Equation 3 · Part 8 · The Attack Surface That Reads

Starting index or lower bound: i=1

P_{\mathrm{bypass}} = \prod_{i=1}^{n} p_i,

i=1

What this part means

This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.

Its job in the formula

i=1 appears in the bound of this product. The bound states where the repeated operation starts, ends, or which values it includes.

Full expressionStarting index or lower bound: i=1Article meaning

The passage around this formula

Here is the modelling error to avoid. Suppose a request passes n independent detection layers, each of which fails to catch a given malicious input with probability $p_i$ . It is tempting to write the bypass probability of the stack as $P_{\mathrm{bypass}} = \prod_{i=1}^{n} p_i$ . and conclude that four layers at ten percent leakage each give one bypass in ten thousand. That number is an artefact of the independence assumption, and the assumption is the weakest part of the model. The layers are typically built from the same model family, trained on overlapping data, and sensitive to the same features of an input; their failures are positively correlated, so the true joint failure probability is larger than the…

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Learn the underlying idea

Σ adds a collection of terms. Π multiplies them. The lower and upper labels tell you which terms belong to the collection.

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Sources cited in the article section

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