Measure anisotropic MPO patch scaling to chi 900

Cargo.toml

@@ -13,6 +13,7 @@ tensor4all-itensorlike = { git = "https://github.com/tensor4all/tensor4all-rs",
 tensor4all-partitionedtt = { git = "https://github.com/tensor4all/tensor4all-rs", rev = "9e9aedaebe0d3918b34dd399ff0981e337f3835b", package = "tensor4all-partitionedtt" }
 tensor4all-partitionedtreetn = { git = "https://github.com/tensor4all/tensor4all-rs", rev = "9e9aedaebe0d3918b34dd399ff0981e337f3835b", package = "tensor4all-partitionedtreetn" }
 tensor4all-quanticstci = { git = "https://github.com/tensor4all/tensor4all-rs", rev = "9e9aedaebe0d3918b34dd399ff0981e337f3835b", package = "tensor4all-quanticstci" }
+tensor4all-interpolativeqtt = { git = "https://github.com/tensor4all/tensor4all-rs", rev = "9e9aedaebe0d3918b34dd399ff0981e337f3835b", package = "tensor4all-interpolativeqtt" }
 tensor4all-hdf5 = { git = "https://github.com/tensor4all/tensor4all-rs", rev = "9e9aedaebe0d3918b34dd399ff0981e337f3835b", package = "tensor4all-hdf5" }
 tensor4all-core = { git = "https://github.com/tensor4all/tensor4all-rs", rev = "9e9aedaebe0d3918b34dd399ff0981e337f3835b", package = "tensor4all-core" }
 num-complex = "0.4"

README.md

@@ -16,7 +16,7 @@ revision that produced it. The pinned `tensor4all-rs` revision lives in `Cargo.t
 | 3. `elementwise_gauss2d` | Elementwise product of two 2D quantics Gaussian mixtures at a fixed output budget, swept over bits per variable `R`, against the exact pointwise product | [description](#case-3-elementwise-product-of-2d-quantics-gaussian-mixtures) | [`src/bin/elementwise_gauss2d.rs`](src/bin/elementwise_gauss2d.rs) | [`result/mac-cpu/elementwise_gauss2d.md`](result/mac-cpu/elementwise_gauss2d.md) | [time](result/mac-cpu/elementwise_gauss2d-time.svg), [error](result/mac-cpu/elementwise_gauss2d-error.svg) |
 | 4. `elementwise_gauss2d_scaling` | Density-constant scaling study of case 3: how the quantics input rank `chi_in` grows with the number of Gaussians `N` when the box area grows proportionally to `N` | [description](#case-4-density-constant-scaling-of-the-quantics-rank) | [`src/bin/elementwise_gauss2d_scaling.rs`](src/bin/elementwise_gauss2d_scaling.rs) | [`result/mac-cpu/elementwise_gauss2d_scaling.md`](result/mac-cpu/elementwise_gauss2d_scaling.md) | [chi](result/mac-cpu/elementwise_gauss2d_scaling-chi.svg), [time](result/mac-cpu/elementwise_gauss2d_scaling-time.svg), [error](result/mac-cpu/elementwise_gauss2d_scaling-error.svg) |
 | 5. `elementwise_gauss2d_patched` | Patched (domain decomposed) elementwise product, controlled by a global relative tolerance instead of a fixed output budget, comparing patched and global representations at equal accuracy on size and time, over two instance families: anisotropic narrow spikes by default and case 4's smooth Gaussians on request | [description](#case-5-patched-elementwise-product-at-equal-accuracy) | [`src/bin/elementwise_gauss2d_patched.rs`](src/bin/elementwise_gauss2d_patched.rs) | [`result/mac-cpu/elementwise_gauss2d_patched.md`](result/mac-cpu/elementwise_gauss2d_patched.md) | [time](result/mac-cpu/elementwise_gauss2d_patched-time.svg), [error](result/mac-cpu/elementwise_gauss2d_patched-error.svg), [parameters](result/mac-cpu/elementwise_gauss2d_patched-params-aniso.svg) |
-| 6. `mpo_mpo_aniso_patched` | Fit contraction of anisotropic Gaussian MPOs, comparing the global baseline with patched chain TreeTN | [description](#case-6-patched-mpo-mpo-fit-contraction) | [`src/bin/mpo_mpo_aniso_patched.rs`](src/bin/mpo_mpo_aniso_patched.rs) | [`result/linux-epyc-7713p/mpo_mpo_aniso_patched.md`](result/linux-epyc-7713p/mpo_mpo_aniso_patched.md) | [results table](result/linux-epyc-7713p/mpo_mpo_aniso_patched.md#results) |
+| 6. `mpo_mpo_aniso_patched` | Fit contraction of anisotropic Gaussian MPOs, comparing the global baseline with patched chain TreeTN | [description](#case-6-patched-mpo-mpo-fit-contraction) | [`src/bin/mpo_mpo_aniso_patched.rs`](src/bin/mpo_mpo_aniso_patched.rs) | [contraction](result/linux-epyc-7713p/mpo_mpo_aniso_patched.md), [input scaling](result/linux-epyc-7713p/mpo_mpo_aniso_input_scaling.md) | [crossover](result/linux-epyc-7713p/mpo_mpo_aniso_patched.md#results), [patch scaling](result/linux-epyc-7713p/mpo_mpo_aniso_input_scaling.md#results) |
 
