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Flatiron Institute

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Selected work

Representative Papers

Linear space streaming lower bounds for approximating CSPs

Jun 24, 2021Electron. Colloquium Comput. Complex.

This work investigates the approximability threshold of constraint satisfaction problems (CSPs) in the streaming model. For $n$-variable CSPs over domain ${0,dots,q-1}$ with $O(n)$ constraints, we prove that any algorithm achieving approximation ratio strictly better than the trivial $1/q$ requires $Omega(n)$ space—establishing the first linear-space lower bound for approximation ratios below $1/2$. Methodologically, we extend the Kapralov–Krachun linear lower-bound technique to general CSPs (surpassing prior $Omega(sqrt{n})$ bounds) via modular-$q$ linear equation encoding, communication complexity analysis, and pseudorandom hard-instance reduction. This yields optimal $q^{-(k-1)}$ inapproximability for Max $k$-LIN mod $q$ with $k>2$, $q>2$. Our results uniformly characterize the streaming hardness of broad CSP subclasses: all nontrivial approximation requires essentially linear space, significantly advancing the theoretical understanding of streaming algorithm limitations.

15 citationsRead paper

Toward Task Capable Active Matter: Learning to Avoid Clogging in Confined Collectives via Collisions

Jun 09, 2022Frontiers of Physics

In high-density confined environments, active matter systems—such as social insect colonies or microrobot swarms—frequently suffer from traffic jams that impede functional flow and task performance. Method: We propose a decentralized congestion-avoidance mechanism relying solely on local collision sensing and simple online learning rules. Using a robophysical experimental platform, we implement robot swarms cooperatively transporting granular loads through narrow tunnels, incorporating noisy tunnel-length estimation, collision-driven probabilistic behavioral modeling, and dynamic strategy updates—including adaptive direction reversal and load-distribution modulation. Contribution/Results: For the first time, we experimentally demonstrate that purely local, collision-based learning dynamics spontaneously induce task differentiation, load redistribution, and periodic directional reversals—without global sensing or centralized coordination. Congestion events decrease by over 70%, and transport efficiency significantly improves. This validates the efficacy and broad applicability of low-complexity learning rules for achieving self-organized functional adaptation in dense active matter systems.

5 citationsRead paper

How many simulations do we need for simulation-based inference in cosmology?

Mar 17, 2025

This study addresses the critical question of the minimum simulation size required for machine learning–based cosmological parameter inference, focusing on information extraction efficiency from summary statistics such as the dark matter power spectrum. We propose and empirically validate an empirical scaling law relating neural network information extraction capacity to the number of training simulations, and combine it with Cramér–Rao bound analysis to quantitatively predict the near-optimal simulation budget. Our methodology integrates neural network training analysis, information-theoretic bound estimation, large-scale N-body simulation generation using Sobol sequences (the BSQ dataset comprises 32,768 ΛCDM simulations), and empirical convergence studies. Results show that current mainstream simulation suites—e.g., Quijote LH (~2,000 realizations)—are vastly insufficient for optimal inference. The derived scaling law enables principled, resource-efficient allocation of simulation effort and establishes the first quantifiable, generalizable sample complexity benchmark for simulation-based cosmological inference.

2 citationsRead paper

Adjoint Matching through the Lens of the Stochastic Maximum Principle in Optimal Control

Mar 28, 2026arXiv.org

This work addresses the challenge of reward fine-tuning in diffusion models and Boltzmann distribution sampling by formulating generative model optimization as a stochastic optimal control problem governed by stochastic differential equations. Leveraging the Stochastic Maximum Principle (SMP), the paper rigorously derives, for the first time, a general Hamiltonian adjoint matching objective applicable to settings where both drift and diffusion coefficients depend on the control, and establishes its intrinsic connection to the Hamilton–Jacobi–Bellman (HJB) equation. By integrating the adjoint system with a continuous-time successive approximation algorithm, the method recovers the lightweight adjoint loss when the diffusion coefficient is state-independent, validates the necessity of higher-order terms in state-dependent cases, and provides a tractable iterative scheme based on SMP that circumvents intractable martingale terms.

1 citationsRead paper

Boltzmann Generators for Condensed Matter via Riemannian Flow Matching

Feb 10, 2026

This work addresses the challenges of inefficient equilibrium sampling and inaccurate free energy estimation in condensed-phase systems by proposing a continuous normalizing flow method that incorporates periodic structural constraints. The approach constructs a Boltzmann generator via Riemannian flow matching—a technique applied here for the first time to condensed-phase systems—and integrates Hutchinson’s stochastic trace estimator with a cumulant-expansion-based bias correction scheme to enable thermodynamically consistent and efficient reweighting. Demonstrated on a monoatomic water model, the method successfully trains the largest generative model to date for such systems and achieves high-accuracy free energies without requiring multi-stage estimation protocols.

1 citationsRead paper
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