Sayantan Sen
@sayantansen.bsky.social
Postdoc @quantumlah @NUSingapore
Previously: Postdoc @NUSComputing
https://sites.google.com/view/sayantans
Previously: Postdoc @NUSComputing
https://sites.google.com/view/sayantans
Reposted by Sayantan Sen
Quantum Toolbox (12): Bretagnolle-Huber Inequality (1/6)
November 5, 2025 at 12:41 AM
Quantum Toolbox (12): Bretagnolle-Huber Inequality (1/6)
Reposted by Sayantan Sen
Quantum Toolbox (11): Generalized Operator Schwarz Inequality (1/6)
October 16, 2025 at 1:49 AM
Quantum Toolbox (11): Generalized Operator Schwarz Inequality (1/6)
Reposted by Sayantan Sen
Here's a classic (but fun to show) fact: if X is any random variable (with a finite variance) and λ is a real, then
𝔼[(X-λ)²] = Var[X]+(𝔼[X]-λ)²
(In particular, this shows that 𝔼[X] is the quantity minimizing 𝔼[(X-λ)²] over all λ, and that Var[X] is the resulting value.)
𝔼[(X-λ)²] = Var[X]+(𝔼[X]-λ)²
(In particular, this shows that 𝔼[X] is the quantity minimizing 𝔼[(X-λ)²] over all λ, and that Var[X] is the resulting value.)
![A short proof: here is the LaTeX code.
**Proof.** We have, for any $\color{blue}{\lambda} \in\mathbb{R}$,
\begin{align*}
\mathbb{E}[(X-\color{blue}{\lambda})^2]
&= \mathbb{E}[(X-\color{red}{\mathbb{E}[X]} + \color{red}{\mathbb{E}[X]} - \color{blue} {\lambda})^2] \\
&=\mathbb{E}[(X-\color{red}{\mathbb{E}[X]})^2 + 2(X-\color{red}{\mathbb{E}[X]})(\color{red}{\mathbb{E}[X]} - \color{blue} {\lambda}) + (\color{red}{\mathbb{E}[X]} - \color{blue} {\lambda})^2]\\
&=\underbrace{\mathbb{E}[(X-\color{red}{\mathbb{E}[X]})^2]}_{=\textrm{Var}[X]} + 2\underbrace{\mathbb{E}[X-\color{red}{\mathbb{E}[X]}]}_{=0}(\color{red}{\mathbb{E}[X]} - \color{blue} {\lambda})] + (\color{red}{\mathbb{E}[X]} - \color{blue} {\lambda})^2
\end{align*}
and that's all. (The first step is a trick known as *"hiding zero:"* writing $0=a-a$. 🤷)](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:ac6qioenkpl3jmmnib3tpbhb/bafkreieevv3petzx4kqxx3o6i4oqtugsjh52n7i2ellidxmetefboag6fi@jpeg)
October 11, 2025 at 4:04 AM
Here's a classic (but fun to show) fact: if X is any random variable (with a finite variance) and λ is a real, then
𝔼[(X-λ)²] = Var[X]+(𝔼[X]-λ)²
(In particular, this shows that 𝔼[X] is the quantity minimizing 𝔼[(X-λ)²] over all λ, and that Var[X] is the resulting value.)
𝔼[(X-λ)²] = Var[X]+(𝔼[X]-λ)²
(In particular, this shows that 𝔼[X] is the quantity minimizing 𝔼[(X-λ)²] over all λ, and that Var[X] is the resulting value.)
Reposted by Sayantan Sen
Quantum Toolbox (10): Uhlmann's Theorem (1/6)
September 29, 2025 at 2:02 AM
Quantum Toolbox (10): Uhlmann's Theorem (1/6)
Reposted by Sayantan Sen
Oh, and guess what — not only is this pre #FOCS2025 satellite event free, there is some financial support (covering accommodation, on the #USyd campus) for students available!
Register to the event, apply for travel support! (The latter by Sep 19)
sites.google.com/view/celebra...
