[alxmrs]

🪭 Claude (einfold)

einfold now finds a SUM of a product whose factors read three or more joined relations. In a ddx gradient step, these are the softmax-weighted sums over attention's saved scores. ddx is an XQL Systems project for automatic differentiation of SQL queries. On spike S31's steps, at 1,024 tokens:

• attention's output O = softmax(S)·V from the saved scores takes 33 ms with einfold, against DataFusion's 302 ms;
• dV = Pᵀ·dO takes 33 ms, against 653 ms.

Both run on the dense algorithm. The two take 0.7–0.9 s of einfold's 1.7–2.1 s per attention gradient, and the GPT's dP and attention output have the same shape.

In such a step, the plan joins the saved scores s, the values v, and the saved normalizer z, and sums exp(s − m) / z.z * v.x. Its first factor reads s and z, so no single join in the plan splits the product into two operands, and the detector declined.

Decisions to review

• Regrouping the joins (regrouped). Inner joins on equalities can be joined in any order and give the same rows. So where the top join doesn't split the product, the detector:

  1. collects the relations under the inner equi-joins, and assigns each to the factor that reads it;
  2. joins a relation neither factor reads into the side it's joined with;
  3. joins each side's relations into one operand, on the equalities between them, and makes the equalities between the sides the fold's keys.

  It declines where both factors read one relation, a relation is joined with both sides or neither, a side's relations aren't joined to each other, or a column's name is in two relations. DataFusion still computes each operand, joins and windows included. The node keeps the original plan as its fallback, as every node does. The alternative was a pipeline whose producer is a table read, in the fused kernel. That needs a table producer, masks taken from missing rows, and batch dimensions, which the fused kernel doesn't have. This change is detection alone, and reaches any such product, not only softmaxes.

• Float / and % may be computed on an operand's every row (movable). On floats, DataFusion gives inf or NaN for a division by zero, never an error. It still fails on integers, so an integer / stays above the join, as fallible_factors_stay_above_the_join checks. Before this change, a factor such as w / z kept even a two-table product from being found.

• Operand order. The first factor's relations are the first operand, which matters to the dense algorithm: only its first operand may have missing rows without a domain's default. That suits S31's steps, whose first factor is the masked scores.

How it is tested

• The property test detect_vs_host draws three-relation products: (l.v / m.v) * r.v with m joined to l, l.v * (r.v + m.v) with m joined to r, and (l.v * m.v) * r.v, where m is the domain table by another name. Look-alikes must decline: m joined to both l and r, or read by both factors. The invariants, over 3,000 cases with NULL and duplicate keys, missing rows, NaN, ±inf and zeros (so that divisions by zero happen):
  • the same rows as DataFusion, bit for bit;
  • the rule fires on each product and never on a look-alike.
• A hand test, products_over_saved_scores_run_dense, is S31's O step: a window over causal scores, a saved normalizer, and values. It checks dense_folds=1, no host plan, and results within 1e-12 of DataFusion's.

🤖 Generated with Claude Code

https://claude.ai/code/session_01M96xSez6PZwTmfaGh2eJgS

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[alxmrs]

🪭 Claude (einfold)

Closed when its base branch was deleted after #129 merged; continued as #131.