From bebb7bf139fb8ec71029c266af557c1a8f4c5472 Mon Sep 17 00:00:00 2001 From: Nina Miolane Date: Fri, 3 Apr 2026 06:44:16 -0700 Subject: [PATCH 1/8] Rm helper build_model_from_config --- src/main.py | 52 +++++++++++++++++++++-------------------------- test/test_main.py | 23 +++++++++++++++++++++ 2 files changed, 46 insertions(+), 29 deletions(-) diff --git a/src/main.py b/src/main.py index dd29621..6fb35a3 100644 --- a/src/main.py +++ b/src/main.py @@ -100,33 +100,6 @@ def save_results( return metadata -def _build_model_from_config(config, template_flat, device): - """Reconstruct a model from config (no weights loaded).""" - model_type = config["model"]["model_type"] - group_size = len(template_flat) - - if model_type == "TwoLayerMLP": - m = model.TwoLayerMLP( - group_size=group_size, - hidden_dim=config["model"]["hidden_dim"], - k=config["data"]["k"], - nonlinearity=config["model"].get("nonlinearity", "square"), - init_scale=config["model"]["init_scale"], - output_scale=config["model"].get("output_scale", 1.0), - ) - elif model_type == "QuadraticRNN": - m = model.QuadraticRNN( - group_size=group_size, - hidden_dim=config["model"]["hidden_dim"], - k=config["data"]["k"], - init_scale=config["model"]["init_scale"], - return_all_outputs=config["model"]["return_all_outputs"], - ) - else: - raise ValueError(f"Unknown model_type: {model_type}") - return m.to(device) - - def _reconstruct_param_save_indices(config, num_saved): """Reconstruct param_save_indices from config when not saved to disk.""" dense = config["training"].get("dense_save_until", 0) @@ -177,9 +150,30 @@ def regenerate_plots(run_dir, device="cpu"): else: param_save_indices = _reconstruct_param_save_indices(config, len(param_hist)) - mdl = _build_model_from_config(config, template.flatten(), device) - group_name = config["data"]["group_name"] + group_size = len(template.flatten()) + model_type = config["model"]["model_type"] + + if model_type == "TwoLayerMLP": + mdl = model.TwoLayerMLP( + group_size=group_size, + hidden_dim=config["model"]["hidden_dim"], + k=config["data"]["k"], + nonlinearity=config["model"].get("nonlinearity", "square"), + init_scale=config["model"]["init_scale"], + output_scale=config["model"].get("output_scale", 1.0), + ).to(device) + elif model_type == "QuadraticRNN": + mdl = model.QuadraticRNN( + group_size=group_size, + hidden_dim=config["model"]["hidden_dim"], + k=config["data"]["k"], + init_scale=config["model"]["init_scale"], + return_all_outputs=config["model"]["return_all_outputs"], + ).to(device) + else: + raise ValueError(f"Unknown model_type: {model_type}") + training_mode = config["training"]["mode"] if group_name == "cnxcn": diff --git a/test/test_main.py b/test/test_main.py index 807113c..2989c58 100644 --- a/test/test_main.py +++ b/test/test_main.py @@ -157,5 +157,28 @@ def test_main_a5_config(): assert config["device"] == "cpu" +def test_regenerate_plots_cn(temp_run_dir, mock_all_plots): + """Test regenerate_plots loads a saved run and dispatches to the right produce_plots. + + Runs a tiny train_single_run to produce artifacts, then calls + regenerate_plots on the same directory with fresh mocks. + """ + import src.main as main + + config = main.load_config(str(CONFIG_FILES["c10"])) + main.train_single_run(config, run_dir=temp_run_dir) + + mock_all_plots["produce_plots_cn"].reset_mock() + + main.regenerate_plots(str(temp_run_dir), device="cpu") + + mock_all_plots["produce_plots_cn"].assert_called_once() + call_kwargs = mock_all_plots["produce_plots_cn"].call_args[1] + mdl = call_kwargs["model"] + assert isinstance(mdl, main.model.TwoLayerMLP) + assert mdl.group_size == 10 + assert mdl.k == 2 + + if __name__ == "__main__": pytest.main([__file__, "-v"]) From 42b59e32286540f55c863d8598d14103c3b622f0 Mon Sep 17 00:00:00 2001 From: Nina Miolane Date: Fri, 3 Apr 2026 11:10:57 -0700 Subject: [PATCH 2/8] Rm escnn and create own group computations --- pyproject.toml | 3 +- scripts/extract_escnn_data.py | 59 +++++ src/dataset.py | 11 +- src/fourier.py | 63 ------ src/groups/__init__.py | 19 ++ src/groups/a5.py | 49 +++++ src/groups/cn.py | 89 ++++++++ src/groups/cnxcn.py | 103 +++++++++ src/groups/dn.py | 116 ++++++++++ src/groups/group.py | 109 +++++++++ src/groups/irrep.py | 37 ++++ src/groups/oh.py | 49 +++++ src/main.py | 37 ++-- src/power.py | 402 ++++++++++------------------------ src/template.py | 8 +- src/viz.py | 41 ++-- test/test_dataset.py | 8 +- test/test_fourier.py | 17 +- test/test_group_escnn.py | 203 +++++++++++++++++ test/test_main.py | 8 +- test/test_power.py | 64 +++--- test/test_template.py | 4 +- 22 files changed, 1035 insertions(+), 464 deletions(-) create mode 100644 scripts/extract_escnn_data.py delete mode 100644 src/fourier.py create mode 100644 src/groups/__init__.py create mode 100644 src/groups/a5.py create mode 100644 src/groups/cn.py create mode 100644 src/groups/cnxcn.py create mode 100644 src/groups/dn.py create mode 100644 src/groups/group.py create mode 100644 src/groups/irrep.py create mode 100644 src/groups/oh.py create mode 100644 test/test_group_escnn.py diff --git a/pyproject.toml b/pyproject.toml index 15d1ac2..4b6325f 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -28,7 +28,6 @@ scikit-learn = "^1.7.2" tqdm = "^4.67.1" seaborn = "^0.13.2" jupyter-black = "^0.4.0" -escnn = "^1.0.11" [build-system] @@ -60,7 +59,7 @@ ignore = [ "E501", # line too long (handled by formatter) "B008", # do not perform function calls in argument defaults "B905", # zip without strict - "F403", # star imports (used intentionally for escnn.group) + "F403", # star imports "F405", # may be undefined from star imports "F841", # local variable assigned but never used (common in notebooks/experiments) "B007", # loop control variable not used (common pattern) diff --git a/scripts/extract_escnn_data.py b/scripts/extract_escnn_data.py new file mode 100644 index 0000000..88456ea --- /dev/null +++ b/scripts/extract_escnn_data.py @@ -0,0 +1,59 @@ +#!/usr/bin/env python +"""One-time script: extract irrep and regular-rep matrices from escnn. + +Saves .npy files into src/groups/data/ that are loaded at import time +by oh.py and a5.py. + +Usage: + conda activate group-agf + python scripts/extract_escnn_data.py +""" + +from pathlib import Path + +import numpy as np +from escnn.group import Icosahedral, Octahedral + + +DATA_DIR = Path(__file__).resolve().parent.parent / "src" / "groups" / "data" + + +def extract_group(escnn_group, prefix: str): + """Extract and save all group data as .npy files.""" + DATA_DIR.mkdir(parents=True, exist_ok=True) + + elements = list(escnn_group.elements) + irreps = escnn_group.irreps() + + print(f" Order: {escnn_group.order()}") + print(f" Irreps: {len(irreps)} dims={[ir.size for ir in irreps]}") + print(f" Irrep names: {[str(ir) for ir in irreps]}") + + names = [str(ir) for ir in irreps] + np.save(DATA_DIR / f"{prefix}_irrep_names.npy", np.array(names)) + + for i, irrep in enumerate(irreps): + mats = np.array([irrep(g) for g in elements]) + path = DATA_DIR / f"{prefix}_irrep_{i}.npy" + np.save(path, mats) + print(f" Saved {path.name} shape={mats.shape}") + + regular_rep = escnn_group.representations["regular"] + reg_mats = np.array([regular_rep(g) for g in elements]) + path = DATA_DIR / f"{prefix}_regular_rep.npy" + np.save(path, reg_mats) + print(f" Saved {path.name} shape={reg_mats.shape}") + + +def main(): + print("Extracting Octahedral ...") + extract_group(Octahedral(), "oh") + + print("\nExtracting Icosahedral (A5) ...") + extract_group(Icosahedral(), "a5") + + print(f"\nAll files saved to {DATA_DIR}") + + +if __name__ == "__main__": + main() diff --git a/src/dataset.py b/src/dataset.py index bc2eb3a..638c798 100644 --- a/src/dataset.py +++ b/src/dataset.py @@ -177,18 +177,15 @@ def _build_group( num_samples=65536, return_all_outputs=False, ): - """Build dataset arrays for any escnn group with a regular representation.""" - group_size = group.order() + """Build dataset arrays for any group with a regular representation.""" + group_size = group.order assert template.shape == (group_size,), ( f"template must be ({group_size},), got {template.shape}" ) - regular_rep = group.representations["regular"] - elements = list(group.elements) - n_elements = len(elements) - - rep_matrices = np.array([regular_rep(g) for g in elements]) + n_elements = group_size + rep_matrices = group.regular_rep() if mode == "exhaustive": total = n_elements**k diff --git a/src/fourier.py b/src/fourier.py deleted file mode 100644 index 3bf199e..0000000 --- a/src/fourier.py +++ /dev/null @@ -1,63 +0,0 @@ -import numpy as np -from escnn.group import * - - -def group_fourier(group, template): - """Compute the group Fourier transform of the template. - - For each irrep rho, compute the Fourier coefficient: - hat x [rho] = sum_{g in G} x[g] * rho(g).conj().T - - Parameters - ---------- - group : Group (escnn object) - The group. - template : np.ndarray, shape=[group.order()] - The template to compute the Fourier transform of. - - Returns - ------- - fourier_coefs : list of np.ndarray, each of shape=[irrep.size, irrep.size] - A list of (matrix) Fourier coefficients of template at each irrep. - """ - irreps = group.irreps() - fourier_coefs = [] - for irrep in irreps: - coef = sum([template[i_g] * irrep(g).conj().T for i_g, g in enumerate(group.elements)]) - fourier_coefs.append(coef) - return fourier_coefs - - -def group_fourier_inverse(group, fourier_coefs): - """Compute the inverse group Fourier transform. - - Using the formula: - x(g) = 1/|G| * sum_{rho in irreps} dim(rho) * Tr(rho(g) * hat x[rho]) - - Parameters - ---------- - group : Group (escnn object) - The group. - fourier_coefs : list of np.ndarray, each of shape=[irrep.size, irrep.size] - The (matrix) Fourier coefficients of template at each irrep. - - Returns - ------- - signal : np.ndarray, shape=[group.order()] - The inverse Fourier transform: a signal over the group. - """ - irreps = group.irreps() - - def _inverse_at_element(g): - return ( - 1 - / group.order() - * sum( - [ - irrep.size * np.trace(irrep(g) @ fourier_coefs[i]) - for i, irrep in enumerate(irreps) - ] - ) - ) - - return np.array([_inverse_at_element(g) for g in group.elements]) diff --git a/src/groups/__init__.py b/src/groups/__init__.py new file mode 100644 index 0000000..924c13d --- /dev/null +++ b/src/groups/__init__.py @@ -0,0 +1,19 @@ +"""Self-contained finite group implementations for Group-AGF.""" + +from src.groups.a5 import IcosahedralGroup +from src.groups.cn import CyclicGroup +from src.groups.cnxcn import ProductCyclicGroup +from src.groups.dn import DihedralGroup +from src.groups.group import Group +from src.groups.irrep import IrreducibleRepresentation +from src.groups.oh import OctahedralGroup + +__all__ = [ + "Group", + "IrreducibleRepresentation", + "CyclicGroup", + "ProductCyclicGroup", + "DihedralGroup", + "OctahedralGroup", + "IcosahedralGroup", +] diff --git a/src/groups/a5.py b/src/groups/a5.py new file mode 100644 index 0000000..b195ace --- /dev/null +++ b/src/groups/a5.py @@ -0,0 +1,49 @@ +"""Icosahedral / A5 group (order 60, 5 irreps). + +All irrep and regular-representation matrices are loaded from pre-computed +``.npy`` files in ``src/groups/data/``. +""" + +from pathlib import Path + +import numpy as np + +from src.groups.group import Group +from src.groups.irrep import IrreducibleRepresentation + +_DATA = Path(__file__).resolve().parent / "data" + +_IRREP_NAMES = [ + "Icosahedral|[irrep_0]:1", + "Icosahedral|[irrep_1]:3", + "Icosahedral|[irrep_2]:5", + "Icosahedral|[irrep_3]:3", + "Icosahedral|[irrep_4]:4", +] + +_N_IRREPS = 5 +_ORDER = 60 + + +class IcosahedralGroup(Group): + """The icosahedral rotation group, isomorphic to A5 (order 60).""" + + def __init__(self): + self._irreps = [] + for i in range(_N_IRREPS): + mats = np.load(_DATA / f"a5_irrep_{i}.npy") + self._irreps.append(IrreducibleRepresentation(_IRREP_NAMES[i], mats)) + self._regular = np.load(_DATA / "a5_regular_rep.npy") + + @property + def order(self) -> int: + return _ORDER + + def elements(self) -> list[int]: + return list(range(_ORDER)) + + def irreps(self) -> list[IrreducibleRepresentation]: + return list(self._irreps) + + def regular_rep(self) -> np.ndarray: + return self._regular diff --git a/src/groups/cn.py b/src/groups/cn.py new file mode 100644 index 0000000..5561d51 --- /dev/null +++ b/src/groups/cn.py @@ -0,0 +1,89 @@ +"""Cyclic group C_N (order N). + +The Fourier transform and power spectrum override the base-class +implementations to use ``np.fft``, which is equivalent but faster. +""" + +import numpy as np + +from src.groups.group import Group +from src.groups.irrep import IrreducibleRepresentation + + +class CyclicGroup(Group): + """Cyclic group C_N of order N. + + Parameters + ---------- + N : int + Order of the cyclic group (N >= 1). + """ + + def __init__(self, N: int): + if N < 1: + raise ValueError(f"N must be >= 1, got {N}") + self._N = N + self._irreps = self._build_irreps() + self._regular = self._build_regular_rep() + + @property + def order(self) -> int: + return self._N + + def elements(self) -> list[int]: + return list(range(self._N)) + + def irreps(self) -> list[IrreducibleRepresentation]: + return list(self._irreps) + + def regular_rep(self) -> np.ndarray: + return self._regular + + # ------------------------------------------------------------------ + # Fast FFT overrides + # ------------------------------------------------------------------ + + def fourier(self, signal: np.ndarray) -> list[np.ndarray]: + """DFT-based group Fourier transform for cyclic groups.""" + return [ + irrep_mat + for irrep_mat in [ + np.array([[coef]]) for coef in np.fft.fft(signal) + ] + ] + + def inverse_fourier(self, fourier_coefs: list[np.ndarray]) -> np.ndarray: + """IDFT-based inverse group Fourier transform for cyclic groups.""" + spectrum = np.array([fc[0, 0] for fc in fourier_coefs]) + return np.fft.ifft(spectrum).real + + def power_spectrum(self, signal: np.ndarray) -> np.ndarray: + """Power