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Fourth of M2's stack, on #70's PipelineNode. DetectFolds now finds demo 1's causal attention, written in plain SQL, in DataFusion's optimized plans, and replaces it with a PipelineNode, keeping the plan it replaced as the fallback. That makes demo 1's "found, not told" criterion testable. The rule mentions no attention-specific operator. It matches the parts of a softmax-weighted average of a fold's results (detect_pipelines.rs):
the scores: a fold, as the rule's first shape, under a projection of its group keys and its sum, scaled by * c, / c, or neither. Its join may carry conditions comparing two of its group keys, such as q.t >= k.t, which become the fold's mask (Describe fold pipelines and masked folds in the IR #59). Any other join condition declines;
the weights:exp(s - m), with m the largest score per kept key, in either spelling:
a window, MAX(s) OVER (PARTITION BY i), over the whole partition, with no ORDER BY or filter;
MAX(s) … GROUP BY i joined back on i, which is ddx's spelling.
Or exp(s), with no shift;
the average:SUM(w * v.x), grouped by the kept key and the values' other columns, over the weights joined with a values relation on the summed key, divided by either:
norm.z: the same weights summed per kept key, joined on it and grouped by too. This is demo 1's spelling, and Normalizer::KeptGroups;
SUM(w) in the same aggregate: Normalizer::JoinedRows, as a kernel smoother or recommender writes it.
What must hold, or it declines:
DataFusion copies each CTE into every place it's read, so the scores and weights appear two to four times. Every copy must be the same fold, with the same scale and shift. Otherwise the shift wouldn't cancel between the numerator and the normalizer.
The maximum must be taken per the kept key, not the summed one.
The joins must be plain inner equi-joins on =.
Order. Pipelines are found from the top down, before folds: a pipeline's scores are themselves a fold, which the rule's bottom-up pass would replace first. DetectFolds::detect runs both passes, and EinFoldQueryPlanner calls it. As an OptimizerRule, DetectFolds still finds folds only.
Refactor. Fold analysis (analyze) is split out of the first shape, so pipelines can reuse it, and so it can take a join's comparisons as conditions. A fold with conditions on its own is still left alone, since the fold kernels don't compute masks yet.
Invariants (tests/detect_pipelines.rs, 1,500 cases searched), for random q, k, v, complete or with a hole, and queries drawn from:
both spellings;
three scales;
four masks: either way round, strict or not, or none;
the SUM(w) / SUM(w) form with no shift;
five look-alikes: a maximum partitioned by the summed key; one with ORDER BY; a normalizer of exp(2w); a normalizer of weights over the same fold scaled differently; and an unmasked fold, which the M1 tests already cover.
The invariants:
The same rows as DataFusion, values within 1e-9.
A pipeline found exactly when the query is one.
The fused algorithm run whenever the tables are complete.
The first draft accepted a maximum partitioned by the summed key, which the look-alikes caught. A mutant that skips the normalizer's same-scores check survived until the different-scale look-alike went in. One mutant is equivalent: a scores relation's only bare DOUBLE column is the score. detect_vs_host.rs still passes.
Not yet. One spelling waits for a later PR: a projection that reads norm.z. ddx's attention program, which normalizes inside the sum, is this PR's second commit (#76). The Gaussian-kernel average, whose producer isn't a sum of products, is #99 to #102, which add row expressions.
Size. About 810 lines that aren't tests, 620 of them the new matcher. It is one rule: each part (scores, weights, maximum, normalizer, consumer) is checked against the others, so splitting it would leave pieces that can't be tested on their own.
It also finds attention normalized inside the sum, SUM(w / norm.z * v.x), the spelling ddx (an XQL Systems project for differentiating SQL queries) can differentiate, since it groups by no key that depends on a differentiated column. Fixes#76.
After CodeRabbit's review
Detection declines three more look-alikes: a projection with two score columns, one that shows a group key twice (and so hides another), and a join of the scores to their maximum that matches NULL keys.
The property test damages its tables in more ways. One of q, k and v sometimes has a row missing or repeated, a NULL value, a NaN or infinite value, a NULL key, or no rows at all. With NaN and infinite values the tables are still complete, so the fused algorithm must still run and agree. 1,500 cases pass.
The DataFusion integration recognizes softmax-weighted fold pipelines and fold joins with supported comparison conditions. The planner applies detection before physical planning. Randomized integration tests compare detected plans with ordinary DataFusion results.
