ProbeMatricesProperties.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import tensorflow as tf\n",
    "import numpy as np\n",
    "\n",
    "import constants\n",
    "from datasets import DependencyDataset\n",
    "from network import DistanceProbe, DepthProbe\n",
    "\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def orthogonality_check(matrix):\n",
    "    assert len(matrix.shape) == 2, \"Only 2D matrices suported\"\n",
    "    fro_norm = np.linalg.norm(matrix @ matrix.transpose() -  np.eye(matrix.shape[0]), ord='fro')\n",
    "    if matrix.shape[0] != matrix.shape[1]:\n",
    "        fro_norm += np.linalg.norm(matrix.transpose() @ matrix - np.eye(matrix.shape[1]), ord='fro')\n",
    "        fro_norm /= 2.\n",
    "    return fro_norm\n",
    "\n",
    "\n",
    "def matrix_cos_distance(matrixA, matrixB):\n",
    "    EPSILON = 1e-4\n",
    "    assert np.linalg.norm(matrixA) > EPSILON\n",
    "    assert np.linalg.norm(matrixB) > EPSILON\n",
    "    return np.linalg.norm(matrixA - matrixB, ord='fro') / (np.linalg.norm(matrixA, ord='fro') * np.linalg.norm(matrixB, ord='fro'))\n",
    "\n",
    "def matrix_max_distance(matrixA, matrixB):\n",
    "    return np.max(np.abs(matrixA - matrixB))\n",
    "\n",
    "def matrix_smpl_distance(matrixA, matrixB):\n",
    "    NUM_SMPL = 100\n",
    "    sample = np.random.randn(NUM_SMPL, matrixA.shape[0])\n",
    "    sample = sample / np.linalg.norm(sample, axis=-1, keepdims=True)\n",
    "    A_smpl = sample @ matrixA\n",
    "    B_smpl = sample @ matrixB\n",
    "    return np.mean(np.linalg.norm(A_smpl - B_smpl, axis=-1))\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# DEPTH MATRICES"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:Unresolved object in checkpoint: (root).optimizer.iter\n",
      "WARNING:tensorflow:Unresolved object in checkpoint: (root).optimizer.beta_1\n",
      "WARNING:tensorflow:Unresolved object in checkpoint: (root).optimizer.beta_2\n",
      "WARNING:tensorflow:Unresolved object in checkpoint: (root).optimizer.decay\n",
      "WARNING:tensorflow:Unresolved object in checkpoint: (root).optimizer.learning_rate\n",
      "WARNING:tensorflow:A checkpoint was restored (e.g. tf.train.Checkpoint.restore or tf.keras.Model.load_weights) but not all checkpointed values were used. See above for specific issues. Use expect_partial() on the load status object, e.g. tf.train.Checkpoint.restore(...).expect_partial(), to silence these warnings, or use assert_consumed() to make the check explicit. See https://www.tensorflow.org/guide/checkpoint#loading_mechanics for details.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "'experiments/train_en_de_fr/task_depth-layer_6-trainl_en_de_fr/params/ckpt-12'"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_dim = 768\n",
    "probe_rank = 768\n",
    "\n",
    "languages = ['en', 'fr', 'de']\n",
    "out_dir = 'experiments/train_en_de_fr/task_depth-layer_6-trainl_en_de_fr/'\n",
    "\n",
    "\n",
    "DistanceProbe = tf.Variable(tf.random_uniform_initializer(minval=-0.05, maxval=0.05, seed=42)\n",
    "                             ((probe_rank, model_dim)),\n",
    "                             trainable=True, name='distance_probe', dtype=tf.float32)\n",
    "\n",
    "DepthProbe = tf.Variable(tf.random_uniform_initializer(minval=-0.05, maxval=0.05, seed=42)\n",
    "                             ((probe_rank, model_dim)),\n",
    "                             trainable=True, name='depth_probe', dtype=tf.float32)\n",
    "\n",
    "optimizer=tf.optimizers.Adam()\n",
    "\n",
    "LanguageMaps = {lang: tf.Variable(tf.initializers.Identity(gain=1.0)((model_dim, model_dim)),\n",
    "                                               trainable=False, name='{}_map'.format(lang))\n",
    "                             for lang in languages}\n",
    "ckpt = tf.train.Checkpoint(optimizer=optimizer, depth_probe=DepthProbe, distance_probe=DistanceProbe, **LanguageMaps)\n",
    "\n",
    "checkpoint_manger = tf.train.CheckpointManager(ckpt, os.path.join(out_dir, 'params'), max_to_keep=1)\n",
    "\n",
    "checkpoint_manger.restore_or_initialize()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "en_map_depth = ckpt.en.numpy()\n",
    "fr_map_depth = ckpt.fr.numpy()\n",
    "de_map_depth  = ckpt.de.numpy()\n",
    "depth_probe = ckpt.depth_probe.numpy()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conduct SVD and compare non orthogonal part of the matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "15.058353652093482"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "orthogonality_check(en_map_depth)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "15.259980829491433"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "orthogonality_check(de_map_depth)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "15.843890662679716"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "orthogonality_check(fr_map_depth)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "depth probe matrix and language map matrices are not orthogonal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "en_u, en_s, en_v =  np.linalg.svd(en_map_depth)\n",
    "de_u, de_s, de_v =  np.linalg.svd(de_map_depth)\n",
    "fr_u, fr_s, fr_v =  np.linalg.svd(fr_map_depth)\n",
    "depth_u, depth_s, depth_v =  np.linalg.svd(depth_probe)\n",
    "\n",
    "# en_sv = np.diag(en_s) @ en_v\n",
    "# de_sv = np.diag(de_s) @ de_v\n",
