# ![@yangpliu Avatar](https://lunarcrush.com/gi/w:26/cr:twitter::1164770512985214991.png) @yangpliu Yang Liu

Yang Liu posts on X about in the, light, thread, ai the most. They currently have [---] followers and [--] posts still getting attention that total [------] engagements in the last [--] hours.

### Engagements: [------] [#](/creator/twitter::1164770512985214991/interactions)
![Engagements Line Chart](https://lunarcrush.com/gi/w:600/cr:twitter::1164770512985214991/c:line/m:interactions.svg)

- [--] Year [------] +11,265%

### Mentions: [--] [#](/creator/twitter::1164770512985214991/posts_active)
![Mentions Line Chart](https://lunarcrush.com/gi/w:600/cr:twitter::1164770512985214991/c:line/m:posts_active.svg)


### Followers: [---] [#](/creator/twitter::1164770512985214991/followers)
![Followers Line Chart](https://lunarcrush.com/gi/w:600/cr:twitter::1164770512985214991/c:line/m:followers.svg)

- [--] Year [---] +127%

### CreatorRank: [-------] [#](/creator/twitter::1164770512985214991/influencer_rank)
![CreatorRank Line Chart](https://lunarcrush.com/gi/w:600/cr:twitter::1164770512985214991/c:line/m:influencer_rank.svg)

### Social Influence

**Social category influence**
[technology brands](/list/technology-brands) 

**Social topic influence**
[in the](/topic/in-the) #5935, [light](/topic/light) #918, [thread](/topic/thread) #89, [ai](/topic/ai) #3334, [feels](/topic/feels) #252, [open ai](/topic/open-ai), [polymath](/topic/polymath), [safely](/topic/safely) #600, [key](/topic/key) #2346, [background](/topic/background)

**Top accounts mentioned or mentioned by**
[@tfwnicholson](/creator/undefined) [@sushnt](/creator/undefined) [@overtheplaces](/creator/undefined) [@john07331405](/creator/undefined) [@dhuritwits](/creator/undefined) [@puneeshdeora](/creator/undefined) [@dayshuai](/creator/undefined) [@littmath](/creator/undefined)

**Top assets mentioned**
[Polymath (POLY)](/topic/polymath)
### Top Social Posts
Top posts by engagements in the last [--] hours

"This question asks to prove that for fixed c [--] that for all sufficiently large N that a subset S of 012N of size c * 3N contains a combinatorial line. That is xyz in S so that (x_iy_iz_i) = (000) (111) (222) or (012) for all i = [--] . n"  
[X Link](https://x.com/yangpliu/status/1860533037123219552)  2024-11-24T03:56Z [---] followers, [---] engagements


"This was the topic of the first Polymath project which proved this for N which is at least a tower of exponentials of height 1/c2. We improve this bound to N = 2222(1/cO(1)). https://arxiv.org/abs/0910.3926 https://arxiv.org/abs/0910.3926"  
[X Link](https://x.com/yangpliu/status/1860533085592584592)  2024-11-24T03:57Z [---] followers, [---] engagements


"This project builds on a recent line of work of Amey Subhash and Dor on optimal approximability of satisfiable CSP instances. In the new preprints we prove an inverse theorem for 3-wise correlations and combine this the Polymath proof and Shkredov's ingenuous corners bound"  
[X Link](https://x.com/yangpliu/status/1860533153494106194)  2024-11-24T03:57Z [---] followers, [---] engagements


"@TFWNicholson Yes it should be the pseudoinverse. If the graph is connected (for these problems this can be assumed without loss of generality) the only vector in the nullspace is (1 [--] . 1) so it's easy to get a handle on the pseudoinverse"  
[X Link](https://x.com/yangpliu/status/2022831329654562903)  2026-02-15T00:32Z [---] followers, [--] engagements


"2/ Background: For a graph G with n vertices and m edges the Laplacian is L = D A where D is the diagonal degree matrix and A is the adjacency matrix. Another viewpoint: L = sum_e b(e) b(e)T where for an edge e = (u v) b(e) is the n-dim vector with +1 at u [--] at v and [--] elsewhere. Many arguments work even when the b(e)s are general vectors"  
[X Link](https://x.com/yangpliu/status/2022745944102683090)  2026-02-14T18:53Z [---] followers, [----] engagements


"5/ Restricted invertibility: instead of reweighting many terms we select a subset S of vectors (S = n n). Let L_S = sum_e in S b(e) b(e)T and M_S = L1/2 L_S L1/2. Goal: make the smallest nonzero eigenvalue of M_S as large as possible. A much simpler proof and improved bound was given by Spielman and Srivastava. (arXiv:0911.1114) Both this and the BSS bound for sparsification use the same barrier potential method"  
[X Link](https://x.com/yangpliu/status/2022745949710459124)  2026-02-14T18:53Z [---] followers, [----] engagements


