Tensor Statistics
Every view in Tensormorph that shades, colors, or summarizes a tensor - the Architecture view's magnitude-heatmap shading, the Matrix/Heatmap view, the Inspector panel's summary card - draws from the same underlying set of tile statistics, computed once and reused everywhere rather than recomputed per view.
What gets computed
For any region of a tensor (down to a single tile, up to the whole thing), Tensormorph maintains:
- Moments - mean, variance/standard deviation, and higher moments where relevant.
- Extremes - min, max, and absmax (the largest absolute value, which matters more than min/max alone for symmetric weight distributions).
- Norms - L1 and squared-L2, the basis for magnitude shading and for outlier detection.
- Special-value counts - NaN count, Inf count, and zero count (the latter doubling as the basis for sparsity measurement).
- A log-scale histogram - the binned value distribution, which is what powers Histograms and Distributions.
Why "mergeable" matters
Tile statistics are monoid-mergeable: the statistics for a coarse region can be computed directly from the statistics of its constituent finer tiles, without ever re-reading the raw values underneath them.
This is what makes level-of-detail streaming work for a trillion-parameter model: an overview of an entire layer doesn't require touching every scalar in it, only combining the already-computed statistics of its tiles. It also means a statistic is well-defined and cheap at any granularity - a single scalar, a tile, a tensor, or an entire model - using exactly the same aggregation logic throughout.
Where statistics stop being enough
Tile statistics are deliberately cheap: they're designed to be computed once during indexing and reused everywhere. Some questions need more than that - effective rank, principal components, or pairwise similarity between two tensors require actually reading more of the underlying data, not just combining precomputed summaries. Tensormorph treats those as a distinct, explicitly-requested tier of analysis rather than something that happens automatically as you navigate; see SVD, PCA and Effective Rank.
Reading statistics in the Inspector
Selecting any node - a whole tensor, a tile, a row - shows its statistics in the Inspector panel's summary card. The same numbers are queryable directly through TQL, so a question like "which layers have the largest absmax" is a query over already-computed statistics, not a scan over raw weights.
Related resources
- Histograms and Distributions - the log-histogram statistic, visualized.
- NaN and Inf Detection - built directly on the special-value counts above.
- Level of Detail and Streaming - how mergeable statistics enable LOD rendering.