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Consider the differential equation with phase state $M$
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Consider the differential equation with phase state $M$
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What is the difference between Hypothesis Testing and Classification?
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Economical Ideas.
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Let us first recall some classical result on random matrix.
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Mixing.
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Some quantum mechanical calculation.
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Statistical watermark leverage the psuedorandomness during decoding.
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Consider the general constrained optimization problem (P) shown below, where we have not assumed anything regarding
the functions $f$, $h$, $l$ (like convexity).
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Under certain conditions the evolution of a quantum system interacting with its environment can be described by a quantum dynamical semigroup and shown to satisfy a Lindblad master equation
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Denote
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metric entropy, chaining…
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RLHF (Reinforcement Learning from Human Feedback) has been the dominant technique to align an intelligent agent to human preferences.
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lexing’s paper
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How to derive an estimate better than Gronwall’s inequality?
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Hypocoercivity is a mathematical concept used to describe the behavior of certain dynamical systems and partial differential equations (PDEs) that do not exhibit traditional coercivity properties but still exhibit convergence to equilibrium over time.
In the study of kinetic equations and systems where traditional coercive methods (like those used in parabolic PDEs) do not apply, we may resort to hypocoercivity.
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Deriving the asymptotics
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In this article, I breifly introduce some current methods of estimating the tail of a heavy tail distributions.
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The spectral representation of a stationary process ${X_t}$ essentially decomposes ${X_t}$ into a sum of sinusoidal components with uncorrelated random coefficients. This is an analogue of the more familiar Fourier representation of deterministic functions.
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In this article, I breifly explain the idea of Le Cam methods.
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In this article, I breifly explain the idea of double machine learning.
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In this article, I breifly explain the theory of Koopman Operator.
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In this article, I breifly review the theory of point estimation.
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In this article, I recap the classical gradient descent analysis.
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In this article, we explain the Neural Tangent Kernel.
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In this article, we explain the PAC-Bayesian generalization bound.
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In this article, we first recall the basic postulates of quantum computing.
Then we mainly focus on the mathematical structures behind it.
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One notable difference between traditional machine learning algorithms and deep learning is that in deep learning, the features are learnable and can be interpreted.
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We can leverage symmetry.
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In this article, I describe $C^*$-algebra, complete positive map, and its relationship to quantum mechanics.
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Circuit complexity is a measure of how hard it is to express or compute a boolean function.
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Communication complexity was first introduced by Andrew Yao in 1973,
while studying the problem of computation distributed among several machines.
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Let us first recall how to reverse a classical diffusion process.
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In this series I try to imagine and examine the great figures in the history as researchers. The goal is not to diefy anyone, but to examine great figures in the history and to inspire researchers today.
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This is how I understand research.
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This article records some of my proofs in plane geometry.
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This article records some problems in plane geometry that I, my friend Yonggang Ren, and my middle school teacher Lingfeng Chen have discovered.
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This article records some solutions of a problem in plane geometry that I discovered.