Probe: motion = bit shift × transform no-op × shaping — the factorization, measured by AdaWorldAPI · Pull Request #232 · AdaWorldAPI/ndarray

AdaWorldAPI · 2026-07-04T09:51:00Z

The factorization

The operator's reframe of M1: motion compensation in this substrate factors as

bit shift (integer motion = addressing, zero arithmetic — the deterministic PLACE / VPGATHERDD) × transform no-op (the DCT a real codec puts after MC collapses to identity when prediction is good) × shaping (the residue applied directly as a shape, not transform-coded).

M1 already is this — recon = shifted_ref + residual, no transform, and 62.5% of blocks had residual == 0 (transform fully absent). This probe measures the factorization as a tradeoff curve, not three independent stages, because a transform cannot compress white noise, and good motion whitens the residual.

Fairness

All three codings are orthonormal, so quantising with a fixed step Q gives equal L2 distortion (Parseval) — an equal-PSNR byte comparison. Bytes = order-0 Shannon H₀ (ideal rANS). Residual lag-1 autocorrelation ρ is the motion-quality proxy: good motion ⇒ white residual (ρ→0); poor motion ⇒ structured (ρ→1). direct = quantise the residual with no transform (pure shaping); wht/dct = transform then quantise coefficients.

Measured (128×128, 8×8 blocks, Q=6)

residual	ρ (measured)	direct	wht	dct	dct/dir	wht/dct
ρ≈0.00	−0.001	9135	9579	9581	0.95×	1.00×
ρ≈0.30	0.053	8386	8609	8608	0.97×	1.00×
ρ≈0.60	0.419	7664	7147	7146	1.07×	1.00×
ρ≈0.90	0.961	7641	3846	3754	2.04×	1.02×

Both falsifiable claims hold

transform no-op grows with motion quality. dct/dir runs 0.95× → 0.97× → 1.07× → 2.04× as the residual whitens. For a white residual (good motion) the DCT is below no-op (0.95× — it actively costs). It only earns its keep (2.04×) on the structured residual that good bit-shift motion avoids. The transform's value is inversely coupled to the motion's quality — that's "transform no-op," quantified.
a multiply-free sign transform suffices. wht/dct ≈ 1.00–1.02× across the entire sweep — even at ρ≈0.9 where the transform matters most (3846 vs 3754). The ±1 add/subtract Walsh–Hadamard transform — the cognitive shader's "zero FP, zero matmul" idiom — matches the full multiply DCT within 2%. The substrate never needs a multiply-based DCT.

Conclusion

Motion = bit shift (free addressing) × transform no-op (WHT, and vanishing as motion improves) × shaping (the direct residue). Three factors, one tradeoff curve. The codec's "transform" stage is either absent (good motion) or a multiply-free sign transform (bad motion) — never a DCT — which is exactly what a codec that is the zero-FP cognitive shader requires.

Ties to H-7 via the residue CellMode histogram. cargo fmt --check + cargo clippy clean, feature-gated required-features = ["codec"].

Run: cargo run --release --example motion_transform_noop --features codec

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coderabbitai · 2026-07-04T09:51:08Z

