on the geometry of the training dynamics, covering three distinct effects: positional bias, type of bias, and range shrinking. Our analytical approach encompasses a broad class of problems, including sparse coding, matrix sensing, single-layer attention, and LoRA, for which we demonstrate the utility of our insights. To exploit the lasting effect of regularization and highlight the potential benefit of dynamic weight decay schedules, we propose to switch off weight decay during training, which can improve generalization, as we demonstrate in experiments.},
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}
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‎_data/alumni_members.yml‎

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end_date: Jul 24
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url: https://nelaturuharsha.github.io/
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- role: Research engineers
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members:
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- name: Nikita (Nik) Vedeneev
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last_name: Vedeneev
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photo: c01mive.jpg
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start_date: Dec 24
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end_date: May 25
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email: mikita.vedzeneyeu@cispa.de
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description: "I am interesting in making modern AI models efficient. In particular, I work on discovering and exploiting structure in Neural Networks (sparsity, low-dimensional representations and similar) for efficient training, fine-tuning and inference. I am a former full-time core developer for [PyTorch](https://github.com/pytorch/pytorch) and [Lightning Thunder](https://github.com/Lightning-AI/lightning-thunder). Check my [GitHub](https://github.com/nikitaved) to see what I work on now."
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members:
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- name: Otto Piramuthu

‎_data/news.yml‎

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- date: 2. June 2025
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headline: "Rebekka and Celia are presenting at the International Network Science Conference ([NetSci](https://netsci2025.github.io/)) in Maastricht."
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- date: 1. June 2025
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headline: Welcome Baraah!
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- date: 1. May 2025
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headline: "Our paper on [implicit bias](https://arxiv.org/pdf/2504.12883) has been accepted at ICML 2025."
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- date: 24. March 2025
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headline: "Rebekka is at [CPAL](https://cpal.cc/spotlight_track/) in Stanford presenting three of our [papers](/publications) as recent spotlights."
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- date: 22. January 2025
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headline: "Two papers
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[(1)](https://openreview.net/forum?id=g6v09VxgFw)
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[(2)](https://openreview.net/forum?id=U47ymTS3ut)
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have been accepted at ICLR 2025 (see [publications](/publications))."
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have been accepted at ICLR 2025."
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headline: "Welcome to Gowtham and Nik!"
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headline: "Welcome to Chao, Rahul, and Dong!"
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headline: "Celia, Advait and Adarsh are presenting at the Helmholtz AI Conference: AI for Science ([HAICON](https://eventclass.it/haic2024/scientific/external-program/session?s=S-05a))."
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headline: "Celia, Advait and Adarsh are presenting at the Helmholtz AI Conference: AI for Science ([HAICON](https://eventclass.it/haic2024/scientific/external-program/session?s=S-05a)) in Düsseldorf."
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- date: 1. May 2024
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headline: "Our paper on [improving GATs](https://openreview.net/forum?id=Sjv5RcqfuH) has been accepted at ICML 2024."

‎_data/team_members.yml‎

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url: https://cispa.de/en/people/c01dosu
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description: "My current research focuses on theoretically elucidating the superior performance of Mixture of Experts models, with an emphasis on their generalization performance, sample complexity, training dynamics, and robustness to adversarial noises."
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- role: Research engineers
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members:
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- name: Nikita (Nik) Vedeneev
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last_name: Vedeneev
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photo: c01mive.jpg
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start_date: Dec 2024
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email: mikita.vedzeneyeu@cispa.de
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url: https://cispa.de/en/people/c01mive
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description: "I am interesting in making modern AI models efficient. In particular, I work on discovering and exploiting structure in Neural Networks (sparsity, low-dimensional representations and similar) for efficient training, fine-tuning and inference. I am a former full-time core developer for [PyTorch](https://github.com/pytorch/pytorch) and [Lightning Thunder](https://github.com/Lightning-AI/lightning-thunder). Check my [GitHub](https://github.com/nikitaved) to see what I work on now."
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- name: Baraah Sidahmed
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last_name: Sidahmed
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photo:
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start_date: Jun 2025
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email: baraah.adil@cispa.de
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url: https://cispa.de/en/people/c01baad

