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Ankur Moitra

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Debate: Sparks versus embersUnknown Futures of Generalization 20242024-12-02
Motion: whether current LLM scaling plus realistic post-training can produce new proof techniques to settle problems like P≠NP. Panelists present concrete…
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Learning from DynamicsJoint IFML/MPG Symposium 20242024-11-19
Given one long input-output trajectory, the paper proves polynomial-time parameter recovery for linear dynamical systems under marginal stability plus bounded…
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When do dependencies in your data help?Emerging Generalization Settings 20242024-09-09
Assumes samples come from Glauber dynamics and proves bounded‑degree k‑wise Markov random fields are learnable in roughly n^2 log n time from a single n log n…
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How Do Transformers Work?Special Year on Large Language Models and Transformers, Part 1 Boot Camp2024-09-04
Explains transformers as an encoder–decoder stack that replaces huge n‑gram parameter blowups (V^4 for a 4‑gram) with learned vector word embeddings (hundreds…
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Learning Restricted Boltzman MachinesAlgorithmic Aspects of Causal Inference 20222022-03-18
Proves bounded‑degree RBMs exactly capture order‑T binary Markov random fields, giving a sharp representational characterization; shows improper learning of…
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Recent Progress in High-Dimensional LearningProbability, Geometry, and Computation in High Dimensions Boot Camp (Simons Institute, Fall 2020)2020-08-19
Argues that low‑rank tensor decompositions uniquely recover latent factors under mild linear‑independence conditions and gives an explicit spectral method…
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Recent Progress in High-Dimensional LearningProbability, Geometry, and Computation in High Dimensions Boot Camp (Simons Institute, Fall 2020)2020-08-19
1D robust estimation uses the median absolute deviation to get O(ε) TV guarantees, but high dimensions face hardness: the Tukey median is robust but NP‑hard…
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Recent Progress in High-Dimensional LearningProbability, Geometry, and Computation in High Dimensions Boot Camp (Simons Institute, Fall 2020)2020-08-19
Shows polynomial‑time algorithms that learn half‑spaces under Massart noise up to error η+ε, first via an improper partitioned classifier and now via a proper…
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Recent Progress in High-Dimensional LearningProbability, Geometry, and Computation in High Dimensions Boot Camp (Simons Institute, Fall 2020)2020-08-19
Provable algorithms reconstruct mixtures of Airy disks from photon samples: for any fixed K a polynomial-time algorithm recovers centers to accuracy ε given…
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LP/SDP Hierarchies and Sum of Squares Proofs 1Bridging Continuous and Discrete Optimization Boot Camp 20172017-08-21
Explains that nonnegativity checks reduce to semidefinite programming by writing a polynomial as a quadratic form over a chosen monomial basis and searching…
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LP/SDP Hierarchies and Sum of Squares Proofs 2Bridging Continuous and Discrete Optimization Boot Camp 20172017-08-21
Real infeasibility certificates appear as an f + g = -1 certificate with f in the ideal of equations and g in the cone generated by inequalities; bounding the…
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LP/SDP Hierarchies and Sum of Squares Proofs 3Bridging Continuous and Discrete Optimization Boot Camp 20172017-08-21
Part three shows an SOS/SDP proof that a triangle-free graph has at most asymptotically half the possible edges (an SOS version of Mantel’s theorem), by…
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LP/SDP Hierarchies and Sum of Squares Proofs 4Bridging Continuous and Discrete Optimization Boot Camp 20172017-08-21
Presents a concrete SOS-based algorithm: a quasi-polynomial time N^{O(log N / ε^2)} method that approximates the max of a degree‑4 polynomial (M defined as…
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Above Average-Case Analysis?Learning, Algorithm Design and Beyond Worst-Case Analysis2016-11-14
Claims a polynomial-time procedure that, under an adversary who corrupts an ε fraction of samples (or distributions ε-close in total variation), recovers mean…
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Planted Clique, Sum-of-Squares and Pseudo-CalibrationRandom Instances and Phase Transitions (Simons Institute, 2016)2016-05-02
Shows that level-D Sum-of-Squares cannot rule out planted cliques much below √n: the integrality gap is ≥ n^{1/2 - O(√D / log n)} for D = o(log n), so any SOS…
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Extended Formulations and Information ComplexityInformation Theory in Complexity Theory and Combinatorics 20152015-04-24
Defines non-negative rank of the slack matrix and uses an entropy sampling reduction to show any factorization with R terms would let one sample a size-3^n…
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Simple, Efficient and Neural Algorithms for Sparse CodingInformation Theory, Learning and Big Data (Simons Institute, 2015)2015-03-16
Proposes a simple online, local, Hebbian algorithm that decodes by multiplying by the current dictionary transpose and hard‑thresholding and then updates via…
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A Polynomial Time Algorithm for Lossy Population RecoverySemidefinite Optimization, Approximation and Applications 20142014-09-24
Proves a polynomial time algorithm for lossy population recovery for any fixed mu>0, showing recovery even when only ~1% of bits survive. Turns the problem…
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