Synthetic linear regression

300 observations generated from y = 2x + 1 + noise, with x sampled uniformly from [−2, 2) and noise uniformly from [−0.6, 0.6). A fixed shuffled split assigns 240 rows to training and 60 to validation.

• Generation seed: 42. A 32-bit LCG (1664525 × state + 1013904223, modulo 2³²) produces inputs and noise, then a Fisher–Yates shuffle assigns the split.
• The same 300 rows and split are used for every learning-rate comparison. Neither initialization nor learning rate regenerates the dataset.
• Only x is a model feature. The target, split, and row identifier are never used as input features. There is no fitted preprocessing.
• Validation loss is useful for these comparisons, but repeated tuning on it does not produce an unbiased test score. There is no separate test set.
• Noise prevents a single straight line from fitting every target exactly. This is synthetic regression, not MNIST or a GPU benchmark.

Counts exclude the row identifier. Duplicate counts are extra occurrences after the first. Feature duplicates ignore labels and experimental conditions. — means a statistic is undefined or not applicable.

Row

Stable identifier within this synthetic fixture.

Input x

Raw input, rounded to six decimals. No fitted normalization.

Target y

2x + 1 plus sampled noise, rounded to six decimals.

Split

Training rows determine gradients; validation rows are used only to evaluate the fitted line.