QMCSoftware · AndersPride · Apr 22, 2026 · May 15, 2026 · May 18, 2026 · May 26, 2026
diff --git a/.github/workflows/alltests.yml b/.github/workflows/alltests.yml
@@ -297,12 +297,12 @@ jobs:
       - name: Validate MPMC dependencies (Unix)
         if: runner.os != 'Windows'
         shell: bash -el {0}
-        run: python -c "import torch, pyg_lib, torch_geometric; print(f'torch={torch.__version__}'); print('MPMC dependencies ready')"
+        run: python -c "import torch, torch_geometric; print(f'torch={torch.__version__}'); print('MPMC dependencies ready')"
 
       - name: Validate MPMC dependencies (Windows)
         if: runner.os == 'Windows'
         shell: pwsh
-        run: python -c "import torch, pyg_lib, torch_geometric; print(f'torch={torch.__version__}'); print('MPMC dependencies ready')"
+        run: python -c "import torch, torch_geometric; print(f'torch={torch.__version__}'); print('MPMC dependencies ready')"
       # -----------------------------------------------------------
       # Colab readiness tests (Linux only)
       # -----------------------------------------------------------

diff --git a/.gitignore b/.gitignore
@@ -39,6 +39,7 @@ demos/prob_failure_gp_ci_plots/
 demos/fgpr_figs/
 demos/GBM/images/*.png
 demos/GBM/outputs/*.*
+*.tmp_colab*
 .tmp_*
 
 # Generated notebook/demo images

diff --git a/CONTRIBUTING.md b/CONTRIBUTING.md
@@ -60,7 +60,7 @@ While `dev` contains the most complete set of install dependencies, a number of
 pip install -e ".[dev]"
 ~~~
 
-The `dev` extra includes QMCPy's PyPI-hosted MPMC dependencies. MPMC additionally requires a platform-specific `pyg_lib` wheel that is not available from PyPI. After installing `dev`, let the QMCPy installer select the wheel page matching the installed PyTorch build:
+The `dev` extra includes QMCPy's PyPI-hosted MPMC dependencies. The optional `pyg_lib` accelerator uses platform-specific wheels that are not available from PyPI. MPMC can run without it using a native PyTorch radius-graph fallback. After installing `dev`, the QMCPy installer can select the wheel page matching the installed PyTorch build; it warns and continues if neither a wheel nor a source build is available:
 
