Computer Science & Data Science · Machine learning and image processing

Convolution output dimension

Q: What does Convolution output dimension describe?

The relation H_{out}=\left\lfloor\frac{H_{in}+2p-d(k-1)-1}{s}+1\right\rfloor summarizes The convolution-size formula determines a discrete kernel’s spatial output dimension with padding, stride and dilation. Read it as a model for defined quantities, not as an automatic claim about every real situation. In the example For Hin=32, k=3, p=1, s=1 and d=1, Hout=floor((32+2−2−1)/1+1)=32., symbols are connected to concrete values and the result is interpreted in context. Validity limit: Apply the same relation to width for the other spatial axis. The effective kernel extent is d(k−1)+1. The floor appears when the kernel does not fit exactly at the boundary; Source: Stanford CS231n, Convolutional Neural Networks: convolution dimension notes.

The convolution-size formula determines a discrete kernel’s spatial output dimension with padding, stride and dilation.

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Formula

H_{o u t} = ⌊ \frac{H _{in} + 2 p - d ( k - 1 ) - 1}{s} + 1 ⌋

Dimensions and parameters are grid cells; output is a count

Variables & units

Variables & units
Symbol	Meaning	Unit
$Hin$	Input height or width	grid cells
$k$	Kernel size	grid cells
$p$	Padding per side	grid cells
$s$	Stride	grid cells
$d$	Dilation	dimensionless

LaTeX

H_{out}=\left\lfloor\frac{H_{in}+2p-d(k-1)-1}{s}+1\right\rfloor

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Derivation & background

Apply the same relation to width for the other spatial axis. The effective kernel extent is d(k−1)+1. The floor appears when the kernel does not fit exactly at the boundary; libraries can differ according to padding mode and rounding rules. Channels and filter count change tensor depth, not spatial height.

Exam blueprint

Validity range

Derivation steps

The convolution-size formula determines a discrete kernel’s spatial output dimension with padding, stride and dilation.

1Read the relation from its definition: H_out=\left\lfloor\frac{H_in+2p-d(k-1)-1}{s}+1\right\rfloor.
2Identify the input, requested output and assumptions of the relation.
3For Hin=32, k=3, p=1, s=1 and d=1, Hout=floor((32+2−2−1)/1+1)=32.

Rearrangements

Defining relation

H_{out}=\left\lfloor\frac{H_{in}+2p-d(k-1)-1}{s}+1\right\rfloor

The equation states the defining relation within its stated domain.

Task variant

Use the example for Convolution output dimension to explain which inputs determine the requested output.

The example connects concrete inputs to its result.
The convolution-size formula determines a discrete kernel’s spatial output dimension with padding, stride and dilation.
The relation applies only under its stated assumptions.

Common mistakes

Applying the relation to a different case without checking its stated assumptions.

Check the validity range before substituting values: Apply the same relation to width for the other spatial axis. The effective kernel extent is d(k−1)+1. The floor appears when the kernel does not fit exactly at the boundary;.

Exam context

Check CNN tensor shapes and plan memory use and layer composition.

Formula cluster

Machine learning and image processing

The convolution-size formula determines a discrete kernel’s spatial output dimension with padding, stride and dilation.

x_k+1=x_k−η∇f(x_k)

Gradient Descent

X[k] = Σ x[n]·e^(−j2πkn/N)

Discrete Fourier transform (DFT)

f(n) ∈ O(g(n))

Big-O notation (asymptotic upper bound)

Worked example

For Hin=32, k=3, p=1, s=1 and d=1, Hout=floor((32+2−2−1)/1+1)=32.

Applications

Check CNN tensor shapes and plan memory use and layer composition.

How do you calculate with Convolution output dimension?

Here is how to work through a typical Convolution output dimension (Hout = floor((Hin+2p−d(k−1)−1)/s+1)) task step by step:

1
Task
Use the example for Convolution output dimension to explain which inputs determine the requested output.
Solution path
1. The example connects concrete inputs to its result.
2. The convolution-size formula determines a discrete kernel’s spatial output dimension with padding, stride and dilation.
3. The relation applies only under its stated assumptions.

Frequently asked questions about Convolution output dimension

What does Convolution output dimension describe?+

The relation H_out=\left\lfloor\frac{H_in+2p-d(k-1)-1}{s}+1\right\rfloor summarizes The convolution-size formula determines a discrete kernel’s spatial output dimension with padding, stride and dilation. Read it as a model for defined quantities, not as an automatic claim about every real situation. In the example For Hin=32, k=3, p=1, s=1 and d=1, Hout=floor((32+2−2−1)/1+1)=32., symbols are connected to concrete values and the result is interpreted in context. Validity limit: Apply the same relation to width for the other spatial axis. The effective kernel extent is d(k−1)+1. The floor appears when the kernel does not fit exactly at the boundary; Source: Stanford CS231n, Convolutional Neural Networks: convolution dimension notes.