‎_site/images/publications/mirror-mirror.jpg‎

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‎_site/index.html‎

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<h3>News</h3>
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<b>24 Mar 2025</b>
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<p>Rebekka is at <a href="https://cpal.cc/spotlight_track/">CPAL</a> in Stanford presenting three of our <a href="/publications">papers</a> as recent spotlights.</p>
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<b>02 Jun 2025</b>
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<p>Rebekka and Celia are presenting at the International Network Science Conference (<a href="https://netsci2025.github.io/">NetSci</a>) in Maastricht.</p>
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<b>22 Jan 2025</b>
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<p>Two papers <a href="https://openreview.net/forum?id=g6v09VxgFw">(1)</a> <a href="https://openreview.net/forum?id=U47ymTS3ut">(2)</a> have been accepted at ICLR 2025 (see <a href="/publications">publications</a>).</p>
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<b>01 Jun 2025</b>
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<p>Welcome Baraah!</p>
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<b>01 Dec 2024</b>
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<p>Welcome to Gowtham and Nik!</p>
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<b>01 May 2025</b>
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<p>Our paper on <a href="https://arxiv.org/pdf/2504.12883">implicit bias</a> has been accepted at ICML 2025.</p>
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<b>25 Sep 2024</b>
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<p>Three papers <a href="https://openreview.net/forum?id=EMkrwJY2de">(1)</a> <a href="https://openreview.net/forum?id=IfZwSRpqHl">(2)</a> <a href="https://openreview.net/forum?id=FNtsZLwkGr">(3)</a> have been accepted at NeurIPS 2024.</p>
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<b>24 Mar 2025</b>
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<p>Rebekka is at <a href="https://cpal.cc/spotlight_track/">CPAL</a> in Stanford presenting three of our <a href="/publications">papers</a> as recent spotlights.</p>
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<b>01 Jul 2024</b>
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<p>Welcome to Chao, Rahul, and Dong!</p>
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<b>22 Jan 2025</b>
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<p>Two papers <a href="https://openreview.net/forum?id=g6v09VxgFw">(1)</a> <a href="https://openreview.net/forum?id=U47ymTS3ut">(2)</a> have been accepted at ICLR 2025.</p>
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‎_site/news.html‎

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<h4>02 June 2025</h4>
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<p>Rebekka and Celia are presenting at the International Network Science Conference (<a href="https://netsci2025.github.io/">NetSci</a>) in Maastricht.</p>
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<hr />
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<h4>01 June 2025</h4>
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<p>Welcome Baraah!</p>
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<hr />
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<h4>01 May 2025</h4>
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<p>Our paper on <a href="https://arxiv.org/pdf/2504.12883">implicit bias</a> has been accepted at ICML 2025.</p>
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<hr />
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<h4>24 March 2025</h4>
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<p>Rebekka is at <a href="https://cpal.cc/spotlight_track/">CPAL</a> in Stanford presenting three of our <a href="/publications">papers</a> as recent spotlights.</p>
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<hr />
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<h4>22 January 2025</h4>
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<p>Two papers <a href="https://openreview.net/forum?id=g6v09VxgFw">(1)</a> <a href="https://openreview.net/forum?id=U47ymTS3ut">(2)</a> have been accepted at ICLR 2025 (see <a href="/publications">publications</a>).</p>
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<p>Two papers <a href="https://openreview.net/forum?id=g6v09VxgFw">(1)</a> <a href="https://openreview.net/forum?id=U47ymTS3ut">(2)</a> have been accepted at ICLR 2025.</p>
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<h4>14 June 2024</h4>
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<p>Celia, Advait and Adarsh are presenting at the Helmholtz AI Conference: AI for Science (<a href="https://eventclass.it/haic2024/scientific/external-program/session?s=S-05a">HAICON</a>).</p>
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<p>Celia, Advait and Adarsh are presenting at the Helmholtz AI Conference: AI for Science (<a href="https://eventclass.it/haic2024/scientific/external-program/session?s=S-05a">HAICON</a>) in Düsseldorf.</p>
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‎_site/publications/index.html‎