 ~~~bash
 qmcpy-install-mpmc

diff --git a/demos/GBM/gbm_demo.ipynb b/demos/GBM/gbm_demo.ipynb
@@ -858,6 +858,8 @@
     "results_data = []\n",
     "params_ql = {'initial_value': 100, 'mu': 0.05, 'sigma': 0.2, 'maturity': 1.0, 'n_steps': 252, 'n_paths': 2**14, 'seed': cf.QUANTLIB_SEED}\n",
     "params_qp = {'initial_value': 100, 'mu': 0.05, 'diffusion': 0.2**2, 'maturity': 1.0, 'n_steps': 252, 'n_paths': 2**14, 'replications': 8}\n",
+    "if IN_COLAB:\n",
+    "    params_ql['n_paths'] = params_qp['n_paths'] = 2**10\n",
     "theoretical_mean, theoretical_std = calculate_theoretical_statistics(params_ql)\n",
     "\n",
     "# Add theoretical values once\n",
@@ -1140,6 +1142,8 @@
     "# Generate specific data for visualization (ensure we have data for both libraries)\n",
     "params_vis_ql = {'initial_value': 100, 'mu': 0.05, 'sigma': 0.2, 'maturity': 1.0, 'n_steps': 252, 'n_paths': 2**14, 'sampler_type': 'Sobol'}\n",
     "params_vis_qp = {'initial_value': 100, 'mu': 0.05, 'diffusion': 0.2**2, 'maturity': 1.0, 'n_steps': 252, 'n_paths': 2**14, 'sampler_type': 'Sobol'}\n",
+    "if IN_COLAB:\n",
+    "    params_vis_ql['n_paths'] = params_vis_qp['n_paths'] = 2**10\n",
     "\n",
     "# Generate paths for visualization\n",
     "vis_quantlib_paths, _ = qlu.generate_quantlib_paths(**params_vis_ql)\n",
@@ -1201,7 +1205,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "We benchmark path generation with `%timeit`, using ten loops and three repeats.\n",
+    "We benchmark path generation with `%timeit`, using ten loops and three repeats. On Colab, the comparison and benchmark use 1024 paths per library, with one timing loop and one repeat.\n",
     "\n",
     "QMCPy Halton is slowest here because its work scales with an $(n,d,t)$ array of base-$b$ digits. We use `t = cf.HALTON_DIGITS` ($32$ rather than $63$) with the default linear-matrix scramble (LMS) and digital permutation (DP), `'LMS DP'`. QMCPy paths use consecutive batches from the same sampler, limiting the two temporary digit buffers to 64 MiB without changing path counts, time steps, or randomizations. This limit excludes the returned paths and the sampler's permutation tables; the latter use about 3.6 GiB at 512 time steps with eight replications.\n",
     "\n",
@@ -1222,7 +1226,10 @@
     "    for sampler_type in samplers_to_test:\n",
     "        print(f\"QuantLib ({sampler_type}) timing:\")\n",
     "        benchmark_func = lambda st=sampler_type: qlu.generate_quantlib_paths(**base_params, sampler_type=st)\n",
-    "        timing_result = %timeit -n 10 -r 3 -o benchmark_func()\n",
+    "        if IN_COLAB:\n",
+    "            timing_result = %timeit -n 1 -r 1 -o benchmark_func()\n",
+    "        else:\n",
+    "            timing_result = %timeit -n 10 -r 3 -o benchmark_func()\n",
     "        timing_results[sampler_type] = {\n",
     "            'average': timing_result.average,\n",
     "            'stdev': timing_result.stdev,\n",
@@ -1243,7 +1250,10 @@
     "    for sampler_type in samplers_to_test:\n",
     "        print(f\"QMCPy ({sampler_type}) timing:\")\n",
     "        benchmark_func = lambda st=sampler_type: qpu.generate_qmcpy_paths(**qp_params, sampler_type=st)\n",
-    "        timing_result = %timeit -n 10 -r 3 -o benchmark_func()\n",
+    "        if IN_COLAB:\n",
+    "            timing_result = %timeit -n 1 -r 1 -o benchmark_func()\n",
+    "        else:\n",
+    "            timing_result = %timeit -n 10 -r 3 -o benchmark_func()\n",
     "        timing_results[sampler_type] = {\n",
     "            'average': timing_result.average,\n",
     "            'stdev': timing_result.stdev,\n",
@@ -1400,6 +1410,8 @@
     "    'n_steps': 252, \n",
     "    'n_paths': 2**14\n",
     "}\n",
+    "if IN_COLAB:\n",
+    "    base_ql_params['n_paths'] = base_qp_params['n_paths'] = 2**10\n",
     "# Run benchmarks\n",
     "quantlib_timing_results = benchmark_quantlib_samplers(quantlib_samplers_to_benchmark, base_ql_params)\n",
     "qmcpy_timing_results = benchmark_qmcpy_samplers(qmcpy_samplers_to_benchmark, base_qp_params)\n",

diff --git a/demos/lattice_kronecker_methods.ipynb b/demos/lattice_kronecker_methods.ipynb
diff --git a/demos/talk_paper_demos/SorokinThesis2025/sorokin_thesis_2025.ipynb b/demos/talk_paper_demos/SorokinThesis2025/sorokin_thesis_2025.ipynb
@@ -516,20 +516,13 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "import io\n",
-    "import zipfile\n",
-    "from urllib.request import urlopen\n",
-    "\n",
     "import pandas as pd\n",
     "from sklearn.model_selection import train_test_split\n",
     "\n",
-    "with urlopen(\n",
-    "    'https://cdn.uci-ics-mlr-prod.aws.uci.edu/43/haberman%2Bs%2Bsurvival.zip',\n",
-    "    timeout=30,\n",
-    ") as resp:\n",
-    "    with zipfile.ZipFile(io.BytesIO(resp.read())) as zf:\n",
-    "        with zf.open('haberman.data') as f:\n",
-    "            df = pd.read_csv(f, header=None)\n",
+    "df = pd.read_csv(\n",
+    "    'https://archive.ics.uci.edu/ml/machine-learning-databases/haberman/haberman.data',\n",
+    "    header=None,\n",
+    ")\n",
     "df.columns = ['Age','1900 Year','Axillary Nodes','Survival Status']\n",
     "df.loc[df['Survival Status']==2,'Survival Status'] = 0\n",
     "x,y = df[['Age','1900 Year','Axillary Nodes']],df['Survival Status']\n",