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… — measured The operator's claim: a gridlake's cell interdependency, treated as a field operation, reduces to a BF16 16×16 AMX tile GEMM (TDPBF16PS) — the same shape as the intercorrelation / perturbation in a Gaussian splat (the EWA covariance sandwich Σ' = Mᵀ·Σ·M, shipped as hpc::splat3d::spd3::sandwich_x16). Mechanically: a field operation whose output cell is a linear combination of input cells is a linear operator C = A·B — a GEMM; the interdependency IS the coupling matrix. At the gridlake tile granularity (16×16 — a quadrant of the 64×64 gridlake) that GEMM is exactly one hpc::bf16_tile_gemm::bf16_tile_gemm_16x16 call = one TDPBF16PS tile op. Same primitive as the codec separable transform (#232: M·X, WHT/DCT on a tile) and the splat covariance projection (sandwich_x16). Measured on the shipped kernel (this host: AMX TDPBF16PS, amx_available = true), vs a direct f64 reference. Precision reported as Frobenius-relative ‖tile−direct‖_F/‖direct‖_F (the honest aggregate — a per-element max-relative blows up on the near-zero entries a cancellation-heavy Mᵀ·Σ·M naturally has): (1) intercorrelation C = Xᵀ·X frobenius_rel_err = 0.095% (one tile op) (2) covariance sandwich Σ' = Mᵀ·Σ·M frobenius_rel_err = 0.401% (two tile ops) (3) bit-exact on bf16-exact integer operands (|Σ| < 2^24): true (4) throughput: 1.22 M tile-ops/s Conclusion: YES — the gridlake field interdependency reduces to one BF16 16×16 tile op, matching the direct reference to BF16 precision and bit-exact for bf16-exact integer operands. Interdependency / intercorrelation / perturbation / codec transform / covariance projection are ONE op: the 16×16 BF16 tile GEMM. The 64×64 gridlake is 4×4 = 16 of these tiles. fmt + clippy clean, gated required-features = ["std"]. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01MLBnPuScZy6w9di2QEjsXM

…VC 8-tap) Next probe from the HEVC amortization map: HEVC fractional-pel motion compensation applies a separable 8-tap FIR (half-pel luma taps [-1,4,-11,40,40,-11,4,-1]/64). An FIR is a linear operator, so filtering a 16×16 block is a matrix product — one bf16_tile_gemm_16x16 per pass, and the full separable H+V is Hᵀ·(X·H): the SAME two-tile sandwich shape as the splat covariance projection (Mᵀ·Σ·M, #233) and the codec transform (M·X, #232). Measured on real AMX (this host: AMX TDPBF16PS, amx_available = true), vs a direct 8-tap FIR f64 reference (same 16×16 band operator, reflected edges, so only BF16 rounding differs): (1) horizontal 8-tap out = X·H frobenius_rel_err = 0.157% (one tile op) (2) separable H+V out = Hᵀ·(X·H) frobenius_rel_err = 0.215% (two tile ops) (3) throughput: 1.22 M sub-pel tile ops/s Both asserts pass (rel err < BF16 tolerance). Fractional-pel motion is therefore "just another tile op", closing the MC story past integer-pel. R-5 dispatch noted (per-block 8-tap butterfly below the batch crossover, batched tile GEMM above). x86-gated via the same `mod amx` / non-x86 fallback-main pattern as gridlake_field_tile; canonical ndarray::simd imports; fmt + clippy clean. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01MLBnPuScZy6w9di2QEjsXM

The operator's factorization of M1: motion compensation in this substrate is bit shift (integer motion = addressing, zero arithmetic — the deterministic PLACE / VPGATHERDD) × transform no-op (the DCT a real codec puts after MC collapses to identity when prediction is good) × shaping (the residue applied directly as a shape, not transform-coded). M1 already IS this: recon = shifted_ref + residual, no transform, and 62.5% of blocks had residual == 0 (transform fully absent). This probe MEASURES the factorization as a tradeoff curve. All three codings are orthonormal (equal PSNR at a fixed quant step Q); bytes = order-0 Shannon entropy (ideal rANS). Residual lag-1 autocorrelation ρ is the motion-quality proxy (good motion → white residual → ρ→0), because a transform cannot compress white noise. Measured (128x128, 8x8 blocks, Q=6): residual ρ(meas) direct wht dct dct/dir wht/dct ρ≈0.00 -0.001 9135 9579 9581 0.95x 1.00x ρ≈0.30 0.053 8386 8609 8608 0.97x 1.00x ρ≈0.60 0.419 7664 7147 7146 1.07x 1.00x ρ≈0.90 0.961 7641 3846 3754 2.04x 1.02x Both falsifiable claims hold: 1. transform no-op grows with motion quality — dct/dir → 1 (even below, 0.95x) as the residual whitens; the transform is a literal no-op in the good-motion regime and only earns its keep (2.04x) on structured residuals (poor motion), the regime good bit-shift avoids. The transform's value is inversely coupled to motion quality. 2. a multiply-free sign transform suffices — wht/dct ≈ 1.00–1.02x across the whole sweep. The ±1 add/subtract Walsh–Hadamard transform (the shader's "zero FP, zero matmul" idiom) matches the full multiply DCT within 2%, even where the transform matters most. The substrate never needs a DCT. So motion = bit shift (free) × transform no-op (WHT, vanishing as motion improves) × shaping (direct residue) — one tradeoff curve, not three stages. Ties to H-7 via the residue CellMode histogram. fmt + clippy clean, gated. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01MLBnPuScZy6w9di2QEjsXM

