Symbol in context

$i$

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

Meanings in context

Article-grounded definition

Symbol i

the cell at row.

Read equation 3 in How Post-CMOS, Neuromorphic, Photonic, and Quantum AI Compute Actually Works →

Article-grounded definition

Symbol i

assigned a latent strength $\theta_i$ , and the estimated probability that system A ’s output is preferred over system B ’s in a given comparison is.

Read equation 1 in Frontier AI Model Comparisons: A First-Principles Introduction →

Article-grounded definition

Symbol i

the pair.

Read equation 6 in How Llama's Architecture Actually Works, Generation by Generation →

Article-grounded definition

Symbol i

the fraction of those calls actually covered by a working.

Read equation 3 in Ten Failure Modes That Define Production Tool-Protocol Integrations →

Article-grounded definition

Symbol i

close to zero, because nothing in the base protocol gives a server a caller-supplied key to deduplicate against.

Read equation 5 in Ten Failure Modes That Define Production Tool-Protocol Integrations →

Article-grounded definition

Symbol i

the step.

Read equation 8 in The Economics and Physical Limits of Running AI Agents at Scale →

Article-grounded definition

Symbol i

a position index.

Read equation 11 in Measuring What a RAG System Retrieves, Not Just What It Answers →

Article-grounded definition

Symbol i

the if workers.

Read equation 13 in Ten Failure Modes in Agentic Coding, from Prompt Injection to False Completion →

Article-grounded definition

Symbol i

resolved.

Read equation 2 in How to Evaluate Codex Beyond SWE-bench and Vendor Scores →

Used in 145 equations

i

The Type Chart Is a Payoff Matrix, and the Metagame Only Half-Solves It · Equation 10

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

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i

The Type Chart Is a Payoff Matrix, and the Metagame Only Half-Solves It · Equation 13

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

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f_i(x) = \sum_j x_j\, U(i,j)

The Type Chart Is a Payoff Matrix, and the Metagame Only Half-Solves It · 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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i

The Type Chart Is a Payoff Matrix, and the Metagame Only Half-Solves It · Equation 16

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

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\phi(x) = \sum_i x_i f_i(x)

The Type Chart Is a Payoff Matrix, and the Metagame Only Half-Solves It · Equation 17

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

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D_{\mathrm{KL}}(p \,\|\, q) = \sum_i p_i \log_2(p_i/q_i)

The Type Chart Is a Payoff Matrix, and the Metagame Only Half-Solves It · Equation 18

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} = \frac{\sum_{i} (P_2(i) - P_1(i))\,(P_4(i) - P_1(i))}{\sum_{i} (P_3(i) - P_1(i))\,(P_4(i) - P_1(i))}

Hominin Evolution and Deep Prehistory: A First-Principles Introduction · 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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i

Hominin Evolution and Deep Prehistory: A First-Principles Introduction · Equation 5

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

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P_{rx} = P_{tx} - \sum_i L_i - \alpha \ell,

AI Datacenter Interconnects in Practice: An Advanced Technical Guide · 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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(a+bi)(c+di)

Mathematicians Finished the Job After an Evolutionary Search Beat 56 Years of Human Proofs · Equation 7

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

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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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\mathcal{L}_{\text{SMEFT}} = \mathcal{L}_{\text{SM}} + \sum_i \frac{c_i}{\Lambda^{2}} \mathcal{O}_i^{(6)} + \mathcal{O}\!\left(\frac{1}{\Lambda^{4}}\right)

From Origins to Frontier: A History of Particle Physics Beyond the Standard Model · 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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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.

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\mathcal{L}_{\text{SMEFT}} = \mathcal{L}_{\text{SM}} + \sum_i \frac{c_i}{\Lambda^{2}} \mathcal{O}_i^{(6)} + \mathcal{O}\!\left(\frac{1}{\Lambda^{4}}\right)

Comparing the Main Approaches to Particle Physics Beyond the Standard Model · 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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\text{cumulative damage} \approx \sum_i \frac{n_i}{N_i}

Comparing the Main Approaches to Materials Discovery and Degradation · Equation 5

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

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h^2 \times i \times V = 0.50 \times 0.01 \times 0.01 = 0.00005

One Gene, Forty Eyes: What Evo-Devo Did to the Convergence Story · 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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\operatorname{Var}(\mathrm{Sel}) = \sigma^2 \sum_i s_i^2 (z_i - \bar z)^2, \qquad N_e = \frac{1}{\mathrm{HHI}}

Selection Accounting: The Price Equation Runs the Economy · Equation 10

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

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Y_{\text{package}} \approx \prod_{i=1}^{n} y_i

Chiplets and Advanced Packaging in Practice: An Advanced Technical Guide · Equation 3

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

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i

The Hardest Unsolved Problems in Frontier AI Model Comparisons · Equation 1

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

Equation guide → · This term → · Article →

i

The Hardest Unsolved Problems in Frontier AI Model Comparisons · Equation 5

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

Equation guide → · This term → · Article →

i

Chemical Dynamics and Catalysis in Practice: An Advanced Technical Guide · Equation 4

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

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\hat{p} = \frac{1}{n}\sum_{i=1}^{n} \mathbb{1}[\text{trial } i \text{ succeeded}],

The Hardest Unsolved Problems in AI Agent Evaluation and Reliability · Equation 14

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

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R = 1 - \sum_{i=1}^{n} w_i \cdot \mathbb{1}[\text{trial } i \text{ failed}],

The Hardest Unsolved Problems in AI Agent Evaluation and Reliability · 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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T_{\mathrm{turn}} = T_{\mathrm{system}} + T_{\mathrm{tools}} + \sum_{i=1}^{n} T_{\mathrm{result},i} + T_{\mathrm{exchange}}

The Economics, Energy, and Physical Limits of Tool Protocols and the Model Context Protocol · Equation 1

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

Equation guide → · This term → · Article →

i

The Economics, Energy, and Physical Limits of Tool Protocols and the Model Context Protocol · Equation 8

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

Equation guide → · This term → · Article →

i\Delta

The Economics, Energy, and Physical Limits of Tool Protocols and the Model Context Protocol · Equation 9

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

Equation guide → · This term → · Article →

B(k) = \Delta \sum_{i=1}^{k} i = \Delta\,\frac{k(k+1)}{2}.

The Economics, Energy, and Physical Limits of Tool Protocols and the Model Context Protocol · Equation 10

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

Equation guide → · This term → · Article →

i

Frontier AI Model Comparisons: A First-Principles Introduction · Equation 1

assigned a latent strength $\theta_i$ , and the estimated probability that system A ’s output is preferred over system B ’s in a given comparison is.

Equation guide → · This term → · Article →

I = \sum_{i=1}^{n} w_i \, s_i, \qquad \sum_{i=1}^{n} w_i = 1,

What Independent Evidence Actually Supports About Grok's Capabilities · Equation 1

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

Equation guide → · This term → · Article →

i

What Independent Evidence Actually Supports About Grok's Capabilities · Equation 3

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

Equation guide → · This term → · Article →

iii

Meanings in context

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Used in 145 equations

$i$