# Learning Munsell

Technical documentation covering performance benchmarks, training methodology, architecture design, and experimental findings.

## Overview

This project implements ML models for bidirectional conversion between CIE xyY colorspace values and Munsell specifications:

- **xyY to Munsell (from_xyY)**: 25+ architectures, best Delta-E 0.52
- **Munsell to xyY (to_xyY)**: 9 architectures, best Delta-E 0.48

### Delta-E Interpretation

- **< 1.0**: Not perceptible by human eye
- **1-2**: Perceptible through close observation
- **2-10**: Perceptible at a glance
- **> 10**: Colors are perceived as completely different

Our best models achieve **Delta-E 0.48-0.52**, meaning the difference between ML prediction and iterative algorithm is **not perceptible by the human eye**.

## xyY to Munsell (from_xyY)

### Performance Benchmarks

Comprehensive comparison using all 2,734 REAL Munsell colors:

| Model                                                    | Delta-E     | Speed (ms) |
|----------------------------------------------------------|-------------|------------|
| Colour Library (Baseline)                                | 0.00        | 111.90     |
| **Multi-ResNet + Multi-Error Predictor (Large Dataset)** | **0.52**    | 0.089      |
| Multi-MLP (W+B) + Multi-Error Predictor (W+B) Large      | 0.52        | 0.057      |
| Multi-MLP + Multi-Error Predictor (Large Dataset)        | 0.52        | 0.058      |
| Multi-MLP + Multi-Error Predictor                        | 0.53        | 0.058      |
| MLP + Error Predictor                                    | 0.53        | 0.030      |
| Multi-ResNet (Large Dataset)                             | 0.54        | 0.044      |
| Multi-Head + Multi-Error Predictor                       | 0.54        | 0.042      |
| Multi-Head + Multi-Error Predictor (Large Dataset)       | 0.56        | 0.043      |
| Deep + Wide                                              | 0.60        | 0.074      |
| Multi-Head (Large Dataset)                               | 0.66        | 0.013      |
| Mixture of Experts                                       | 0.80        | 0.020      |
| Transformer (Large Dataset)                              | 0.82        | 0.123      |
| Multi-MLP                                                | 0.86        | 0.027      |
| MLP + Self-Attention                                     | 0.88        | 0.173      |
| MLP (Base Only)                                          | 1.09        | **0.007**  |
| Unified MLP                                              | 1.12        | 0.072      |

Note: The Colour library baseline had 171 convergence failures out of 2,734 samples (6.3% failure rate).

**Best Models**:

- **Best Accuracy**: Multi-ResNet + Multi-Error Predictor (Large Dataset) - Delta-E 0.52
- **Fastest**: MLP Base Only (0.007 ms/sample) - 15,492x faster than Colour library
- **Best Balance**: Multi-MLP (W+B: Weighted Boundary) + Multi-Error Predictor (W+B) Large - 1,951x faster with Delta-E 0.52

### Model Architectures

25+ architectures were systematically evaluated:

**Single-Stage Models**

1.  **MLP (Base Only)** - Simple MLP network, 3 inputs to 4 outputs
2.  **Unified MLP** - Single large MLP with shared features
3.  **Multi-Head** - Shared encoder with 4 independent decoder heads
4.  **Multi-Head (Large Dataset)** - Multi-Head trained on 1.4M samples
5.  **Multi-MLP** - 4 completely independent MLP branches (one per output)
6.  **Multi-MLP (Large Dataset)** - Multi-MLP trained on 1.4M samples
7.  **MLP + Self-Attention** - MLP with attention mechanism for feature weighting
8.  **Deep + Wide** - Combined deep and wide network paths
9.  **Mixture of Experts** - Gating network selecting specialized expert networks
10. **Transformer (Large Dataset)** - Feature Tokenizer Transformer for tabular data
11. **FT-Transformer** - Feature Tokenizer Transformer (standard size)

**Two-Stage Models**

12. **MLP + Error Predictor** - Base MLP with unified error correction
13. **Multi-Head + Multi-Error Predictor** - Multi-Head with 4 independent error predictors
14. **Multi-Head + Multi-Error Predictor (Large Dataset)** - Large dataset variant
15. **Multi-MLP + Multi-Error Predictor** - 4 independent branches with 4 independent error predictors
16. **Multi-MLP + Multi-Error Predictor (Large Dataset)** - Large dataset variant
17. **Multi-ResNet + Multi-Error Predictor (Large Dataset)** - Deep ResNet-style branches (BEST)

The **Multi-ResNet + Multi-Error Predictor (Large Dataset)** architecture achieved the best results with Delta-E 0.52.