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<option value="Jacobs">Tom Jacobs</option>
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<option value="Nittala">Rahul Nittala</option>
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<option value="Sun">Dong Sun</option>
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<option value="Vedeneev">Nikita (Nik) Vedeneev</option>
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<option value="Sidahmed">Baraah Sidahmed</option>
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</select></p>
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<ol class="bibliography"><li><!-- _layouts/bib.html -->
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<div class="row" style="margin-top: 30px;" id="bib-jacobs2025mirror" authors="JacobsZhouBurkholz">
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<div class="preview"><img class="preview z-depth-1 rounded" src="/images/publications/mirror-mirror.jpg" />
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<!-- include figure.html
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path=entry_path
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class="preview z-depth-1 rounded"
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<!-- Entry bib key -->
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<div id="jacobs2025mirror" class="col-sm-10">
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<!-- Title -->
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<div class="title"><a href="https://arxiv.org/abs/2504.12883"><b>Mirror, Mirror of the Flow: How Does Regularization Shape Implicit Bias?</b></a></div>
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<!-- Author -->
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<div class="author">
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Tom Jacobs,&nbsp;Chao Zhou,&nbsp;and&nbsp;Rebekka Burkholz</div>
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<!-- Journal/Book title and date -->
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<em>In Forty-second International Conference on Machine Learning</em>, 2025
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</div>
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</div>
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<!-- Links/Buttons -->
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<div class="links"><a class="conf btn btn-sm z-depth-0">ICML</a><a class="bibtex btn btn-sm z-depth-0" role="button">Bib</a>
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<a class="abstract btn btn-sm z-depth-0" role="button">Abs</a>
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<!-- <a href="https://arxiv.org/pdf/2504.12883" class="btn btn-sm z-depth-0" role="button">PDF</a> -->
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</div>
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<!-- Hidden abstract block -->
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<div class="abstract hidden">
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<p>Implicit bias plays an important role in explaining how overparameterized models generalize well. Explicit regularization like weight decay is often employed in addition to prevent overfitting. While both concepts have been studied separately, in practice, they often act in tandem. Understanding their interplay is key to controlling the shape and strength of implicit bias, as it can be modified by explicit regularization. To this end, we incorporate explicit regularization into the mirror flow framework and analyze its lasting effects on the geometry of the training dynamics, covering three distinct effects: positional bias, type of bias, and range shrinking. Our analytical approach encompasses a broad class of problems, including sparse coding, matrix sensing, single-layer attention, and LoRA, for which we demonstrate the utility of our insights. To exploit the lasting effect of regularization and highlight the potential benefit of dynamic weight decay schedules, we propose to switch off weight decay during training, which can improve generalization, as we demonstrate in experiments.</p>
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</div><!-- Hidden bibtex block -->
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<div class="bibtex hidden">
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<figure class="highlight"><pre><code class="language-bibtex" data-lang="bibtex"><span class="nc">@inproceedings</span><span class="p">{</span><span class="nl">jacobs2025mirror</span><span class="p">,</span>
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<span class="na">title</span> <span class="p">=</span> <span class="s">{Mirror, Mirror of the Flow: How Does Regularization Shape Implicit Bias?}</span><span class="p">,</span>
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<span class="na">author</span> <span class="p">=</span> <span class="s">{Jacobs, Tom and Zhou, Chao and Burkholz, Rebekka}</span><span class="p">,</span>
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<span class="na">booktitle</span> <span class="p">=</span> <span class="s">{Forty-second International Conference on Machine Learning}</span><span class="p">,</span>
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<span class="na">year</span> <span class="p">=</span> <span class="s">{2025}</span><span class="p">,</span>
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<span class="na">url</span> <span class="p">=</span> <span class="s">{https://arxiv.org/abs/2504.12883}</span><span class="p">,</span>
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<span class="p">}</span></code></pre></figure>
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<li><!-- _layouts/bib.html -->
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<div class="preview"><img class="preview z-depth-1 rounded" src="/images/publications/mask_in_the_mirror.png" />
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<!-- include figure.html

‎_site/team/index.html‎

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<p><img src="/images/team members/c01mive.jpg" class="img-responsive" width="20%" style="float: left; margin: 0px 22px 24px 0;" /></p>
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<h4>Nikita (Nik) Vedeneev</h4>
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<p><a href="https://cispa.de/en/people/c01mive">Homepage</a>
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| <a href="mailto:mikita.vedzeneyeu@cispa.de">Email</a>
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| <a class="membercv" role="button">Description</a> <br />
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<i>since Dec 2024</i></p>
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<p><img src="/images/team members/blank.jpg" class="img-responsive" width="20%" style="float: left; margin: 0px 22px 24px 0;" /></p>
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<p>I am interesting in making modern AI models efficient. In particular, I work on discovering and exploiting structure in Neural Networks (sparsity, low-dimensional representations and similar) for efficient training, fine-tuning and inference. I am a former full-time core developer for <a href="https://github.com/pytorch/pytorch">PyTorch</a> and <a href="https://github.com/Lightning-AI/lightning-thunder">Lightning Thunder</a>. Check my <a href="https://github.com/nikitaved">GitHub</a> to see what I work on now.</p>
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</div>
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<h4>Baraah Sidahmed</h4>
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<p><a href="https://cispa.de/en/people/c01baad">Homepage</a>
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| <a href="mailto:baraah.adil@cispa.de">Email</a>
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<br />
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<i>since Jun 2025</i></p>
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<h3>Research engineers</h3>
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<ul>
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<li style="margin-left:-16px;">Nikita (Nik) Vedeneev:
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<i>Dec 24-May 25</i>.
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</li>
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</ul>
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<h3>Visiting students</h3>
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‎images/publications/mirror-mirror.jpg‎

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