Calculation Results
Review predictions, losses, gradients, checks, updates, and warnings.
Predictions
Layer Summary
Gradient Details
Parameter Updates
Numerical Gradient Check
Network Diagram
Gradient Magnitudes
Step-by-Step Report
Formula Used
How to Use
- Enter layer sizes and matching activation functions.
- Provide input samples and target values.
- Select initialisation, loss, optimiser, and gradient settings.
- Enable numerical checking when gradient verification is needed.
- Calculate and review every displayed result table.
Example Data
| Setting | Example | Purpose |
|---|---|---|
| Architecture | 2,3,1 | Two inputs, three hidden neurons, one output. |
| Activations | tanh,sigmoid | Hidden nonlinear transformation and binary output. |
| Inputs | [[0.2,0.7],[0.8,0.1]] | Two training samples with two features. |
| Targets | [[1],[0]] | Binary labels matching one output neuron. |
| Loss | Binary Cross-Entropy | Measures binary probability prediction error. |
Backpropagation Notes
Backpropagation sends output error toward earlier network layers. Each layer applies the chain rule to its inputs. This reveals how every parameter changes the final loss.
Large gradients may create unstable and destructive parameter updates. Tiny gradients can prevent useful learning in deep networks. Clipping and suitable activations often improve training stability greatly.
Numerical checking estimates derivatives by perturbing individual parameters. It is slower than analytical backpropagation during normal training. Use it mainly for debugging formulas and implementations carefully.
Frequently Asked Questions
What does this calculator compute?
It computes forward values, losses, gradients, and updates. It also checks selected gradients numerically. Results explain each network layer with clear tables.
Which network types are supported?
The calculator supports dense feed-forward neural networks. Hidden layers may use different activation functions. Recurrent and convolutional operations require separate specialised calculations.
Why must matrix dimensions match?
Every layer expects a fixed number of inputs. Incorrect dimensions prevent valid multiplication and gradient propagation. Validation identifies mismatches before performing any calculation steps.
What is numerical gradient checking?
It approximates derivatives using small parameter changes. The estimate is compared with analytical backpropagation. Small relative differences usually indicate correct gradient calculations.
What causes vanishing gradients?
Repeated small derivatives reduce gradients across deep layers. Saturating sigmoid functions can worsen this behaviour. ReLU variants and careful initialisation often reduce problems.
What causes exploding gradients?
Repeated large derivatives can magnify gradients dramatically. Updates may then become unstable or non-finite. Gradient clipping limits harmful update magnitudes during training.
Which optimiser should I choose?
SGD offers simple and transparent parameter updates. Adam often works well for quick experimentation. Final choices should depend on validation performance and stability.
Can I enter custom parameters?
Choose custom JSON in the initialisation selector. Then provide every weight matrix and bias vector. Their dimensions must match the declared network structure.
Are exported results suitable for reports?
CSV exports structured tables for further analysis. PDF and printing provide readable calculation summaries. Always verify important results before making final decisions.