[alxmrs]

Why

grad and vjp refused a UNION ALL between a wrt table and the loss (#144). That blocks GraphCast-shaped models: each message-passing MLP reads an edge's, its sender's and its receiver's features concatenated with UNION ALL, at offset feature indices. jvp already had a rule.

How

Reverse mode recomputes the row-local work between saved aggregates as one relation, a region, and every transpose rule reads a row's own columns. A union's rows come from different inputs, so it is rebuilt to fit:

• Each input's rows carry its own columns, a column that is TRUE in them (Def::Branch), and NULL in every other input's columns.
• Those NULLs need the engine's types, which ddx doesn't know. So each input is FULL JOINed ON TRUE to LIMIT 0 copies of the others.
• Each column of the union (Def::Union) reads the column of the input that gave the row.
• Its transpose is a select, as jnp.concatenate's is a slice: the cotangent goes to that input's column, and NULL (no cotangent) to the others'.

Everything beneath an input reads only its own columns. So its cotangents are NULL in other inputs' rows, and those rows send it no gradient.

Edge cases

• DataFusion's union names. DataFusion names a union's columns after its first input's, without their tables, and suffixes a repeat (x_1). A table can already have an x_1 column, and a union over a union always does, so DataFusion refused the union. Each input's columns are now renamed after their qualified names first, as ddx already does for windows.
• More than one row. A union of one-row inputs has several rows, so grad no longer takes it for a scalar loss.
• Windows over a union. Rows from different inputs can share dims, so the input column is part of the key that sums a window's cotangents back to its rows.
• Contractions. The contraction rule declines a union region and accepts a union as one input of its join.
• UNION (distinct) is still refused. DataFusion plans it as a GROUP BY over UNION ALL, and the key that depends on wrt is what's refused.
• Performance. Plans without a union are unchanged.

Tests

• crates/ddx-datafusion/tests/union_all.rs has 14 cases, each checked against finite differences, on Substrait and with DDX_STEPS_AS_SQL=1:
  • two tables concatenated, and one table read by both inputs;
  • an input that reads no wrt table;
  • groups that take rows from both inputs, and a union of aggregates;
  • features concatenated and then multiplied by a weight;
  • a maximum tied across the inputs, and a window over both inputs' rows;
  • nested unions, and a table with columns named i_1 and x_1;
  • a NULL value, and a group whose key is NULL;
  • two refusals.
• tests/test_query_jax.py adds GraphCast's message passing against jax.grad of jnp.concatenate.
• ddxdb runs the issue's case on DataFusion and on DuckDB, where steps run as SQL.
• The full Rust suite and the soak pass.

Next

#127 and #88 (soak coverage), then #186 (fewer, larger steps).

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https://claude.ai/code/session_01CvszJhH8pn8H9G69wEPMU2

Summary by CodeRabbit

• New Features

  • Gradient calculations now support queries that combine results with UNION ALL, including when the combined rows are used in grouping, joins, or window operations.
  • Gradients are routed to the source of each row, including when multiple branches contribute to shared groups.
  • Added a way to create a zero-row relation while preserving the input’s columns.

• Documentation

  • Updated the design documentation to reflect UNION ALL support in reverse-mode gradients.

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Files selected for processing: 1

• crates/ddx-ad/src/transpose.rs

Files skipped from review as they are similar to previous changes: 1

• crates/ddx-ad/src/transpose.rs

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Walkthrough

The change adds reverse-mode support for UNION ALL, including branch-aware forward lowering and cotangent routing. It adds gradient tests across SQL backends and a separate SQL-to-JAX message-passing gradient comparison.

Changes: UNION ALL reverse-mode support

Layer / File(s)	Summary
Union representation and lowering crates/ddx-ad/src/forward.rs, crates/ddx-ad/src/emit.rs, crates/ddx-ad/src/contraction.rs	Forward lowering adds branch markers and source-column mappings for UNION ALL. It rejects other set operations, empty unions, and inputs with different output widths. Region slicing and appending preserve or remap union definitions. no_rows creates a fetch relation with a count of zero.
Cotangent routing crates/ddx-ad/src/transpose.rs, docs/design.md	Reverse mode includes branch markers in row identity and routes each output cotangent to its source input. The design documentation describes the concatenate transpose rule.
UNION ALL gradient validation crates/ddx-datafusion/tests/union_all.rs, python/ddxdb/tests/test_ad.py, python/ddxdb/tests/test_duckdb.py	Tests cover gradients through unions, nested unions, aggregates, joins, windows, NULL cases, and unsupported operations.