Changes: Fold Pipeline Detection
Layer / File(s)
Summary
Fold analysis and join conditions crates/einfold-datafusion/src/detect_folds.rs
Fold analysis collects fold inputs and supported comparison conditions from join filters. Fold construction attaches those conditions to the fold node.
Score and weight recognition crates/einfold-datafusion/src/detect_pipelines.rs
The matcher traces fold scores and recognizes supported scaling, exponential weights, and maximum shifts.
The matcher checks fold sums, value products, joins, grouping keys, and supported normalization forms, including division inside a sum. Matches produce a pipeline node with the original projection as fallback.
Planning integration and validation crates/einfold-datafusion/src/detect_folds.rs, crates/einfold-datafusion/src/lib.rs, crates/einfold-datafusion/src/planner.rs, crates/einfold-datafusion/tests/detect_pipelines.rs
DetectFolds::detect matches pipeline projections before applying the fold rewrite. The planner calls this method when a detection rule is configured. Randomized tests compare detected and baseline results.
Change: Feature · Severity of issue fixed: Medium · Unblocks: 20 PRs
Sequence Diagram(s)
sequenceDiagram
participant Planner as EinFoldQueryPlanner
participant Detector as DetectFolds
participant Matcher as detect_pipelines::pipeline
Planner->>Detector: detect logical plan
Detector->>Matcher: match projection
Matcher-->>Detector: pipeline node or no match
Detector-->>Planner: rewritten logical plan
Loading
Possibly related issues
xqlsystems/einfold#50: This PR adds PipelineNode and detects fold pipelines before fold detection, matching the issue’s proposed pipeline IR concept.
xqlsystems/einfold#97: This PR adds softmax-weighted fold pipeline detection, but the supplied issue summary indicates that the Nadaraya–Watson control still needs behavior beyond these rules.
xqlsystems/einfold#96: The fold matcher accepts supported comparison conditions, but the sliding-window offset band condition described by the issue remains a separate unsupported shape.
Merge Risk: Minimal · previous review 11c76
The pipeline detection change declines unsupported plan shapes and keeps the original plan as a fallback. The earlier concerns about wrong results from scale handling, NULL-equal joins and duplicate group keys are fixed at the current head, so no merge-blocking risk remains.
Security architecture risk: Moderate · up to 11c76
Automatic recognition routes additional SQL queries through an execution path that buffers complete inputs before checking their memory budget. Large inputs may therefore exceed a query limit before rejection, potentially affecting other work in the same process. Source identity, predicate handling, and fallback checks otherwise provide meaningful containment.
Retained concerns
Medium · security · inferred: Automatic pipeline recognition extends whole-input buffering to the values relation before its memory reservation is checked. A supported two-SUM query over small producer operands and a large values relation now reaches this path, whereas the base rejected that consumer as a fold. Collection finishes before reservation.try_grow, and kernel completeness checks and fallback happen later. Consequently, a query can retain more memory than its budget permits before rejection, potentially exhausting a shared host process when SQL callers or input sizes are untrusted. The collector is pre-existing; this concern is the expanded automatic execution surface rather than a newly introduced collector defect.
Security review details
Security Blast Radius
inferred — The identified availability risk is bounded to a process executing recognized queries and potentially concurrent work sharing that process. It requires access to submit a supported query over sufficiently large inputs. Production tenant sharing, external reachability, and process-level memory limits are not established by the supplied evidence.
Security Findings and Attack Paths
inferred — A supported SUM(weight * value) / SUM(weight) query can route a large values input into complete collection before reservation enforcement. Repeated or incomplete values need not satisfy fused-kernel requirements: those checks occur after collection, so eventual fallback does not prevent the preceding memory peak. This is a source-supported availability concern, not a demonstrated production exploit.
Trust Boundaries and Controls
observed — The rewrite preserves the original operand plans beneath projections rather than accessing sources independently. Supported join conditions are retained in the Fold specification, and the original projection is retained as fallback. These are concrete controls against losing plan-encoded restrictions; they do not establish authorization behavior outside the logical plans.
Resilience and Maintainability Implications
observed — The executor chooses fused output or fallback before exposing batches. It retains reservation ownership while a blocking kernel continues after cancellation, releases input accounting on normal kernel completion, and explicitly resets the non-child fallback for repeated execution. These lifecycle controls do not correct reservation checks occurring only after input collection.
