HistogramObserver

Per-tensor observer that records a value histogram and picks a clip range.

The accuracy-maximising activation observer. Instead of committing to the raw [min, max] — which on a heavy-tailed activation would stretch the grid over a handful of rare extremes and quantize the dense bulk coarsely — it accumulates a bins-bucket histogram of every value seen (via the engine histc primitive), then at calculate_qparams time searches for the clip range [new_min, new_max] that minimises the expected L2 quantization error. Clipping the tails costs a little error on the rare outliers but wins far finer resolution on the common values, which is usually a large net accuracy gain.

When to pick it. Use it for activations with skewed / heavy-tailed distributions — it is the activation observer in lucid.quantization.get_default_qconfig (static PTQ). It is more expensive than min/max (it maintains a histogram and runs a search) and applies to per-tensor affine schemes, so it is not used for per-channel weights (see PerChannelMinMaxObserver). When calibration is cheap and distributions are light-tailed, plain MinMaxObserver / MovingAverageMinMaxObserver suffice.

The running range widens with the data; when it grows the existing histogram is rebinned onto the wider support before the new batch is added. With bin centers $c_i$ and counts $n_i$, the search evaluates candidate clip endpoints $[a, b]$ (drawn from a few tail quantiles) and picks the pair minimising the per-value clip error plus the uniform-quantization noise variance:

where the first term is the squared clipping error (mass pushed onto the boundary) and $\Delta^2/12$ is the variance of rounding to a uniform grid of step $\Delta$. The winning $[a, b]$ is then fed to lucid.quantization.calculate_qparams for the final affine (scale, zero_point).