Message-passing gradient comparison

Layer / File(s)	Summary
SQL and JAX gradient comparison tests/test_query_jax.py	A seeded message-passing test compares SQL gradients for edge features, node features, and weights with jax.grad.

Priority: Normal

Estimated code review effort: 3 (Moderate) | ~25 minutes

Change: Feature

Sequence Diagram(s)

sequenceDiagram
  participant Builder
  participant union_all
  participant region_once
  participant InputColumns
  Builder->>union_all: Lower set relation
  union_all->>Builder: Return branch-marked relation
  Builder->>region_once: Provide union output definitions
  region_once->>InputColumns: Route cotangents by branch marker

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Possibly related issues

• xqlsystems/ddx#150 — The issue identifies UNION ALL as a blocker for GraphCast gradient support. This change adds reverse-mode UNION ALL handling and a message-passing gradient comparison.

Merge Risk: Minimal · up to 045a5

The union-arm routing change has no identified issue that needs to be resolved before merge.

Security architecture risk: Low · up to ec0b6

The change extends gradient computation within the existing query workflow without an identified expansion of privileges or table access. Source-level checks support branch isolation and per-build state ownership, but deployed isolation and runtime resource effects were not verified.

Retained concerns
No architecture-level concerns identified.

Security review details

Security Blast Radius

• inferred — The affected source scope is the caller-supplied query plan and its explicit input relations. Lowering does not discover additional tables through branch metadata. Maximum deployed tenant, service, or environment exposure cannot be established from the supplied evidence.

Trust Boundaries and Controls

• observed — The existing entrypoint still lowers a checked root and verifies that requested differentiation tables were read. Each union input passes through the same wrt-aware dispatcher, including the existing constant path for non-wrt inputs; no authorization mechanism is added or removed by this dispatch.

Resilience and Maintainability Implications

• inferred — Construction failures remain contained within a build: union validation returns errors from locally owned lowering state, and backward construction creates a fresh transposer while borrowing the forward representation immutably. The inspected ownership model does not expose partial transpose state to subsequent or concurrent builds.

Pre-merge checks: 4 · 1

Failed checks: 1 warning

Check name	Status	Explanation	Resolution
Docstring Coverage		Docstring coverage is 70.00% which is insufficient. The required threshold is 80.00%. Docstring coverage is scoped to functions touched by this diff with cyclomatic complexity of at least 2. Documenta…	Write docstrings for the functions missing them to satisfy the coverage threshold.

Passed checks: 4 passed

Check name	Status	Explanation
Description Check		Check skipped - CodeRabbit’s high-level summary is enabled.
Title check		The title clearly and concisely states that reverse-mode differentiation through UNION ALL was added, which matches the main change.
Linked Issues check		Check skipped because no linked issues were found for this pull request.
Out of Scope Changes check		Check skipped because no linked issues were found for this pull request.

Full details: Docstring Coverage

Explanation

Docstring coverage is 70.00% which is insufficient. The required threshold is 80.00%. Docstring coverage is scoped to functions touched by this diff with cyclomatic complexity of at least 2. Documentation-only edits and deletions within surviving functions are included; unchanged diff context and fully deleted functions are excluded. Analyzed 10 functions across 8 files.

Resolution

Write docstrings for the functions missing them to satisfy the coverage threshold.

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Inline comments:
Review comments at @crates/ddx-ad/src/transpose.rs:
- Around line 659-664: In the Def::Union transpose loop over arms, skip each
source column whose region.varied[col] is false before adding a cotangent term
to pending. Preserve the existing term generation for varied columns.

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Reviewing files that changed from the base of the PR and between 9576911 and ec0b661.

Files selected for processing: 9

• crates/ddx-ad/src/contraction.rs
• crates/ddx-ad/src/emit.rs
• crates/ddx-ad/src/forward.rs
• crates/ddx-ad/src/transpose.rs
• crates/ddx-datafusion/tests/union_all.rs
• docs/design.md
• python/ddxdb/tests/test_ad.py
• python/ddxdb/tests/test_duckdb.py
• tests/test_query_jax.py

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[alxmrs]

LGTM