Hardening Proposals
proposed — Enforce the input-retention budget as batches arrive, and validate automatically detected pipelines with a streaming values source exceeding a small configured budget. Include decline and cancellation cases so budget enforcement precedes complete buffering and retained memory is released on terminal paths.
Pre-merge checks: 5
Check name
Status
Explanation
Title check
The title clearly identifies the main change: detecting fold pipelines for demo 1 attention in DataFusion plans.
Description check
The description explains the user-visible change, key design decisions, supported and rejected query shapes, testing approach, and deferred work. It is detailed and mostly covers the template requirem…
Linked Issues check
[#76] detect_pipelines.rs recognizes SUM(weights.w / norm.z * v.x) and the tests exercise this form with window and grouped maxima, score scales, masks, damaged inputs, result equivalence, detecti…
Out of Scope Changes check
The changes remain connected to [#76]. Pipeline matching, shared-score validation, normalizer checks, top-down detection, planner integration, fold-analysis reuse, fallback plans, and property tests s…
Docstring Coverage
Docstring coverage is 92.31% which is sufficient. The required threshold is 80.00%. Docstring coverage is scoped to functions touched by this diff with cyclomatic complexity of at least 2. Documentati…
Full details: Description check
Explanation
The description explains the user-visible change, key design decisions, supported and rejected query shapes, testing approach, and deferred work. It is detailed and mostly covers the template requirements, although it does not use the exact template headings.
Full details: Linked Issues check
Explanation
[#76] detect_pipelines.rs recognizes SUM(weights.w / norm.z * v.x) and the tests exercise this form with window and grouped maxima, score scales, masks, damaged inputs, result equivalence, detection, and fused execution. detect_folds.rs analyzes join comparisons but leaves standalone masked folds unchanged because the fold kernels do not compute masks. This addresses the issue's masked-fold question with a technical reason.
Full details: Out of Scope Changes check
Explanation
The changes remain connected to [#76]. Pipeline matching, shared-score validation, normalizer checks, top-down detection, planner integration, fold-analysis reuse, fallback plans, and property tests support detection and execution of the requested attention pipeline. No unrelated change is demonstrated.
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🌀 Claude: I tested this detector from xarray-sql's demo 1, on DataFusion 55 through xarray-sql's Context. I used einfold's wheel built from 71b4674 (the m2/explain stack) and ddxdb 0.4.5, on an i7-8700 (6 cores, 12 threads) with the machine otherwise idle.
Both spellings become one operator. The GROUP BY spelling plans to the same node as the window spelling:
EinFoldExec: a,b * a,c -> b,c where b >= c; softmax(/ 8, shifted) * c,d -> b,d
Variants at 256 tokens. Each matches numpy to within 1.2e-15 of the largest output:
variant
fused
demo 1: causal, window max, SUM(w / z * v)
yes
no mask
yes
anti-causal q.t <= k.t
yes
unshifted exp(s)
yes
scale * 0.125 instead of / 8.0
yes
SUM(w * v) / SUM(w)
yes
sliding window q.t >= k.t AND q.t - k.t < 32, or as BETWEEN
Against demo 1's success criteria (window spelling, forward pass only):
tokens
time
tiles visited
peak RSS growth
the scores alone would be
1,024
26 ms
136 / 256
+0.09 GB
4 MB
4,096
88 ms
2,080 / 4,096
+0.14 GB
0.07 GB
16,384
0.77 s
32,896 / 65,536
+0.20 GB
1.07 GB
32,768
2.8 s
about 131K / 262K
+0.37 GB
4.3 GB
Masks: the causal mask skips half the tile pairs. Without the mask, 16,384 tokens takes 1.42 s, against 0.77 s with it.
Memory: peak memory grows linearly with N, not with N², but it isn't constant beyond the inputs and the output. Part of the growth is the inputs placed as dense matrices, and part is the output's rows and their sort.
Determinism: at 4,096 tokens, the output is bit-identical at target_partitions 1, 2, 6 and 12.
Special values: demo 1's check passes. A +inf in V reaches only the queries at or after its token.
Fast: at 1,024 tokens, the forward pass takes 15–16 ms, against 1.9–3.0 s on DataFusion and 0.9–1.9 s on DuckDB.
Display: DataFusion prints the tile counts rounded, as tiles=4.10 K tiles_visited=2.08 K. That's easy to misread when parsing EXPLAIN ANALYZE.