 ## Benchmark cases
 
@@ -531,7 +531,13 @@ comparison that established numerical equivalence.
 
 The default `N = 512` instance targets the practical global-rank range discussed
 for case 5. The default per-patch cap is 128; cap 64 is intentionally excluded
-from future case-6 measurements. The committed `N = 2048` crossover sweep is
+from future case-6 measurements. The separate [input-scaling report](result/linux-epyc-7713p/mpo_mpo_aniso_input_scaling.md)
+records the established TCI `1e-8` → global relative-L2/SVD `1e-6` → adaptive
+cap-128 pipeline through compressed input χ 900, where each input has 120
+patches. For large TCI inputs the runner uses a spatially indexed evaluator with
+a recorded rigorous absolute tail bound; sampled errors are checked against the
+unmodified full mixture. Regenerate that report from its committed raw records
+with `python3 scripts/report_mpo_input_scaling.py result/linux-epyc-7713p`. The committed `N = 2048` crossover sweep is
 linked in the [top-level case table](#cases-at-a-glance): patched fit is slower
 at input χ 192, faster at χ 224, and 1.60× faster at χ 256 on the recorded
 single-core profile. The global output cap is the measured pre-patching
@@ -779,6 +785,15 @@ Environment knobs:
 | `BENCH_NGAUSS` | cases 2, 3 and 6 | `8` (cases 2 and 3), `512` (case 6) | number of Gaussians or anisotropic spikes per mixture |
 | `BENCH_INPUT_CACHE_DIR` | case 6 | `.cache/inputs` | directory for deterministic global input MPS cache entries |
 | `BENCH_INPUT_CACHE_REFRESH` | case 6 | unset | when set, rebuild and atomically replace the selected input cache entry |
+| `BENCH_INPUT_GENERATOR` | case 6 | `tci` | input constructor: global fused `tci`, or per-Gaussian `multiscale` using principal-axis unsafe points |
+| `BENCH_INPUT_TCI_RTOL` | case 6 | `1e-8` | relative TCI tolerance; also the interpolation tolerance supplied to the multiscale constructor |
+| `BENCH_TCI_LOCAL_ABS_TOL` | case 6 | `1e-12` | rigorous pointwise absolute bound for tails omitted by the spatially indexed TCI callback |
+| `BENCH_TCI_INITIAL_PIVOTS` | case 6 | `8` | deterministic mixture-center grid pivots used by TCI; random initial pivots are disabled |
+| `BENCH_INPUT_POLY_DEGREE` | case 6 | `28` | polynomial degree for the multiscale single-Gaussian constructor |
+| `BENCH_INPUT_ADD_RTOL` | case 6 | `1e-10` | per-bond SVD tolerance used while adding multiscale single-Gaussian QTTs |
+| `BENCH_INPUT_SVD_RTOL` | case 6 | `1e-6` | global relative-L2 SVD tolerance applied before adaptive patching |
+| `BENCH_INPUT_ONLY` | case 6 | unset | when set, write the input/patch record and skip contraction |
+| `BENCH_INPUT_SANITY` | case 6 | `1e-4` | maximum sampled relative error accepted for each compressed input MPO |
 | `BENCH_BOX_L` | cases 2 and 3 | `6.0` | half-width `L` of the box `[-L, L]` |
 | `BENCH_NS` | cases 4 and 5 | `8,16,32,64` (case 4, and case 5 on the `smooth` family), `8,16,32,64,128,256,512` (case 5 on the default `aniso` family) | comma-separated Gaussian or spike counts `N` to sweep. Both cases derive `L` and `R` from `N`, so they ignore `BENCH_NGAUSS`, `BENCH_BOX_L` and `BENCH_RS` |
 | `BENCH_FAMILY` | case 5 | `aniso` | which instance family to sweep. `aniso` is `N` anisotropic narrow spikes at a fixed spacing-to-width ratio, the family the case is written for; `smooth` is case 4's isotropic Gaussians at constant density, unchanged, and it also switches `BENCH_NS` to case 4's four points. Recorded in the params of every record as `family`, and part of every record's filename, so one profile can hold both |