### Training Methodology

**Data Generation**

1.  **Dense xyY Grid** (~500K samples)
    - Regular grid in valid xyY space (MacAdam limits for Illuminant C)
    - Captures general input distribution
2.  **Boundary Refinement** (~700K samples)
    - Adaptive dense sampling near Munsell gamut boundaries
    - Uses `maximum_chroma_from_renotation` to detect edges
    - Focuses on regions where iterative algorithm is most complex
    - Includes Y/GY/G hue regions with high value/chroma (challenging areas)
3.  **Forward Augmentation** (~200K samples)
    - Dense Munsell space sampling via `munsell_specification_to_xyY`
    - Ensures coverage of known valid colors

Total: ~1.4M samples for large dataset training.

**Loss Functions**

Two loss function approaches were tested:

*Precision-Focused Loss* (Default):

```
total_loss = 1.0 * MSE + 0.5 * MAE + 0.3 * log_penalty + 0.5 * huber_loss
```

- MSE: Standard mean squared error
- MAE: Mean absolute error
- Log penalty: Heavily penalizes small errors (pushes toward high precision)
- Huber loss: Small delta (0.01) for precision on small errors

*Pure MSE Loss* (Optimized config):

```
total_loss = MSE
```

Interestingly, the precision-focused loss achieved better Delta-E despite higher validation MSE, suggesting the custom weighting better correlates with perceptual accuracy.

### Design Rationale

**Two-Stage Architecture**

The error predictor stage corrects systematic biases in the base model:

1.  Base model learns the general xyY to Munsell mapping
2.  Error predictor learns residual corrections specific to each component
3.  Combined prediction: `final = base_prediction + error_correction`

This decomposition allows each stage to specialize and reduces the complexity each network must learn.

**Independent Branch Design**

Munsell components have different characteristics:

- **Hue**: Circular (0-10, wrapping), most complex
- **Value**: Linear (0-10), easiest to predict
- **Chroma**: Highly variable range depending on hue/value
- **Code**: Discrete hue sector (0-9)

Shared encoders force compromises between these different prediction tasks. Independent branches allow full specialization.

**Architecture Details**

*MLP (Base Only)*

Simple feedforward network predicting all 4 outputs simultaneously:

    Input (3) ──► Linear Layers ──► Output (4: hue, value, chroma, code)

- Smallest model (~8KB ONNX)
- Fastest inference (0.007 ms)
- Baseline for comparison

*Unified MLP*

Single large MLP with shared internal features:

    Input (3) ──► 128 ──► 256 ──► 512 ──► 256 ──► 128 ──► Output (4)

- Shared representations across all outputs
- Moderate size, good speed

*Multi-Head MLP*

Shared encoder with specialized decoder heads:

    Input (3) ──► SHARED ENCODER (3→128→256→512) ──┬──► Hue Head (512→256→128→1)
                                                   ├──► Value Head (512→256→128→1)
                                                   ├──► Chroma Head (512→384→256→128→1)
                                                   └──► Code Head (512→256→128→1)

- Shared encoder learns common color space features
- 4 specialized decoder heads branch from shared representation
- Parameter efficient (encoder weights shared)
- Fast inference (encoder computed once)

*Multi-MLP*

Fully independent branches with no weight sharing:

    Input (3) ──► Hue Branch    (3→128→256→512→256→128→1)
    Input (3) ──► Value Branch  (3→128→256→512→256→128→1)
    Input (3) ──► Chroma Branch (3→256→512→1024→512→256→1)  [2x wider]
    Input (3) ──► Code Branch   (3→128→256→512→256→128→1)

- 4 completely independent MLPs
- Each branch learns its own features from scratch
- Chroma branch is wider (2x) to handle its complexity
- Better accuracy than Multi-Head on large dataset (Delta-E 0.52 vs 0.56 with error predictors)

