All reports by Author Ankit Garg:

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TR22-151
| 12th November 2022
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Prashanth Amireddy, Ankit Garg, Neeraj Kayal, Chandan Saha, Bhargav Thankey#### Low-depth arithmetic circuit lower bounds via shifted partials

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TR20-045
| 15th April 2020
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Ankit Garg, Neeraj Kayal, Chandan Saha#### Learning sums of powers of low-degree polynomials in the non-degenerate case

Revisions: 1

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TR19-042
| 18th March 2019
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Ankit Garg, Nikhil Gupta, Neeraj Kayal, Chandan Saha#### Determinant equivalence test over finite fields and over $\mathbf{Q}$

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TR18-151
| 29th August 2018
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Ankit Garg, Rafael Oliveira#### Recent progress on scaling algorithms and applications

Prashanth Amireddy, Ankit Garg, Neeraj Kayal, Chandan Saha, Bhargav Thankey

We prove super-polynomial lower bounds for low-depth arithmetic circuits using the shifted partials measure [Gupta-Kamath-Kayal-Saptharishi, CCC 2013], [Kayal, ECCC 2012] and the affine projections of partials measure [Garg-Kayal-Saha, FOCS 2020], [Kayal-Nair-Saha, STACS 2016]. The recent breakthrough work of Limaye, Srinivasan and Tavenas [FOCS 2021] proved these lower bounds by proving ... more >>>

Ankit Garg, Neeraj Kayal, Chandan Saha

We develop algorithms for writing a polynomial as sums of powers of low degree polynomials. Consider an $n$-variate degree-$d$ polynomial $f$ which can be written as

$$f = c_1Q_1^{m} + \ldots + c_s Q_s^{m},$$

where each $c_i\in \mathbb{F}^{\times}$, $Q_i$ is a homogeneous polynomial of degree $t$, and $t m = ...
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Ankit Garg, Nikhil Gupta, Neeraj Kayal, Chandan Saha

The determinant polynomial $Det_n(\mathbf{x})$ of degree $n$ is the determinant of a $n \times n$ matrix of formal variables. A polynomial $f$ is equivalent to $Det_n$ over a field $\mathbf{F}$ if there exists a $A \in GL(n^2,\mathbf{F})$ such that $f = Det_n(A \cdot \mathbf{x})$. Determinant equivalence test over $\mathbf{F}$ is ... more >>>

Ankit Garg, Rafael Oliveira

Scaling problems have a rich and diverse history, and thereby have found numerous

applications in several fields of science and engineering. For instance, the matrix scaling problem

has had applications ranging from theoretical computer science to telephone forecasting,

economics, statistics, optimization, among many other fields. Recently, a generalization of matrix

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