Dense Layer Output Game

Build dense neural layers, solve shapes, count parameters, calculate activations, debug networks, and master forward propagation through animated challenges, practical simulations, and instant feedback.

Learning dashboard

Choose a mode, configure a layer, and solve the generated challenge.

Score0Ready
Accuracy0%0 attempts
Current streak0Best: 0
Experience0 XP
Timer--Untimed
Parameter budgetNo limit

Game setup

Shape Detective

Keyboard: Enter checks answers, N creates a new challenge, and H reveals a hint.

Neural network arena

Visualise a dense layer and animate its forward pass.

Input (2, 3) → Output (2, 4) Parameters: 16

Current challenge

Start the game to generate a question.

Round 0

Configure the game, then press Start game.

Z = XW + b; A = activation(Z)
Your feedback and worked solution will appear here.

Interactive workspace

Edit matrices, build layers, inspect calculations, and compare outputs.

Input matrix X

Weight matrix W

Bias vector b

Pre-activation Z

Activated output A

Architecture summary


  1. Start a challenge to generate a worked solution.

Session history

RoundModeResultPointsTime
No attempts yet.

Achievements

Core formulas

Output shape = (batch size, units)
Weight shape = (input features, units)
Bias shape = (units)
Parameters = input features × units + units
Z = XW + b; A = activation(Z)

Concept guide

A dense layer connects every input feature to every neuron. Its weight matrix stores one weight for every connection.

The batch dimension remains unchanged. The units setting determines the final dimension of the layer output.

Bias adds one trainable value per neuron. Disabling bias removes those values from the parameter total.

Activation functions transform weighted sums. Softmax converts each output row into probabilities that sum to one.

Common errors

ErrorCauseFix
Input mismatchInput columns differ from weight rows.Set weight rows equal to input features.
Bias mismatchBias length differs from output units.Use one bias value per neuron.
Layer mismatchA layer's units differ from the next layer's inputs.Connect each layer using the previous output size.
Wrong softmax axisSoftmax is applied across samples.Apply softmax across each output row.

Custom challenges and exports

Save configurations, share results, and continue learning later.


Generated on 2026-08-10 15:36:50. Progress and custom challenges remain in this browser unless cleared.

Related Calculators

Build a Neural NetworkNeuron Activation GameActivation Function MatchBackpropagation PuzzleWeight Adjustment ChallengeVanishing Gradient EscapeNeural Network Architecture BuilderDropout DefenderLoss Function Challenge

Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.