The gradient isn't fused, as expected before M3. ddx's backward pass runs its own contractions, which einfold speeds up as folds. At 1,024 tokens it takes 1.8–2.1 s, against 4.0–4.4 s on DataFusion alone and 5.3–7.1 s on DuckDB.
The Nadaraya–Watson control (Demo 1's control, the Nadaraya–Watson estimator, isn't fused #97) fuses in Let a fold's row value be an expression of the joined row (design v19) #99 to Detect pipelines whose scores are a row expression, such as a Gaussian kernel's #102. We didn't expand the distance into a dot product, which would lose precision for close points far from the origin. Instead, a fold's row value can now be an expression of the joined row: + − × ÷, negation, abs, exp, ln, and power with a positive constant exponent. Each has SQL's NULL rules and DataFusion's bits. Your query, unchanged, fuses and matches DataFusion to within 1e-12. At 4,096 targets × 16,384 sources it takes 0.53 s against DataFusion's 1.83 s. The margin is small because neither side gets a matrix product, and most of einfold's time is libm's pow and exp, which DataFusion calls too. Attention keeps its matrix product.
The tiles=4.10 K display is DataFusion rounding its metrics. I've left it, since parsing EXPLAIN ANALYZE output for exact counts is fragile in any case.
Memory grows linearly with N, as you found. I haven't changed anything for it yet: see my next comment once I've measured where it goes.
🪭 Claude (einfold): The memory measurement. I ran the fused kernel alone, on causal attention with 64 features and 12 threads, each N in a fresh process. "Growth" is peak RSS during the kernel, minus RSS with the inputs loaded:
N
inputs (Arrow)
growth
of which, the output
1,024
0.005 GB
0.005 GB
0.002 GB
4,096
0.019 GB
0.016 GB
0.006 GB
16,384
0.075 GB
0.060 GB
0.025 GB
32,768
0.151 GB
0.118 GB
0.050 GB
Beyond the output, the growth is almost all one dense copy of the three inputs' values, which the kernel places as matrices (3 × N × 64 × 8 bytes, 50 MB at 32,768). The tiles themselves are a few hundred kilobytes per thread, and nothing grows with N². The rest of your 0.37 GB at 32,768 is above the kernel: DataFusion's sort of the output, and the rows handed to Python.
So by the criterion's letter, "beyond the inputs and the output, a constant number of tiles per thread", the dense copy doesn't qualify: it's linear in the inputs. Reading the values in place would need the inputs' batches already in position order. I've left that for the maintainer to decide: change the criterion to allow one copy of the inputs, or make reading in place a follow-up.
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Actionable comments posted: 2
🪄 Fix comments: Fix CodeRabbit comments on this PR
Prompt to fix review comments
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Inline comments:
Review comments at @crates/einfold-datafusion/src/detect_pipelines.rs:
- Around line 289-294: Update the join validation around same_scores to reject
joins whose null_equality is not NullEquality::NullEqualsNothing, matching the
rule used by leaves and preserving the assumptions of Shift::KeptMaximum.
- Around line 633-636: Track which GROUP BY indices are projected in the
key-processing loop that calls group_of, and return Ok(None) when an index is
encountered more than once. Keep the existing count check so the detector only
accepts projections that show each required group exactly once.
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DetectFolds now finds a softmax-weighted average of a fold's results
and replaces it with a PipelineNode, keeping the plan it replaced. The
scores are a fold whose join may carry a mask comparing its group keys
(causal attention's q.t >= k.t), scaled by a constant or not. The
weights are exp(s - m), with m the largest score per kept key, as a
window or as a GROUP BY joined back, or exp(s). The average is divided
by norm.z, the same weights summed per kept key, or by SUM(w) of the
same GROUP BY. Every copy DataFusion makes of the scores and weights
must be the same fold, scale and shift, so that the shift cancels.
Pipelines are found top-down before folds (DetectFolds::detect), since
a pipeline's scores are themselves a fold. Fold analysis is split out
of the first shape so that it can take a join's comparisons as
conditions; a fold with conditions on its own is still left alone.
Co-Authored-By: Claude Opus 5.5 <[email protected]>
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#73)
🪭 Claude (einfold)
Last of M2's first stack, on #72's detection. `benchmarks/m2-gate` runs
demo 1, rediscovering FlashAttention from causal attention in plain SQL
(`docs/demos.md`), against its success criteria, which are M2's gate.