    "# fr_sv = np.diag(fr_s) @ fr_v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "26.680162"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.norm(en_s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.908904"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(en_s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.699213"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.norm(depth_s)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Most of scaling is done in language specific matrix. It hinders multilanguage aspect of the probe.\n",
    "On the other hand depth probe is responsible for downscaling, mean eigenvalue of lang specific matrix is close to one. I think it is mostly due to intialization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7724513"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.norm(en_s - de_s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.39260736"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.norm(en_s - fr_s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6916721"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.norm(de_s - fr_s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1152x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[16,9])\n",
    "plt.plot(en_s, label='en eigenvalues')\n",
    "plt.plot(de_s, label='de eigenvalues')\n",
    "plt.plot(fr_s, label='fr eigenvalues')\n",
    "plt.plot(depth_s, label='probe eigenvalues')\n",
    "#plt.ylim([0.8, 1.05])\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Takeway: Language specific matrices have similar singular values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0238862"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(np.max(en_v @ fr_v.transpose(), axis=-1) / np.max(en_u.transpose() @ fr_u, axis=0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0285408"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(np.max(en_v @ de_v.transpose(), axis=-1) / np.max(en_u.transpose() @ de_u, axis=0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0191784"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(np.max(fr_v @ de_v.transpose(), axis=-1) / np.max(fr_u.transpose() @ de_u, axis=0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "?Takeway: right multiplication by U makes vector space less language dependent (where U @ S @ V = SVD(M))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# DISTANCE MATRICES"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'experiments/train_en_de_fr/task_distance-layer_6-trainl_en_de_fr/params/ckpt-15'"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_dim = 768\n",
    "probe_rank = 768\n",
    "\n",
    "languages = ['en', 'fr', 'de']\n",
    "out_dir = 'experiments/train_en_de_fr/task_distance-layer_6-trainl_en_de_fr/'\n",
    "\n",
    "\n",
    "DistanceProbe = tf.Variable(tf.random_uniform_initializer(minval=-0.05, maxval=0.05, seed=42)\n",
    "                             ((probe_rank, model_dim)),\n",
    "                             trainable=True, name='distance_probe', dtype=tf.float32)\n",
    "\n",
    "DepthProbe = tf.Variable(tf.random_uniform_initializer(minval=-0.05, maxval=0.05, seed=42)\n",
    "                             ((probe_rank, model_dim)),\n",
    "                             trainable=True, name='depth_probe', dtype=tf.float32)\n",
    "\n",
    "optimizer=tf.optimizers.Adam()\n",
    "\n",
    "LanguageMaps = {lang: tf.Variable(tf.initializers.Identity(gain=1.0)((model_dim, model_dim)),\n",
    "                                               trainable=False, name='{}_map'.format(lang))\n",
    "                             for lang in languages}\n",
    "ckpt = tf.train.Checkpoint(optimizer=optimizer, depth_probe=DepthProbe, distance_probe=DistanceProbe, **LanguageMaps)\n",
    "\n",
    "checkpoint_manger = tf.train.CheckpointManager(ckpt, os.path.join(out_dir, 'params'), max_to_keep=1)\n",
    "\n",
    "checkpoint_manger.restore_or_initialize()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [],
   "source": [
    "en_map_dist = ckpt.en.numpy()\n",
    "fr_map_dist = ckpt.fr.numpy()\n",
    "de_map_dist = ckpt.de.numpy()\n",
    "distance_probe = ckpt.distance_probe.numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [],
   "source": [
    "en_u, en_s, en_v =  np.linalg.svd(en_map_dist)\n",
    "de_u, de_s, de_v =  np.linalg.svd(de_map_dist)\n",
    "fr_u, fr_s, fr_v =  np.linalg.svd(fr_map_dist)\n",
    "dist_u, dist_s, dist_v =  np.linalg.svd(distance_probe)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "18.396372620066515"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "orthogonality_check(en_map_dist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "27.887388"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.norm(en_s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.6431499"
      ]
     },
     "execution_count": 138,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.norm(dist_s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.6431499"
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.norm(dist_s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5069455"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.norm(en_s - de_s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.21521693"
      ]
     },