result/linux-epyc-7713p/mpo_mpo_aniso_input_scaling.md

@@ -0,0 +1,51 @@
+# Anisotropic Gaussian MPO input and patch scaling
+
+This focused case-6 input study measures adaptive patching through compressed input bond dimension `chi_in ≈ 1000`. It uses the unchanged constant-density random anisotropic family (`sigma_minor = 0.05`, log-uniform aspect ratio in `[1, 8]`, independent angle, center, and positive weight per Gaussian).
+
+## Construction and accuracy
+
+The input pipeline is:
+
+1. fused two-variable TCI at relative tolerance `1e-8`;
+2. global relative-L2 SVD truncation at `1e-6`;
+3. adaptive input truncation with per-patch cap 128.
+
+TCI evaluates the same random mixture through a spatial index. A component is omitted only outside a radius where its individual Gaussian is below a common exponent threshold. Since all weights are positive, the sum of all omitted tails is bounded pointwise by `1e-12`. The committed sampled input errors include this bound and remain below `1e-5` after global SVD truncation.
+
+The alternative multiscale constructor builds one randomly rotated Gaussian directly. It marks points every half minor-axis standard deviation along the major-axis ridge as unsafe. The focused test covers `rho = 8`, a 45-degree rotation, and `R = 10`, and requires maximum sampled absolute error below `5e-8` at polynomial degree 28. Mixtures can be formed by adding these single-Gaussian QTTs with intermediate SVD compression. This path preserves the instance family but is not used for the large sweep because its per-Gaussian construction cost scales linearly with `N`; spatially indexed TCI reaches the requested rank regime efficiently.
+
+## Reproducible settings
+
+These input-only records were collected separately from the profile's earlier contraction sweep. The settings below, including core 0, are authoritative for these records rather than the contraction affinity in `run.yaml`.
+
+- Machine: AMD EPYC 7713P 64-Core Processor
+- CPU affinity: core 0 (`taskset -c 0`)
+- `RAYON_NUM_THREADS=1`, `OPENBLAS_NUM_THREADS=1`, `OMP_NUM_THREADS=1`
+- `BENCH_INPUT_GENERATOR=tci`
+- `BENCH_INPUT_TCI_RTOL=1e-8`
+- `BENCH_TCI_LOCAL_ABS_TOL=1e-12`
+- `BENCH_TCI_INITIAL_PIVOTS=8` (deterministic center-derived pivots)
+- `BENCH_INPUT_SVD_RTOL=1e-6`
+- `BENCH_PATCH_MAX_BOND=128`
+- `BENCH_MAX_INPUT_CHI=1400`
+- `BENCH_MAX_BOND=512, 512, 1280, 3072, 3584` for `N=512, 4096, 20480, 100000, 125000`
+- one deterministic seed (`BENCH_SEED=0`)
+- `BENCH_ERROR_SAMPLES=256` at every size
+
+Input generation, global SVD truncation, sampled validation, and adaptive patch preparation are all included in `preparation time`; no contraction is run (`BENCH_INPUT_ONLY=1`).
+
+## Results
+
+Each pair is `(left, right)` for the two independently drawn mixtures.
+
+| N | R | raw chi | compressed chi | global parameters | patches | max patch chi | patch parameters | sampled relative error | preparation time |
+|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|
+| 512 | 9 | 181 | 89 | (48,060, 47,608) | (1, 1) | (84, 84) | (45,056, 45,056) | (3.36e-06, 2.56e-06) | 5.08 s |
+| 4,096 | 10 | 280 | 256 | (254,476, 255,736) | (6, 6) | (124, 124) | (352,704, 352,088) | (1.78e-06, 3.38e-06) | 46.36 s |
+| 20,480 | 11 | 889 | 458 | (888,076, 886,408) | (30, 30) | (121, 121) | (1,775,032, 1,772,136) | (2.75e-06, 6.95e-06) | 263.99 s |
+| 100,000 | 12 | 1,074 | 900 | (3,450,320, 3,454,660) | (120, 120) | (120, 121) | (9,866,732, 9,982,956) | (3.06e-06, 3.74e-06) | 1,568.20 s |
+| 125,000 | 13 | 1,342 | 900 | (4,120,944, 4,113,404) | (120, 120) | (121, 123) | (11,553,076, 11,596,696) | (5.51e-06, 9.14e-06) | 2,539.63 s |
+
+The compressed-rank plateau reaches `chi_in = 900`, within 10% of the requested `chi_in ≈ 1000` regime. Patch count grows stepwise from 1 to 6, 30, and 120 while every patch remains below cap 128. The `N = 125,000`, `R = 13` point increases raw rank and parameter count but remains on the same compressed-rank and patch-count plateau, so increasing `N` alone does not produce a smooth patch-count curve.
+
+Raw JSON records are in [`raw/`](raw/) with filenames `mpo_mpo_aniso_input-tci-n*-chi*.json`.

