401 lines
13 KiB
Python
401 lines
13 KiB
Python
#####################################################
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# Copyright (c) Xuanyi Dong [GitHub D-X-Y], 2020.03 #
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#####################################################
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# Reformulate the codes in https://github.com/CalculatedContent/WeightWatcher
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#####################################################
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import numpy as np
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from typing import List
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import torch.nn as nn
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from collections import OrderedDict
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from sklearn.decomposition import TruncatedSVD
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def available_module_types():
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return (nn.Conv2d, nn.Linear)
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def get_conv2D_Wmats(tensor: np.ndarray) -> List[np.ndarray]:
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"""
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Extract W slices from a 4 index conv2D tensor of shape: (N,M,i,j) or (M,N,i,j).
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Return ij (N x M) matrices
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"""
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mats = []
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N, M, imax, jmax = tensor.shape
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assert (
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N + M >= imax + jmax
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), "invalid tensor shape detected: {}x{} (NxM), {}x{} (i,j)".format(
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N, M, imax, jmax
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)
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for i in range(imax):
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for j in range(jmax):
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w = tensor[:, :, i, j]
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if N < M:
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w = w.T
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mats.append(w)
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return mats
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def glorot_norm_check(W, N, M, rf_size, lower=0.5, upper=1.5):
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"""Check if this layer needs Glorot Normalization Fix"""
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kappa = np.sqrt(2 / ((N + M) * rf_size))
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norm = np.linalg.norm(W)
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check1 = norm / np.sqrt(N * M)
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check2 = norm / (kappa * np.sqrt(N * M))
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if (rf_size > 1) and (check2 > lower) and (check2 < upper):
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return check2, True
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elif (check1 > lower) & (check1 < upper):
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return check1, True
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else:
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if rf_size > 1:
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return check2, False
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else:
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return check1, False
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def glorot_norm_fix(w, n, m, rf_size):
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"""Apply Glorot Normalization Fix."""
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kappa = np.sqrt(2 / ((n + m) * rf_size))
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w = w / kappa
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return w
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def analyze_weights(
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weights,
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min_size,
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max_size,
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alphas,
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lognorms,
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spectralnorms,
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softranks,
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normalize,
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glorot_fix,
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):
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results = OrderedDict()
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count = len(weights)
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if count == 0:
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return results
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for i, weight in enumerate(weights):
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M, N = np.min(weight.shape), np.max(weight.shape)
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Q = N / M
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results[i] = cur_res = OrderedDict(N=N, M=M, Q=Q)
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check, checkTF = glorot_norm_check(weight, N, M, count)
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cur_res["check"] = check
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cur_res["checkTF"] = checkTF
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# assume receptive field size is count
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if glorot_fix:
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weight = glorot_norm_fix(weight, N, M, count)
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else:
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# probably never needed since we always fix for glorot
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weight = weight * np.sqrt(count / 2.0)
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if spectralnorms: # spectralnorm is the max eigenvalues
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svd = TruncatedSVD(n_components=1, n_iter=7, random_state=10)
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svd.fit(weight)
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sv = svd.singular_values_
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sv_max = np.max(sv)
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if normalize:
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evals = sv * sv / N
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else:
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evals = sv * sv
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lambda0 = evals[0]
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cur_res["spectralnorm"] = lambda0
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cur_res["logspectralnorm"] = np.log10(lambda0)
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else:
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lambda0 = None
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if M < min_size:
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summary = "Weight matrix {}/{} ({},{}): Skipping: too small (<{})".format(
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i + 1, count, M, N, min_size
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)
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cur_res["summary"] = summary
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continue
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elif max_size > 0 and M > max_size:
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summary = (
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"Weight matrix {}/{} ({},{}): Skipping: too big (testing) (>{})".format(
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i + 1, count, M, N, max_size
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)
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)
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cur_res["summary"] = summary
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continue
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else:
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summary = []
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if alphas:
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import powerlaw
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svd = TruncatedSVD(n_components=M - 1, n_iter=7, random_state=10)
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svd.fit(weight.astype(float))
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sv = svd.singular_values_
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if normalize:
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evals = sv * sv / N
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else:
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evals = sv * sv
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lambda_max = np.max(evals)
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fit = powerlaw.Fit(evals, xmax=lambda_max, verbose=False)