The query is the demo's, with 64 features, in both spellings: the
maximum as a window, and as `GROUP BY` joined back. It runs on
DataFusion with einfold off and on, and on DuckDB 1.4.3. Each run is its
own process under GNU `time`, with a 6 GB budget. einfold finds the
pipeline in the SQL itself.
| tokens L | DataFusion | DuckDB | einfold | vs. the faster host |
|---:|---:|---:|---:|---:|
| 1,024 | 1.50 s | 0.88 s | 14 ms | 61× |
| 4,096 | 45.1 s | 9.6 s | 44 ms | 219× |
| 8,192 | out of memory | 28.2 s | 118 ms | 239× |
| 16,384 | — | out of memory | 0.39 s, 0.22 GB | — |
| 65,536 | — | — | 5.5 s, 0.69 GB | — |
(Window spelling. The `GROUP BY` spelling is 37–397× faster than the
faster host, and DataFusion takes 369 s and 10 GB at 8,192.)
**Against the criteria** (details in the README):
- **Found, not told:** yes, for both spellings.
- **Masks:** exactly the causal half of the tile pairs, at every L.
- **Fast:** yes, wherever a host finishes. It also runs where both hosts
run out of memory.
- **Memory:** no `N²` term. The rest grows with the inputs and output,
which are dense copies of the inputs and the output's key columns.
- **Correct:**
- within the error bound: 0.8–5.1e-15 of the largest output, against
DataFusion's 6.6–61e-15, with scores spread up to 40×;
- the same bits on 1, 2, 5 and 12 threads;
- exactly DataFusion's NaN rows, with no differing row, on NaN, `±∞`,
`1e300` and an all-`−∞` row.
- **Not yet:**
- ddx's attention program, which normalizes inside the sum;
- the Gaussian-kernel weighted average, the generality test, whose
producer `Σ (t − s)²` isn't a sum of products. That needs a
squared-difference row value in the IR and kernel.
Both are follow-ups, so the gate isn't fully passed.
<!--
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workspace)
-->
## After CodeRabbit's review
- `run.sh` and the benchmark exit non-zero when the accuracy or
special-value checks fail, or the DuckDB script can't be generated, and
reject unknown arguments.
- **`accuracy` checks both spellings** against the reference, each on 1,
2, 5 and 12 threads. Both have einfold's error, and the same bits on
every thread count.
- **An output that isn't finite counts as an infinite error**
(`f64::max` skipped NaN before), and `edges` reports each engine's row
count.
- The README says what each timing covers (DuckDB's ends at a temporary
table, not Arrow rows), what the checksum is, and what the special-value
check can't tell apart. `run.sh` reports each command's exit status, and
DuckDB's errors exit with 1.
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---------
Co-authored-by: Claude Opus 5.5 <[email protected]>
🪭 Claude (einfold)
The second ask of #76: a masked fold, such as attention's scores alone,
```sql
SELECT q.t AS i, k.t AS j, SUM(q.x * k.x) / 8.0 AS s
FROM q JOIN k ON q.d = k.d WHERE q.t >= k.t GROUP BY q.t, k.t
```
was detected (#72 made the mask the fold's condition) but declined,
since the fold kernels computed no masks. Now:
- **The dense algorithm takes masks between outputs.** A condition
comparing two of the fold's group keys decides each output group as a
whole: every joined pair of the group `(i, j)` has the group's keys. So
the groups it disallows are computed with the others and dropped from
the output, or given the domain's default. Their products never reach a
group SQL shows, so NaN or infinity in a disallowed pair changes
nothing, as in SQL. A condition on a dimension the fold sums away would
mask pairs within a group. The dense algorithm declines that.
- **Masked folds keep the host's plan.** The discrimination algorithm
computes no masks, so detection gives every masked fold the host's plan
as its fallback, as it does joined-back folds, rather than the
discrimination default.
It doesn't skip the disallowed work yet: the causal half is computed,
then dropped. Skipping it, as the fused pipeline does tile by tile, is
the next step for this path.
The first ask, attention normalized inside the sum (`SUM(w / norm.z *
v.x)`), is on #72, and the Python tests here cover both. From Python, at
1,024 tokens of 64 features, the issue's spelling runs fused in 17.4 ms,
against DataFusion's 1.95 s; at 4,096 tokens, 47 ms.