spectrum via FFT for cyclic groups. + + Returns one power value per frequency bin (same count as irreps = N). + """ + ft = np.fft.fft(signal) + return np.abs(ft) ** 2 + + # ------------------------------------------------------------------ + # Private helpers + # ------------------------------------------------------------------ + + def _build_irreps(self) -> list[IrreducibleRepresentation]: + N = self._N + irreps = [] + for j in range(N): + mats = np.empty((N, 1, 1), dtype=np.complex128) + for k in range(N): + mats[k, 0, 0] = np.exp(2j * np.pi * j * k / N) + irreps.append(IrreducibleRepresentation(f"C{N}|[irrep_{j}]:1", mats)) + return irreps + + def _build_regular_rep(self) -> np.ndarray: + N = self._N + reg = np.zeros((N, N, N)) + for g in range(N): + for h in range(N): + i = (g + h) % N + reg[g, i, h] = 1.0 + return reg diff --git a/src/groups/cnxcn.py b/src/groups/cnxcn.py new file mode 100644 index 0000000..527ad4d --- /dev/null +++ b/src/groups/cnxcn.py @@ -0,0 +1,103 @@ +"""Product cyclic group C_{p1} x C_{p2} (order p1*p2). + +The Fourier transform and power spectrum override the base-class +implementations to use ``np.fft.fft2`` / ``np.fft.rfft2``, which is +equivalent but faster. +""" + +import numpy as np + +from src.groups.group import Group +from src.groups.irrep import IrreducibleRepresentation + + +class ProductCyclicGroup(Group): + """Product cyclic group C_{p1} x C_{p2} (order p1*p2). + + Parameters + ---------- + p1, p2 : int + Orders of the two cyclic factors. + """ + + def __init__(self, p1: int, p2: int): + if p1 < 1 or p2 < 1: + raise ValueError(f"p1, p2 must be >= 1, got ({p1}, {p2})") + self._p1 = p1 + self._p2 = p2 + self._order = p1 * p2 + + @property + def order(self) -> int: + return self._order + + def elements(self) -> list[int]: + return list(range(self._order)) + + def irreps(self) -> list[IrreducibleRepresentation]: + p1, p2 = self._p1, self._p2 + n = self._order + irreps = [] + for j1 in range(p1): + for j2 in range(p2): + mats = np.empty((n, 1, 1), dtype=np.complex128) + for k1 in range(p1): + for k2 in range(p2): + idx = k1 * p2 + k2 + phase = 2j * np.pi * (j1 * k1 / p1 + j2 * k2 / p2) + mats[idx, 0, 0] = np.exp(phase) + name = f"C{p1}xC{p2}|[irrep_{j1},{j2}]:1" + irreps.append(IrreducibleRepresentation(name, mats)) + return irreps + + def regular_rep(self) -> np.ndarray: + p1, p2, n = self._p1, self._p2, self._order + reg = np.zeros((n, n, n)) + for g in range(n): + g1, g2 = divmod(g, p2) + for h in range(n): + h1, h2 = divmod(h, p2) + i1, i2 = (g1 + h1) % p1, (g2 + h2) % p2 + i = i1 * p2 + i2 + reg[g, i, h] = 1.0 + return reg + + # ------------------------------------------------------------------ + # Fast FFT overrides + # ------------------------------------------------------------------ + + def fourier_2d(self, signal_2d: np.ndarray) -> np.ndarray: + """2D DFT-based Fourier transform returning the full spectrum array.""" + return np.fft.fft2(signal_2d) + + def power_spectrum_2d(self, signal_2d: np.ndarray) -> np.ndarray: + """2D power spectrum (full, not rfft2-reduced). + + Parameters + ---------- + signal_2d : np.ndarray, shape (p1, p2) + + Returns + ------- + np.ndarray, shape (p1, p2) + Normalised by p1*p2. + """ + ft = np.fft.fft2(signal_2d) + return np.abs(ft) ** 2 / self._order + + def fourier(self, signal: np.ndarray) -> list[np.ndarray]: + """Flat-signal group Fourier transform.""" + signal_2d = signal.reshape(self._p1, self._p2) + ft = np.fft.fft2(signal_2d) + return [np.array([[ft[j1, j2]]]) for j1 in range(self._p1) for j2 in range(self._p2)] + + def inverse_fourier(self, fourier_coefs: list[np.ndarray]) -> np.ndarray: + """Inverse group Fourier transform.""" + spectrum = np.array([fc[0, 0] for fc in fourier_coefs]).reshape(self._p1, self._p2) + return np.fft.ifft2(spectrum).real.ravel() + + def power_spectrum(self, signal: np.ndarray) -> np.ndarray: + """Flat-signal power spectrum (one value per irrep).""" + signal_2d = signal.reshape(self._p1, self._p2) + ft = np.fft.fft2(signal_2d) + return (np.abs(ft) ** 2).ravel() diff --git a/src/groups/dn.py b/src/groups/dn.py new file mode 100644 index 0000000..77d3d8c --- /dev/null +++ b/src/groups/dn.py @@ -0,0 +1,116 @@ +"""Dihedral group D_N (order 2N). + +Elements are indexed 0..2N-1: + - 0..N-1 : rotations r^0, r^1, ..., r^{N-1} + - N..2N-1 : r^0*s, r^1*s, ..., r^{N-1}*s (reflection composed with rotation) + +Irrep ordering matches escnn.group.DihedralGroup exactly. +""" + +import numpy as np + +from src.groups.group import Group +from src.groups.irrep import IrreducibleRepresentation + + +class DihedralGroup(Group): + """Dihedral group D_N (order 2N), parameterised by N >= 2.""" + + def __init__(self, N: int): + if N < 2: + raise ValueError(f"N must be >= 2, got {N}") + self._N = N + self._order = 2 * N + self._irreps = self._build_irreps() + self._regular = self._build_regular_rep() + + @property + def order(self) -> int: + return self._order + + def elements(self) -> list[int]: + return list(range(self._order)) + + def irreps(self) -> list[IrreducibleRepresentation]: + return list(self._irreps) + + def regular_rep(self) -> np.ndarray: + return self._regular + + # ------------------------------------------------------------------ + # Private helpers + # ------------------------------------------------------------------ + + def _build_irreps(self) -> list[IrreducibleRepresentation]: + N = self._N + n_elems = self._order + irreps = [] + + trivial = np.ones((n_elems, 1, 1)) + irreps.append(IrreducibleRepresentation( + f"D{N}|[irrep_0,0]:1", trivial + )) + + sign = np.ones((n_elems, 1, 1)) + sign[N:] = -1.0 + irreps.append(IrreducibleRepresentation( + f"D{N}|[irrep_1,0]:1", sign + )) + + n_2d = (N - 1) // 2 + for j in range(1, n_2d + 1): + mats = np.empty((n_elems, 2, 2)) + for k in range(N): + angle = 2.0 * np.pi * j * k / N + c, s = np.cos(angle), np.sin(angle) + mats[k] = [[c, -s], [s, c]] + mats[N + k] = [[c, s], [s, -c]] + irreps.append(IrreducibleRepresentation( + f"D{N}|[irrep_1,{j}]:2", mats + )) + + if N % 2 == 0: + half = N // 2 + + rep_1_half = np.empty((n_elems, 1, 1)) + for k in range(N): + rep_1_half[k, 0, 0] = (-1.0) ** k + rep_1_half[N + k, 0, 0] = -((-1.0) ** k) + irreps.append(IrreducibleRepresentation( + f"D{N}|[irrep_1,{half}]:1", rep_1_half + )) + + rep_0_half = np.empty((n_elems, 1, 1)) + for k in range(N): + rep_0_half[k, 0, 0] = (-1.0) ** k + rep_0_half[N + k, 0, 0] = (-1.0) ** k + irreps.append(IrreducibleRepresentation( + f"D{N}|[irrep_0,{half}]:1", rep_0_half + )) + + return irreps + + def _cayley(self, g: int, h: int) -> int: + """Index of the product g * h in the group.""" + N = self._N + g_rot = g < N + h_rot = h < N + a = g if g_rot else g - N + b = h if h_rot else h - N + + if g_rot and h_rot: + return (a + b) % N + if g_rot and not h_rot: + return N + (a + b) % N + if not g_rot and h_rot: + return N + (a - b) % N + return (a - b) % N + + def _build_regular_rep(self) -> np.ndarray: + n = self._order + reg = np.zeros((n, n, n)) + for g in range(n): + for h in range(n): + i = self._cayley(g, h) + reg[g, i, h] = 1.0 + return reg diff --git a/src/groups/group.py b/src/groups/group.py new file mode 100644 index 0000000..b7a9e71 --- /dev/null +++ b/src/groups/group.py @@ -0,0 +1,109 @@ +from abc import ABC, abstractmethod + +import numpy as np + + +class Group(ABC): + """Abstract Base Class for Finite Groups in Group-AGF. + + Subclasses must implement ``order``, ``elements``, ``irreps``, and + ``regular_rep``. The Fourier analysis methods (``fourier``, + ``inverse_fourier``, ``power_spectrum``) are provided as concrete + implementations that rely solely on the abstract interface. + """ + + @property + @abstractmethod + def order(self) -> int: + """Cardinality |G| of the group.""" + + @abstractmethod + def elements(self) -> list[int]: + """List of element indices ``[0, 1, ..., |G|-1]``.""" + + @abstractmethod + def irreps(self) -> list: + """List of :class:`IrreducibleRepresentation` objects.""" + + @abstractmethod + def regular_rep(self) -> np.ndarray: + """All regular-representation (permutation) matrices. + + Returns + ------- + np.ndarray, shape (|G|, |G|, |G|) + ``result[i]`` is the |G| x |G| permutation matrix for element *i*. + """ + + # ------------------------------------------------------------------ + # Concrete methods built on the abstract interface + # ------------------------------------------------------------------ + + def fourier(self, signal: np.ndarray) -> list[np.ndarray]: + """Group Fourier Transform. + + For each irrep rho, compute the Fourier coefficient: + hat_x[rho] = sum_{g in G} x[g] * rho(g).conj().T + + Parameters + ---------- + signal : np.ndarray, shape (|G|,) + + Returns + ------- + list of np.ndarray, each of shape (d_rho, d_rho) + """ + irreps = self.irreps() + fourier_coefs = [] + for irrep in irreps: + coef = sum( + signal[i_g] * irrep(i_g).conj().T for i_g in range(self.order) + ) + fourier_coefs.append(coef) + return fourier_coefs + + def inverse_fourier(self, fourier_coefs: list[np.ndarray]) -> np.ndarray: + """Inverse Group Fourier Transform. + + x(g) = 1/|G| * sum_{rho} dim(rho) * Tr(rho(g) @ hat_x[rho]) + + Parameters + ---------- + fourier_coefs : list of np.ndarray, each of shape (d_rho, d_rho) + + Returns + ------- + np.ndarray, shape (|G|,) + """ + irreps = self.irreps() + n = self.order + + def _at_element(g): + return (1.0 / n) * sum( + irrep.size * np.trace(irrep(g) @ fourier_coefs[i]) + for i, irrep in enumerate(irreps) + ) + + return np.array([_at_element(g) for g in range(n)]) + + def power_spectrum(self, signal: np.ndarray) -> np.ndarray: + """Group power spectrum. + + For each irrep rho the power is:: + ||hat x(rho)||^2_rho = dim(rho) * Tr( hat_x(rho)^H @ hat_x(rho) ) + + Parameters + ---------- + signal : np.ndarray, shape (|G|,) + + Returns + ------- + np.ndarray, shape (n_irreps,) + """ + fourier_coefs = self.fourier(signal) + irreps = self.irreps() + ps = np.zeros(len(irreps)) + for i, irrep in enumerate(irreps): + fc = fourier_coefs[i] + ps[i] = irrep.size * np.trace(fc.conj().T @ fc) + return ps diff --git a/src/groups/irrep.py b/src/groups/irrep.py new file mode 100644 index 0000000..2196deb --- /dev/null +++ b/src/groups/irrep.py @@ -0,0 +1,37 @@ +import numpy as np + + +class IrreducibleRepresentation: + """Stores the matrices of a single irreducible representation for every group element. + + Parameters + ---------- + name : str + Human-readable label (e.g. ``"trivial"``, ``"standard_2d"``). + matrices : np.ndarray, shape (|G|, d, d) + Representation matrices indexed by element index. + """ + + def __init__(self, name: str, matrices: np.ndarray): + if matrices.ndim != 3 or matrices.shape[1] != matrices.shape[2]: + raise ValueError( + f"matrices must have shape (n_elements, d, d), got {matrices.shape}" + ) + self._name = name + self._matrices = np.asarray(matrices, dtype=np.float64) + self._size = int(matrices.shape[1]) + + @property + def size(self) -> int: + """Dimension of the irrep (d).""" + return self._size + + def __call__(self, element_index: int) -> np.ndarray: + """Return the representation matrix for the given element index.""" + return self._matrices[element_index] + + def __repr__(self) -> str: + return f"IrreducibleRepresentation(name={self._name!r}, size={self._size})" + + def __str__(self) -> str: + return self._name diff --git a/src/groups/oh.py b/src/groups/oh.py new file mode 100644 index 0000000..510fa8c --- /dev/null +++ b/src/groups/oh.py @@ -0,0 +1,49 @@ +"""Octahedral group (order 24, 5 irreps). + +All irrep and regular-representation matrices are loaded from pre-computed +``.npy`` files in ``src/groups/data/``. +""" + +from pathlib import Path + +import numpy as np + +from src.groups.group import Group +from src.groups.irrep import IrreducibleRepresentation + +_DATA = Path(__file__).resolve().parent / "data" + +_IRREP_NAMES = [ + "Octahedral|[irrep_0]:1", + "Octahedral|[irrep_1]:3", + "Octahedral|[irrep_-1]:3", + "Octahedral|[irrep_2]:2", + "Octahedral|[irrep_3]:1", +] + +_N_IRREPS = 5 +_ORDER = 24 + + +class OctahedralGroup(Group): + """The chiral octahedral rotation group (order 24).""" + + def __init__(self): + self._irreps = [] + for i in range(_N_IRREPS): + mats = np.load(_DATA / f"oh_irrep_{i}.npy") + self._irreps.append(IrreducibleRepresentation(_IRREP_NAMES[i], mats)) + self._regular = np.load(_DATA / "oh_regular_rep.npy") + + @property + def order(self) -> int: + return _ORDER + + def elements(self) -> list[int]: + return list(range(_ORDER)) + + def irreps(self) -> list[IrreducibleRepresentation]: + return list(self._irreps) + + def regular_rep(self) -> np.ndarray: + return self._regular diff --git a/src/main.py b/src/main.py index 6fb35a3..82d7c9f 100644 --- a/src/main.py +++ b/src/main.py @@ -202,17 +202,17 @@ def regenerate_plots(run_dir, device="cpu"): ) elif group_name in ("dihedral", "octahedral", "A5"): if group_name == "dihedral": - from escnn.group import DihedralGroup + from src.groups import DihedralGroup group = DihedralGroup(N=config["data"].get("group_n", 3)) elif group_name == "octahedral": - from escnn.group import Octahedral + from src.groups import OctahedralGroup - group = Octahedral() + group = OctahedralGroup() else: - from escnn.group import Icosahedral + from src.groups import IcosahedralGroup - group = Icosahedral() + group = IcosahedralGroup() produce_plots_group( run_dir=run_dir, config=config, @@ -801,7 +801,7 @@ def produce_plots_group( group=None, ): """ - Generate all analysis plots after training for any escnn group. + Generate all analysis plots after training for any group. Args: run_dir: Directory to save plots @@ -812,18 +812,18 @@ def produce_plots_group( train_loss_hist: Training loss history template: 1D template array of shape (group_size,) device: Device string ('cpu' or 'cuda') - group: escnn group object (required) + group: Group object (required) """ group_name = config["data"]["group_name"] # Build a human-readable label for plot titles if group_name == "dihedral": n = config["data"].get("group_n", 3) - group_label = f"D{n} (Dihedral, order {group.order()})" + group_label = f"D{n} (Dihedral, order {group.order})" elif group_name == "octahedral": - group_label = f"Octahedral (order {group.order()})" + group_label = f"Octahedral (order {group.order})" elif group_name == "A5": - group_label = f"A5 / Icosahedral (order {group.order()})" + group_label = f"A5 / Icosahedral (order {group.order})" else: group_label = group_name @@ -835,7 +835,7 @@ def produce_plots_group( plot_power_spectrum = plots_bool_dict.get("power_spectrum", True) plot_w_dominant_irrep_fraction_bool = plots_bool_dict.get("w_dominant_irrep_fraction", True) - group_size = group.order() + group_size = group.order k = config["data"]["k"] batch_size = config["data"]["batch_size"] @@ -1015,7 +1015,7 @@ def produce_plots_group( if fig_w is None: print( " (skipped w_dominant_irrep_fraction: need W or W_out with second dim" - f" {group_size} matching escnn group order)" + f" {group_size} matching group order)" ) viz.maybe_save_w_dominant_irrep_fraction_npz( @@ -1123,25 +1123,24 @@ def train_single_run(config: dict, run_dir: Path = None) -> dict: plt.close(fig) print(" ✓ Saved template") elif group_name in ("dihedral", "octahedral", "A5"): - # Construct the escnn group object if group_name == "dihedral": - from escnn.group import DihedralGroup + from src.groups import DihedralGroup n = group_n if group_n is not None else 3 group = DihedralGroup(N=n) group_label = f"Dihedral D{n}" elif group_name == "octahedral": - from escnn.group import Octahedral + from src.groups import OctahedralGroup - group = Octahedral() + group = OctahedralGroup() group_label = "Octahedral" elif group_name == "A5": - from escnn.group import Icosahedral + from src.groups import IcosahedralGroup - group = Icosahedral() + group = IcosahedralGroup() group_label = "Icosahedral (A5)" - group_size = group.order() + group_size = group.order print(f"{group_label} group order: {group_size}") print(f"{group_label} irreps: {[irrep.size for irrep in group.irreps()]} (dimensions)") diff --git a/src/power.py b/src/power.py index e19abde..cd185e1 100644 --- a/src/power.py +++ b/src/power.py @@ -1,263 +1,119 @@ import numpy as np import torch -import src.fourier as fourier + +# --------------------------------------------------------------------------- +# Loss plateau prediction functions (extracted from former CyclicPower / +# GroupPower classes) +# --------------------------------------------------------------------------- -class CyclicPower: - """Compute and store the power spectrum of the template, which can be used - to compute theoretical loss plateau predictions for the ZnZ group and compare to learned power spectrum. +def loss_plateau_predictions_cyclic(template, template_dim, p1=None, p2=None): + """Compute theoretical loss plateau predictions for a cyclic template. Parameters ---------- - template : ndarray (group_size,) or (group_size*group_size,) - Flattened template array. + template : np.ndarray + The template array. For ``template_dim == 1``, shape ``(group_size,)``. + For ``template_dim == 2``, shape ``(p1, p2)`` or flattened ``(p1*p2,)``. template_dim : int - ``1`` for C_n (1D cyclic), ``2`` for C_n × C_m as a 2D grid. + ``1`` for C_n (1D cyclic), ``2`` for C_n x C_m (2D). p1, p2 : int, optional - For ``template_dim == 2``, grid shape ``(p1, p2)`` when the grid is not square. - If omitted, the template must be square ``(g, g)`` with ``len(template) == g**2``. + Required when ``template_dim == 2`` to specify the grid shape. + + Returns + ------- + list of float + Theoretical loss plateau predictions for each nonzero power, in descending order. """ + template = np.asarray(template) - def __init__(self, template, template_dim, p1=None, p2=None): - self.template = np.asarray(template).ravel() - self.template_dim = template_dim - self._p1 = p1 - self._p2 = p2 - if template_dim == 2: - if p1 is not None and p2 is not None: - if self.template.size != p1 * p2: - raise ValueError( - f"template length {self.template.size} must equal p1*p2={p1 * p2}" - ) - self.template_2D = self.template.reshape((p1, p2)) - self.group_size = p1 * p2 - else: - g = int(np.sqrt(len(self.template))) - if g * g != len(self.template): - raise ValueError( - "2D cyclic template must be square or pass p1, p2 for a rectangular grid" - ) - self.group_size = g - self.template_2D = self.template.reshape((self.group_size, self.group_size)) - self.x_freqs, self.y_freqs, self.power = self.cnxcn_power_spectrum(return_freqs=True) + if template_dim == 2: + if p1 is not None and p2 is not None: + template_2d = template.reshape((p1, p2)) + group_size = p1 * p2 + print("Computing loss plateau predictions for template of shape:", (p1, p2)) else: - self.group_size = len(self.template) - self.freqs, self.power = self.cn_power_spectrum(return_freqs=True) - - def cn_power_spectrum(self, return_freqs=False): - """Compute the 1D power spectrum of 1D FT.""" - num_coefficients = (self.group_size // 2) + 1 - - # Perform FFT and calculate power spectrum - ft = np.fft.fft( - self.template - ) # Could consider using np.fft.rfft which is designed for real valued input. - power = np.abs(ft[:num_coefficients]) ** 2 / self.group_size - - # Double power for frequencies strictly between 0 and Nyquist (Nyquist is not doubled if p is even) - if ( - self.group_size % 2 == 0 - ): # group size is even, Nyquist frequency at index num_coefficients - 1 - power[1 : num_coefficients - 1] *= 2 - else: # p is odd, no Nyquist frequency - power[1:] *= 2 - - # Confirm the power sum approximates the squared norm of points - total_power = np.sum(power) - norm_squared = np.linalg.norm(self.template) ** 2 - if not np.isclose(total_power, norm_squared, rtol=1e-3): - print( - f"Warning: Total power {total_power:.3f} does not match norm squared {norm_squared:.3f}" - ) - - if return_freqs: - freqs = np.fft.rfftfreq(self.group_size) - return freqs, power - - return power + flat = template.ravel() + g = int(np.sqrt(len(flat))) + if g * g != len(flat): + raise ValueError( + "2D cyclic template must be square or pass p1, p2 for a rectangular grid" + ) + template_2d = flat.reshape((g, g)) + group_size = g * g + print("Computing loss plateau predictions for template of shape:", (g, g)) - def cnxcn_power_spectrum(self, return_freqs=False): - """ - Compute the 2D power spectrum of 2D FT. - - Why are some powers doubled? - rfft2 removes redundant frequencies along first axis automatically - but does not truncate the second axis - Therefore, the output shape is (M, N//2 + 1). - This eliminates redundancy, save for a specific cases: - --> All frequencies along the first axis at (u, 0) for u = N//2 + 1, ..., N - 1 - are redundant and contain the same information as (u, 0) for u = 1, ..., N//2 - 1. - - Since most of the power coefficients now represnet 2 frequencies (positive and negative), - we double all the power coefficients to conserve total power. - However, we do not double the DC component (0, 0) and the Nyquist frequency (N/2, 0) if N is even, - since these are unique and do not have a negative counterpart. - - Parameters - ---------- - template : ndarray (M, N) - Real-valued 2D input array. - - Returns - ------- - row_freqs : ndarray (M,) - Frequency bins for the first axis (rows). - column_freqs : ndarray (N//2 + 1,) - Frequency bins for the second axis (columns). - power : ndarray (M, N//2 + 1) - Power spectrum of the input. - """ - M, N = self.template_2D.shape - - # Perform 2D rFFT - ft = np.fft.rfft2(self.template_2D) - - # Power spectrum normalized by total number of samples + ft = np.fft.rfft2(template_2d) + M, N = template_2d.shape power = np.abs(ft) ** 2 / (M * N) - - # For the first row (u=0), remove redundant frequencies and double the appropriate ones - power[(N // 2 + 1) :, 0] = 0 - + power[(N // 2 + 1):, 0] = 0 power *= 2 power[0, 0] /= 2 if N % 2 == 0: power[N // 2, 0] /= 2 + power = power.flatten() + else: + template = template.ravel() + group_size = len(template) + num_coefficients = (group_size // 2) + 1 + ft = np.fft.fft(template) + power = np.abs(ft[:num_coefficients]) ** 2 / group_size + if group_size % 2 == 0: + power[1: num_coefficients - 1] *= 2 + else: + power[1:] *= 2 - # Check Parseval’s theorem - total_power = np.sum(power) - norm_squared = np.linalg.norm(self.template_2D) ** 2 - if not np.isclose(total_power, norm_squared, rtol=1e-3): - print( - f"Warning: Total power {total_power:.3f} does not match norm squared {norm_squared:.3f}" - ) - - if return_freqs: - # Frequency bins - row_freqs = np.fft.fftfreq(M) # full symmetric frequencies (rows) - column_freqs = np.fft.rfftfreq(N) # only non-negative frequencies (columns) - - return row_freqs, column_freqs, power - - return power - - def loss_plateau_predictions(self): - """Compute theoretical loss plateau predictions from the template's power spectrum. - (as predicted by AGF) - - Returns - ------- - plateau_predictions : list of float - Theoretical loss plateau predictions for each nonzero power, in descending order. - """ - power = self.power - - if self.template_dim == 2: - if self._p1 is not None and self._p2 is not None: - print( - "Computing loss plateau predictions for template of shape:", - (self._p1, self._p2), - ) - else: - img_size = int(np.sqrt(len(self.template))) - print( - "Computing loss plateau predictions for template of shape:", - (img_size, img_size), - ) - power = power.flatten() - - nonzero_power_mask = power > 1e-20 - power = power[nonzero_power_mask] - i_power_descending_order = np.argsort(power)[::-1] - power = power[i_power_descending_order] - - plateau_predictions = [np.sum(power[k:]) for k in range(len(power))] - coef = 1 / self.group_size - plateau_predictions = [alpha * coef for alpha in plateau_predictions] + nonzero_power_mask = power > 1e-20 + power = power[nonzero_power_mask] + i_power_descending_order = np.argsort(power)[::-1] + power = power[i_power_descending_order] - return plateau_predictions + coef = 1 / group_size + return [coef * np.sum(power[k:]) for k in range(len(power))] -class GroupPower: - """Compute and store the power spectrum of the template for a generic group. +def loss_plateau_predictions_group(template, group): + """Compute theoretical loss plateau predictions for a generic group template. Parameters ---------- - template : ndarray (group_size,) - 1D template array of length ``group.order()``. - group : Group (escnn object) - The group the template is defined over. - Also specifies which fourier transform to apply, and thus - which transform to compute the power spectrum for. + template : np.ndarray, shape (group.order,) + The template array. + group : Group + A group instance with a ``power_spectrum`` method. + + Returns + ------- + list of float + Theoretical loss plateau predictions for each nonzero power, in descending order. """ + p = len(template) + print("Computing loss plateau predictions for template of shape:", (p,)) + power = group.power_spectrum(template) + nonzero_power_mask = power > 1e-20 + power = power[nonzero_power_mask] + print("Found ", len(power), "non-zero power coefficients.") + i_power_descending_order = np.argsort(power)[::-1] + power = power[i_power_descending_order] + coef = 1 / p + return [coef * np.sum(power[k:]) for k in range(len(power))] - def __init__(self, template, group): - self.template = template - self.group_size = len(template) - self.group = group - self.power = self.group_power_spectrum() - self.freqs = list(range(len(self.power))) - - def group_power_spectrum(self): - """Compute the (group) power spectrum of the template. - - For each irrep rho, the power is given by: - ||hat x(rho)||_rho = dim(rho) * Tr(hat x(rho)^dagger * hat x(rho)) - where hat x(rho) is the (matrix) Fourier coefficient of template x at irrep rho. - - We multiply by the dimension of the irrep because for 2D irreps, the power - would otherwise be split across two dimensions, so we must double it to get the correct - total power. - - Returns - ------- - power_spectrum : np.ndarray, shape=[len(group.irreps())] - The power spectrum of the template. - """ - fourier_coefs = fourier.group_fourier(self.group, self.template) - irreps = self.group.irreps() - - power_spectrum = np.zeros(len(irreps)) - for i, irrep in enumerate(irreps): - fc = fourier_coefs[i] - power_spectrum[i] = irrep.size * np.trace(fc.conj().T @ fc) - power_spectrum = power_spectrum / self.group.order() - - return np.array(power_spectrum) - - def loss_plateau_predictions(self): - """Compute theoretical loss plateau predictions from the template's power spectrum. - - The loss plateau predictions give the levels of the loss plot. - - Returns - ------- - plateau_predictions : list of float - Theoretical loss plateau predictions for each nonzero power, in descending order. - """ - p = len(self.template) - print("Computing loss plateau predictions for template of shape:", (p,)) - power = self.power - nonzero_power_mask = power > 1e-20 - power = power[nonzero_power_mask] - print("Found ", len(power), "non-zero power coefficients.") - i_power_descending_order = np.argsort(power)[::-1] - power = power[i_power_descending_order] - plateau_predictions = [np.sum(power[k:]) for k in range(len(power))] - coef = 1 / p - plateau_predictions = [alpha * coef for alpha in plateau_predictions] - return plateau_predictions + +# --------------------------------------------------------------------------- +# Per-neuron power helpers +# --------------------------------------------------------------------------- def powers_per_neuron_rows(W: np.ndarray, group) -> np.ndarray: - """Irrep power spectrum for each row of ``W`` using :class:`GroupPower`. + """Irrep power spectrum for each row of ``W`` using ``group.power_spectrum``. - Each row is treated as a real signal on ``group`` (length ``group.order()``). + Each row is treated as a real signal on ``group`` (length ``group.order``). Parameters ---------- - W : ndarray, shape (hidden_dim, group.order()) - group : escnn ``Group`` + W : ndarray, shape (hidden_dim, group.order) + group : Group Must match the group structure of the weight rows. Returns @@ -267,13 +123,13 @@ def powers_per_neuron_rows(W: np.ndarray, group) -> np.ndarray: """ if W.ndim != 2: raise ValueError(f"W must be 2-D, got shape {W.shape}") - if W.shape[1] != group.order(): - raise ValueError(f"W.shape[1] ({W.shape[1]}) must equal group.order() ({group.order()})") + if W.shape[1] != group.order: + raise ValueError(f"W.shape[1] ({W.shape[1]}) must equal group.order ({group.order})") hidden = W.shape[0] n_irreps = len(group.irreps()) out = np.empty((hidden, n_irreps)) for h in range(hidden): - out[h] = GroupPower(W[h], group).power + out[h] = group.power_spectrum(W[h]) return out @@ -284,7 +140,7 @@ def powers_per_neuron_rows_cyclic( p1: int | None = None, p2: int | None = None, ) -> np.ndarray: - """Cyclic power spectrum for each row of ``W`` using :class:`CyclicPower`. + """Cyclic power spectrum for each row of ``W``. Parameters ---------- @@ -297,8 +153,9 @@ def powers_per_neuron_rows_cyclic( Returns ------- ndarray - For 1D, shape ``(hidden_dim, group_size // 2 + 1)``. For 2D, shape ``(hidden_dim, M * (N//2 + 1))`` - with ``M, N = p1, p2`` (flattened :class:`CyclicPower` 2D power). + For 1D, shape ``(hidden_dim, group_size // 2 + 1)``. + For 2D, shape ``(hidden_dim, M * (N//2 + 1))`` + with ``M, N = p1, p2``. """ if W.ndim != 2: raise ValueError(f"W must be 2-D, got shape {W.shape}") @@ -308,20 +165,21 @@ def powers_per_neuron_rows_cyclic( num_coeffs = (p // 2) + 1 out = np.empty((hidden, num_coeffs)) for h in range(hidden): - out[h] = CyclicPower(W[h], template_dim=1).power + pw, _ = get_power_1d(W[h]) + out[h] = pw return out if template_dim != 2: raise ValueError(f"template_dim must be 1 or 2, got {template_dim}") if p1 is None or p2 is None: - raise ValueError("p1 and p2 are required for cyclic 2D (CyclicPower template_dim=2)") + raise ValueError("p1 and p2 are required for cyclic 2D power (template_dim=2)") if W.shape[1] != p1 * p2: raise ValueError(f"W.shape[1] ({W.shape[1]}) must equal p1*p2 ({p1 * p2})") - cp0 = CyclicPower(W[0], template_dim=2, p1=p1, p2=p2) - n_bins = cp0.power.size + pw0 = get_power_2d(W[0].reshape(p1, p2), no_freq=True) + n_bins = pw0.size out = np.empty((hidden, n_bins)) - out[0] = cp0.power.ravel() + out[0] = pw0.ravel() for h in range(1, hidden): - out[h] = CyclicPower(W[h], template_dim=2, p1=p1, p2=p2).power.ravel() + out[h] = get_power_2d(W[h].reshape(p1, p2), no_freq=True).ravel() return out @@ -338,48 +196,43 @@ def model_power_over_time(group_name, model, param_history, model_inputs, group= List of model parameters at each training step. model_inputs : torch.Tensor Input data tensor. - group : Group (escnn object) - The escnn group object. Optional, since we don't use escnn for cnxcn. + group : Group, optional + Required for non-cyclic groups. Returns ------- avg_power_history : list of ndarray (num_steps, num_freqs) List of average power spectra at each step. """ - # Determine output shape: support both 1D and 2D model.eval() with torch.no_grad(): test_output = model(model_inputs[:1]) output_shape = test_output.shape[1:] - if group_name == "cnxcn": # 2D template + if group_name == "cnxcn": p1 = int(np.sqrt(output_shape[0])) p2 = p1 template_power_length = p1 * (p2 // 2 + 1) reshape_dims = (-1, p1, p2) - elif group_name == "cn": # 1D template + elif group_name == "cn": template_power_length = (output_shape[0] // 2) + 1 p1 = output_shape[0] reshape_dims = (-1, p1) - else: # other groups are 1D signals + else: template_power_length = len(group.irreps()) p1 = output_shape[0] reshape_dims = (-1, p1) num_points = 200 max_step = len(param_history) - 1 - num_inputs_to_compute_power = max(1, len(model_inputs) // 50) # Ensure at least 1 input - X_tensor = model_inputs[ - :num_inputs_to_compute_power - ] # Added by Nina to speed up computation with octahedral. + num_inputs_to_compute_power = max(1, len(model_inputs) // 50) + X_tensor = model_inputs[:num_inputs_to_compute_power] if max_step <= 1: - # Very short training: just use all available checkpoints steps = np.arange(max_step + 1) else: steps = np.unique(np.logspace(1, np.log10(max_step), num_points, dtype=int)) steps = steps[steps > 50] steps = np.hstack([np.linspace(1, min(50, max_step), 5).astype(int), steps]) - # Ensure all indices are within bounds steps = np.unique(steps) steps = steps[steps <= max_step] powers_over_time = np.zeros([len(steps), template_power_length]) @@ -398,29 +251,25 @@ def model_power_over_time(group_name, model, param_history, model_inputs, group= powers = [] for out in outputs_arr: if group_name == "cnxcn": - output_power = CyclicPower(out.flatten(), template_dim=2) + one_power = get_power_2d(out, no_freq=True).flatten() elif group_name == "cn": - output_power = CyclicPower(out.flatten(), template_dim=1) + one_power, _ = get_power_1d(out.flatten()) else: - output_power = GroupPower(out.flatten(), group=group) - - one_power = output_power.power - # flatten to 1D for both 1D and 2D cases - one_power_flat = one_power.flatten() - powers.append(one_power_flat) + one_power = group.power_spectrum(out.flatten()) + powers.append(one_power.flatten()) powers = np.array(powers) - average_power = np.mean(powers, axis=0) # shape: (num_samples, template_power_length) + average_power = np.mean(powers, axis=0) powers_over_time[i_step, :] = average_power - powers_over_time = np.array(powers_over_time) # shape: (steps, num_freqs) + powers_over_time = np.array(powers_over_time) powers_over_time[powers_over_time < 1e-20] = 0 return powers_over_time, steps # --------------------------------------------------------------------------- -# Power spectrum computation functions (moved from utils.py) +# Power spectrum computation functions # --------------------------------------------------------------------------- @@ -502,11 +351,11 @@ def get_power_2d(points, no_freq=False): weight = 2 * np.ones((M, N // 2 + 1)) weight[0, 0] = 1 - weight[(M // 2 + 1) :, 0] = 0 + weight[(M // 2 + 1):, 0] = 0 if M % 2 == 0: weight[M // 2, 0] = 1 if N % 2 == 0: - weight[(M // 2 + 1) :, N // 2] = 0 + weight[(M // 2 + 1):, N // 2] = 0 weight[0, N // 2] = 1 if (M % 2 == 0) and (N % 2 == 0): weight[M // 2, N // 2] = 1 @@ -605,32 +454,3 @@ def theoretical_final_loss_2d(template_2d): def theoretical_final_loss_1d(template_1d): """Returns expected initial loss (for setting convergence targets).""" return theoretical_loss_levels_1d(template_1d)["initial"] - - -def group_power_spectrum(group, template): - """Compute the (group) power spectrum of the template. - - For each irrep rho, the power is given by: - ||hat x(rho)||_rho = dim(rho) * Tr(hat x(rho)^dagger * hat x(rho)) - - Parameters - ---------- - group : Group (escnn object) - The group. - template : np.ndarray, shape=[group.order()] - The template to compute the power spectrum of. - - Returns - ------- - power_spectrum : np.ndarray, shape=[len(group.irreps())] - The power spectrum of the template. - """ - fourier_coefs = fourier.group_fourier(group, template) - irreps = group.irreps() - - power_spectrum = np.zeros(len(irreps)) - for i, irrep in enumerate(irreps): - fc = fourier_coefs[i] - power_spectrum[i] = irrep.size * np.trace(fc.conj().T @ fc) - power_spectrum = power_spectrum / group.order() - return np.array(power_spectrum) diff --git a/src/template.py b/src/template.py index 9afe367..01ca8ca 100644 --- a/src/template.py +++ b/src/template.py @@ -1,7 +1,5 @@ import numpy as np -import src.fourier as fourier - def one_hot(group_size): """One-hot, with 0th frequency removed (!) encoding of an integer value in R^group_size.""" @@ -117,7 +115,7 @@ def fixed_group(group, powers): Parameters ---------- - group : Group (escnn object) + group : Group The group. powers : list of float Desired spectral power for each irrep (one entry per irrep). @@ -127,7 +125,7 @@ def fixed_group(group, powers): template : np.ndarray, shape (group.order(),), dtype float32 The mean-centered template. """ - group_order = group.order() + group_order = group.order irreps = group.irreps() irrep_dims = [ir.size for ir in irreps] @@ -146,7 +144,7 @@ def fixed_group(group, powers): np.fill_diagonal(mat, np.full(irrep.size, diag_val, dtype=float)) spectrum.append(mat) - template = fourier.group_fourier_inverse(group, spectrum) + template = group.inverse_fourier(spectrum) template = template - np.mean(template) template = template.astype(np.float32) diff --git a/src/viz.py b/src/viz.py index dc2bc00..0164305 100644 --- a/src/viz.py +++ b/src/viz.py @@ -559,7 +559,7 @@ def compute_w_dominant_irrep_fraction_data( if use_cyclic: if group_name == "cnxcn" and group_size != p1 * p2: return None - elif group_size != group.order(): + elif group_size != group.order: return None hidden_dim = W0.shape[0] @@ -688,7 +688,7 @@ def maybe_save_w_dominant_irrep_fraction_npz( data = compute_w_dominant_irrep_fraction_data( param_hist, param_save_indices, - group.order(), + group.order, gn, group=group, ) @@ -744,24 +744,24 @@ def load_w_dominant_irrep_fraction_for_run_dir(run_dir: str | Path) -> dict | No p2=p2, ) if gn == "dihedral": - from escnn.group import DihedralGroup + from src.groups import DihedralGroup group = DihedralGroup(N=config["data"].get("group_n", 3)) elif gn == "octahedral": - from escnn.group import Octahedral + from src.groups import OctahedralGroup - group = Octahedral() + group = OctahedralGroup() elif gn == "A5": - from escnn.group import Icosahedral + from src.groups import IcosahedralGroup - group = Icosahedral() + group = IcosahedralGroup() else: return None return compute_w_dominant_irrep_fraction_data( param_hist, param_save_indices, - group.order(), + group.order, gn, group=group, ) @@ -854,8 +854,8 @@ def plot_w_dominant_irrep_fraction( **What “power” and “fraction” mean** Each neuron's weights form a vector on the group (length ``group_size``). That vector is decomposed into a - **power spectrum**: either cyclic bins via :class:`src.power.CyclicPower` (for ``cn`` / ``cnxcn``) - or irrep-wise power via :class:`src.power.GroupPower` (for escnn groups). **Total power** is the + **power spectrum**: either cyclic bins via FFT (for ``cn`` / ``cnxcn``) + or irrep-wise power via ``group.power_spectrum`` (for generic groups). **Total power** is the sum of that spectrum—how much “energy” the row has in Fourier / group space. **Fraction of power** here means: at time ``t``, take the power in **one** chosen mode and divide by a **single** normalization: the **maximum** of total power that neuron ever had over training. So the y-axis @@ -886,8 +886,8 @@ def plot_w_dominant_irrep_fraction( param_save_indices: Step or epoch index for each snapshot (same length as ``param_hist``) group_size: Flattened group dimension (second axis of ``W`` / ``W_out.T``) x_label: X-axis label (e.g. ``\"Epoch\"`` or ``\"Step\"``) - group_name: ``\"cn\"``, ``\"cnxcn\"``, or an escnn-backed name (e.g. ``\"dihedral\"``) - group: escnn ``Group`` (required unless ``group_name`` is ``cn`` or ``cnxcn``) + group_name: ``\"cn\"``, ``\"cnxcn\"``, or a group name (e.g. ``\"dihedral\"``) + group: ``Group`` (required unless ``group_name`` is ``cn`` or ``cnxcn``) p1, p2: Grid shape for ``cnxcn`` (required when ``group_name == \"cnxcn\"``) save_path: If set, save figure to this path show: If True, display the figure @@ -1107,13 +1107,12 @@ def plot_power_cn( ): """Plot power spectrum of model outputs vs template for cyclic group Cn. - Mirrors plot_power_group but uses CyclicPower (no escnn). + Mirrors plot_power_group but uses 1D FFT power. Each frequency mode is treated as a 1D irrep. """ import src.power as power - template_power_obj = power.CyclicPower(template_1d, template_dim=1) - template_power = template_power_obj.power + template_power, _ = power.get_power_1d(template_1d) n_modes = len(template_power) print(f" Template power spectrum (cn): {template_power}") @@ -1258,13 +1257,12 @@ def plot_power_cnxcn( ): """Plot power spectrum of model outputs vs template for CnxCn group. - Mirrors plot_power_cn but uses 2D CyclicPower (rfft2). + Mirrors plot_power_cn but uses 2D rfft2 power. Each 2D frequency mode (u, v) is tracked separately. """ import src.power as power - template_power_obj = power.CyclicPower(template_2d.flatten(), template_dim=2) - template_power_2d = template_power_obj.power # (p1, p2//2+1) + template_power_2d = power.get_power_2d(template_2d, no_freq=True) # (p1, p2//2+1) template_power = template_power_2d.flatten() n_modes = len(template_power) n_cols = p2 // 2 + 1 @@ -1630,7 +1628,7 @@ def plot_power_group( ): """Plot power spectrum of model outputs vs template over training. - Uses GroupPower from src/power.py for template power and model_power_over_time + Uses group.power_spectrum for template power and model_power_over_time for model output power over training checkpoints. Args: @@ -1639,7 +1637,7 @@ def plot_power_group( param_save_indices: List mapping param_hist index to epoch number X_eval: Input evaluation tensor template: Template array (group_size,) - group: escnn group object + group: Group object k: Sequence length optimizer: Optimizer name init_scale: Initialization scale @@ -1652,8 +1650,7 @@ def plot_power_group( irreps = group.irreps() n_irreps = len(irreps) - template_power_obj = power.GroupPower(template, group=group) - template_power = template_power_obj.power + template_power = group.power_spectrum(template) print(f" Template power spectrum: {template_power}") print(" (These are dim^2 * diag_value^2 / |G| for each irrep)") diff --git a/test/test_dataset.py b/test/test_dataset.py index bf0fef0..b6a3f3d 100644 --- a/test/test_dataset.py +++ b/test/test_dataset.py @@ -155,17 +155,17 @@ def test_exhaustive_shapes(self): class TestGroupCompositionDatasetOfflineGroup: - """Tests for GroupCompositionDataset with generic escnn groups (offline).""" + """Tests for GroupCompositionDataset with generic groups (offline).""" @pytest.fixture def d3_group(self): - from