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Equation 1 · Part 12 · Every Test Changed the Scene and Kept the Chair Red

Numerator: 1

dx(t)dt=−[1τ+f(x(t),I(t),t,θ)]⊙x(t)+f(x(t),I(t),t,θ)⊙A,\frac{d\mathbf{x}(t)}{dt} = -\left[\frac{1}{\tau} + f(\mathbf{x}(t),\mathbf{I}(t),t,\theta)\right]\odot \mathbf{x}(t) + f(\mathbf{x}(t),\mathbf{I}(t),t,\theta)\odot A ,
11

What this part means

The complete quantity above the fraction bar.

Its job in the formula

1 occurs above the fraction bar. The numerator is divided by the entire denominator below it.

The passage around this formula

…a model class : an LTC network, described by the ordinary differential equation the paper reproduces as dx(t)dt=−[1τ+f(x(t),I(t),t,θ)]⊙x(t)+f(x(t),I(t),t,θ)⊙A\frac{d\mathbf{x}(t)}{dt} = -\left[\frac{1}{\tau} + f(\mathbf{x}(t),\mathbf{I}(t),t,\theta)\right]\odot \mathbf{x}(t) + f(\mathbf{x}(t),\mathbf{I}(t),t,\theta)\odot A . reduces to a DCM whenever its learned function f satisfies three stated analytic conditions [ 1 , 2 ] . That is a real theorem about the architecture’s dynamical form, established independently of this drone task, and nothing in this article disputes it. What it does not supply, on its own, is a certificate that the specific f this paper’s networks actually learned from confounded pixel…

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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

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Sources cited in the surrounding passage

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