*Multi-ResNet*

Deep branches with residual-style connections:

    Input (3) ──► Hue Branch    (3→256→512→512→512→256→1)    [6 layers]
    Input (3) ──► Value Branch  (3→256→512→512→512→256→1)    [6 layers]
    Input (3) ──► Chroma Branch (3→512→1024→1024→1024→512→1) [6 layers, 2x wider]
    Input (3) ──► Code Branch   (3→256→512→512→512→256→1)    [6 layers]

- Deeper architecture than Multi-MLP
- BatchNorm + SiLU activation
- Best accuracy when combined with error predictor (Delta-E 0.52)
- Largest model (~14MB base, ~28MB with error predictor)

*Deep + Wide*

Combined deep and wide network paths:

    Input (3) ──┬──► Deep Path (multiple layers) ──┬──► Concat ──► Output (4)
                └──► Wide Path (direct connection) ─┘

- Deep path captures complex patterns
- Wide path preserves direct input information
- Good for mixed linear/nonlinear relationships

*MLP + Self-Attention*

MLP with attention mechanism for feature weighting:

    Input (3) ──► MLP ──► Self-Attention ──► Output (4)

- Attention weights learn feature importance
- Slower due to attention computation (0.173 ms)
- Did not improve over simpler MLPs

*Mixture of Experts*

Gating network selecting specialized expert networks:

    Input (3) ──► Gating Network ──► Weighted sum of Expert outputs ──► Output (4)

- Multiple expert networks specialize in different input regions
- Gating network learns which expert to use
- More complex but did not outperform Multi-MLP

*FT-Transformer*

Feature Tokenizer Transformer for tabular data:

    Input (3) ──► Feature Tokenizer ──► Transformer Blocks ──► Output (4)

- Each input feature tokenized separately
- Self-attention across feature tokens
- Good for tabular data with feature interactions
- Slower inference due to attention computation

*Error Predictor (Two-Stage)*

Second-stage network that corrects base model errors:

    Stage 1: Input (3) ──► Base Model ──► Base Prediction (4)
    Stage 2: [Input (3), Base Prediction (4)] ──► Error Predictor ──► Error Correction (4)
    Final:   Base Prediction + Error Correction = Final Output

- Learns residual corrections for each component
- Can have unified (1 network) or multi (4 networks) error predictors
- Consistently improves accuracy across all base architectures
- Best results: Multi-ResNet + Multi-Error Predictor (Delta-E 0.52)

**Loss-Metric Mismatch**

An important finding: **optimizing MSE does not optimize Delta-E**.

The Optuna hyperparameter search minimized validation MSE, but the best MSE configuration did not achieve the best Delta-E. This is because:

- MSE treats all component errors equally
- Delta-E (CIE2000) weights errors based on human perception
- The precision-focused loss with custom weights better approximates perceptual importance

**Weighted Boundary Loss (Experimental)**

Analysis of model errors revealed systematic underperformance on Y/GY/G hues (Yellow/Green-Yellow/Green) with high value and chroma. The weighted boundary loss approach was explored to address this by:

1.  Applying 3x loss weight to samples in challenging regions:
    - Hue: 0.18-0.35 (normalized range covering Y/YG/G)
    - Value > 0.7 (high brightness)
    - Chroma > 0.5 (high saturation)
2.  Adding boundary penalty to prevent predictions exceeding Munsell gamut limits

**Finding**: The large dataset approach (~1.4M samples with dense boundary sampling) naturally provides sufficient coverage of these challenging regions. Both the weighted boundary loss model (Multi-MLP W+B + Multi-Error Predictor W+B Large, Delta-E 0.524) and the standard large dataset model (Multi-MLP + Multi-Error Predictor Large, Delta-E 0.525) achieve nearly identical results, making explicit loss weighting optional. The best overall model is Multi-ResNet + Multi-Error Predictor (Large Dataset) with Delta-E 0.52.

### Experimental Findings

The following experiments were conducted but did not improve results:

**Delta-E Training**

Training with differentiable Delta-E CIE2000 loss via round-trip through the Munsell-to-xyY approximator.

*Hypothesis*: Perceptual Delta-E loss might outperform MSE-trained models.

