Why does a one-batch overfit test floor at 0.4 loss when random cropping and colour jitter stay on?

## What the test assumes Driving the loss to zero on one batch is only meaningful if the batch is *the same batch every step*. The whole argument rests on memorization: a model with more parameters than the batch has examples can, by rote, map those specific inputs to those specific labels. The moment the inputs stop being fixed, the argument evaporates. ## What augmentation does to it Random cropping picks a different sub-window on every pass; colour jitter shifts brightness, contrast and saturation by fresh random amounts. Eight images therefore become an effectively infinite family of images, all sharing eight labels. The model is no longer memorizing eight points — it is learning a function that must be correct across the whole augmented family, which is the real learning problem in miniature. That problem has a nonzero optimum for any finite-capacity model, so the loss descends, slows, and parks at some positive value like 0.4. The misdiagnosis is natural, because the curve looks exactly like a model that cannot represent the target: descent, then a flat floor. Two signatures distinguish them. A floor caused by input randomness is stable and low-variance across restarts and sits at the same level whether you train for 500 steps or 5000. And the discriminating experiment is one line of configuration away: disable augmentation and rerun. ## The order in which you switch things off Several mechanisms can put a floor under the loss, and they should be removed in decreasing order of effect: 1. **Input augmentation.** It changes what the model sees, so it breaks the memorization premise outright. Off first, always. 2. **Dropout and any stochastic-depth-style randomness.** These perturb activations each step, so the network is optimizing an average over sub-networks rather than one function. The loss can still get small, but it is noisy and floors above zero. 3. **Label smoothing.** This one is a genuine mathematical floor rather than noise. If the target is a smoothed distribution instead of a one-hot vector, the smallest achievable cross-entropy is the entropy of that smoothed target, which is strictly positive. A perfectly memorizing model will never print zero, and no amount of training changes that. If you must keep it on, compute the floor for your smoothing coefficient and class count, and compare against that number instead of against zero. 4. **Weight decay.** It pulls weights toward the origin and so competes weakly with exact memorization. In practice it slows the descent more than it raises the floor, which is why it is removed last. ## A cleaner way to read the run Even with augmentation on, you can recover a usable signal by evaluating on the *un-augmented* fixed batch while training on the augmented stream. Training accuracy on those eight canonical inputs should climb to 100% quickly even though the augmented loss stays at 0.4. If accuracy on the fixed inputs also refuses to move, the problem really is in the model or the loop, and augmentation was a red herring rather than the cause. ## A related pattern worth naming The reverse asymmetry is more confusing and more informative: the one-batch test fails, but a 200-example subset trains happily to near-zero loss. A harder rung passing after an easier rung failed means the *test setup* is the anomaly, not the model. The usual causes are batch-size-dependent behaviour in normalization layers — with a single example a fully-connected batch-normalization layer emits only its learned shift, discarding the input entirely — a batch that happens to contain duplicate inputs with conflicting labels, so no function can fit both, or a sampler that quietly draws fresh examples each step when you believed the batch was pinned. Fix the test, then rerun it; do not conclude that the rung can be skipped. ## The habit to build Write the sanity run as a deliberate configuration in which augmentation, dropout, smoothing and decay are all disabled together, rather than something you assemble by hand each time and half-remember. Most of the false alarms this rung produces come from inheriting a training configuration written for the full run and forgetting that half of it exists specifically to *prevent* memorization — which is precisely the thing you are trying to demonstrate.