"6/ The barrier method idea (restricted invertibility case): start with S = empty so M_S = [--]. Track a potential like Phi(S) = Tr((M_S b I)1) to analyze the evolution of an algorithm which adds elements to S one by one. Each step: decrease b a bit and add one element to S keeping Phi from blowing up. The technical work: analyze how Phi changes under adding one rank-one term using ShermanMorrison (rank-one inverse update). These kinds of barrier functions have later been used towards the Kadison-Singer problem (1306.3969) and in other discrepancy theory problems (An Improved Bound for the"  
[X Link](https://x.com/yangpliu/status/2022745951715140073)  2026-02-14T18:53Z [---] followers, [----] engagements


"7/ 1stProof Problem 6: very similar setup to restricted invertibility but now were selecting vertices. We want a vertex set S so that if L_S := sum_e with both endpoints in S b(e) b(e)T and M_S := L1/2 L_S L1/2 that the max eigenvalue of M_S to be . Again you can set up a barrier potential e.g. Phi(S) = Tr(( I M_S)1). Iterate: each time add a vertex to S and increase as needed so that Phi does not increase. https://twitter.com/i/web/status/2022745953699324027 https://twitter.com/i/web/status/2022745953699324027"  
[X Link](https://x.com/yangpliu/status/2022745953699324027)  2026-02-14T18:53Z [---] followers, [----] engagements


"9/ Official solution: it maintains an additional property that the total leverage score of S (a spectral notion of accumulated importance/mass) stays bounded. This blocks the bad scenario where S becomes too heavy too quickly. In the screenshot below ell(S) is the total leverage score of S: as you can see the algorithm maintains that the total leverage score only increases by [--] for each new vertex insertion. https://twitter.com/i/web/status/2022745959248335042 https://twitter.com/i/web/status/2022745959248335042"  
[X Link](https://x.com/yangpliu/status/2022745959248335042)  2026-02-14T18:53Z [---] followers, [----] engagements


"10/ OpenAI solution: it maintains r 1/ different sets S_1 S_r whose total size eventually is a constant fraction of n. The solution proves that you can always find one of the sets to add a new vertex to without increasing the potential: this makes sense because on average some set should be light. In the screenshots below M_t is the sum of Laplacians of each color class and as you can see the solution maintains a barrier function over M_t and does not need to maintain any property of the leverage scores of S. https://twitter.com/i/web/status/2022745962595197144"  
[X Link](https://x.com/anyuser/status/2022745962595197144)  2026-02-14T18:53Z [---] followers, [----] engagements


"Just for intuition: the official proof informally says that as long as a set does not have too much "mass" on its neighboring edges then it's possible to add a new vertex to it. So if I have many sets then by an averaging argument one of them must have less mass than average so we can safely add a vertex to it. https://twitter.com/i/web/status/2022831851350442442 https://twitter.com/i/web/status/2022831851350442442"  
[X Link](https://x.com/yangpliu/status/2022831851350442442)  2026-02-15T00:34Z [---] followers, [--] engagements


"My thoughts on #1stProof Problem [--] (closely related to areas I've worked in): OpenAIs solution is essentially correct and the difficulty feels consistent with AI capabilities over the past several months. More detail in the thread"  
[X Link](https://x.com/anyuser/status/2022690162220716327)  2026-02-14T15:11Z [---] followers, 65.5K engagements


"1/ Technical thread on #1stProof Problem 6: finding spectrally light vertex subsets in a graph and how its solution fits into the landscape of spectral sparsification + restricted invertibility. Original thread: https://x.com/yangpliu/status/2022690162220716327 My thoughts on #1stProof Problem [--] (closely related to areas I've worked in): OpenAIs solution is essentially correct and the difficulty feels consistent with AI capabilities over the past several months. More detail in the thread. https://x.com/yangpliu/status/2022690162220716327 My thoughts on #1stProof Problem [--] (closely related to"  
[X Link](https://x.com/anyuser/status/2022745942047244708)  2026-02-14T18:53Z [---] followers, 34K engagements


"3/ This suggests a meta-question: can we approximate L using far fewer rank-one terms while preserving spectral structure Two natural/famous directions: (1) Spectral sparsification and (2) Restricted invertibility. Beyond being natural sparsification has several algorithmic applications because it can reduce computations on a dense graph to that on a sparse graph. For example it was a key component of the near-linear time algorithms for solving Laplacian linear systems of Spielman-Teng (0808.4134 0607105). Solving a Laplacian system encompasses the fundamental problems of: (1) Compute"  
[X Link](https://x.com/yangpliu/status/2022745946115768655)  2026-02-14T18:53Z [---] followers, [----] engagements


"8/ Everything above is fairly standard to experts but Problem [--] has a key subtlety: unlike the edge-selection/restricted-invertibility setting without additional properties of S its not always true that a new vertex can be safely added to S while keeping the potential small. For example if the current set S has many neighboring edges that leave S then adding one more vertex can create many new inside S edges at once which causes M_S and thus Phi to increase too much. So you need some extra property to get around this. https://twitter.com/i/web/status/2022745956278476862"  
[X Link](https://x.com/yangpliu/status/2022745956278476862)  2026-02-14T18:53Z [---] followers, [----] engagements