… — measured The operator's claim: a gridlake's cell interdependency, treated as a field operation, reduces to a BF16 16×16 AMX tile GEMM (TDPBF16PS) — the same shape as the intercorrelation / perturbation in a Gaussian splat (the EWA covariance sandwich Σ' = Mᵀ·Σ·M, shipped as hpc::splat3d::spd3::sandwich_x16). Mechanically: a field operation whose output cell is a linear combination of input cells is a linear operator C = A·B — a GEMM; the interdependency IS the coupling matrix. At the gridlake tile granularity (16×16 — a quadrant of the 64×64 gridlake) that GEMM is exactly one hpc::bf16_tile_gemm::bf16_tile_gemm_16x16 call = one TDPBF16PS tile op. Same primitive as the codec separable transform (#232: M·X, WHT/DCT on a tile) and the splat covariance projection (sandwich_x16). Measured on the shipped kernel (this host: AMX TDPBF16PS, amx_available = true), vs a direct f64 reference. Precision reported as Frobenius-relative ‖tile−direct‖_F/‖direct‖_F (the honest aggregate — a per-element max-relative blows up on the near-zero entries a cancellation-heavy Mᵀ·Σ·M naturally has): (1) intercorrelation C = Xᵀ·X frobenius_rel_err = 0.095% (one tile op) (2) covariance sandwich Σ' = Mᵀ·Σ·M frobenius_rel_err = 0.401% (two tile ops) (3) bit-exact on bf16-exact integer operands (|Σ| < 2^24): true (4) throughput: 1.22 M tile-ops/s Conclusion: YES — the gridlake field interdependency reduces to one BF16 16×16 tile op, matching the direct reference to BF16 precision and bit-exact for bf16-exact integer operands. Interdependency / intercorrelation / perturbation / codec transform / covariance projection are ONE op: the 16×16 BF16 tile GEMM. The 64×64 gridlake is 4×4 = 16 of these tiles. fmt + clippy clean, gated required-features = ["std"]. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01MLBnPuScZy6w9di2QEjsXM

…ubstrate The durable ledger for the operator's thesis: use the BF16 16×16 AMX GEMM / blasgraph neighborhood / Morton-tile pyramid / perturbation-shader cascade to amortize H.265/HEVC — the per-block cost collapsing to a gather (bit shift) + one TDPBF16PS tile op over a deterministic pyramid built once. Maps every HEVC DSP stage to the substrate primitive, each row tagged MEASURED (#PR) / MECHANISM-unmeasured (probe named) / DOESN'T-FIT: - Motion estimation/compensation → i8/bf16 GEMM + gather [MEASURED #230] - Inverse transform → separable tile GEMM; WHT no-op [MEASURED #232] - Intra prediction / covariance → field-coupling tile op [MEASURED shape #233] - Sub-pel interpolation (8-tap) → separable tile GEMM [MECHANISM — probe] - CTU quad-tree → Morton/HHTL cascade [MECHANISM — shipped] - Deblock/SAO → masked tile op + LUT (the "AMX masking") [PARTIAL — masking] - CABAC entropy → serial arithmetic coding [DOESN'T FIT] Two honest boundaries recorded: (1) CABAC is not a GEMM — the entropy layer is the M2 serial front-end the tile substrate does not amortize; (2) the golden-spiral codec is for directional/sparse data, not dense scalar residuals (#231, measured negative). Cross-repo tie grounded: OGAR's perturbation pyramid IS the Walsh-Hadamard transform of the address tree = the same WHT #232 measured as the codec transform. Includes a probe queue (subpel_tap_tile, intra_angular_tile, deblock_masked_tile, CTU routing parity, M2 CABAC). Anchors: PRs #230–#233; hpc::bf16_tile_gemm, splat3d::spd3, cascade, codec; blasgraph HHTL; OGAR perturbation pyramid. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01MLBnPuScZy6w9di2QEjsXM