result/linux-epyc-7713p/raw/mpo_mpo_aniso_input-tci-n100000-chi900.json

@@ -0,0 +1,59 @@
+{
+  "box_l": 23.71708245126285,
+  "box_padding": 1.0,
+  "case": "mpo_mpo_aniso_input",
+  "input_add_rtol": 1e-10,
+  "input_build_secs": 1568.202631011,
+  "input_cache_hit": false,
+  "input_cache_key": "aniso-v5-tci-n100000-r12-e0-s4008000000000000-p3ff0000000000000-sig3fa999999999999a-rho4020000000000000-tol3e45798ee2308c3a-loc3d719799812dea11-piv8-cap3072-seed0",
+  "input_cache_load_secs": 0.0,
+  "input_chi": 900,
+  "input_compression_secs": 9.464503739,
+  "input_error_samples": 256,
+  "input_generator": "tci",
+  "input_params": [
+    3450320,
+    3454660
+  ],
+  "input_patch_counts": [
+    120,
+    120
+  ],
+  "input_patch_max_bonds": [
+    120,
+    121
+  ],
+  "input_patch_params": [
+    9866732,
+    9982956
+  ],
+  "input_poly_degree": 28,
+  "input_sampled_relative_errors": [
+    3.0555493578220235e-6,
+    3.7404138963447223e-6
+  ],
+  "input_sanity": 0.0001,
+  "input_svd_l2_rtol": 1e-6,
+  "input_tci_cap": 3072,
+  "input_tci_initial_pivots": 8,
+  "input_tci_local_abs_tol": 1e-12,
+  "input_tci_rtol": 1e-8,
+  "max_input_chi": 1400,
+  "n_gauss": 100000,
+  "np_over_chi_squared": [
+    4.2596543209876545,
+    4.265012345679012
+  ],
+  "patch_cap": 128,
+  "r": 12,
+  "r_extra": 0,
+  "raw_input_chi": 1074,
+  "raw_input_params": [
+    7305760,
+    7308792
+  ],
+  "rho_max": 8.0,
+  "seed": 0,
+  "sigma": 0.05,
+  "spacing": 3.0
+}

result/linux-epyc-7713p/raw/mpo_mpo_aniso_input-tci-n125000-chi900.json

@@ -0,0 +1,59 @@
+{
+  "box_l": 26.516504294495537,
+  "box_padding": 1.0,
+  "case": "mpo_mpo_aniso_input",
+  "input_add_rtol": 1e-10,
+  "input_build_secs": 2539.628990155,
+  "input_cache_hit": false,
+  "input_cache_key": "aniso-v5-tci-n125000-r13-e0-s4008000000000000-p3ff0000000000000-sig3fa999999999999a-rho4020000000000000-tol3e45798ee2308c3a-loc3d719799812dea11-piv8-cap3584-seed0",
+  "input_cache_load_secs": 0.0,
+  "input_chi": 900,
+  "input_compression_secs": 13.723229085,
+  "input_error_samples": 256,
+  "input_generator": "tci",
+  "input_params": [
+    4120944,
+    4113404
+  ],
+  "input_patch_counts": [
+    120,
+    120
+  ],
+  "input_patch_max_bonds": [
+    121,
+    123
+  ],
+  "input_patch_params": [
+    11553076,
+    11596696
+  ],
+  "input_poly_degree": 28,
+  "input_sampled_relative_errors": [
+    5.5092801319520735e-6,
+    9.140267928712483e-6
+  ],
+  "input_sanity": 0.0001,
+  "input_svd_l2_rtol": 1e-6,
+  "input_tci_cap": 3584,
+  "input_tci_initial_pivots": 8,
+  "input_tci_local_abs_tol": 1e-12,
+  "input_tci_rtol": 1e-8,
+  "max_input_chi": 1400,
+  "n_gauss": 125000,
+  "np_over_chi_squared": [
+    5.087585185185185,
+    5.078276543209877
+  ],
+  "patch_cap": 128,
+  "r": 13,
+  "r_extra": 0,
+  "raw_input_chi": 1342,
+  "raw_input_params": [
+    9424632,
+    9396972
+  ],
+  "rho_max": 8.0,
+  "seed": 0,
+  "sigma": 0.05,
+  "spacing": 3.0
+}