Register to the event, apply for travel support! (The latter by Sep 19)
sites.google.com/view/celebra...
September 13, 2025 at 2:01 PM
Oh, and guess what — not only is this pre #FOCS2025 satellite event free, there is some financial support (covering accommodation, on the #USyd campus) for students available!
Register to the event, apply for travel support! (The latter by Sep 19)
sites.google.com/view/celebra...
Register to the event, apply for travel support! (The latter by Sep 19)
sites.google.com/view/celebra...
Reposted by Sayantan Sen
Quantum Toolbox (9): Sample Complexity Lower Bounds via Mutual Information (1/6)
September 10, 2025 at 11:03 AM
Quantum Toolbox (9): Sample Complexity Lower Bounds via Mutual Information (1/6)
Reposted by Sayantan Sen
🍾💐 Celebrating a successful thesis defence by Josep Lumbreras Zarapico!! 🍉🧀🍪 Advised by @marcotomamichel.bsky.social, Josep defended his thesis "Bandits Roaming Hilbert Space". He will next join Mile Gu’s group as a research fellow. Congrats and all the best, Dr Josep!
August 12, 2025 at 11:56 AM
🍾💐 Celebrating a successful thesis defence by Josep Lumbreras Zarapico!! 🍉🧀🍪 Advised by @marcotomamichel.bsky.social, Josep defended his thesis "Bandits Roaming Hilbert Space". He will next join Mile Gu’s group as a research fellow. Congrats and all the best, Dr Josep!
Reposted by Sayantan Sen
Quantum Toolbox (8): Hadamard's Three-Lines Theorem (1/6)
August 1, 2025 at 10:36 AM
Quantum Toolbox (8): Hadamard's Three-Lines Theorem (1/6)
Reposted by Sayantan Sen
New podcast episode of "Probably Approximately Correct Learners," featuring guest Clément Canonne @ccanonne.github.io!
Check it out on Youtube, Spotify, Apple Podcasts, or wherever you get your podcasts. Subscribe so you don't miss out! (links in the next post) 1/2
Check it out on Youtube, Spotify, Apple Podcasts, or wherever you get your podcasts. Subscribe so you don't miss out! (links in the next post) 1/2
July 10, 2025 at 4:26 PM
New podcast episode of "Probably Approximately Correct Learners," featuring guest Clément Canonne @ccanonne.github.io!
Check it out on Youtube, Spotify, Apple Podcasts, or wherever you get your podcasts. Subscribe so you don't miss out! (links in the next post) 1/2
Check it out on Youtube, Spotify, Apple Podcasts, or wherever you get your podcasts. Subscribe so you don't miss out! (links in the next post) 1/2
Reposted by Sayantan Sen
Quantum Toolbox (7): Continuity of the von Neumann Entropy (1/6)
July 5, 2025 at 1:23 PM
Quantum Toolbox (7): Continuity of the von Neumann Entropy (1/6)
Reposted by Sayantan Sen
We are happy to share our work in classical distribution testing "Testing (Conditional) Mutual Information" (arxiv.org/abs/2506.03894), which was recently accepted at COLT 2025. (1/6)
Testing (Conditional) Mutual Information
We investigate the sample complexity of mutual information and conditional mutual information testing. For conditional mutual information testing, given access to independent samples of a triple of ra...
arxiv.org
June 13, 2025 at 1:04 PM
We are happy to share our work in classical distribution testing "Testing (Conditional) Mutual Information" (arxiv.org/abs/2506.03894), which was recently accepted at COLT 2025. (1/6)
Reposted by Sayantan Sen
Quantum Toolbox (6): Hoeffding's Inequality (1/7)
June 11, 2025 at 6:58 AM
Quantum Toolbox (6): Hoeffding's Inequality (1/7)
Reposted by Sayantan Sen
Quantum Toolbox (5): Cauchy-Schwarz Inequality (1/6)
June 6, 2025 at 8:15 AM
Quantum Toolbox (5): Cauchy-Schwarz Inequality (1/6)
Reposted by Sayantan Sen
Quantum state-agnostic work extraction (almost) without dissipation:
We are excited to share a new application of the multi-armed quantum bandit framework—this time in quantum thermodynamics!