How should I work through a calculation?+

First write down the requested quantity and all given values with their symbols. Substitute them into the defining relation and check unit consistency. The example For Hin=32, k=3, p=1, s=1 and d=1, Hout=floor((32+2−2−1)/1+1)=32. provides a worked check: formula and result must have compatible scale and meaning; round only at the end. Validity limit: Apply the same relation to width for the other spatial axis. The effective kernel extent is d(k−1)+1. The floor appears when the kernel does not fit exactly at the boundary; Source: Stanford CS231n, Convolutional Neural Networks: convolution dimension notes.

Which assumption must I keep in mind?+

The formula applies only when quantities are defined as in the source and background. Check boundary cases, measurement conditions and whether an approximation rather than equality is intended. Substitution can be algebraically correct yet technically wrong when assumptions fail or the population or system boundary changes. Validity limit: Apply the same relation to width for the other spatial axis. The effective kernel extent is d(k−1)+1. The floor appears when the kernel does not fit exactly at the boundary; Source: Stanford CS231n, Convolutional Neural Networks: convolution dimension notes.

Which units and quantities are involved?+

The stated units are: Dimensions and parameters are grid cells; output is a count. Convert values to a consistent unit system before substitution; counts, percentages and dimensionless ratios are not interchangeable. The variable list states the role of each symbol. Dimensional analysis catches many errors but does not replace checking the formula's assumptions. Validity limit: Apply the same relation to width for the other spatial axis. The effective kernel extent is d(k−1)+1. The floor appears when the kernel does not fit exactly at the boundary; Source: Stanford CS231n, Convolutional Neural Networks: convolution dimension notes.

When is comparison with gradientenabstieg and diskrete-fouriertransformation useful?+

Comparison helps when both quantities address the same question but emphasize different properties. Report the definition, input data, threshold or averaging with the value. The source Stanford CS231n, Convolutional Neural Networks: convolution dimension notes. supports the definition used here; other conventions can differ. Choose the measure to match the learning or analysis goal. Validity limit: Apply the same relation to width for the other spatial axis. The effective kernel extent is d(k−1)+1. The floor appears when the kernel does not fit exactly at the boundary; Source: Stanford CS231n, Convolutional Neural Networks: convolution dimension notes.

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Subject references and further reading

This list names subject references and further reading. A page or section number appears when it is part of the reference; these are not verbatim quotations.

[1]Stanford CS231n, Convolutional Neural Networks: convolution dimension notes.

More formulas: Data analysis and machine learning

F_1 = \frac{2\,TP}{2\,TP + FP + FN}

F₁ score

H(p,q)=-\sum_{i=1}^{K}p_i\ln q_i

Cross-entropy (classification loss)

\theta_{t+1}=\theta_t-\eta\nabla J(\theta_t)

Gradient descent parameter update

\mathrm{BA}=\frac{1}{2}\left(\frac{TP}{TP+FN}+\frac{TN}{TN+FP}\right)

Balanced accuracy

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Convolution output dimension

The convolution-size formula determines a discrete kernel’s spatial output dimension with padding, stride and dilation.

AdvancedUniversity/collegeBachelor foundationsSubject specialization

Free to browse · flashcards or a multiple-choice quiz · import from Essential

Symbol

Meaning

Unit

Hin

Input height or width

grid cells

k

Kernel size

grid cells

p

Padding per side

grid cells

s

Stride

grid cells

d

Dilation

dimensionless

Derivation & background

Exam blueprint

Validity range

Derivation steps

The convolution-size formula determines a discrete kernel’s spatial output dimension with padding, stride and dilation.

1Read the relation from its definition: H_out=\left\lfloor\frac{H_in+2p-d(k-1)-1}{s}+1\right\rfloor.
2Identify the input, requested output and assumptions of the relation.
3For Hin=32, k=3, p=1, s=1 and d=1, Hout=floor((32+2−2−1)/1+1)=32.

How do you calculate with Convolution output dimension?

Here is how to work through a typical Convolution output dimension (Hout = floor((Hin+2p−d(k−1)−1)/s+1)) task step by step:

Task

Use the example for Convolution output dimension to explain which inputs determine the requested output.

Solution path

The example connects concrete inputs to its result.
The convolution-size formula determines a discrete kernel’s spatial output dimension with padding, stride and dilation.
The relation applies only under its stated assumptions.

Frequently asked questions about Convolution output dimension

What does Convolution output dimension describe?+

How should I work through a calculation?+

Which assumption must I keep in mind?+

Which units and quantities are involved?+

When is comparison with gradientenabstieg and diskrete-fouriertransformation useful?+

Retain Convolution output dimension for exams

Create a curated FSRS exam set for Hout = floor((Hin+2p−d(k−1)−1)/s+1): formula recall, variables, derivation, rearrangement, worked example, common mistakes and exam context.

Curated formula set · LaTeX · FSRS spaced repetition · import from Essential