Weight Histogram Inputs
Formula Used
μ = Σwᵢ / n. This locates the distribution center.σ² = Σ(wᵢ − μ)² / n. This measures squared dispersion.σ = √σ². This reports spread using original units.IQR = Q3 − Q1. IQR fences detect robust outliers.dⱼ = cⱼ / (nΔ). Here, Δ represents bin width.γ₁ = mean(((wᵢ − μ) / σ)³). This measures distribution asymmetry.γ₂ = mean(((wᵢ − μ) / σ)⁴) − 3. This evaluates tail heaviness.√(2 / (fan-in + fan-out)). He uses √(2 / fan-in).The health score combines scale, shift, outliers, skewness, and sparsity. It is a diagnostic heuristic, not a training guarantee.
How to Use This Calculator
- Paste weight values from one model layer or tensor.
- Choose a bin rule matching your sample size.
- Select count, probability, percent, or density normalization.
- Apply clipping only when investigating extreme parameters.
- Set fan values and the intended initialization reference.
- Enable smoothing curves for easier shape comparison.
- Submit the form and inspect results above.
- Compare findings with gradients, activations, losses, and checkpoints.
Understanding Weight Distribution Histograms
Reading the Distribution
Weight histograms summarize thousands of parameters without hiding important distribution patterns. They reveal central tendency, spread, symmetry, tails, gaps, and concentrated regions. These features help reviewers understand whether training produced balanced parameter behavior.
Recognizing Healthy Shapes
A healthy layer often shows a compact center with controlled tails. Extreme spikes can indicate unstable updates, poor scaling, or corrupted checkpoints. Very narrow shapes may suggest weak learning or excessive regularization pressure.
Center and Direction
The mean shows where the distribution balances across all processed weights. A large nonzero mean can signal drift or persistent directional bias. Median values provide stronger resistance against a few extreme parameters.
Spread and Variation
Standard deviation measures typical distance from the calculated distribution mean. Variance expresses the same spread using squared measurement units. Coefficient variation compares spread against mean magnitude, requiring careful interpretation.
Tails and Outliers
Outliers deserve attention because they may dominate activations and gradients. IQR detection uses quartiles and remains robust under asymmetric distributions. Z-score detection works best when the central shape remains approximately normal.
Sparsity Signals
Sparsity measures how many weights remain near zero after training. Higher sparsity may reduce complexity, storage, and computational requirements. Unexpected sparsity can also reveal dead connections or aggressive pruning.
Choosing Histogram Bins
Histogram bins control how much local structure appears within the chart. Too few bins hide modes, tails, gaps, and small clusters. Too many bins create noise and exaggerate random sample variation.
Adaptive Bin Rules
Freedman-Diaconis adapts width using sample size and interquartile range. Scott uses standard deviation and performs well for smoother distributions. Sturges, Rice, and square-root rules provide simpler practical alternatives.
Normalization Choices
Count normalization shows the number of weights inside each interval. Probability normalization displays each bin as a share of observations. Density normalization supports comparisons between layers containing different parameter counts.
Initialization References
Expected initialization scale depends on fan-in, fan-out, and activation behavior. He scaling often supports ReLU layers with stronger variance preservation. Xavier scaling commonly suits tanh or balanced linear signal propagation.
Interpreting Scale Differences
Compare observed deviation against expected initialization before drawing strong conclusions. Training naturally changes weights, so differences are not automatically defects. Use trends across checkpoints, layers, and experiments for reliable diagnosis.
Tracking Checkpoints
Checkpoint comparisons show whether spread expands gradually or changes suddenly during training. Sudden widening may follow learning rate jumps, data shifts, or optimizer resets. Stable patterns usually support confidence when validation metrics remain healthy.
Combining Evidence
Never judge model quality from one histogram without supporting evidence. Review losses, gradients, activations, predictions, and layer responsibilities together. Combined evidence turns visual patterns into practical and defensible engineering decisions.
Frequently Asked Questions
What does a weight histogram show?
It groups model weights into numeric intervals. Bar heights show frequency, probability, percent, or density. The shape reveals spread, symmetry, tails, gaps, modes, and possible anomalies.
Which bin rule should I choose?
Freedman-Diaconis handles skewed data well. Scott suits smoother distributions. Sturges works for modest samples. Manual bins help when comparing layers with one fixed visual scale.
Why compare observed and expected deviation?
The comparison highlights scale changes from initialization. A large difference may reflect learning, regularization, instability, or architecture effects. Always compare checkpoints and validation behavior before diagnosing failure.
What does high weight sparsity mean?
High sparsity means many weights remain near zero. This can support pruning and compression. It can also reveal dead connections, excessive regularization, or a threshold chosen too broadly.
When should I use density normalization?
Use density when layers contain different weight counts. The total bar area becomes approximately one. This supports fairer shape comparisons despite unequal sample sizes and bin widths.
What is the KDE curve?
Kernel density estimation creates a smooth distribution estimate. Bandwidth controls its smoothness. Small bandwidths reveal local details, while large bandwidths emphasize broad structure.
Should every layer look normally distributed?
No. Training objectives, constraints, pruning, attention, and normalization alter shapes. The fitted normal curve is a reference, not a requirement. Layer purpose should guide interpretation.
How are outliers detected?
IQR mode uses quartile fences. Z-score mode measures standard deviations from the mean. IQR is usually safer for skewed or heavy-tailed distributions.
Can this calculator prove model instability?
No. It provides statistical and visual warning signals. Confirm suspected instability using gradients, activations, losses, validation metrics, optimizer states, and comparisons across training checkpoints.