Symbol in context

$f$

This entry links every published equation using this exact notation. Its meaning may change between equations.

Meanings in context

Article-grounded definition

Symbol f

the sampling rate.

Read equation 7 in What Multimodal AI Actually Costs, Modality by Modality →

Article-grounded definition

Symbol f

the frequency of query term $q_i$ in D , |D| is the document’s length, $\mathrm{avgdl}$ is the average document length in the collection, and $k_1$ .

Read equation 8 in From BM25 to Agentic Retrieval: A History of Retrieval-Augmented Generation →

Article-grounded definition

Symbol f

the nameplate capacity c and capacity factor.

Read equation 5 in Power Density and What It Permits →

Article-grounded definition

Symbol f

the frequency.

Read equation 4 in Why the Physical World Is Harder →

Used in 71 equations

\forall\, x \in B_\epsilon(x_0): \quad f(x) \in S,

Comparing the Main Approaches to AI and Cybersecurity · Equation 5

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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P = f(\mathbf{s}; \theta)

How Materials Discovery and Degradation Actually Work · Equation 1

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

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f

How Materials Discovery and Degradation Actually Work · Equation 8

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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f(x,y) = (296+x/4)(264+0.275y)

The EV Formula Is an Exact Production Function Trainers Solved by Accident · Equation 15

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

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y = f(x_1, x_2, \ldots, x_N)

How Scientific Instruments and Metrology Actually Work · Equation 3

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

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u_c^2(y) = \sum_{i=1}^{N} \left(\frac{\partial f}{\partial x_i}\right)^2 u^2(x_i) \;+\; 2\sum_{i=1}^{N-1}\sum_{j=i+1}^{N} \frac{\partial f}{\partial x_i}\frac{\partial f}{\partial x_j}\, u(x_i, x_j)

How Scientific Instruments and Metrology Actually Work · Equation 4

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

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\hat{f}(x) = f(x) + \varepsilon_{\text{disc}}(h) + \varepsilon_{\text{round}}(u) + \varepsilon_{\text{model}}

Comparing the Main Approaches to Mathematics, Proof, and Scientific Computation · Equation 1

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

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f(x)

Comparing the Main Approaches to Mathematics, Proof, and Scientific Computation · Equation 2

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

Equation guide → · This term → · Article →

f(x)

Comparing the Main Approaches to Mathematics, Proof, and Scientific Computation · Equation 5

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

Equation guide → · This term → · Article →

y = f(x_1, x_2, \ldots, x_N)

Comparing the Main Approaches to Scientific Instruments and Metrology · Equation 3

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

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u_c^2(y) = \sum_{i=1}^{N} \left( \frac{\partial f}{\partial x_i} \right)^2 u^2(x_i)

Comparing the Main Approaches to Scientific Instruments and Metrology · Equation 4

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

Equation guide → · This term → · Article →

f(x,t)

Einstein's Random Walk and the Mathematics of Genetic Drift · Equation 1

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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\frac{\partial f(x,t)}{\partial t} = D\,\frac{\partial^{2} f(x,t)}{\partial x^{2}}

Einstein's Random Walk and the Mathematics of Genetic Drift · Equation 2

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

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\frac{\partial f(x,t)}{\partial t} = D\,\frac{\partial^{2} f(x,t)}{\partial x^{2}} \qquad \text{(Einstein, 1905)}

Einstein's Random Walk and the Mathematics of Genetic Drift · Equation 20

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

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f

Human Evolution Did Not Stop, and Medicine Is Now Steering It · Equation 7

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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s = f(\theta, H)

What Open Weights Actually Let You Verify · Equation 1

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

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f(\theta, H) = f(\theta', H')

What Open Weights Actually Let You Verify · Equation 6

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

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N_{\mathrm{tok}}(\mathrm{video}) = t \left( f \cdot \tau_{\mathrm{frame}} + \tau_{\mathrm{audio}} \right),

What Multimodal AI Actually Costs, Modality by Modality · Equation 7

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

Equation guide → · This term → · Article →

f

What Multimodal AI Actually Costs, Modality by Modality · Equation 9

the sampling rate.

Equation guide → · This term → · Article →

\mathcal{L}(x) = \lVert x - \hat{x}(x) \rVert_2^2 + \lambda \lVert f(x) \rVert_1, \qquad \hat{x}(x) = W_d\, f(x) + b_d,

What Interpretability Actually Costs to Do at Scale · Equation 5

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

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c_{\text{video}} \approx (f \times \tau_{\text{frame}}) + \tau_{\text{audio}}

Where Multimodal Frontier Models Actually Differ, Beyond the Marketing · Equation 1

This equation gives an approximation: it relates the quantities while allowing an approximation.

Equation guide → · This term → · Article →

f

Where Multimodal Frontier Models Actually Differ, Beyond the Marketing · Equation 2

the sampling rate.

Equation guide → · This term → · Article →

f(x)

Probing, Sparse Autoencoders, Patching, and Steering: The Main Interpretability Methods, Compared · Equation 8

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

Equation guide → · This term → · Article →

\hat x = W_d f(x) + b_d, \qquad f(x) = \mathrm{JumpReLU}_\theta\big(W_e x + b_e\big), \qquad \mathcal L(x) = \lVert x - \hat x \rVert_2^2 + \lambda \lVert f(x) \rVert_0.

Probing, Sparse Autoencoders, Patching, and Steering: The Main Interpretability Methods, Compared · Equation 9

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

Equation guide → · This term → · Article →

\lVert f(x) \rVert_0

Probing, Sparse Autoencoders, Patching, and Steering: The Main Interpretability Methods, Compared · Equation 13

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

Equation guide → · This term → · Article →

\phi(f, x)

How Do We Know an Interpretability Claim Is Actually Right? · Equation 3

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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f

How Do We Know an Interpretability Claim Is Actually Right? · Equation 5

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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\mathrm{score}(D,Q) = \sum_{i=1}^{n} \mathrm{IDF}(q_i) \cdot \frac{f(q_i, D)\,(k_1+1)}{f(q_i, D) + k_1\left(1 - b + b\,\dfrac{|D|}{\mathrm{avgdl}}\right)}

What Actually Happens Between a Query and an Answer in RAG · Equation 1

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

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\mathrm{score}(D, Q) = \sum_{q_i \in Q} \mathrm{IDF}(q_i) \cdot \frac{f(q_i, D) \cdot (k_1 + 1)}{f(q_i, D) + k_1 \cdot \left(1 - b + b \cdot \dfrac{|D|}{\mathrm{avgdl}}\right)},

From BM25 to Agentic Retrieval: A History of Retrieval-Augmented Generation · Equation 8

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

Equation guide → · This term → · Article →

f(q_i, D)

From BM25 to Agentic Retrieval: A History of Retrieval-Augmented Generation · Equation 9

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

Equation guide → · This term → · Article →

fff

Meanings in context

Symbol f

Symbol f

Symbol f

Symbol f

Used in 71 equations

$f$