Researcher posts underfitting vs overfitting visualizations

A researcher posting from the X account Mathemetica shared a thread on May 24 comparing underfitting, optimal fitting and overfitting with side-by-side visualizations of model behavior. The post, identified by ID 2058533673767670102, presented training and validation error curves as the main diagnostic for how a model performs as complexity changes. The thread also referenced regression metrics including mean absolute error, mean squared error, root mean squared error and R-squared, according to the post description. (scikit-learn.org) The post linked readers to Python examples on GitHub for plotting the evaluation outputs. (x.com) ### Why do training and validation curves matter in a post like this? Training and validation curves are the standard way to show whether a model is learning signal or memorizing noise. Scikit-learn’s documentation says underfitting appears when a model is too simple to capture the underlying pattern, while overfitting appears when a model is too complex and tracks the training data too closely. In practical terms, a low-capacity model tends to produce high error on both training and validation data, while an overfit model often shows training error continuing to improve as validation error stops improving or worsens. (x.com) The Mathemetica thread used that familiar contrast as a visual teaching device. Posts of this kind usually put the three regimes — underfit, well-fit and overfit — in one sequence so readers can compare not only the fitted curves but also the divergence between train and validation performance. That framing matches the example published in scikit-learn’s official gallery, which uses different polynomial degrees to show the same progression. ### What do MAE, MSE, RMSE and R² add beyond a single accuracy chart? (scikit-learn.org) MAE, MSE, RMSE and R² describe different aspects of regression performance. IBM says underfitting and overfitting are core model-selection problems, and practitioners typically need more than one metric to see whether errors are large, whether outliers are being punished heavily, and how much variance the model explains. MSE and RMSE amplify larger misses because they square the residuals, while MAE tracks average absolute error in the original unit scale. R-squared measures how much of the outcome variance is explained relative to a baseline model. (scikit-learn.org) Accuracy curves are more common in classification tasks, where the same train-versus-validation comparison can flag a model that is too simple or too tuned to the training set. The value of placing those plots next to regression metrics is that readers can see the same generalization problem across task types instead of treating overfitting as a single-number issue. ### What does an “optimal fitting” picture usually show? An “optimal fitting” panel usually shows the narrowest useful gap between training and validation performance. (ibm.com) Scikit-learn’s example illustrates that middle case with a model complex enough to capture the curve in the data but not so flexible that it chases individual sample noise. In such a chart, validation error is near its minimum and training error is low without collapsing into an unrealistic perfect fit. A visual like that is often more legible than a text definition. (github.com) Readers can see that the target is not the absolute lowest training error, but the best out-of-sample behavior. That distinction is the point of using a held-out validation set in the first place. ### Where can readers go next if they want to reproduce the plots? The May 24 X post pointed readers to GitHub code examples for plotting the metrics and curves. Scikit-learn already publishes a working underfitting-versus-overfitting example using polynomial regression, cross-validation and MSE reporting, which gives readers a baseline implementation they can adapt to their own data. (scikit-learn.org) GitHub repositories and notebooks built on that pattern typically extend it with additional metrics and styling for educational use. The next step for readers is to inspect the linked repository from post 2058533673767670102 and compare its plotting code with the official scikit-learn example. (ibm.com) That will show which metrics, datasets and model settings the author used in the May 24 thread. (x.com)