We are excited to share a new application of the multi-armed quantum bandit framework—this time in quantum thermodynamics!
May 21, 2025 at 11:46 AM
Quantum state-agnostic work extraction (almost) without dissipation:
We are excited to share a new application of the multi-armed quantum bandit framework—this time in quantum thermodynamics!
We are excited to share a new application of the multi-armed quantum bandit framework—this time in quantum thermodynamics!
Reposted by Sayantan Sen
3. Data-Processing Inequality: bsky.app/profile/qit-...
Quantum Toolbox (3): Data-Processing Inequality (1/7)
May 9, 2025 at 2:30 AM
3. Data-Processing Inequality: bsky.app/profile/qit-...
Reposted by Sayantan Sen
Quantum Toolbox (2): Schur-Weyl Duality (1/6)
May 4, 2025 at 12:22 PM
Quantum Toolbox (2): Schur-Weyl Duality (1/6)
Reposted by Sayantan Sen
I wrote a post on how to connect with people (i.e., make friends) at CS conferences. These events can be intimidating so here's some suggestions on how to navigate them
I'm late for #ICLR2025 #NAACL2025, but in time for #AISTATS2025 #ICML2025! 1/3
kamathematics.wordpress.com/2025/05/01/t...
I'm late for #ICLR2025 #NAACL2025, but in time for #AISTATS2025 #ICML2025! 1/3
kamathematics.wordpress.com/2025/05/01/t...
Tips on How to Connect at Academic Conferences
I was a kinda awkward teenager. If you are a CS researcher reading this post, then chances are, you were too. How to navigate social situations and make friends is not always intuitive, and has to …
kamathematics.wordpress.com
May 1, 2025 at 12:57 PM
I wrote a post on how to connect with people (i.e., make friends) at CS conferences. These events can be intimidating so here's some suggestions on how to navigate them
I'm late for #ICLR2025 #NAACL2025, but in time for #AISTATS2025 #ICML2025! 1/3
kamathematics.wordpress.com/2025/05/01/t...
I'm late for #ICLR2025 #NAACL2025, but in time for #AISTATS2025 #ICML2025! 1/3
kamathematics.wordpress.com/2025/05/01/t...
Reposted by Sayantan Sen
Reminder/plug: my graduate-level monograph on "Topics and Techniques in Distribution Testing" (FnT Comm. and Inf Theory, 2022).
📖 ccanonne.github.io/survey-topic... [Latest draft+exercise solns, free]
📗 nowpublishers.com/article/Deta... [Official pub]
📝 github.com/ccanonne/sur... [LaTeX source]
📖 ccanonne.github.io/survey-topic... [Latest draft+exercise solns, free]
📗 nowpublishers.com/article/Deta... [Official pub]
📝 github.com/ccanonne/sur... [LaTeX source]
November 15, 2024 at 8:02 PM
Reminder/plug: my graduate-level monograph on "Topics and Techniques in Distribution Testing" (FnT Comm. and Inf Theory, 2022).
📖 ccanonne.github.io/survey-topic... [Latest draft+exercise solns, free]
📗 nowpublishers.com/article/Deta... [Official pub]
📝 github.com/ccanonne/sur... [LaTeX source]
📖 ccanonne.github.io/survey-topic... [Latest draft+exercise solns, free]
📗 nowpublishers.com/article/Deta... [Official pub]
📝 github.com/ccanonne/sur... [LaTeX source]
Reposted by Sayantan Sen
PSA: if you're part of the Theoretical Computer Science (TCS) community, student, postdoc, faculty, or industry or independent researcher: follow/bookmark the TCS Aggregator, theory.report!