"@sushnt Yes good point. I realized later that each subset being light is not equivalent to the sum being light (even if they're vertex disjoint)"  
[X Link](https://x.com/yangpliu/status/2022833281633296506)  2026-02-15T00:40Z [---] followers, [---] engagements


"My thoughts on #1stProof Problem [--] (closely related to areas I've worked in): OpenAIs solution is essentially correct and the difficulty feels consistent with AI capabilities over the past several months. More detail in the thread"  
[X Link](https://x.com/anyuser/status/2022690162220716327)  2026-02-14T15:11Z [---] followers, 65.5K engagements


"Still Im genuinely impressed by how far AI-for-math has come in the past few years and Im excited to see whats next. If people want Im happy to write up more about the problem the solution and how it fits in the context of prior results"  
[X Link](https://x.com/anyuser/status/2022690165869940967)  2026-02-14T15:11Z [---] followers, 12.1K engagements


"Technical thread here: https://x.com/yangpliu/status/2022745942047244708s=20 1/ Technical thread on #1stProof Problem 6: finding spectrally light vertex subsets in a graph and how its solution fits into the landscape of spectral sparsification + restricted invertibility. Original thread: https://t.co/c9Z9RH2Ont https://x.com/yangpliu/status/2022745942047244708s=20 1/ Technical thread on #1stProof Problem 6: finding spectrally light vertex subsets in a graph and how its solution fits into the landscape of spectral sparsification + restricted invertibility. Original thread:"  
[X Link](https://x.com/anyuser/status/2022747334975840425)  2026-02-14T18:58Z [---] followers, [----] engagements


"1/ Technical thread on #1stProof Problem 6: finding spectrally light vertex subsets in a graph and how its solution fits into the landscape of spectral sparsification + restricted invertibility. Original thread: https://x.com/yangpliu/status/2022690162220716327 My thoughts on #1stProof Problem [--] (closely related to areas I've worked in): OpenAIs solution is essentially correct and the difficulty feels consistent with AI capabilities over the past several months. More detail in the thread. https://x.com/yangpliu/status/2022690162220716327 My thoughts on #1stProof Problem [--] (closely related to"  
[X Link](https://x.com/anyuser/status/2022745942047244708)  2026-02-14T18:53Z [---] followers, 34K engagements


"10/ OpenAI solution: it maintains r 1/ different sets S_1 S_r whose total size eventually is a constant fraction of n. The solution proves that you can always find one of the sets to add a new vertex to without increasing the potential: this makes sense because on average some set should be light. In the screenshots below M_t is the sum of Laplacians of each color class and as you can see the solution maintains a barrier function over M_t and does not need to maintain any property of the leverage scores of S. https://twitter.com/i/web/status/2022745962595197144"  
[X Link](https://x.com/anyuser/status/2022745962595197144)  2026-02-14T18:53Z [---] followers, [----] engagements


"End/ Overall Comparison: In my opinion the problem and solution cleanly fall within the scope of previous methods but one does have to nontrivially adapt the method to handle the subtlety described above. In terms of comparing the solutions both give equally clean fixes to the issue. Worth noting that the OpenAI solution proves something slightly stronger than is asked by the problem statement: if proves that a constant fraction of the vertices can be partitioned into O(1/) groups so that the induced Laplacian on every group is spectrally at most *L while the problem only asks for a single"  
[X Link](https://x.com/anyuser/status/2022745964898087350)  2026-02-14T18:53Z [---] followers, [----] engagements


"In a sequence of new preprints with Amey Bhangale Subhash Khot and Dor Minzer we obtain improved bounds for the density Hales-Jewett (DHJ) problem for combinatorial lines of length 3"  
[X Link](https://x.com/anyuser/status/1860532960463847589)  2024-11-24T03:56Z [---] followers, [----] engagements


"Despite building on prior work the papers are self-contained. (1) (2) (3) Some notes for anyone adventurous enough to read: https://eccc.weizmann.ac.il/report/2024/193/ https://eccc.weizmann.ac.il/report/2024/192/ https://eccc.weizmann.ac.il/report/2024/191/ https://eccc.weizmann.ac.il/report/2024/193/ https://eccc.weizmann.ac.il/report/2024/192/ https://eccc.weizmann.ac.il/report/2024/191/"  
[X Link](https://x.com/anyuser/status/1860533187782541623)  2024-11-24T03:57Z [---] followers, [----] engagements


"A. (3) uses Theorem [--] from (1) + Lemma [---] from (2). B. Theorem [--] from (1) is the 3-CSP inverse theorem which is a generalization of the U2-Gowers inverse theorem. The proof is in Sections 1-5. C. Lemma [---] from (2) is a quick extension of Theorem [--] to some 4-ary distributions"  
[X Link](https://x.com/anyuser/status/1860533255164022947)  2024-11-24T03:57Z [---] followers, [---] engagements

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