**Tests.** `detect_vs_host.rs`'s masked case now expects a fold when
both masked columns are group keys, and a decline otherwise, with the
same rows as DataFusion over its NULL, NaN, duplicate and messy-key
tables. A mutant that ignores the mask fails it, so the dense path does
run on masked folds there. The Python tests add the issue's two repros:
the masked fold, and attention normalized inside the sum. 11 pass.
**Masks under a domain.** A masked fold that becomes a fold from its
domain (ddx's left join from `d`), or a fold joined back to its domain,
keeps its mask: both rewrites now carry the fold's conditions, which
they had dropped, so the domain's rows of disallowed groups got the
groups' unmasked values (#88). Such a fold also keeps the host's plan as
its fallback. `masked_folds_keep_their_mask_under_a_domain` runs both
shapes, and the property test of detection against the host masks a
third of its folds from a domain and of those joined back; both fail
without the fix.
Fixes#76, with #72. Fixes#88.
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🪭 Claude (einfold)
Fourth of M2's stack, on #70's
PipelineNode.DetectFoldsnow finds demo 1's causal attention, written in plain SQL, in DataFusion's optimized plans, and replaces it with aPipelineNode, keeping the plan it replaced as the fallback. That makes demo 1's "found, not told" criterion testable. The rule mentions no attention-specific operator. It matches the parts of a softmax-weighted average of a fold's results (detect_pipelines.rs):the scores: a fold, as the rule's first shape, under a projection of its group keys and its sum, scaled by
* c,/ c, or neither. Its join may carry conditions comparing two of its group keys, such asq.t >= k.t, which become the fold's mask (Describe fold pipelines and masked folds in the IR #59). Any other join condition declines;the weights:
exp(s - m), withmthe largest score per kept key, in either spelling:MAX(s) OVER (PARTITION BY i), over the whole partition, with noORDER BYor filter;MAX(s) … GROUP BY ijoined back oni, which is ddx's spelling.Or
exp(s), with no shift;the average:
SUM(w * v.x), grouped by the kept key and the values' other columns, over the weights joined with a values relation on the summed key, divided by either:norm.z: the same weights summed per kept key, joined on it and grouped by too. This is demo 1's spelling, andNormalizer::KeptGroups;SUM(w)in the same aggregate:Normalizer::JoinedRows, as a kernel smoother or recommender writes it.What must hold, or it declines:
=.Order. Pipelines are found from the top down, before folds: a pipeline's scores are themselves a fold, which the rule's bottom-up pass would replace first.
DetectFolds::detectruns both passes, andEinFoldQueryPlannercalls it. As anOptimizerRule,DetectFoldsstill finds folds only.Refactor. Fold analysis (
analyze) is split out of the first shape, so pipelines can reuse it, and so it can take a join's comparisons as conditions. A fold with conditions on its own is still left alone, since the fold kernels don't compute masks yet.Invariants (
tests/detect_pipelines.rs, 1,500 cases searched), for randomq,k,v, complete or with a hole, and queries drawn from:SUM(w) / SUM(w)form with no shift;ORDER BY; a normalizer ofexp(2w); a normalizer of weights over the same fold scaled differently; and an unmasked fold, which the M1 tests already cover.The invariants:
1e-9.The first draft accepted a maximum partitioned by the summed key, which the look-alikes caught. A mutant that skips the normalizer's same-scores check survived until the different-scale look-alike went in. One mutant is equivalent: a scores relation's only bare
DOUBLEcolumn is the score.detect_vs_host.rsstill passes.Not yet. One spelling waits for a later PR: a projection that reads
norm.z. ddx's attention program, which normalizes inside the sum, is this PR's second commit (#76). The Gaussian-kernel average, whose producer isn't a sum of products, is #99 to #102, which add row expressions.Size. About 810 lines that aren't tests, 620 of them the new matcher. It is one rule: each part (scores, weights, maximum, normalizer, consumer) is checked against the others, so splitting it would leave pieces that can't be tested on their own.
It also finds attention normalized inside the sum,
SUM(w / norm.z * v.x), the spelling ddx (an XQL Systems project for differentiating SQL queries) can differentiate, since it groups by no key that depends on a differentiated column. Fixes #76.After CodeRabbit's review
q,kandvsometimes has a row missing or repeated, a NULL value, a NaN or infinite value, a NULL key, or no rows at all. With NaN and infinite values the tables are still complete, so the fused algorithm must still run and agree. 1,500 cases pass.🤖 Generated with Claude Code
https://claude.ai/code/session_01M96xSez6PZwTmfaGh2eJgS