Daily summary of papers, relevant announcements from a range of TCS blogs. 10/10, no notes. #TCSSky
Daily summary of papers, relevant announcements from a range of TCS blogs. 10/10, no notes. #TCSSky
Theory of Computing Report
theory.report
May 2, 2025 at 10:37 PM
PSA: if you're part of the Theoretical Computer Science (TCS) community, student, postdoc, faculty, or industry or independent researcher: follow/bookmark the TCS Aggregator, theory.report!
Daily summary of papers, relevant announcements from a range of TCS blogs. 10/10, no notes. #TCSSky
Daily summary of papers, relevant announcements from a range of TCS blogs. 10/10, no notes. #TCSSky
Reposted by Sayantan Sen
Quantum Toolbox (1): Jensen's Inequality (1/6)
April 24, 2025 at 9:35 AM
Quantum Toolbox (1): Jensen's Inequality (1/6)
Reposted by Sayantan Sen
Now in one place, my sixty favorite theorems covering the six decades of computational complexity.
blog.computationalco...
blog.computationalco...
Favorite Theorems: The Complete List
Now in one place all of my sixty favorite theorems from the six decades of computational complexity (1965-2024). 2015-2024 Graph Isomorphism...
blog.computationalcomplexity.org
December 4, 2024 at 2:07 PM
Now in one place, my sixty favorite theorems covering the six decades of computational complexity.
blog.computationalco...
blog.computationalco...
Reposted by Sayantan Sen
Oh look, our paper with Sayantan Sen (@sayantansen.bsky.social) and Joy Yang (to be presented by Sayantan at ITCS'25 in January) is up! The main result: a tight sample complexity lower bound for testing "grainedness" of probability distributions.
What is it?
eccc.weizmann.ac.il/report/2024/... 1/3
What is it?
eccc.weizmann.ac.il/report/2024/... 1/3
ECCC - TR24-196
eccc.weizmann.ac.il
December 3, 2024 at 5:08 AM
Oh look, our paper with Sayantan Sen (@sayantansen.bsky.social) and Joy Yang (to be presented by Sayantan at ITCS'25 in January) is up! The main result: a tight sample complexity lower bound for testing "grainedness" of probability distributions.
What is it?
eccc.weizmann.ac.il/report/2024/... 1/3
What is it?
eccc.weizmann.ac.il/report/2024/... 1/3
Reposted by Sayantan Sen
Recorded an extended version of my MFCS'24 invited talk. The talk presents my personal experiences in entering learning theory with a TCS background. The target audience is mostly TCS researchers. Hope some of you might enjoy it.
youtu.be/ZYe2mITwww4
youtu.be/ZYe2mITwww4
From Theoretical Computer Science to Learning Theory
YouTube video by Kasper Green Larsen
youtu.be
November 22, 2024 at 12:05 PM
Recorded an extended version of my MFCS'24 invited talk. The talk presents my personal experiences in entering learning theory with a TCS background. The target audience is mostly TCS researchers. Hope some of you might enjoy it.
youtu.be/ZYe2mITwww4
youtu.be/ZYe2mITwww4
Reposted by Sayantan Sen
Things you need as a PhD student:
- coffee ☕
- a living stipend 💰
- a website 🔗
For the last one, @kiragoldner.bsky.social has good resources: www.kiragoldner.com/blog/website..., www.kiragoldner.com/resources.html
- coffee ☕
- a living stipend 💰
- a website 🔗
For the last one, @kiragoldner.bsky.social has good resources: www.kiragoldner.com/blog/website..., www.kiragoldner.com/resources.html
Every Academic Needs a Website
www.kiragoldner.com
November 23, 2024 at 5:29 AM
Things you need as a PhD student:
- coffee ☕
- a living stipend 💰
- a website 🔗
For the last one, @kiragoldner.bsky.social has good resources: www.kiragoldner.com/blog/website..., www.kiragoldner.com/resources.html
- coffee ☕
- a living stipend 💰
- a website 🔗
For the last one, @kiragoldner.bsky.social has good resources: www.kiragoldner.com/blog/website..., www.kiragoldner.com/resources.html