diff --git a/demos/vectorized_qmc.ipynb b/demos/vectorized_qmc.ipynb
@@ -451,20 +451,13 @@
       },
       "outputs": [],
       "source": [
-        "import io\n",
-        "import zipfile\n",
-        "from urllib.request import urlopen\n",
-        "\n",
         "import pandas as pd\n",
         "from sklearn.model_selection import train_test_split\n",
         "\n",
-        "with urlopen(\n",
-        "    'https://cdn.uci-ics-mlr-prod.aws.uci.edu/43/haberman%2Bs%2Bsurvival.zip',\n",
-        "    timeout=30,\n",
-        ") as resp:\n",
-        "    with zipfile.ZipFile(io.BytesIO(resp.read())) as zf:\n",
-        "        with zf.open('haberman.data') as f:\n",
-        "            df = pd.read_csv(f, header=None)\n",
+        "df = pd.read_csv(\n",
+        "    'https://archive.ics.uci.edu/ml/machine-learning-databases/haberman/haberman.data',\n",
+        "    header=None,\n",
+        ")\n",
         "df.columns = ['Age','1900 Year','Axillary Nodes','Survival Status']\n",
         "df.loc[df['Survival Status']==2,'Survival Status'] = 0\n",
         "x,y = df[['Age','1900 Year','Axillary Nodes']],df['Survival Status']\n",

diff --git a/demos/vectorized_qmc_bayes.ipynb b/demos/vectorized_qmc_bayes.ipynb
@@ -450,20 +450,13 @@
    },
    "outputs": [],
    "source": [
-    "import io\n",
-    "import zipfile\n",
-    "from urllib.request import urlopen\n",
-    "\n",
     "import pandas as pd\n",
     "from sklearn.model_selection import train_test_split\n",
     "\n",
-    "with urlopen(\n",
-    "    'https://cdn.uci-ics-mlr-prod.aws.uci.edu/43/haberman%2Bs%2Bsurvival.zip',\n",
-    "    timeout=30,\n",
-    ") as resp:\n",
-    "    with zipfile.ZipFile(io.BytesIO(resp.read())) as zf:\n",
-    "        with zf.open('haberman.data') as f:\n",
-    "            df = pd.read_csv(f, header=None)\n",
+    "df = pd.read_csv(\n",
+    "    'https://archive.ics.uci.edu/ml/machine-learning-databases/haberman/haberman.data',\n",
+    "    header=None,\n",
+    ")\n",
     "df.columns = ['Age','1900 Year','Axillary Nodes','Survival Status']\n",
     "df.loc[df['Survival Status']==2,'Survival Status'] = 0\n",
     "x,y = df[['Age','1900 Year','Axillary Nodes']],df['Survival Status']\n",

diff --git a/docs/api/discrete_distributions.md b/docs/api/discrete_distributions.md
@@ -28,6 +28,10 @@ jupyter:
 
 ::: qmcpy.discrete_distribution.korobov.KorobovLattice
 
+## `lattice_vector_wssd_search`
+
+::: qmcpy.discrete_distribution.lattice.lattice_vector_wssd_search.lattice_vector_wssd_search
+
 ## `Halton`
 
 ::: qmcpy.discrete_distribution.digital_net_any_bases.halton.Halton
@@ -52,6 +56,10 @@ jupyter:
 
 ::: qmcpy.discrete_distribution.latin_hypercube.LatinHypercube
 
+## `kronecker_vector_search_mobius_transform`
+
+::: qmcpy.discrete_distribution.kronecker.kronecker_search_methods.kronecker_vector_search_mobius_transform
+
 ## `DummySampler`
 
 ::: qmcpy.discrete_distribution.dummy_sampler.DummySampler

diff --git a/docs/mpmc-compatibility.md b/docs/mpmc-compatibility.md
@@ -5,17 +5,17 @@
 ## Recommended Baseline
 
 - Treat MPMC as an optional feature, not part of the minimum QMCPy dependency set.
-- Prefer `pyg_lib` plus `torch-geometric`; do not require `torch-cluster` as a separate dependency.
+- Require PyTorch and `torch-geometric`; `pyg_lib` is an optional accelerator. When the compiled radius-graph backend is unavailable or fails to load, MPMC uses a native `torch.cdist` fallback. Neither `pyg_lib` nor `torch-cluster` is required to run MPMC.
 - For reproducible local work and future CI pinning, prefer a modern PyTorch line with matching `data.pyg.org` wheels installed by `qmcpy-install-mpmc`.
 - `unittests.yml` runs the full suite on `3.10`-`3.14` plus a slim `core-tests` tier on `3.9` (see [Minimum Python Version by Role](CONTRIBUTING.md#minimum-python-version-by-role)); neither installs MPMC.
 