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alpha = fit.alpha
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cur_res["alpha"] = alpha
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D = fit.D
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cur_res["D"] = D
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cur_res["lambda_min"] = np.min(evals)
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cur_res["lambda_max"] = lambda_max
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alpha_weighted = alpha * np.log10(lambda_max)
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cur_res["alpha_weighted"] = alpha_weighted
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tolerance = lambda_max * M * np.finfo(np.max(sv)).eps
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cur_res["rank_loss"] = np.count_nonzero(sv > tolerance, axis=-1)
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logpnorm = np.log10(np.sum([ev ** alpha for ev in evals]))
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cur_res["logpnorm"] = logpnorm
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summary.append(
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"Weight matrix {}/{} ({},{}): Alpha: {}, Alpha Weighted: {}, D: {}, pNorm {}".format(
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i + 1, count, M, N, alpha, alpha_weighted, D, logpnorm
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)
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)
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if lognorms:
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norm = np.linalg.norm(weight) # Frobenius Norm
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cur_res["norm"] = norm
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lognorm = np.log10(norm)
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cur_res["lognorm"] = lognorm
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X = np.dot(weight.T, weight)
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if normalize:
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X = X / N
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normX = np.linalg.norm(X) # Frobenius Norm
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cur_res["normX"] = normX
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lognormX = np.log10(normX)
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cur_res["lognormX"] = lognormX
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summary.append(
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"Weight matrix {}/{} ({},{}): LogNorm: {} ; LogNormX: {}".format(
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i + 1, count, M, N, lognorm, lognormX
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)
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)
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if softranks:
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softrank = norm ** 2 / sv_max ** 2
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softranklog = np.log10(softrank)
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softranklogratio = lognorm / np.log10(sv_max)
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cur_res["softrank"] = softrank
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cur_res["softranklog"] = softranklog
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cur_res["softranklogratio"] = softranklogratio
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summary += (
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"{}. Softrank: {}. Softrank log: {}. Softrank log ratio: {}".format(
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summary, softrank, softranklog, softranklogratio
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)
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)
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cur_res["summary"] = "\n".join(summary)
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return results
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def compute_details(results):
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"""
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Return a pandas data frame.
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"""
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final_summary = OrderedDict()
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metrics = {
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# key in "results" : pretty print name
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"check": "Check",
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"checkTF": "CheckTF",
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"norm": "Norm",
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"lognorm": "LogNorm",
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"normX": "Norm X",
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"lognormX": "LogNorm X",
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"alpha": "Alpha",
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"alpha_weighted": "Alpha Weighted",
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"spectralnorm": "Spectral Norm",
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"logspectralnorm": "Log Spectral Norm",
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"softrank": "Softrank",
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"softranklog": "Softrank Log",
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"softranklogratio": "Softrank Log Ratio",
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"sigma_mp": "Marchenko-Pastur (MP) fit sigma",
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"numofSpikes": "Number of spikes per MP fit",
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"ratio_numofSpikes": "aka, percent_mass, Number of spikes / total number of evals",
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"softrank_mp": "Softrank for MP fit",
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"logpnorm": "alpha pNorm",
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}
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metrics_stats = []
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for metric in metrics:
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metrics_stats.append("{}_min".format(metric))
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metrics_stats.append("{}_max".format(metric))
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metrics_stats.append("{}_avg".format(metric))
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metrics_stats.append("{}_compound_min".format(metric))
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metrics_stats.append("{}_compound_max".format(metric))
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metrics_stats.append("{}_compound_avg".format(metric))
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columns = (
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[
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"layer_id",
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"layer_type",
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"N",
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"M",
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"layer_count",
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"slice",
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"slice_count",
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"level",
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"comment",
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]
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+ [*metrics]
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+ metrics_stats
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)
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metrics_values = {}
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metrics_values_compound = {}
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for metric in metrics:
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metrics_values[metric] = []
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metrics_values_compound[metric] = []
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layer_count = 0
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for layer_id, result in results.items():
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layer_count += 1
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layer_type = np.NAN
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if "layer_type" in result:
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layer_type = str(result["layer_type"]).replace("LAYER_TYPE.", "")
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compounds = {} # temp var
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for metric in metrics:
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compounds[metric] = []
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slice_count, Ntotal, Mtotal = 0, 0, 0
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for slice_id, summary in result.items():
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if not str(slice_id).isdigit():
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continue
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slice_count += 1
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N = np.NAN
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if "N" in summary:
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N = summary["N"]
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Ntotal += N
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M = np.NAN
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if "M" in summary:
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M = summary["M"]
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Mtotal += M
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data = {
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"layer_id": layer_id,
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"layer_type": layer_type,
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"N": N,
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"M": M,
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"slice": slice_id,
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"level": "SLICE",
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"comment": "Slice level",
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}
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for metric in metrics:
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if metric in summary:
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value = summary[metric]
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if value is not None:
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metrics_values[metric].append(value)
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compounds[metric].append(value)
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data[metric] = value
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data = {
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"layer_id": layer_id,
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"layer_type": layer_type,
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"N": Ntotal,
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"M": Mtotal,
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"slice_count": slice_count,
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"level": "LAYER",
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"comment": "Layer level",
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}
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# Compute the compound value over the slices
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for metric, value in compounds.items():
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count = len(value)
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if count == 0:
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continue
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compound = np.mean(value)
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metrics_values_compound[metric].append(compound)
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data[metric] = compound
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data = {"layer_count": layer_count, "level": "NETWORK", "comment": "Network Level"}
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for metric, metric_name in metrics.items():
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if metric not in metrics_values or len(metrics_values[metric]) == 0:
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continue
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values = metrics_values[metric]
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minimum = min(values)
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maximum = max(values)
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avg = np.mean(values)
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final_summary[metric] = avg
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# print("{}: min: {}, max: {}, avg: {}".format(metric_name, minimum, maximum, avg))
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data["{}_min".format(metric)] = minimum
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data["{}_max".format(metric)] = maximum
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data["{}_avg".format(metric)] = avg
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values = metrics_values_compound[metric]
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minimum = min(values)
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maximum = max(values)
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avg = np.mean(values)
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final_summary["{}_compound".format(metric)] = avg
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# print("{} compound: min: {}, max: {}, avg: {}".format(metric_name, minimum, maximum, avg))
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data["{}_compound_min".format(metric)] = minimum
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data["{}_compound_max".format(metric)] = maximum
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data["{}_compound_avg".format(metric)] = avg
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return final_summary
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def analyze(
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model: nn.Module,
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min_size=50,
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max_size=0,
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alphas: bool = False,
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lognorms: bool = True,
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spectralnorms: bool = False,
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softranks: bool = False,
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normalize: bool = False,
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glorot_fix: bool = False,
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):
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"""
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Analyze the weight matrices of a model.
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:param model: A PyTorch model
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:param min_size: The minimum weight matrix size to analyze.
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:param max_size: The maximum weight matrix size to analyze (0 = no limit).
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:param alphas: Compute the power laws (alpha) of the weight matrices.
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Time consuming so disabled by default (use lognorm if you want speed)
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:param lognorms: Compute the log norms of the weight matrices.
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:param spectralnorms: Compute the spectral norm (max eigenvalue) of the weight matrices.
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:param softranks: Compute the soft norm (i.e. StableRank) of the weight matrices.
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:param normalize: Normalize or not.
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:param glorot_fix:
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:return: (a dict of all layers' results, a dict of the summarized info)
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"""
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names, modules = [], []
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for name, module in model.named_modules():
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if isinstance(module, available_module_types()):
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names.append(name)
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modules.append(module)
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# print('There are {:} layers to be analyzed in this model.'.format(len(modules)))
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all_results = OrderedDict()
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for index, module in enumerate(modules):
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if isinstance(module, nn.Linear):
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weights = [module.weight.cpu().detach().numpy()]
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else:
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weights = get_conv2D_Wmats(module.weight.cpu().detach().numpy())
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results = analyze_weights(
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weights,
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min_size,
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max_size,
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alphas,
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lognorms,
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spectralnorms,
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softranks,
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normalize,
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glorot_fix,
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)
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results["id"] = index
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results["type"] = type(module)
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all_results[index] = results
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summary = compute_details(all_results)
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return all_results, summary
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