escnn.group import DihedralGroup + from src.groups import DihedralGroup return DihedralGroup(N=3) @pytest.fixture def template_d3(self, d3_group): - group_size = d3_group.order() + group_size = d3_group.order return np.random.randn(group_size).astype(np.float32) def test_sampled_shapes(self, template_d3, d3_group): @@ -226,7 +226,7 @@ def test_return_all_outputs(self, template_d3, d3_group): assert ds.sequence.shape == (num_samples, k) def test_template_mismatch_error(self, d3_group): - wrong_size = d3_group.order() + 1 + wrong_size = d3_group.order + 1 template = np.random.randn(wrong_size).astype(np.float32) with pytest.raises(AssertionError): diff --git a/test/test_fourier.py b/test/test_fourier.py index 2900e5e..e8a1805 100644 --- a/test/test_fourier.py +++ b/test/test_fourier.py @@ -1,18 +1,17 @@ import numpy as np -from escnn.group import Octahedral -import src.fourier as fourier +from src.groups import OctahedralGroup import src.template as template def test_group_fourier_inverse_is_identity(): - """Test that group_fourier followed by group_fourier_inverse reconstructs the original.""" - group = Octahedral() + """Test that fourier followed by inverse_fourier reconstructs the original.""" + group = OctahedralGroup() tpl = template.fixed_group(group, powers=[100.0, 20.0, 0.0, 0.0, 0.0]) - fourier_coefs = fourier.group_fourier(group, tpl) - reconstructed = fourier.group_fourier_inverse(group, fourier_coefs) + fourier_coefs = group.fourier(tpl) + reconstructed = group.inverse_fourier(fourier_coefs) assert np.allclose(tpl, reconstructed, atol=1e-10), ( f"Inversion failed! max diff: {np.max(np.abs(tpl - reconstructed))}" @@ -20,11 +19,11 @@ def test_group_fourier_inverse_is_identity(): def test_group_fourier_coefs_shape(): - """Test that group_fourier returns one coefficient matrix per irrep.""" - group = Octahedral() + """Test that fourier returns one coefficient matrix per irrep.""" + group = OctahedralGroup() tpl = template.fixed_group(group, powers=[100.0, 20.0, 0.0, 0.0, 0.0]) - fourier_coefs = fourier.group_fourier(group, tpl) + fourier_coefs = group.fourier(tpl) assert len(fourier_coefs) == len(group.irreps()) for coef, irrep in zip(fourier_coefs, group.irreps()): diff --git a/test/test_group_escnn.py b/test/test_group_escnn.py new file mode 100644 index 0000000..bd64ed1 --- /dev/null +++ b/test/test_group_escnn.py @@ -0,0 +1,203 @@ +"""Parity tests: verify our Group implementations match escnn exactly. + +This file deliberately imports escnn and is intended to be run *before* +the escnn dependency is removed. It will be skipped automatically if +escnn is not installed. +""" + +import numpy as np +import pytest + +escnn = pytest.importorskip("escnn", reason="escnn not installed; parity tests skipped") + +from escnn.group import DihedralGroup as ESCNNDihedral # noqa: E402 +from escnn.group import Icosahedral as ESCNNIcosahedral # noqa: E402 +from escnn.group import Octahedral as ESCNNOctahedral # noqa: E402 + +from src.groups.a5 import IcosahedralGroup # noqa: E402 +from src.groups.dn import DihedralGroup # noqa: E402 +from src.groups.oh import OctahedralGroup # noqa: E402 + + +# --------------------------------------------------------------------------- +# Helpers +# --------------------------------------------------------------------------- + +def _escnn_irrep_matrices(escnn_group): + """Extract all irrep matrices from an escnn group as a list of (|G|, d, d) arrays.""" + irreps = escnn_group.irreps() + elements = list(escnn_group.elements) + result = [] + for irrep in irreps: + mats = np.array([irrep(g) for g in elements]) + result.append(mats) + return result + + +def _escnn_regular_rep_matrices(escnn_group): + """Extract all regular representation matrices from an escnn group.""" + regular_rep = escnn_group.representations["regular"] + elements = list(escnn_group.elements) + return np.array([regular_rep(g) for g in elements]) + + +# --------------------------------------------------------------------------- +# Fixtures: pairs of (our_group, escnn_group) +# --------------------------------------------------------------------------- + +@pytest.fixture(params=[3, 5], ids=["D3", "D5"]) +def dihedral_pair(request): + n = request.param + return DihedralGroup(N=n), ESCNNDihedral(N=n) + + +@pytest.fixture() +def octahedral_pair(): + return OctahedralGroup(), ESCNNOctahedral() + + +@pytest.fixture() +def a5_pair(): + return IcosahedralGroup(), ESCNNIcosahedral() + + +@pytest.fixture( + params=["dihedral_3", "dihedral_5", "octahedral", "a5"], + ids=["D3", "D5", "Oh", "A5"], +) +def group_pair(request): + """Yield (our_group, escnn_group) for every group under test.""" + name = request.param + if name == "dihedral_3": + return DihedralGroup(N=3), ESCNNDihedral(N=3) + if name == "dihedral_5": + return DihedralGroup(N=5), ESCNNDihedral(N=5) + if name == "octahedral": + return OctahedralGroup(), ESCNNOctahedral() + if name == "a5": + return IcosahedralGroup(), ESCNNIcosahedral() + raise ValueError(name) + + +# =================================================================== +# Tests +# =================================================================== + + +class TestOrder: + def test_order(self, group_pair): + ours, escnn_g = group_pair + assert ours.order == escnn_g.order() + + +class TestElements: + def test_num_elements(self, group_pair): + ours, escnn_g = group_pair + assert len(ours.elements()) == escnn_g.order() + + +class TestIrrepDimsOrdering: + """Exact check that irrep dimensions appear in the expected order.""" + + def test_octahedral_dims(self): + g = OctahedralGroup() + dims = [ir.size for ir in g.irreps()] + assert dims == [1, 3, 3, 2, 1] + + def test_a5_dims(self): + g = IcosahedralGroup() + dims = [ir.size for ir in g.irreps()] + assert dims == [1, 3, 5, 3, 4] + + +class TestIrrepCountAndDims: + def test_same_count_and_dims(self, group_pair): + ours, escnn_g = group_pair + our_dims = [ir.size for ir in ours.irreps()] + escnn_dims = [ir.size for ir in escnn_g.irreps()] + assert our_dims == escnn_dims + + +class TestIrrepMatrices: + """Irrep matrices must match exactly (not up to unitary equivalence).""" + + def test_irrep_matrices_exact(self, group_pair): + ours, escnn_g = group_pair + escnn_mats_list = _escnn_irrep_matrices(escnn_g) + + for i, (our_irrep, escnn_mats) in enumerate( + zip(ours.irreps(), escnn_mats_list) + ): + for g in range(ours.order): + np.testing.assert_allclose( + our_irrep(g), + escnn_mats[g], + atol=1e-12, + err_msg=f"irrep {i} element {g}", + ) + + +class TestRegularRep: + def test_regular_rep(self, group_pair): + ours, escnn_g = group_pair + our_reps = ours.regular_rep() + escnn_reps = _escnn_regular_rep_matrices(escnn_g) + assert our_reps.shape == escnn_reps.shape + np.testing.assert_allclose(our_reps, escnn_reps, atol=1e-12) + + +class TestFourier: + def _random_signal(self, n, seed=42): + rng = np.random.default_rng(seed) + return rng.standard_normal(n) + + def test_fourier_roundtrip(self, group_pair): + ours, _ = group_pair + signal = self._random_signal(ours.order) + coefs = ours.fourier(signal) + reconstructed = ours.inverse_fourier(coefs) + np.testing.assert_allclose(signal, reconstructed, atol=1e-10) + + def test_fourier_vs_escnn(self, group_pair): + ours, escnn_g = group_pair + signal = self._random_signal(ours.order) + our_coefs = ours.fourier(signal) + escnn_irreps = escnn_g.irreps() + escnn_elements = list(escnn_g.elements) + escnn_coefs = [] + for irrep in escnn_irreps: + coef = sum( + signal[i_g] * irrep(g).conj().T + for i_g, g in enumerate(escnn_elements) + ) + escnn_coefs.append(coef) + assert len(our_coefs) == len(escnn_coefs) + for i, (oc, ec) in enumerate(zip(our_coefs, escnn_coefs)): + np.testing.assert_allclose( + oc, ec, atol=1e-10, err_msg=f"fourier coef {i}" + ) + + +class TestPowerSpectrum: + def _random_signal(self, n, seed=42): + rng = np.random.default_rng(seed) + return rng.standard_normal(n) + + def test_power_spectrum_vs_escnn(self, group_pair): + ours, escnn_g = group_pair + signal = self._random_signal(ours.order) + our_ps = ours.power_spectrum(signal) + escnn_irreps = escnn_g.irreps() + escnn_elements = list(escnn_g.elements) + escnn_coefs = [] + for irrep in escnn_irreps: + coef = sum( + signal[i_g] * irrep(g).conj().T + for i_g, g in enumerate(escnn_elements) + ) + escnn_coefs.append(coef) + escnn_ps = np.zeros(len(escnn_irreps)) + for i, irrep in enumerate(escnn_irreps): + fc = escnn_coefs[i] + escnn_ps[i] = irrep.size * np.trace(fc.conj().T @ fc) + np.testing.assert_allclose(our_ps, escnn_ps, atol=1e-10) diff --git a/test/test_main.py b/test/test_main.py index 2989c58..d5e5413 100644 --- a/test/test_main.py +++ b/test/test_main.py @@ -130,8 +130,8 @@ def test_main_d3(temp_run_dir, mock_savefig): def test_main_octahedral_config(): """Test that octahedral config loads and validates correctly. - Full training is skipped because escnn's Octahedral group construction - is expensive (~8s). The D3 test already covers the full group pipeline + Full training is skipped because Octahedral group construction + is relatively expensive. The D3 test already covers the full group pipeline integration (same code path, just a different group). """ import src.main as main @@ -145,8 +145,8 @@ def test_main_octahedral_config(): def test_main_a5_config(): """Test that A5 config loads and validates correctly. - Full training is skipped because escnn's Icosahedral group construction - is expensive (~47s). The D3 test already covers the full group pipeline + Full training is skipped because Icosahedral group construction + is relatively expensive. The D3 test already covers the full group pipeline integration (same code path, just a different group). """ import src.main as main diff --git a/test/test_power.py b/test/test_power.py index a853cb0..c0cbacf 100644 --- a/test/test_power.py +++ b/test/test_power.py @@ -1,8 +1,8 @@ """Tests for src.power module.""" import numpy as np -from escnn.group import Octahedral +from src.groups import DihedralGroup, OctahedralGroup import src.power as power import src.template as template @@ -203,68 +203,60 @@ def test_empty_for_zero_signal(self): class TestPowersPerNeuronRowsCyclic: """Tests for power.powers_per_neuron_rows_cyclic.""" - def test_1d_matches_cyclicpower(self): - """Each row must match CyclicPower on that row (C_n).""" + def test_1d_shape(self): + """Each row must produce the correct power shape for C_n.""" p = 10 h = 3 W = np.random.RandomState(1).randn(h, p) out = power.powers_per_neuron_rows_cyclic(W, template_dim=1) assert out.shape == (h, (p // 2) + 1) for i in range(h): - np.testing.assert_allclose( - out[i], power.CyclicPower(W[i], template_dim=1).power, rtol=1e-10 - ) + expected, _ = power.get_power_1d(W[i]) + np.testing.assert_allclose(out[i], expected, rtol=1e-10) - def test_2d_rectangular_matches_cyclicpower(self): + def test_2d_rectangular_shape(self): p1, p2 = 2, 3 h = 2 W = np.random.RandomState(2).randn(h, p1 * p2) out = power.powers_per_neuron_rows_cyclic(W, template_dim=2, p1=p1, p2=p2) - cp0 = power.CyclicPower(W[0], template_dim=2, p1=p1, p2=p2) - assert out.shape[1] == cp0.power.size - np.testing.assert_allclose(out[0], cp0.power.ravel(), rtol=1e-10) + expected_0 = power.get_power_2d(W[0].reshape(p1, p2), no_freq=True) + assert out.shape[1] == expected_0.size + np.testing.assert_allclose(out[0], expected_0.ravel(), rtol=1e-10) class TestPowersPerNeuronRows: """Tests for power.powers_per_neuron_rows.""" - def test_matches_rowwise_grouppower(self): - """Each row must match GroupPower on that row.""" - from escnn.group import DihedralGroup - + def test_matches_rowwise_group_power_spectrum(self): + """Each row must match group.power_spectrum on that row.""" group = DihedralGroup(3) - h, n = 5, group.order() + h, n = 5, group.order W = np.random.RandomState(0).randn(h, n) out = power.powers_per_neuron_rows(W, group) assert out.shape == (h, len(group.irreps())) for i in range(h): - np.testing.assert_allclose(out[i], power.GroupPower(W[i], group).power, rtol=1e-10) + np.testing.assert_allclose( + out[i], group.power_spectrum(W[i]), rtol=1e-10 + ) -class TestGroupPower: - """Tests for power.GroupPower class.""" +class TestGroupPowerSpectrum: + """Tests for group.power_spectrum via Group objects.""" def test_group_power_spectrum(self): - """Test that power.GroupPower computes correct power spectrum.""" - group = Octahedral() - powers = [0.0, 20.0, 20.0, 100.0, 0.0] - tpl = template.fixed_group(group, powers=powers) + """Test that group.power_spectrum computes correct power from a template. - gp = power.GroupPower(tpl, group) - - assert np.allclose(gp.power, powers), f"Power spectrum mismatch: {gp.power} vs {powers}" - - -class TestGroupPowerSpectrum: - """Tests for standalone power.group_power_spectrum function.""" - - def test_matches_class_method(self): - """Test that standalone function matches GroupPower class result.""" - group = Octahedral() + power_spectrum returns dim(rho) * Tr(hat_x^H @ hat_x) without dividing + by |G|, so the expected values are the input powers scaled by group.order. + """ + group = OctahedralGroup() powers = [0.0, 20.0, 20.0, 100.0, 0.0] tpl = template.fixed_group(group, powers=powers) - spectrum = power.group_power_spectrum(group, tpl) - gp = power.GroupPower(tpl, group) + spectrum = group.power_spectrum(tpl) - np.testing.assert_allclose(spectrum, gp.power, atol=1e-10) + expected = [p * group.order for p in powers] + np.testing.assert_allclose( + spectrum, expected, atol=1e-4, + err_msg=f"Power spectrum mismatch: {spectrum} vs {expected}" + ) diff --git a/test/test_template.py b/test/test_template.py index 2cdf106..70fd971 100644 --- a/test/test_template.py +++ b/test/test_template.py @@ -107,13 +107,13 @@ class TestFixedGroup: @pytest.fixture def dihedral_group(self): """Create a DihedralGroup for testing.""" - from escnn.group import DihedralGroup + from src.groups import DihedralGroup return DihedralGroup(N=3) def test_output_shape(self, dihedral_group): """Test that