 ## Support Policy
 
 | Python | Linux / macOS / Windows | MPMC status | Dependency guidance | CI expectation |
 |---|---|---|---|---|
-| `3.14` | Target | Supported | `torch >= 2.10`, `torch-geometric >= 2.6.1`, `pyg_lib >= 0.6.0` from the matching `data.pyg.org` wheel index | Run MPMC doctests and unit tests |
-| `3.13` | Target | Supported | `torch >= 2.10`, `torch-geometric >= 2.6.1`, `pyg_lib >= 0.6.0` | Run MPMC doctests and unit tests |
-| `3.12` | Target | Supported | `torch >= 2.10`, `torch-geometric >= 2.6.1`, `pyg_lib >= 0.6.0` | Run MPMC doctests and unit tests |
+| `3.14` | Target | Supported | `torch >= 2.10`, `torch-geometric >= 2.6.1`; optional `pyg_lib >= 0.6.0` from the matching `data.pyg.org` wheel index | Run MPMC doctests and unit tests |
+| `3.13` | Target | Supported | `torch >= 2.10`, `torch-geometric >= 2.6.1`; optional `pyg_lib >= 0.6.0` | Run MPMC doctests and unit tests |
+| `3.12` | Target | Supported | `torch >= 2.10`, `torch-geometric >= 2.6.1`; optional `pyg_lib >= 0.6.0` | Run MPMC doctests and unit tests |
 | `3.10` to `3.11` | Best effort | Not a release blocker for MPMC | May work with matching PyTorch / PyG wheels, but not required by current CI policy | Optional manual testing only |
 
 Python `3.9` is covered only by the slim `core-tests` tier, which never installs MPMC's PyTorch Geometric stack (see [Minimum Python Version by Role](CONTRIBUTING.md#minimum-python-version-by-role)).
@@ -29,23 +29,23 @@ The distinction is intentional:
 
 The current CI split is:
 
-- `alltests.yml`: the only workflow that installs the MPMC stack (`qmcpy-install-mpmc`) and runs `make doctests_mpmc` plus the MPMC unit tests, on Python `3.13`. The steps are not OS-gated: Ubuntu alone on feature-branch pushes, all three OSes on full sweeps.
-- `unittests.yml`: `3.10`-`3.14` on all three OSes, plus a `core-tests` tier on Ubuntu for `3.9`. Neither calls `qmcpy-install-mpmc`, so `test/test_dd_mpmc.py` skips throughout via `pytest.importorskip("pyg_lib")`. This workflow gives **no** MPMC coverage.
+- `alltests.yml`: the only workflow that installs the MPMC stack (`qmcpy-install-mpmc`) and runs `make doctests_mpmc` plus the MPMC unit tests, on Python `3.13`. The steps are not OS-gated: Ubuntu alone on feature-branch pushes, all three OSes on full sweeps. Dependency validation requires PyTorch and `torch-geometric`; a missing `pyg_lib` accelerator does not block the tests.
+- `unittests.yml`: `3.10`-`3.14`, each version on one operating system, plus a `core-tests` tier on all three OSes for `3.9`. Neither installs `torch-geometric` or calls `qmcpy-install-mpmc`, so MPMC tests normally skip. `test/test_dd_mpmc.py` checks only for PyTorch and `torch-geometric`; when both are available, the tests run with or without `pyg_lib`.
 
 See [MPMC Coverage by OS](ci-testing.md#mpmc-coverage-by-os) for the per-operating-system breakdown.
 
-This keeps MPMC enforcement in one place. The trade-off: MPMC regressions are invisible to `unittests.yml`, so raising MPMC coverage means adding a job to `alltests.yml`, not widening the `unittests.yml` matrix.
+This keeps required MPMC coverage in `alltests.yml`. Widening the `unittests.yml` matrix alone does not add MPMC coverage; a job must install the required PyTorch and `torch-geometric` dependencies.
 