*Implementation*: JAX/Flax model with combined MSE + Delta-E loss. Requires lower learning rate (1e-4 vs 3e-4) for stability; higher rates cause NaN gradients.

*Results*: While Delta-E is comparable, **hue accuracy is ~10x worse**:

| Metric (Normalized MAE)  | Delta-E Model | MSE Model |
|--------------------------|---------------|-----------|
| Hue MAE                  | 0.30          | 0.03      |
| Value MAE                | 0.002         | 0.004     |
| Chroma MAE               | 0.007         | 0.008     |
| Code MAE                 | 0.07          | 0.01      |
| **Delta-E (perceptual)** | **0.52**      | **0.50**  |

*Key Takeaway*: **Perceptual similarity != specification accuracy**. The MSE model's slightly better Delta-E (0.50 vs 0.52) comes at the cost of ~10x worse hue accuracy, making it unsuitable for specification prediction. Delta-E is too permissive for hue, allowing the model to find "shortcuts" that minimize perceptual difference without correctly predicting the Munsell specification.

**Classical Interpolation**

Classical interpolation methods were tested on 4,995 reference Munsell colors (80% train / 20% test split). ML evaluated on 2,734 REAL Munsell colors.

*Results (Validation MAE)*:

| Component | RBF  | KD-Tree | Delaunay | ML (Best) |
|-----------|------|---------|----------|-----------|
| Hue       | 1.40 | 1.40    | 1.29     | **0.03**  |
| Value     | 0.01 | 0.10    | 0.02     | 0.05      |
| Chroma    | 0.22 | 0.99    | 0.35     | **0.11**  |
| Code      | 0.33 | 0.28    | 0.28     | **0.00**  |

*Key Insight*: The reference dataset (4,995 colors) is too sparse for 3D xyY interpolation. Classical methods fail on hue prediction (MAE ~1.3-1.4), while ML achieves 47x better hue accuracy and 2-3x better chroma/code accuracy.

**Circular Hue Loss**

Circular distance metrics for hue prediction, accounting for cyclic nature (0-10 wraps).

*Results*: The circular loss model performed **21x worse** on hue MAE (5.14 vs 0.24).

*Key Takeaway*: **Mathematical correctness != training effectiveness**. The circular distance creates gradient discontinuities that harm optimization.

**REAL-Only Refinement**

Fine-tuning using only REAL Munsell colors (2,734) instead of ALL colors (4,995).

*Results*: Essentially identical performance (Delta-E 1.5233 vs 1.5191).

*Key Takeaway*: **Data quality is not the bottleneck**. Both REAL and extrapolated colors are sufficiently accurate.

**Gamma Normalization**

Gamma correction to the Y (luminance) channel during normalization.

*Results*: No consistent improvement across gamma values 1.0-3.0:

| Gamma          | Median ΔE (± std) |
|----------------|-------------------|
| 1.0 (baseline) | 0.730 ± 0.054     |
| 2.5 (best)     | 0.683 ± 0.132     |

![Gamma sweep results](_static/gamma_sweep_plot.png)

*Key Takeaway*: **Gamma normalization does not provide consistent improvement**. Standard deviations overlap - differences are within noise.

## Munsell to xyY (to_xyY)

### Performance Benchmarks

Comprehensive comparison using all 2,734 REAL Munsell colors:

| Model                                         | Delta-E     | Speed (ms) |
|-----------------------------------------------|-------------|------------|
| Colour Library (Baseline)                     | 0.00        | 1.27       |
| **Multi-MLP (Optimized)**                     | **0.48**    | 0.008      |
| Multi-MLP (Opt) + Multi-Error Predictor (Opt) | 0.48        | 0.025      |
| Multi-MLP + Multi-Error Predictor             | 0.65        | 0.030      |
| Multi-MLP                                     | 0.66        | 0.016      |
| Multi-MLP + Error Predictor                   | 0.67        | 0.018      |
| Multi-Head (Optimized)                        | 0.71        | 0.015      |
| Multi-Head                                    | 0.78        | 0.008      |
| Multi-Head + Multi-Error Predictor            | 1.11        | 0.028      |
| Simple MLP                                    | 1.42        | **0.0008** |