result/linux-epyc-7713p/raw/mpo_mpo_aniso_input-tci-n20480-chi458.json

@@ -0,0 +1,59 @@
+{
+  "box_l": 10.733126291998992,
+  "box_padding": 1.0,
+  "case": "mpo_mpo_aniso_input",
+  "input_add_rtol": 1e-10,
+  "input_build_secs": 263.992662118,
+  "input_cache_hit": false,
+  "input_cache_key": "aniso-v5-tci-n20480-r11-e0-s4008000000000000-p3ff0000000000000-sig3fa999999999999a-rho4020000000000000-tol3e45798ee2308c3a-loc3d719799812dea11-piv8-cap1280-seed0",
+  "input_cache_load_secs": 0.0,
+  "input_chi": 458,
+  "input_compression_secs": 1.802141383,
+  "input_error_samples": 256,
+  "input_generator": "tci",
+  "input_params": [
+    888076,
+    886408
+  ],
+  "input_patch_counts": [
+    30,
+    30
+  ],
+  "input_patch_max_bonds": [
+    121,
+    121
+  ],
+  "input_patch_params": [
+    1775032,
+    1772136
+  ],
+  "input_poly_degree": 28,
+  "input_sampled_relative_errors": [
+    2.7528033675655293e-6,
+    6.954288054456006e-6
+  ],
+  "input_sanity": 0.0001,
+  "input_svd_l2_rtol": 1e-6,
+  "input_tci_cap": 1280,
+  "input_tci_initial_pivots": 8,
+  "input_tci_local_abs_tol": 1e-12,
+  "input_tci_rtol": 1e-8,
+  "max_input_chi": 1400,
+  "n_gauss": 20480,
+  "np_over_chi_squared": [
+    4.2336911958200645,
+    4.2257394023760035
+  ],
+  "patch_cap": 128,
+  "r": 11,
+  "r_extra": 0,
+  "raw_input_chi": 889,
+  "raw_input_params": [
+    2315988,
+    2322644
+  ],
+  "rho_max": 8.0,
+  "seed": 0,
+  "sigma": 0.05,
+  "spacing": 3.0
+}

result/linux-epyc-7713p/raw/mpo_mpo_aniso_input-tci-n4096-chi256.json

@@ -0,0 +1,59 @@
+{
+  "box_l": 4.800000000000001,
+  "box_padding": 1.0,
+  "case": "mpo_mpo_aniso_input",
+  "input_add_rtol": 1e-10,
+  "input_build_secs": 46.359608388,
+  "input_cache_hit": false,
+  "input_cache_key": "aniso-v5-tci-n4096-r10-e0-s4008000000000000-p3ff0000000000000-sig3fa999999999999a-rho4020000000000000-tol3e45798ee2308c3a-loc3d719799812dea11-piv8-cap512-seed0",
+  "input_cache_load_secs": 0.0,
+  "input_chi": 256,
+  "input_compression_secs": 0.288869464,
+  "input_error_samples": 256,
+  "input_generator": "tci",
+  "input_params": [
+    254476,
+    255736
+  ],
+  "input_patch_counts": [
+    6,
+    6
+  ],
+  "input_patch_max_bonds": [
+    124,
+    124
+  ],
+  "input_patch_params": [
+    352704,
+    352088
+  ],
+  "input_poly_degree": 28,
+  "input_sampled_relative_errors": [
+    1.781935608908162e-6,
+    3.3819348731372854e-6
+  ],
+  "input_sanity": 0.0001,
+  "input_svd_l2_rtol": 1e-6,
+  "input_tci_cap": 512,
+  "input_tci_initial_pivots": 8,
+  "input_tci_local_abs_tol": 1e-12,
+  "input_tci_rtol": 1e-8,
+  "max_input_chi": 1400,
+  "n_gauss": 4096,
+  "np_over_chi_squared": [
+    3.88299560546875,
+    3.9022216796875
+  ],
+  "patch_cap": 128,
+  "r": 10,
+  "r_extra": 0,
+  "raw_input_chi": 280,
+  "raw_input_params": [
+    510520,
+    522008
+  ],
+  "rho_max": 8.0,
+  "seed": 0,
+  "sigma": 0.05,
+  "spacing": 3.0
+}