 ## Local Developer Commands
 
-Install the usual test and MPMC extras first, then add the platform-specific PyG runtime with QMCPy's installed helper command:
+Install the usual test and MPMC extras first, then optionally add the platform-specific accelerator with QMCPy's installed helper command:
 
 ```bash
 python -m pip install -e ".[test,test_torch,test_gpytorch,test_botorch,mpmc]"
 qmcpy-install-mpmc
 ```
 
-The `mpmc` extra contains dependencies available from PyPI. The helper handles `pyg_lib` separately because its wheel page depends on the installed PyTorch version and accelerator build, which standard project metadata cannot select.
+The `mpmc` extra contains dependencies available from PyPI. The helper handles `pyg_lib` separately because its wheel page depends on the installed PyTorch version and accelerator build, which standard project metadata cannot select. If no matching wheel or source build is available, the helper warns and continues; MPMC can use its native PyTorch fallback.
 
 Then run the MPMC-specific checks:
 

diff --git a/makefile b/makefile
@@ -7,7 +7,7 @@ PYTEST_XDIST ?= $(shell $(PYTHON) scripts/pytest_xdist.py 2>/dev/null)
 PYTEST ?=
 SMOKE_CODE_CELLS ?= 2
 WITH_MPMC ?= 0
-HAS_MPMC ?= $(shell $(PYTHON) -c "import importlib.util; mods=('torch','pyg_lib','torch_geometric'); print(int(all(importlib.util.find_spec(m) is not None for m in mods)))" 2>/dev/null || echo 0)
+HAS_MPMC ?= $(shell $(PYTHON) -c "import importlib.util; mods=('torch','torch_geometric'); print(int(all(importlib.util.find_spec(m) is not None for m in mods)))" 2>/dev/null || echo 0)
 
 # set environment variable for documentation
 export JUPYTER_PLATFORM_DIRS=1

diff --git a/mkdocs.yml b/mkdocs.yml
@@ -47,6 +47,7 @@ nav:
       - 2020 MCQMC Software Tutorial: demos/talk_paper_demos/MCQMC_Tutorial_2020/MCQMC_2020_QMC_Software_Tutorial.ipynb
     - Technical Examples:
       - 2023 Random Lattice Generating Vectors: demos/lattice_random_generator.ipynb
+      - Lattice and Kronecker Generating-Vector Search: demos/lattice_kronecker_methods.ipynb
       - 2022 Bayesian Cubature Stopping Criterion: demos/gaussian_diagnostics/gaussian_diagnostics_demo.ipynb
       - 2020 Why Add Q to MC?: demos/talk_paper_demos/why_add_q_to_mc_blog/why_add_q_to_mc_blog.ipynb
       - 2020 Bayesian Optimization Expected Improvement:

diff --git a/qmcpy/discrete_distribution/__init__.py b/qmcpy/discrete_distribution/__init__.py
@@ -1,10 +1,10 @@
 from .abstract_discrete_distribution import AbstractDiscreteDistribution
 from .iid_std_uniform import IIDStdUniform
-from .lattice import Lattice
+from .lattice import Lattice, lattice_vector_wssd_search
 from .digital_net_b2 import DigitalNetB2
 from .digital_net_any_bases import DigitalNetAnyBases,Halton,Faure,Hammersley
 from .mpmc import MPMC
-from .kronecker import Kronecker
+from .kronecker import Kronecker, kronecker_vector_search_mobius_transform
 from .korobov import KorobovLattice
 from .dummy_sampler import DummySampler
 from .latin_hypercube import LatinHypercube
@@ -15,4 +15,3 @@
 DigitalNet = DigitalNetB2
 Net = DigitalNetB2
 NetB2 = DigitalNetB2
-
diff --git a/qmcpy/discrete_distribution/kronecker/__init__.py b/qmcpy/discrete_distribution/kronecker/__init__.py
@@ -0,0 +1,2 @@
+from .kronecker import Kronecker
+from .kronecker_search_methods import kronecker_vector_search_mobius_transform
Original file line number	Diff line number	Diff line change
		@@ -0,0 +1,2 @@
		from .kronecker import Kronecker
		from .kronecker_search_methods import kronecker_vector_search_mobius_transform