… — measured The operator's claim: a gridlake's cell interdependency, treated as a field operation, reduces to a BF16 16×16 AMX tile GEMM (TDPBF16PS) — the same shape as the intercorrelation / perturbation in a Gaussian splat (the EWA covariance sandwich Σ' = Mᵀ·Σ·M, shipped as hpc::splat3d::spd3::sandwich_x16). Mechanically: a field operation whose output cell is a linear combination of input cells is a linear operator C = A·B — a GEMM; the interdependency IS the coupling matrix. At the gridlake tile granularity (16×16 — a quadrant of the 64×64 gridlake) that GEMM is exactly one hpc::bf16_tile_gemm::bf16_tile_gemm_16x16 call = one TDPBF16PS tile op. Same primitive as the codec separable transform (#232: M·X, WHT/DCT on a tile) and the splat covariance projection (sandwich_x16). Measured on the shipped kernel (this host: AMX TDPBF16PS, amx_available = true), vs a direct f64 reference. Precision reported as Frobenius-relative ‖tile−direct‖_F/‖direct‖_F (the honest aggregate — a per-element max-relative blows up on the near-zero entries a cancellation-heavy Mᵀ·Σ·M naturally has): (1) intercorrelation C = Xᵀ·X frobenius_rel_err = 0.095% (one tile op) (2) covariance sandwich Σ' = Mᵀ·Σ·M frobenius_rel_err = 0.401% (two tile ops) (3) bit-exact on bf16-exact integer operands (|Σ| < 2^24): true (4) throughput: 1.22 M tile-ops/s Conclusion: YES — the gridlake field interdependency reduces to one BF16 16×16 tile op, matching the direct reference to BF16 precision and bit-exact for bf16-exact integer operands. Interdependency / intercorrelation / perturbation / codec transform / covariance projection are ONE op: the 16×16 BF16 tile GEMM. The 64×64 gridlake is 4×4 = 16 of these tiles. fmt + clippy clean, gated required-features = ["std"]. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01MLBnPuScZy6w9di2QEjsXM

…VC 8-tap) Next probe from the HEVC amortization map: HEVC fractional-pel motion compensation applies a separable 8-tap FIR (half-pel luma taps [-1,4,-11,40,40,-11,4,-1]/64). An FIR is a linear operator, so filtering a 16×16 block is a matrix product — one bf16_tile_gemm_16x16 per pass, and the full separable H+V is Hᵀ·(X·H): the SAME two-tile sandwich shape as the splat covariance projection (Mᵀ·Σ·M, #233) and the codec transform (M·X, #232). Measured on real AMX (this host: AMX TDPBF16PS, amx_available = true), vs a direct 8-tap FIR f64 reference (same 16×16 band operator, reflected edges, so only BF16 rounding differs): (1) horizontal 8-tap out = X·H frobenius_rel_err = 0.157% (one tile op) (2) separable H+V out = Hᵀ·(X·H) frobenius_rel_err = 0.215% (two tile ops) (3) throughput: 1.22 M sub-pel tile ops/s Both asserts pass (rel err < BF16 tolerance). Fractional-pel motion is therefore "just another tile op", closing the MC story past integer-pel. R-5 dispatch noted (per-block 8-tap butterfly below the batch crossover, batched tile GEMM above). x86-gated via the same `mod amx` / non-x86 fallback-main pattern as gridlake_field_tile; canonical ndarray::simd imports; fmt + clippy clean. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01MLBnPuScZy6w9di2QEjsXM

