Training Loss Curve — Altair

A line plot showing training and validation loss curves over epochs during neural network training. This visualization is essential for monitoring model training, detecting overfitting (when validation loss diverges from training loss), and determining optimal early stopping points. The dual-curve display reveals the gap between training and generalization performance.

Training Loss Curve rendered with Altair

Python source (Altair)

""" anyplot.ai
line-loss-training: Training Loss Curve
Library: altair 6.1.0 | Python 3.13.13
Quality: 80/100 | Updated: 2026-05-14
"""

import altair as alt
import numpy as np
import pandas as pd


# Data - Simulating neural network training loss curves
np.random.seed(42)
epochs = np.arange(1, 51)

# Training loss: exponential decay with noise (continues decreasing)
train_loss = 2.5 * np.exp(-0.08 * epochs) + 0.15 + np.random.normal(0, 0.02, len(epochs))

# Validation loss: decay then overfitting (U-shape after minimum)
val_base = 2.5 * np.exp(-0.07 * epochs) + 0.35
val_loss = val_base + np.random.normal(0, 0.025, len(epochs))
# Add overfitting: loss increases after epoch 25
val_loss[25:] = val_loss[25:] + np.linspace(0, 0.35, 25)

# Find minimum validation loss epoch for annotation
min_val_epoch = epochs[np.argmin(val_loss)]
min_val_loss = np.min(val_loss)

# Create DataFrame in long format for Altair
df = pd.DataFrame(
    {
        "Epoch": np.tile(epochs, 2),
        "Loss": np.concatenate([train_loss, val_loss]),
        "Type": ["Training Loss"] * len(epochs) + ["Validation Loss"] * len(epochs),
    }
)

# Point for minimum validation loss annotation
min_point_df = pd.DataFrame({"Epoch": [min_val_epoch], "Loss": [min_val_loss], "Type": ["Optimal Stopping Point"]})

# Base line chart
lines = (
    alt.Chart(df)
    .mark_line(strokeWidth=3)
    .encode(
        x=alt.X("Epoch:Q", title="Epoch", axis=alt.Axis(labelFontSize=18, titleFontSize=22)),
        y=alt.Y("Loss:Q", title="Cross-Entropy Loss", axis=alt.Axis(labelFontSize=18, titleFontSize=22)),
        color=alt.Color(
            "Type:N",
            scale=alt.Scale(domain=["Training Loss", "Validation Loss"], range=["#306998", "#FFD43B"]),
            legend=alt.Legend(title="Curve Type", labelFontSize=16, titleFontSize=18),
        ),
    )
)

# Add points on lines for visibility
points = (
    alt.Chart(df)
    .mark_point(size=60, filled=True)
    .encode(
        x="Epoch:Q",
        y="Loss:Q",
        color=alt.Color(
            "Type:N",
            scale=alt.Scale(domain=["Training Loss", "Validation Loss"], range=["#306998", "#FFD43B"]),
            legend=None,
        ),
    )
)

# Annotation for minimum validation loss
min_marker = (
    alt.Chart(min_point_df)
    .mark_point(size=300, shape="diamond", filled=True, color="#E63946")
    .encode(x="Epoch:Q", y="Loss:Q")
)

# Text annotation for optimal stopping point
min_text = (
    alt.Chart(min_point_df)
    .mark_text(align="left", dx=12, dy=-10, fontSize=16, fontWeight="bold", color="#E63946")
    .encode(x="Epoch:Q", y="Loss:Q", text=alt.value(f"Min Val Loss (Epoch {min_val_epoch})"))
)

# Combine all layers
chart = (
    (lines + points + min_marker + min_text)
    .properties(
        width=1600,
        height=900,
        title=alt.Title("line-loss-training · altair · pyplots.ai", fontSize=28, anchor="middle"),
    )
    .configure_axis(labelFontSize=18, titleFontSize=22, gridOpacity=0.3)
    .configure_legend(labelFontSize=16, titleFontSize=18)
    .configure_view(strokeWidth=0)
)

# Save as PNG (4800 x 2700 with scale_factor=3)
chart.save("plot.png", scale_factor=3.0)

# Save as HTML for interactivity
chart.save("plot.html")

Part of Training Loss Curve on anyplot.ai.

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