output shape matches group order.""" - group_order = dihedral_group.order() + group_order = dihedral_group.order num_irreps = len(list(dihedral_group.irreps())) powers = [1.0] * num_irreps From 458ca59a34a6bd2f536f3c2ccdd19be928664c31 Mon Sep 17 00:00:00 2001 From: Nina Miolane Date: Fri, 3 Apr 2026 11:12:15 -0700 Subject: [PATCH 3/8] ruff --- src/groups/cn.py | 7 +------ src/groups/dn.py | 20 +++++--------------- src/groups/group.py | 7 ++----- src/groups/irrep.py | 4 +--- src/power.py | 8 ++++---- test/test_group_escnn.py | 20 ++++++-------------- test/test_power.py | 10 +++++----- 7 files changed, 24 insertions(+), 52 deletions(-) diff --git a/src/groups/cn.py b/src/groups/cn.py index 5561d51..a86a6f2 100644 --- a/src/groups/cn.py +++ b/src/groups/cn.py @@ -45,12 +45,7 @@ def regular_rep(self) -> np.ndarray: def fourier(self, signal: np.ndarray) -> list[np.ndarray]: """DFT-based group Fourier transform for cyclic groups.""" - return [ - irrep_mat - for irrep_mat in [ - np.array([[coef]]) for coef in np.fft.fft(signal) - ] - ] + return [irrep_mat for irrep_mat in [np.array([[coef]]) for coef in np.fft.fft(signal)]] def inverse_fourier(self, fourier_coefs: list[np.ndarray]) -> np.ndarray: """IDFT-based inverse group Fourier transform for cyclic groups.""" diff --git a/src/groups/dn.py b/src/groups/dn.py index 77d3d8c..5ebdc26 100644 --- a/src/groups/dn.py +++ b/src/groups/dn.py @@ -47,15 +47,11 @@ def _build_irreps(self) -> list[IrreducibleRepresentation]: irreps = [] trivial = np.ones((n_elems, 1, 1)) - irreps.append(IrreducibleRepresentation( - f"D{N}|[irrep_0,0]:1", trivial - )) + irreps.append(IrreducibleRepresentation(f"D{N}|[irrep_0,0]:1", trivial)) sign = np.ones((n_elems, 1, 1)) sign[N:] = -1.0 - irreps.append(IrreducibleRepresentation( - f"D{N}|[irrep_1,0]:1", sign - )) + irreps.append(IrreducibleRepresentation(f"D{N}|[irrep_1,0]:1", sign)) n_2d = (N - 1) // 2 for j in range(1, n_2d + 1): @@ -65,9 +61,7 @@ def _build_irreps(self) -> list[IrreducibleRepresentation]: c, s = np.cos(angle), np.sin(angle) mats[k] = [[c, -s], [s, c]] mats[N + k] = [[c, s], [s, -c]] - irreps.append(IrreducibleRepresentation( - f"D{N}|[irrep_1,{j}]:2", mats - )) + irreps.append(IrreducibleRepresentation(f"D{N}|[irrep_1,{j}]:2", mats)) if N % 2 == 0: half = N // 2 @@ -76,17 +70,13 @@ def _build_irreps(self) -> list[IrreducibleRepresentation]: for k in range(N): rep_1_half[k, 0, 0] = (-1.0) ** k rep_1_half[N + k, 0, 0] = -((-1.0) ** k) - irreps.append(IrreducibleRepresentation( - f"D{N}|[irrep_1,{half}]:1", rep_1_half - )) + irreps.append(IrreducibleRepresentation(f"D{N}|[irrep_1,{half}]:1", rep_1_half)) rep_0_half = np.empty((n_elems, 1, 1)) for k in range(N): rep_0_half[k, 0, 0] = (-1.0) ** k rep_0_half[N + k, 0, 0] = (-1.0) ** k - irreps.append(IrreducibleRepresentation( - f"D{N}|[irrep_0,{half}]:1", rep_0_half - )) + irreps.append(IrreducibleRepresentation(f"D{N}|[irrep_0,{half}]:1", rep_0_half)) return irreps diff --git a/src/groups/group.py b/src/groups/group.py index b7a9e71..8d88191 100644 --- a/src/groups/group.py +++ b/src/groups/group.py @@ -56,9 +56,7 @@ def fourier(self, signal: np.ndarray) -> list[np.ndarray]: irreps = self.irreps() fourier_coefs = [] for irrep in irreps: - coef = sum( - signal[i_g] * irrep(i_g).conj().T for i_g in range(self.order) - ) + coef = sum(signal[i_g] * irrep(i_g).conj().T for i_g in range(self.order)) fourier_coefs.append(coef) return fourier_coefs @@ -80,8 +78,7 @@ def inverse_fourier(self, fourier_coefs: list[np.ndarray]) -> np.ndarray: def _at_element(g): return (1.0 / n) * sum( - irrep.size * np.trace(irrep(g) @ fourier_coefs[i]) - for i, irrep in enumerate(irreps) + irrep.size * np.trace(irrep(g) @ fourier_coefs[i]) for i, irrep in enumerate(irreps) ) return np.array([_at_element(g) for g in range(n)]) diff --git a/src/groups/irrep.py b/src/groups/irrep.py index 2196deb..cdeed54 100644 --- a/src/groups/irrep.py +++ b/src/groups/irrep.py @@ -14,9 +14,7 @@ class IrreducibleRepresentation: def __init__(self, name: str, matrices: np.ndarray): if matrices.ndim != 3 or matrices.shape[1] != matrices.shape[2]: - raise ValueError( - f"matrices must have shape (n_elements, d, d), got {matrices.shape}" - ) + raise ValueError(f"matrices must have shape (n_elements, d, d), got {matrices.shape}") self._name = name self._matrices = np.asarray(matrices, dtype=np.float64) self._size = int(matrices.shape[1]) diff --git a/src/power.py b/src/power.py index cd185e1..1578ab2 100644 --- a/src/power.py +++ b/src/power.py @@ -47,7 +47,7 @@ def loss_plateau_predictions_cyclic(template, template_dim, p1=None, p2=None): ft = np.fft.rfft2(template_2d) M, N = template_2d.shape power = np.abs(ft) ** 2 / (M * N) - power[(N // 2 + 1):, 0] = 0 + power[(N // 2 + 1) :, 0] = 0 power *= 2 power[0, 0] /= 2 if N % 2 == 0: @@ -60,7 +60,7 @@ def loss_plateau_predictions_cyclic(template, template_dim, p1=None, p2=None): ft = np.fft.fft(template) power = np.abs(ft[:num_coefficients]) ** 2 / group_size if group_size % 2 == 0: - power[1: num_coefficients - 1] *= 2 + power[1 : num_coefficients - 1] *= 2 else: power[1:] *= 2 @@ -351,11 +351,11 @@ def get_power_2d(points, no_freq=False): weight = 2 * np.ones((M, N // 2 + 1)) weight[0, 0] = 1 - weight[(M // 2 + 1):, 0] = 0 + weight[(M // 2 + 1) :, 0] = 0 if M % 2 == 0: weight[M // 2, 0] = 1 if N % 2 == 0: - weight[(M // 2 + 1):, N // 2] = 0 + weight[(M // 2 + 1) :, N // 2] = 0 weight[0, N // 2] = 1 if (M % 2 == 0) and (N % 2 == 0): weight[M // 2, N // 2] = 1 diff --git a/test/test_group_escnn.py b/test/test_group_escnn.py index bd64ed1..540e453 100644 --- a/test/test_group_escnn.py +++ b/test/test_group_escnn.py @@ -23,6 +23,7 @@ # Helpers # --------------------------------------------------------------------------- + def _escnn_irrep_matrices(escnn_group): """Extract all irrep matrices from an escnn group as a list of (|G|, d, d) arrays.""" irreps = escnn_group.irreps() @@ -45,6 +46,7 @@ def _escnn_regular_rep_matrices(escnn_group): # Fixtures: pairs of (our_group, escnn_group) # --------------------------------------------------------------------------- + @pytest.fixture(params=[3, 5], ids=["D3", "D5"]) def dihedral_pair(request): n = request.param @@ -125,9 +127,7 @@ def test_irrep_matrices_exact(self, group_pair): ours, escnn_g = group_pair escnn_mats_list = _escnn_irrep_matrices(escnn_g) - for i, (our_irrep, escnn_mats) in enumerate( - zip(ours.irreps(), escnn_mats_list) - ): + for i, (our_irrep, escnn_mats) in enumerate(zip(ours.irreps(), escnn_mats_list)): for g in range(ours.order): np.testing.assert_allclose( our_irrep(g), @@ -166,16 +166,11 @@ def test_fourier_vs_escnn(self, group_pair): escnn_elements = list(escnn_g.elements) escnn_coefs = [] for irrep in escnn_irreps: - coef = sum( - signal[i_g] * irrep(g).conj().T - for i_g, g in enumerate(escnn_elements) - ) + coef = sum(signal[i_g] * irrep(g).conj().T for i_g, g in enumerate(escnn_elements)) escnn_coefs.append(coef) assert len(our_coefs) == len(escnn_coefs) for i, (oc, ec) in enumerate(zip(our_coefs, escnn_coefs)): - np.testing.assert_allclose( - oc, ec, atol=1e-10, err_msg=f"fourier coef {i}" - ) + np.testing.assert_allclose(oc, ec, atol=1e-10, err_msg=f"fourier coef {i}") class TestPowerSpectrum: @@ -191,10 +186,7 @@ def test_power_spectrum_vs_escnn(self, group_pair): escnn_elements = list(escnn_g.elements) escnn_coefs = [] for irrep in escnn_irreps: - coef = sum( - signal[i_g] * irrep(g).conj().T - for i_g, g in enumerate(escnn_elements) - ) + coef = sum(signal[i_g] * irrep(g).conj().T for i_g, g in enumerate(escnn_elements)) escnn_coefs.append(coef) escnn_ps = np.zeros(len(escnn_irreps)) for i, irrep in enumerate(escnn_irreps): diff --git a/test/test_power.py b/test/test_power.py index c0cbacf..543a6c1 100644 --- a/test/test_power.py +++ b/test/test_power.py @@ -235,9 +235,7 @@ def test_matches_rowwise_group_power_spectrum(self): out = power.powers_per_neuron_rows(W, group) assert out.shape == (h, len(group.irreps())) for i in range(h): - np.testing.assert_allclose( - out[i], group.power_spectrum(W[i]), rtol=1e-10 - ) + np.testing.assert_allclose(out[i], group.power_spectrum(W[i]), rtol=1e-10) class TestGroupPowerSpectrum: @@ -257,6 +255,8 @@ def test_group_power_spectrum(self): expected = [p * group.order for p in powers] np.testing.assert_allclose( - spectrum, expected, atol=1e-4, - err_msg=f"Power spectrum mismatch: {spectrum} vs {expected}" + spectrum, + expected, + atol=1e-4, + err_msg=f"Power spectrum mismatch: {spectrum} vs {expected}", ) From e8b5fce52ad8e03e83df98f14b25feb8428e0fc2 Mon Sep 17 00:00:00 2001 From: Nina Miolane Date: Fri, 3 Apr 2026 13:50:57 -0700 Subject: [PATCH 4/8] Lint --- scripts/extract_escnn_data.py | 1 - src/main.py | 6 ++---- src/power.py | 1 - src/train.py | 14 +++++--------- src/viz.py | 4 +--- test/test_fourier.py | 2 +- test/test_group_escnn.py | 1 - test/test_power.py | 2 +- 8 files changed, 10 insertions(+), 21 deletions(-) diff --git a/scripts/extract_escnn_data.py b/scripts/extract_escnn_data.py index 88456ea..95b331d 100644 --- a/scripts/extract_escnn_data.py +++ b/scripts/extract_escnn_data.py @@ -14,7 +14,6 @@ import numpy as np from escnn.group import Icosahedral, Octahedral - DATA_DIR = Path(__file__).resolve().parent.parent / "src" / "groups" / "data" diff --git a/src/main.py b/src/main.py index 9c76fe0..2bad715 100644 --- a/src/main.py +++ b/src/main.py @@ -1334,7 +1334,7 @@ def train_single_run(config: dict, run_dir: Path = None) -> dict: else: raise ValueError(f"Unknown model_type: {model_type}") - resume_state = _apply_training_resume(rnn_2d, config, device) + resume_state = _apply_training_resume(net, config, device) criterion = nn.MSELoss() @@ -1507,9 +1507,7 @@ def train_single_run(config: dict, run_dir: Path = None) -> dict: if not save_param_snapshots: with torch.no_grad(): - param_hist = [ - {n: p.detach().cpu().clone() for n, p in rnn_2d.named_parameters()} - ] + param_hist = [{n: p.detach().cpu().clone() for n, p in net.named_parameters()}] param_save_indices = [int(final_step)] print("\nTraining complete!") diff --git a/src/power.py b/src/power.py index 1578ab2..0ffa9b1 100644 --- a/src/power.py +++ b/src/power.py @@ -1,7 +1,6 @@ import numpy as np import torch - # --------------------------------------------------------------------------- # Loss plateau prediction functions (extracted from former CyclicPower / # GroupPower classes) diff --git a/src/train.py b/src/train.py index 9d529e7..ed67d4c 100644 --- a/src/train.py +++ b/src/train.py @@ -6,7 +6,9 @@ from torch.utils.data import DataLoader -def _clone_param_snapshots(snapshots: list[dict[str, torch.Tensor]]) -> list[dict[str, torch.Tensor]]: +def _clone_param_snapshots( + snapshots: list[dict[str, torch.Tensor]], +) -> list[dict[str, torch.Tensor]]: return [{k: v.detach().cpu().clone() for k, v in sd.items()} for sd in snapshots] @@ -136,10 +138,7 @@ def train( epoch <= dense_save_until or ( save_param_interval is not None - and ( - global_epoch % save_param_interval == 0 - or epoch == epochs - ) + and (global_epoch % save_param_interval == 0 or epoch == epochs) ) or (save_param_interval is None and epoch == epochs) ) @@ -307,10 +306,7 @@ def train_online( should_save = save_param_snapshots and ( ( save_param_interval is not None - and ( - global_step % save_param_interval == 0 - or step == num_steps - ) + and (global_step % save_param_interval == 0 or step == num_steps) ) or (save_param_interval is None and step == num_steps) ) diff --git a/src/viz.py b/src/viz.py index 4742495..1945db1 100644 --- a/src/viz.py +++ b/src/viz.py @@ -1100,9 +1100,7 @@ def plot_power_1d( cp_theory = power.CyclicPower(np.asarray(template_1d).ravel(), template_dim=1) y_levels = np.array(cp_theory.loss_plateau_predictions(verbose=False), dtype=float) - n_bands = ( - max(0, min(len(tracked_freqs), len(y_levels) - 1)) if len(y_levels) else 0 - ) + n_bands = max(0, min(len(tracked_freqs), len(y_levels) - 1)) if len(y_levels) else 0 for i in range(n_bands): y_top = y_levels[i] y_bot = y_levels[i + 1] diff --git a/test/test_fourier.py b/test/test_fourier.py index e8a1805..fe6cd93 100644 --- a/test/test_fourier.py +++ b/test/test_fourier.py @@ -1,7 +1,7 @@ import numpy as np -from src.groups import OctahedralGroup import src.template as template +from src.groups import OctahedralGroup def test_group_fourier_inverse_is_identity(): diff --git a/test/test_group_escnn.py b/test/test_group_escnn.py index 540e453..85fc74b 100644 --- a/test/test_group_escnn.py +++ b/test/test_group_escnn.py @@ -18,7 +18,6 @@ from src.groups.dn import DihedralGroup # noqa: E402 from src.groups.oh import OctahedralGroup # noqa: E402 - # --------------------------------------------------------------------------- # Helpers # --------------------------------------------------------------------------- diff --git a/test/test_power.py b/test/test_power.py index 543a6c1..a92bab1 100644 --- a/test/test_power.py +++ b/test/test_power.py @@ -2,9 +2,9 @@ import numpy as np -from src.groups import DihedralGroup, OctahedralGroup import src.power as power import src.template as template +from src.groups import DihedralGroup, OctahedralGroup class TestGetPower1D: From cbcdde44887fd4495a13740507b8c7437f0690d3 Mon Sep 17 00:00:00 2001 From: Nina Miolane Date: Fri, 3 Apr 2026 14:01:59 -0700 Subject: [PATCH 5/8] Change remaining TwoLayerNet to MLP --- README.md | 22 +++++++-------- notebooks/cn.ipynb | 2 +- notebooks/cnxcn.ipynb | 4 +-- notebooks/dn.ipynb | 2 +- runs_data/A5/config.yaml | 2 +- runs_data/C11/config.yaml | 5 ++-- runs_data/C11/param_save_indices.npy | Bin 800136 -> 40136 bytes runs_data/C11/power_data.npz | Bin 21540 -> 19636 bytes runs_data/C11/train_loss_history.npy | Bin 800136 -> 40136 bytes runs_data/C11/w_dominant_irrep_fraction.npz | Bin 1024095 -> 788090 bytes runs_data/C5xC5/config.yaml | 2 +- runs_data/D5/config.yaml | 2 +- runs_data/Oh/config.yaml | 5 ++-- runs_data/Oh/param_save_indices.npy | Bin 800208 -> 1008 bytes runs_data/Oh/power_data.npz | Bin 18732 -> 8268 bytes runs_data/Oh/train_loss_history.npy | Bin 8000136 -> 8136 bytes runs_data/Oh/w_dominant_irrep_fraction.npz | Bin 1586951 -> 119022 bytes src/configs/config_a5.yaml | 4 +-- src/configs/config_c11.yaml | 6 ++-- src/configs/config_c5xc5.yaml | 4 +-- src/configs/config_d5.yaml | 4 +-- src/configs/config_oh.yaml | 4 +-- src/viz.py | 29 ++++++++------------ 23 files changed, 45 insertions(+), 52 deletions(-) diff --git a/README.md b/README.md index 632f82f..c1eaed6 100644 --- a/README.md +++ b/README.md @@ -121,13 +121,13 @@ The repository includes preconfigured experiments for eight groups: | Group | Config | Order | k | Architecture | |:------|:-------|:-----:|:-:|:-------------| | Cyclic $C_{10}$ | `config_c10_k3.yaml` | 10 | 3 | SequentialMLP | -| Cyclic $C_{11}$ | `config_c11.yaml` | 11 | 2 | TwoLayerNet | +| Cyclic $C_{11}$ | `config_c11.yaml` | 11 | 2 | TwoLayerMLP | | Product $C_4 \times C_4$ | `config_c4x4_k3.yaml` | 16 | 3 | SequentialMLP | -| Product $C_5 \times C_5$ | `config_c5xc5.yaml` | 25 | 2 | TwoLayerNet | -| Dihedral $D_3$ | `config_d3.yaml` | 6 | 2 | TwoLayerNet | -| Dihedral $D_5$ | `config_d5.yaml` | 10 | 2 | TwoLayerNet | -| Octahedral $O_h$ | `config_oh.yaml` | 24 | 2 | TwoLayerNet | -| Icosahedral $A_5$ | `config_a5.yaml` | 60 | 2 | TwoLayerNet | +| Product $C_5 \times C_5$ | `config_c5xc5.yaml` | 25 | 2 | TwoLayerMLP | +| Dihedral $D_3$ | `config_d3.yaml` | 6 | 2 | TwoLayerMLP | +| Dihedral $D_5$ | `config_d5.yaml` | 10 | 2 | TwoLayerMLP | +| Octahedral $O_h$ | `config_oh.yaml` | 24 | 2 | TwoLayerMLP | +| Icosahedral $A_5$ | `config_a5.yaml` | 60 | 2 | TwoLayerMLP | ### Reproduce Paper's Figure @@ -170,7 +170,7 @@ Key parameters in the YAML config files: | `data.group_name` | `cn`, `cnxcn`, `dihedral`, `octahedral`, `A5` | Group to learn | | `data.k` | integer | Number of elements to compose | | `data.template_type` | `custom_fourier`, `onehot`, `mnist`, `gaussian` | Template generation method | -| `model.model_type` | `QuadraticRNN`, `SequentialMLP`, `TwoLayerNet` | Architecture | +| `model.model_type` | `QuadraticRNN`, `SequentialMLP`, `TwoLayerMLP` | Architecture | | `model.hidden_dim` | integer | Hidden layer size | | `model.init_scale` | float | Weight initialization scale | | `training.optimizer` | `auto`, `adam`, `per_neuron`, `hybrid` | Optimizer (`auto` recommended) | @@ -190,7 +190,7 @@ data: powers: [0.0, 3000.0, 2000.0, 1000.0] model: - model_type: TwoLayerNet + model_type: TwoLayerMLP hidden_dim: 300 init_scale: 0.0001 @@ -209,7 +209,7 @@ training: group-agf/ ├── src/ # Source code │ ├── main.py # Training entry point (CLI) -│ ├── model.py # TwoLayerNet, QuadraticRNN, SequentialMLP +│ ├── model.py # TwoLayerMLP, QuadraticRNN, SequentialMLP │ ├── optimizer.py # PerNeuronScaledSGD, HybridRNNOptimizer │ ├── dataset.py # Dataset generation and loading │ ├── template.py # Template construction functions @@ -239,7 +239,7 @@ group-agf/ | Model | Description | Input | |:------|:------------|:------| -| **TwoLayerNet** | Two-layer feedforward network with configurable nonlinearity (square, relu, tanh, gelu) | Flattened binary pair `(N, 2 * group_size)` | +| **TwoLayerMLP** | Two-layer feedforward network with configurable nonlinearity (square, relu, tanh, gelu) | Flattened binary pair `(N, 2 * group_size)` | | **QuadraticRNN** | Recurrent network: `h_t = (W_mix h_{t-1} + W_drive x_t)^2` | Sequence `(N, k, p)` | | **SequentialMLP** | Feedforward MLP with k-th power activation, permutation-invariant for commutative groups | Sequence `(N, k, p)` | @@ -247,7 +247,7 @@ group-agf/ | Optimizer | Description | Recommended for | |:----------|:------------|:----------------| -| **PerNeuronScaledSGD** | SGD with per-neuron learning rate scaling exploiting model homogeneity | SequentialMLP, TwoLayerNet | +| **PerNeuronScaledSGD** | SGD with per-neuron learning rate scaling exploiting model homogeneity | SequentialMLP, TwoLayerMLP | | **HybridRNNOptimizer** | Scaled SGD for MLP weights + Adam for recurrent weights | QuadraticRNN | | Adam (PyTorch built-in) | Standard Adam | QuadraticRNN | diff --git a/notebooks/cn.ipynb b/notebooks/cn.ipynb index 01aac8d..7ffed88 100644 --- a/notebooks/cn.ipynb +++ b/notebooks/cn.ipynb @@ -173,7 +173,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "Model: TwoLayerNet(p=11, hidden=200, init_scale=1e-05)\n", + "Model: TwoLayerMLP(p=11, hidden=200, init_scale=1e-05)\n", "Optimizer: PerNeuronScaledSGD(lr=0.01, degree=3)\n", "Training for 5000 epochs\n" ] diff --git a/notebooks/cnxcn.ipynb b/notebooks/cnxcn.ipynb index 4338969..098bdc6 100644 --- a/notebooks/cnxcn.ipynb +++ b/notebooks/cnxcn.ipynb @@ -10,7 +10,7 @@ "**Group:** Product of cyclic groups $C_n \\times C_n$ of order $n^2$. \n", "**Task:** Given encodings of two group elements $g_1, g_2 \\in C_n \\times C_n$, predict the encoding of their product. \n", "**Sequence length:** $k = 2$ (binary composition). \n", - "**Architecture:** `TwoLayerNet` with square nonlinearity. \n", + "**Architecture:** `TwoLayerMLP` with square nonlinearity. \n", "**Key result:** The network learns one irreducible representation at a time." ] }, @@ -176,7 +176,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "Model: TwoLayerNet(group_size=25, hidden=128)\n", + "Model: TwoLayerMLP(group_size=25, hidden=128)\n", "Optimizer: Adam(lr=0.001)\n", "Training for 1000 epochs\n" ] diff --git a/notebooks/dn.ipynb b/notebooks/dn.ipynb index 5c9cf93..f90dcb1 100644 --- a/notebooks/dn.ipynb +++ b/notebooks/dn.ipynb @@ -191,7 +191,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "Model: TwoLayerNet(group_size=6, hidden=180, init_scale=0.001)\n", + "Model: TwoLayerMLP(group_size=6, hidden=180, init_scale=0.001)\n", "Optimizer: PerNeuronScaledSGD(lr=0.01, degree=2)\n", "Training for 5000 epochs\n" ] diff --git a/runs_data/A5/config.yaml b/runs_data/A5/config.yaml index 0258bce..eaedfd8 100644 --- a/runs_data/A5/config.yaml +++ b/runs_data/A5/config.yaml @@ -20,7 +20,7 @@ device: cuda:0 model: hidden_dim: 400 init_scale: 1.0e-05 - model_type: TwoLayerNet + model_type: TwoLayerMLP nonlinearity: square output_scale: 1.0 return_all_outputs: false diff --git a/runs_data/C11/config.yaml b/runs_data/C11/config.yaml index 04c5c5b..bc765e9 100644 --- a/runs_data/C11/config.yaml +++ b/runs_data/C11/config.yaml @@ -22,18 +22,17 @@ device: cuda:0 model: hidden_dim: 200 init_scale: 1.0e-05 - 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nonlinearity: square # Activation function (TwoLayerNet only): 'square' | ... - output_scale: 1.0 # Output layer scaling factor (TwoLayerNet only) + nonlinearity: square # Activation function (TwoLayerMLP only): 'square' | ... + output_scale: 1.0 # Output layer scaling factor (TwoLayerMLP only) return_all_outputs: false # true = seq-to-seq, false = seq-to-one (final output only) training: diff --git a/src/configs/config_c11.yaml b/src/configs/config_c11.yaml index 19f3be6..8d6f3dd 100644 --- a/src/configs/config_c11.yaml +++ b/src/configs/config_c11.yaml @@ -17,11 +17,11 @@ data: powers: [0, 12.5, 10, 7.5, 5, 2.5] #[0.0, 200.0, 100.0, 50.0, 20.0, 5.] model: - model_type: TwoLayerNet # Model architecture: 'QuadraticRNN' | 'SequentialMLP' | 'TwoLayerNet' + model_type: TwoLayerMLP # Model architecture: 'QuadraticRNN' | 'SequentialMLP' | 'TwoLayerMLP' hidden_dim: 200 # Hidden layer width init_scale: 0.00001 # Weight initialization scale - nonlinearity: square # Activation function (TwoLayerNet only): 'square' | ... - output_scale: 1.0 # Output layer scaling factor (TwoLayerNet only) + nonlinearity: square # Activation function (TwoLayerMLP only): 'square' | ... + output_scale: 1.0 # Output layer scaling factor (TwoLayerMLP only) return_all_outputs: false # true = seq-to-seq, false = seq-to-one (final output only) training: diff --git a/src/configs/config_c5xc5.yaml b/src/configs/config_c5xc5.yaml index 5ed63ac..55339e6 100644 --- a/src/configs/config_c5xc5.yaml +++ b/src/configs/config_c5xc5.yaml @@ -20,8 +20,8 @@ model: model_type: TwoLayerMLP # Model architecture: 'QuadraticRNN' | 'TwoLayerMLP' hidden_dim: 300 # Hidden layer width (hidden_factor=20 * group_size=25) init_scale: 0.00001 # Weight initialization scale - nonlinearity: square # Activation function (TwoLayerNet only): 'square' | ... - output_scale: 1.0 # Output layer scaling factor (TwoLayerNet only) + nonlinearity: square # Activation function (TwoLayerMLP only): 'square' | ... + output_scale: 1.0 # Output layer scaling factor (TwoLayerMLP only) return_all_outputs: false # true = seq-to-seq, false = seq-to-one (final output only) training: diff --git a/src/configs/config_d5.yaml b/src/configs/config_d5.yaml index ff3acc1..10d754d 100644 --- a/src/configs/config_d5.yaml +++ b/src/configs/config_d5.yaml @@ -22,8 +22,8 @@ model: model_type: TwoLayerMLP # Model architecture: 'QuadraticRNN' | 'TwoLayerMLP' hidden_dim: 200 # Hidden layer width (hidden_factor=20 * group_size=10) init_scale: 0.000001 # Weight initialization scale - nonlinearity: square # Activation function (TwoLayerNet only): 'square' | ... - output_scale: 1.0 # Output layer scaling factor (TwoLayerNet only) + nonlinearity: square # Activation function (TwoLayerMLP only): 'square' | ... + output_scale: 1.0 # Output layer scaling factor (TwoLayerMLP only) return_all_outputs: false # true = seq-to-seq, false = seq-to-one (final output only) training: diff --git a/src/configs/config_oh.yaml b/src/configs/config_oh.yaml index ad8fde3..72cb3df 100644 --- a/src/configs/config_oh.yaml +++ b/src/configs/config_oh.yaml @@ -21,8 +21,8 @@ model: model_type: TwoLayerMLP # Model architecture: 'QuadraticRNN' | 'TwoLayerMLP' hidden_dim: 300 # Hidden layer width init_scale: 0.00001 # Weight initialization scale - nonlinearity: square # Activation function (TwoLayerNet only): 'square' | ... - output_scale: 1.0 # Output layer scaling factor (TwoLayerNet only) + nonlinearity: square # Activation function (TwoLayerMLP only): 'square' | ... + output_scale: 1.0 # Output layer scaling factor (TwoLayerMLP only) return_all_outputs: false # true = seq-to-seq, false = seq-to-one (final output only) training: diff --git a/src/viz.py b/src/viz.py index 1945db1..27b9b13 100644 --- a/src/viz.py +++ b/src/viz.py @@ -110,9 +110,9 @@ def _training_loss_log_y_floor(ax): def _theory_loss_y_levels_from_run(run_dir: Path, cfg: dict) -> list[float] | None: - """Template MSE plateau levels via :class:`~src.power.CyclicPower` / :class:`~src.power.GroupPower`. + """Template MSE plateau levels via loss_plateau_predictions functions. - Uses ``loss_plateau_predictions()`` only (no duplicate alpha arithmetic here). + Uses ``loss_plateau_predictions_cyclic`` / ``loss_plateau_predictions_group``. """ import src.power as power @@ -125,29 +125,26 @@ def _theory_loss_y_levels_from_run(run_dir: Path, cfg: dict) -> list[float] | No if gn == "cn": t_flat = np.asarray(template_np).ravel() - cp = power.CyclicPower(t_flat, template_dim=1) - out = cp.loss_plateau_predictions(verbose=False) + out = power.loss_plateau_predictions_cyclic(t_flat, template_dim=1) elif gn == "cnxcn": p1, p2 = cfg["data"]["p1"], cfg["data"]["p2"] t_flat = np.asarray(template_np).ravel() - cp = power.CyclicPower(t_flat, template_dim=2, p1=p1, p2=p2) - out = cp.loss_plateau_predictions(verbose=False) + out = power.loss_plateau_predictions_cyclic(t_flat, template_dim=2, p1=p1, p2=p2) elif gn in ("dihedral", "octahedral", "A5"): if gn == "dihedral": - from escnn.group import DihedralGroup + from src.groups import DihedralGroup group = DihedralGroup(N=cfg["data"].get("group_n", 3)) elif gn == "octahedral": - from escnn.group import Octahedral + from src.groups import OctahedralGroup - group = Octahedral() + group = OctahedralGroup() else: - from escnn.group import Icosahedral + from src.groups import IcosahedralGroup - group = Icosahedral() + group = IcosahedralGroup() t = np.asarray(template_np).ravel() - gp = power.GroupPower(t, group) - out = gp.loss_plateau_predictions(verbose=False) + out = power.loss_plateau_predictions_group(t, group) else: return None @@ -330,8 +327,7 @@ def plot_train_loss_with_theory( ax.plot(x_values, loss_history, lw=4, color="#1f77b4", label="Training Loss") - cp = power.CyclicPower(template_2d.ravel(), template_dim=2, p1=p1, p2=p2) - for y in cp.loss_plateau_predictions(verbose=False): + for y in power.loss_plateau_predictions_cyclic(template_2d.ravel(), template_dim=2, p1=p1, p2=p2): ax.axhline(y=y, color="black", linestyle="--", linewidth=2, zorder=-2) ax.set_xlabel(x_label, fontsize=24) @@ -1097,8 +1093,7 @@ def plot_power_1d( ax1.plot(loss_epochs, loss_history_subset, lw=4, color="#1f77b4", label="Training Loss") - cp_theory = power.CyclicPower(np.asarray(template_1d).ravel(), template_dim=1) - y_levels = np.array(cp_theory.loss_plateau_predictions(verbose=False), dtype=float) + y_levels = np.array(power.loss_plateau_predictions_cyclic(np.asarray(template_1d).ravel(), template_dim=1), dtype=float) n_bands = max(0, min(len(tracked_freqs), len(y_levels) - 1)) if len(y_levels) else 0 for i in range(n_bands): From e61f3cd4f9cdb4d56fd0521106ff336cc3f8f365 Mon Sep 17 00:00:00 2001 From: Nina Miolane Date: Fri, 3 Apr 2026 14:02:18 -0700 Subject: [PATCH 6/8] Lint --- src/viz.py | 9 +++++++-- 1 file changed, 7 insertions(+), 2 deletions(-) diff --git a/src/viz.py b/src/viz.py index 27b9b13..932a469 100644 --- a/src/viz.py +++ b/src/viz.py @@ -327,7 +327,9 @@ def plot_train_loss_with_theory( ax.plot(x_values, loss_history, lw=4, color="#1f77b4", label="Training Loss") - for y in power.loss_plateau_predictions_cyclic(template_2d.ravel(), template_dim=2, p1=p1, p2=p2): + for y in power.loss_plateau_predictions_cyclic( + template_2d.ravel(), template_dim=2, p1=p1, p2=p2 + ): ax.axhline(y=y, color="black", linestyle="--", linewidth=2, zorder=-2) ax.set_xlabel(x_label, fontsize=24) @@ -1093,7 +1095,10 @@ def plot_power_1d( ax1.plot(loss_epochs, loss_history_subset, lw=4, color="#1f77b4", label="Training Loss") - y_levels = np.array(power.loss_plateau_predictions_cyclic(np.asarray(template_1d).ravel(), template_dim=1), dtype=float) + y_levels = np.array( + power.loss_plateau_predictions_cyclic(np.asarray(template_1d).ravel(), template_dim=1), + dtype=float, + ) n_bands = max(0, min(len(tracked_freqs), len(y_levels) - 1)) if len(y_levels) else 0 for i in range(n_bands): From 09806799cadf4c0b2e0465d56d02784a7724a1e0 Mon Sep 17 00:00:00 2001 From: Nina Miolane Date: Fri, 3 Apr 2026 15:26:36 -0700 Subject: [PATCH 7/8] Add group data --- .gitignore | 2 +- src/groups/data/a5_irrep_0.npy | Bin 0 -> 608 bytes src/groups/data/a5_irrep_1.npy | Bin 0 -> 4448 bytes src/groups/data/a5_irrep_2.npy | Bin 0 -> 12128 bytes src/groups/data/a5_irrep_3.npy | Bin 0 -> 4448 bytes src/groups/data/a5_irrep_4.npy | Bin 0 -> 7808 bytes src/groups/data/a5_irrep_names.npy | Bin 0 -> 588 bytes src/groups/data/a5_regular_rep.npy | Bin 0 -> 1728128 bytes src/groups/data/oh_irrep_0.npy | Bin 0 -> 320 bytes src/groups/data/oh_irrep_1.npy | Bin 0 -> 1856 bytes src/groups/data/oh_irrep_2.npy | Bin 0 -> 1856 bytes src/groups/data/oh_irrep_3.npy | Bin 0 -> 896 bytes src/groups/data/oh_irrep_4.npy | Bin 0 -> 320 bytes src/groups/data/oh_irrep_names.npy | Bin 0 -> 588 bytes src/groups/data/oh_regular_rep.npy | Bin 0 -> 110720 bytes 15 files changed, 1 insertion(+), 1 deletion(-) create mode 100644 src/groups/data/a5_irrep_0.npy create mode 100644 src/groups/data/a5_irrep_1.npy create mode 100644 src/groups/data/a5_irrep_2.npy create mode 100644 src/groups/data/a5_irrep_3.npy create mode 100644 src/groups/data/a5_irrep_4.npy create mode 100644 src/groups/data/a5_irrep_names.npy create mode 100644 src/groups/data/a5_regular_rep.npy create mode 100644 src/groups/data/oh_irrep_0.npy create mode 100644 src/groups/data/oh_irrep_1.npy create mode 100644 src/groups/data/oh_irrep_2.npy create mode 100644 src/groups/data/oh_irrep_3.npy create mode 100644 src/groups/data/oh_irrep_4.npy create mode 100644 src/groups/data/oh_irrep_names.npy create mode 100644 src/groups/data/oh_regular_rep.npy diff --git a/.gitignore b/.gitignore index 28ac925..f037132 100644 --- a/.gitignore +++ b/.gitignore @@ -14,7 +14,7 @@ notebooks/W-weights.pdf notebooks/predictions.pdf runs/ -data/ +#data/ !notebooks/data/ sweep_results/ diff --git a/src/groups/data/a5_irrep_0.npy b/src/groups/data/a5_irrep_0.npy new file mode 100644 index 0000000000000000000000000000000000000000..02b7f0bad18189eb7f5743007a3d765581751b09 GIT binary patch literal 608 zcmbR27wQ`j$;eQ~P_3SlTAW;@Zl$1ZlV+i=qoAIaUsO_*m=~X4l#&V(cT3DEP6dh= mXCxM+0{I$d2099cK%}XoP^&-|;9>xS5B8%pC?v&>nCg)HK5=AQGM^E~IdclZAJOY0XtKQ{Vy 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zUf6h=haa?Od7eMW|BR167xjbo=icD6Haf(ibAQd_tk~tzO(*-vp76QGc3ybUBcHDR zIm6%i_NG4@_PyYT;&}1XgXiSYRrh|4|E$pOss7{iI5+d;v0>-&Lv{Ad@4WDyJm(O! z_pY0LPu}Bw)L)%*8C%`QIl298&!hV8>s(j*(P6*%-|@G3iqpk*&X@3Xf1mhee#htc zL#fwSJ-&1}k6ZHT@AuU3F*j(QIr!LzxzIc|q+47)zdZcKui?$#Jn`aZ)7ih*l81-6 z&|H1!ox1Q*Kk@8KUC-rTsb9&z#lFSvxIBm_)VFzvH`@0u-+jG=SAULL;pseJ`=4z6 NQs2D3+t&Bve*xL@Qe*%C literal 0 HcmV?d00001 From 4ebeaef65c278df58db55403265da66ccaf0b240 Mon Sep 17 00:00:00 2001 From: Nina Miolane Date: Fri, 3 Apr 2026 16:35:48 -0700 Subject: [PATCH 8/8] solve dn error --- notebooks/dn.ipynb | 228 ++++++++++++--------------------------------- src/viz.py | 2 +- 2 files changed, 60 insertions(+), 170 deletions(-) diff --git a/notebooks/dn.ipynb b/notebooks/dn.ipynb index f90dcb1..8eac525 100644 --- a/notebooks/dn.ipynb +++ b/notebooks/dn.ipynb @@ -2,7 +2,6 @@ "cells": [ { "cell_type": "markdown", - "id": "a6e4bcaa", "metadata": {}, "source": [ "# Binary Group Composition on $D_n$ (Dihedral Group)\n", @@ -12,22 +11,20 @@ "**Sequence length:** $k = 2$ (binary composition). \n", "**Architecture:** `TwoLayerMLP` with square nonlinearity. \n", "**Key result:** The network learns one irreducible representation at a time, producing a staircase in the training loss." - ] + ], + "id": "a6e4bcaa" }, { "cell_type": "markdown", - "id": "210231cf", "metadata": {}, "source": [ "## Imports" - ] + ], + "id": "210231cf" }, { "cell_type": "code", - "execution_count": 1, - "id": "e2dd1d57", "metadata": {}, - "outputs": [], "source": [ "import os\n", "import random\n", @@ -36,7 +33,7 @@ "import numpy as np\n", "import torch\n", "import torch.nn as nn\n", - "from escnn.group import DihedralGroup\n", + "from src.groups import DihedralGroup\n", "from torch.utils.data import DataLoader, TensorDataset\n", "\n", "import src.dataset as dataset\n", @@ -46,30 +43,22 @@ "import src.template as template\n", "import src.train as train_mod\n", "import src.viz as viz" - ] + ], + "execution_count": null, + "outputs": [], + "id": "e2dd1d57" }, { "cell_type": "markdown", - "id": "4b719115", "metadata": {}, "source": [ "## Configuration" - ] + ], + "id": "4b719115" }, { "cell_type": "code", - "execution_count": 2, - "id": "ea401ba7", "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Group: D_3, order 6\n" - ] - } - ], "source": [ "TEST_MODE = os.environ.get(\"NOTEBOOK_TEST_MODE\", \"0\") == \"1\"\n", "\n", @@ -80,7 +69,7 @@ "\n", "n = 3 # D_3 has order 2*3 = 6\n", "group = DihedralGroup(n)\n", - "group_size = group.order()\n", + "group_size = group.order\n", "\n", "hidden_dim = 20 if TEST_MODE else 180\n", "epochs = 2 if TEST_MODE else 5000\n", @@ -91,22 +80,22 @@ "os.makedirs(FIGURES_DIR, exist_ok=True)\n", "\n", "print(f\"Group: D_{n}, order {group_size}\")" - ] + ], + "execution_count": null, + "outputs": [], + "id": "ea401ba7" }, { "cell_type": "markdown", - "id": "51c08dab", "metadata": {}, "source": [ "## Template and Dataset" - ] + ], + "id": "51c08dab" }, { "cell_type": "code", - "execution_count": 3, - "id": "699c266b", "metadata": {}, - "outputs": [], "source": [ "# Build a template with known Fourier structure on D_n\n", "# D_3 has 3 irreps with dimensions [1, 1, 2]\n", @@ -133,25 +122,14 @@ "\n", "print(f\"Dataset: {len(ds)} samples (all {group_size}x{group_size} pairs)\")\n", "print(f\"X shape: {X_tensor.shape}, Y shape: {Y_tensor.shape}\")" - ] + ], + "execution_count": null, + "outputs": [], + "id": "699c266b" }, { "cell_type": "code", - "execution_count": 4, - "id": "520c3b23", "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "

        " - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], "source": [ "# Visualize template and its group power spectrum\n", "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 4))\n", @@ -161,8 +139,7 @@ "ax1.set_ylabel(\"Template value\")\n", "ax1.set_title(f\"Template $t$ on $D_{{{n}}}$\")\n", "\n", - "gp = power.GroupPower(tpl, group)\n", - "pwr = gp.group_power_spectrum()\n", + "pwr = group.power_spectrum(tpl)\n", "ax2.bar(range(len(pwr)), pwr, color=\"steelblue\")\n", "ax2.set_xlabel(\"Irrep index\")\n", "ax2.set_ylabel(\"Power\")\n", @@ -171,32 +148,22 @@ "plt.tight_layout()\n", "plt.savefig(f\"{FIGURES_DIR}/dn_template.pdf\", bbox_inches=\"tight\")\n", "plt.show()" - ] + ], + "execution_count": null, + "outputs": [], + "id": "520c3b23" }, { "cell_type": "markdown", - "id": "d536fbd5", "metadata": {}, "source": [ "## Model and Optimizer" - ] + ], + "id": "d536fbd5" }, { "cell_type": "code", - "execution_count": 5, - "id": "b30529be", "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Model: TwoLayerMLP(group_size=6, hidden=180, init_scale=0.001)\n", - "Optimizer: PerNeuronScaledSGD(lr=0.01, degree=2)\n", - "Training for 5000 epochs\n" - ] - } - ], "source": [ "net = model.TwoLayerMLP(\n", " group_size=group_size,\n", @@ -213,39 +180,22 @@ "print(f\"Model: TwoLayerMLP(group_size={group_size}, hidden_dim={hidden_dim}, k=2, init_scale={init_scale})\")\n", "print(f\"Optimizer: PerNeuronScaledSGD(lr={lr}, degree={opt.param_groups[0]['degree']})\")\n", "print(f\"Training for {epochs} epochs\")" - ] + ], + "execution_count": null, + "outputs": [], + "id": "b30529be" }, { "cell_type": "markdown", - "id": "99594a2b", "metadata": {}, "source": [ "## Training" - ] + ], + "id": "99594a2b" }, { "cell_type": "code", - "execution_count": 6, - "id": "ade94d19", "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[Epoch 500/5000] loss: 5.032102 | reduction: 99.0%\n", - "[Epoch 1000/5000] loss: 5.044927 | reduction: 99.0%\n", - "[Epoch 1500/5000] loss: 5.060741 | reduction: 99.0%\n", - "[Epoch 2000/5000] loss: 5.080063 | reduction: 99.0%\n", - "[Epoch 2500/5000] loss: 5.103499 | reduction: 99.0%\n", - "[Epoch 3000/5000] loss: 5.127010 | reduction: 99.0%\n", - "[Epoch 3500/5000] loss: 5.137788 | reduction: 99.0%\n", - "[Epoch 4000/5000] loss: 5.143885 | reduction: 99.0%\n", - "[Epoch 4500/5000] loss: 5.136471 | reduction: 99.0%\n", - "[Epoch 5000/5000] loss: 5.138467 | reduction: 99.0%\n" - ] - } - ], "source": [ "loss_history, val_loss_history, param_history, param_save_epochs, final_epoch = train_mod.train(\n", " net,\n", @@ -257,44 +207,25 @@ " grad_clip=0.1,\n", " save_param_interval=1,\n", ")" - ] + ], + "execution_count": null, + "outputs": [], + "id": "ade94d19" }, { "cell_type": "markdown", - "id": "31ee1553", "metadata": {}, "source": [ "## Training Loss" - ] + ], + "id": "31ee1553" }, { "cell_type": "code", - "execution_count": 7, - "id": "3e1d3b93", "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Computing loss plateau predictions for template of shape: (6,)\n", - "Found 2 non-zero power coefficients.\n" - ] - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
        " - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], "source": [ "# Compute theoretical loss plateau levels\n", - "theory_levels = gp.loss_plateau_predictions()\n", + "theory_levels = power.loss_plateau_predictions_group(tpl, group)\n", "\n", "fig, ax = plt.subplots(figsize=(8, 6))\n", "ax.plot(loss_history, lw=4)\n", @@ -313,55 +244,22 @@ "plt.tight_layout()\n", "plt.savefig(f\"{FIGURES_DIR}/dn_loss.pdf\", bbox_inches=\"tight\")\n", "plt.show()" - ] + ], + "execution_count": null, + "outputs": [], + "id": "3e1d3b93" }, { "cell_type": "markdown", - "id": "a04bf2c1", "metadata": {}, "source": [ "## Power Spectrum Over Training" - ] + ], + "id": "a04bf2c1" }, { "cell_type": "code", - "execution_count": 8, - "id": "13dab6c1", "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Computing power at step 1 with output shape (1, 6)\n", - "Computing power at step 61 with output shape (1, 6)\n", - "Computing power at step 83 with output shape (1, 6)\n", - "Computing power at step 114 with output shape (1, 6)\n", - "Computing power at step 156 with output shape (1, 6)\n", - "Computing power at step 213 with output shape (1, 6)\n", - "Computing power at step 291 with output shape (1, 6)\n", - "Computing power at step 398 with output shape (1, 6)\n", - "Computing power at step 544 with output shape (1, 6)\n", - "Computing power at step 744 with output shape (1, 6)\n", - "Computing power at step 1016 with output shape (1, 6)\n", - "Computing power at step 1389 with output shape (1, 6)\n", - "Computing power at step 1899 with output shape (1, 6)\n", - "Computing power at step 2595 with output shape (1, 6)\n", - "Computing power at step 3546 with output shape (1, 6)\n", - "Computing power at step 4846 with output shape (1, 6)\n" - ] - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
        " - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], "source": [ "# Use model_power_over_time from src/power.py\n", "powers_over_time, power_steps = power.model_power_over_time(\n", @@ -373,7 +271,7 @@ ")\n", "\n", "# Reference: template power per irrep\n", - "template_pwr = gp.group_power_spectrum()\n", + "template_pwr = group.power_spectrum(tpl)\n", "\n", "# Plot\n", "colors = [\"tab:blue\", \"tab:orange\", \"tab:red\", \"tab:green\", \"tab:brown\", \"tab:purple\"]\n", @@ -396,38 +294,30 @@ "plt.tight_layout()\n", "plt.savefig(f\"{FIGURES_DIR}/dn_power_spectrum.pdf\", bbox_inches=\"tight\")\n", "plt.show()" - ] + ], + "execution_count": null, + "outputs": [], + "id": "13dab6c1" }, { "cell_type": "markdown", - "id": "62e7ee65", "metadata": {}, "source": [ "## Irreducible Representations" - ] + ], + "id": "62e7ee65" }, { "cell_type": "code", - "execution_count": 9, - "id": "59d42a70", "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "
        " - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], "source": [ "fig = viz.plot_irreps(group, show=False)\n", "plt.savefig(f\"{FIGURES_DIR}/dn_irreps.pdf\", bbox_inches=\"tight\")\n", "plt.show()" - ] + ], + "execution_count": null, + "outputs": [], + "id": "59d42a70" } ], "metadata": { diff --git a/src/viz.py b/src/viz.py index 932a469..707f46b 100644 --- a/src/viz.py +++ b/src/viz.py @@ -2226,7 +2226,7 @@ def plot_irreps(group, show=False): FONT_SIZES = {"title": 30, "axes_label": 30, "tick_label": 30, "legend": 15} irreps = group.irreps() - group_elements = group.elements + group_elements = group.elements() num_irreps = len(irreps) fig, axs = plt.subplots(1, num_irreps, figsize=(3 * num_irreps, 4), squeeze=False)

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a/runs_data/C5xC5/config.yaml b/runs_data/C5xC5/config.yaml index 185c8cf..f771375 100644 --- a/runs_data/C5xC5/config.yaml +++ b/runs_data/C5xC5/config.yaml @@ -23,7 +23,7 @@ device: cuda:0 model: hidden_dim: 300 init_scale: 1.0e-05 - model_type: TwoLayerNet + model_type: TwoLayerMLP nonlinearity: square output_scale: 1.0 return_all_outputs: false diff --git a/runs_data/D5/config.yaml b/runs_data/D5/config.yaml index f2e8a5e..570c791 100644 --- a/runs_data/D5/config.yaml +++ b/runs_data/D5/config.yaml @@ -25,7 +25,7 @@ device: cuda:1 model: hidden_dim: 200 init_scale: 1.0e-06 - model_type: TwoLayerNet + model_type: TwoLayerMLP nonlinearity: square output_scale: 1.0 return_all_outputs: false diff --git a/runs_data/Oh/config.yaml b/runs_data/Oh/config.yaml index dc0e0c1..a186386 100644 --- a/runs_data/Oh/config.yaml +++ b/runs_data/Oh/config.yaml @@ -20,18 +20,17 @@ device: cuda:0 model: hidden_dim: 300 init_scale: 1.0e-05 - model_type: TwoLayerNet + model_type: TwoLayerMLP 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