…ubstrate The durable ledger for the operator's thesis: use the BF16 16×16 AMX GEMM / blasgraph neighborhood / Morton-tile pyramid / perturbation-shader cascade to amortize H.265/HEVC — the per-block cost collapsing to a gather (bit shift) + one TDPBF16PS tile op over a deterministic pyramid built once. Maps every HEVC DSP stage to the substrate primitive, each row tagged MEASURED (#PR) / MECHANISM-unmeasured (probe named) / DOESN'T-FIT: - Motion estimation/compensation → i8/bf16 GEMM + gather [MEASURED #230] - Inverse transform → separable tile GEMM; WHT no-op [MEASURED #232] - Intra prediction / covariance → field-coupling tile op [MEASURED shape #233] - Sub-pel interpolation (8-tap) → separable tile GEMM [MECHANISM — probe] - CTU quad-tree → Morton/HHTL cascade [MECHANISM — shipped] - Deblock/SAO → masked tile op + LUT (the "AMX masking") [PARTIAL — masking] - CABAC entropy → serial arithmetic coding [DOESN'T FIT] Two honest boundaries recorded: (1) CABAC is not a GEMM — the entropy layer is the M2 serial front-end the tile substrate does not amortize; (2) the golden-spiral codec is for directional/sparse data, not dense scalar residuals (#231, measured negative). Cross-repo tie grounded: OGAR's perturbation pyramid IS the Walsh-Hadamard transform of the address tree = the same WHT #232 measured as the codec transform. Includes a probe queue (subpel_tap_tile, intra_angular_tile, deblock_masked_tile, CTU routing parity, M2 CABAC). Anchors: PRs #230–#233; hpc::bf16_tile_gemm, splat3d::spd3, cascade, codec; blasgraph HHTL; OGAR perturbation pyramid. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01MLBnPuScZy6w9di2QEjsXM

…VC 8-tap) Next probe from the HEVC amortization map: HEVC fractional-pel motion compensation applies a separable 8-tap FIR (half-pel luma taps [-1,4,-11,40,40,-11,4,-1]/64). An FIR is a linear operator, so filtering a 16×16 block is a matrix product — one bf16_tile_gemm_16x16 per pass, and the full separable H+V is Hᵀ·(X·H): the SAME two-tile sandwich shape as the splat covariance projection (Mᵀ·Σ·M, #233) and the codec transform (M·X, #232). Measured on real AMX (this host: AMX TDPBF16PS, amx_available = true), vs a direct 8-tap FIR f64 reference (same 16×16 band operator, reflected edges, so only BF16 rounding differs): (1) horizontal 8-tap out = X·H frobenius_rel_err = 0.157% (one tile op) (2) separable H+V out = Hᵀ·(X·H) frobenius_rel_err = 0.215% (two tile ops) (3) throughput: 1.22 M sub-pel tile ops/s Both asserts pass (rel err < BF16 tolerance). Fractional-pel motion is therefore "just another tile op", closing the MC story past integer-pel. R-5 dispatch noted (per-block 8-tap butterfly below the batch crossover, batched tile GEMM above). x86-gated via the same `mod amx` / non-x86 fallback-main pattern as gridlake_field_tile; canonical ndarray::simd imports; fmt + clippy clean. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01MLBnPuScZy6w9di2QEjsXM

AdaWorldAPI force-pushed the claude/motion-transform-noop branch from 2bebe18 to 23f7b2f Compare July 4, 2026 10:52

AdaWorldAPI force-pushed the claude/motion-transform-noop branch from 23f7b2f to c62cb3f Compare July 4, 2026 10:55

AdaWorldAPI merged commit 1ea77e8 into master Jul 4, 2026
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Probe: motion = bit shift × transform no-op × shaping — the factorization, measured#232

Probe: motion = bit shift × transform no-op × shaping — the factorization, measured#232
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AdaWorldAPI commented Jul 4, 2026

The factorization

Fairness

Measured (128×128, 8×8 blocks, Q=6)

Both falsifiable claims hold

Conclusion

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