**Best Models**:

- **Best Accuracy**: Multi-MLP (Optimized) - Delta-E 0.48
- **Fastest**: Simple MLP (0.0008 ms/sample) - 1,654x faster than Colour library
- **Best Balance**: Multi-MLP (Optimized) - 154x faster with Delta-E 0.48

### Model Architectures

9 architectures were evaluated for the Munsell to xyY direction:

**Single-Stage Models**

1.  **Simple MLP** - Basic MLP network, 4 inputs to 3 outputs
2.  **Multi-Head** - Shared encoder with 3 independent decoder heads (x, y, Y)
3.  **Multi-Head (Optimized)** - Hyperparameter-optimized variant
4.  **Multi-MLP** - 3 completely independent MLP branches
5.  **Multi-MLP (Optimized)** - Hyperparameter-optimized variant (BEST)

**Two-Stage Models**

6.  **Multi-MLP + Error Predictor** - Base Multi-MLP with unified error correction
7.  **Multi-MLP + Multi-Error Predictor** - 3 independent error predictors
8.  **Multi-MLP (Opt) + Multi-Error Predictor (Opt)** - Optimized two-stage
9.  **Multi-Head + Multi-Error Predictor** - Multi-Head with error correction

The **Multi-MLP (Optimized)** architecture achieved the best results with Delta-E 0.48.

### Differentiable Approximator

A small MLP (68K parameters) trained to approximate the Munsell to xyY conversion for use in differentiable Delta-E loss:

- **Architecture**: 4 -> 128 -> 256 -> 128 -> 3 with LayerNorm + SiLU
- **Accuracy**: MAE ~0.0006 for x, y, and Y components
- **Output formats**: PyTorch (.pth), ONNX, and JAX-compatible weights (.npz)

This enables differentiable Munsell to xyY conversion, which was previously only possible through non-differentiable lookup tables.

## Shared Infrastructure

### Hyperparameter Optimization

Optuna was used for systematic hyperparameter search over:

- Learning rate (1e-4 to 1e-3)
- Batch size (256, 512, 1024)
- Dropout rate (0.0 to 0.2)
- Chroma branch width multiplier (1.0 to 2.0)
- Loss function weights (MSE, Huber)

Key finding: **No dropout (0.0)** consistently performed better across all models in both conversion directions, contrary to typical deep learning recommendations for regularization.

### Training Infrastructure

- **Optimizer**: AdamW with weight decay
- **Scheduler**: ReduceLROnPlateau (patience=10, factor=0.5)
- **Early stopping**: Patience=20 epochs
- **Checkpointing**: Best model saved based on validation loss
- **Logging**: MLflow for experiment tracking

### JAX Delta-E Implementation

Located in `learning_munsell/losses/jax_delta_e.py`:

- Differentiable xyY -> XYZ -> Lab color space conversions
- Full CIE 2000 Delta-E implementation with gradient support
- JIT-compiled functions for performance

Usage:

```python
from learning_munsell.losses import delta_E_loss, delta_E_CIE2000

# Compute perceptual loss between predicted and target xyY
loss = delta_E_loss(pred_xyY, target_xyY)
```

## Limitations

### BatchNorm Instability on MPS

Models using `BatchNorm1d` layers exhibit numerical instability when trained on Apple Silicon GPUs via the MPS backend:

1.  **Validation loss spikes** during training
2.  **Occasional extreme outputs** during inference (e.g., 20M instead of ~0.1)
3.  **Non-reproducible behavior**

**Affected Models**: Large dataset error predictors using BatchNorm.

**Workarounds**:

1.  Use CPU for training
2.  Replace BatchNorm with LayerNorm
3.  Use smaller models (300K samples vs 2M)
4.  Skip error predictor stage for affected models

The recommended production model (`multi_resnet_error_predictor_large.onnx`) was trained on the large dataset and does not exhibit this instability.

**References**:

- [BatchNorm non-trainable exception](https://github.com/pytorch/pytorch/issues/98602)
- [ONNX export incorrect on MPS](https://github.com/pytorch/pytorch/issues/83230)
- [MPS kernel bugs](https://elanapearl.github.io/blog/2025/the-bug-that-taught-me-pytorch/)