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Published equation contexts

Pbypass=∏i=1npiP_{\mathrm{bypass}} = \prod_{i=1}^{n} p_i

Why this formula appears here

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 pip_i . It is tempting to write the bypass probability of the stack as Pbypass=∏i=1npiP_{\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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PbypassP_{\mathrm{bypass}}

Symbol P_bypass

PbP_bypass is part of the quantity the equation computes from the expression on the right.

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ii

Symbol i

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

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nn

Symbol n

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

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i=1i=1

Starting index or lower bound: i=1

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.

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nn

Ending index or upper bound: n

This label says where the repeated addition, multiplication, or accumulation stops. It sets the last term or end of the range.

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Published contexts (1)

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

Equation 3 · AI Security

The Attack Surface That Reads

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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 pip_i . It is tempting to write the bypass probability of the stack as Pbypass=∏i=1npiP_{\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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