     "execution_count": 119,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.norm(en_s - fr_s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5700357"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.norm(de_s - fr_s)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Observation: eigenvalues of maps across languages are closer in distance probing than depth probing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0151405"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(np.max(en_v @ fr_v.transpose(), axis=-1) / np.max(en_u.transpose() @ fr_u, axis=0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0247933"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(np.max(en_v @ de_v.transpose(), axis=-1) / np.max(en_u.transpose() @ de_u, axis=0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.017285"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(np.max(fr_v @ de_v.transpose(), axis=-1) / np.max(fr_u.transpose() @ de_u, axis=0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Comprison of Language specific matrices in Depth and Distance probes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.012554613"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix_cos_distance(en_map_depth, en_map_dist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.012928756"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix_cos_distance(fr_map_depth, fr_map_dist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.012441403"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix_cos_distance(de_map_depth, de_map_dist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.52868587"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix_cos_distance(distance_probe, depth_probe)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.3411"
      ]
     },
     "execution_count": 141,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.norm(en_map_depth - en_map_dist, ord='fro')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.7718587"
      ]
     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.norm(distance_probe - depth_probe, ord='fro')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3365877558739269"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix_smpl_distance(en_map_depth, en_map_dist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.096884206"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix_max_distance(en_map_depth, en_map_dist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.15160161"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix_max_distance(distance_probe, depth_probe)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# DEPTH MATRICES with ORTHOGONALITY CONSTRAINT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:Unresolved object in checkpoint: (root).optimizer.iter\n",
      "WARNING:tensorflow:Unresolved object in checkpoint: (root).optimizer.beta_1\n",
      "WARNING:tensorflow:Unresolved object in checkpoint: (root).optimizer.beta_2\n",
      "WARNING:tensorflow:Unresolved object in checkpoint: (root).optimizer.decay\n",
      "WARNING:tensorflow:Unresolved object in checkpoint: (root).optimizer.learning_rate\n",
      "WARNING:tensorflow:A checkpoint was restored (e.g. tf.train.Checkpoint.restore or tf.keras.Model.load_weights) but not all checkpointed values were used. See above for specific issues. Use expect_partial() on the load status object, e.g. tf.train.Checkpoint.restore(...).expect_partial(), to silence these warnings, or use assert_consumed() to make the check explicit. See https://www.tensorflow.org/guide/checkpoint#loading_mechanics for details.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "'experiments/train_en_de_fr_ortho/task_depth-layer_6-trainl_en_de_fr_ortho_1._dso/params/ckpt-12'"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_dim = 768\n",
    "probe_rank = 768\n",
    "\n",
    "languages = ['en', 'fr', 'de']\n",
    "out_dir = 'experiments/train_en_de_fr_ortho/task_depth-layer_6-trainl_en_de_fr_ortho_1._dso/'\n",
    "\n",
    "\n",
    "DistanceProbe = tf.Variable(tf.random_uniform_initializer(minval=-0.05, maxval=0.05, seed=42)\n",
    "                             ((probe_rank, model_dim)),\n",
    "                             trainable=True, name='distance_probe', dtype=tf.float32)\n",
    "\n",
    "DepthProbe = tf.Variable(tf.random_uniform_initializer(minval=-0.05, maxval=0.05, seed=42)\n",
    "                             ((probe_rank, model_dim)),\n",
    "                             trainable=True, name='depth_probe', dtype=tf.float32)\n",
    "\n",
    "optimizer=tf.optimizers.Adam()\n",
    "\n",
    "LanguageMaps = {lang: tf.Variable(tf.initializers.Identity(gain=1.0)((model_dim, model_dim)),\n",
    "                                               trainable=False, name='{}_map'.format(lang))\n",
    "                             for lang in languages}\n",
    "ckpt = tf.train.Checkpoint(optimizer=optimizer, depth_probe=DepthProbe, distance_probe=DistanceProbe, **LanguageMaps)\n",
    "\n",
    "checkpoint_manger = tf.train.CheckpointManager(ckpt, os.path.join(out_dir, 'params'), max_to_keep=1)\n",
    "\n",
    "checkpoint_manger.restore_or_initialize()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "en_map_depth = ckpt.en.numpy()\n",
    "fr_map_depth = ckpt.fr.numpy()\n",
    "de_map_depth  = ckpt.de.numpy()\n",
    "depth_probe = ckpt.depth_probe.numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7645905480652638"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "orthogonality_check(en_map_depth)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6718994420994511"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "orthogonality_check(fr_map_depth)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9906213459231713"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "orthogonality_check(de_map_depth)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "27.55194293886825"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "orthogonality_check(depth_probe)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "en_u, en_s, en_v =  np.linalg.svd(en_map_depth)\n",
    "de_u, de_s, de_v =  np.linalg.svd(de_map_depth)\n",
    "fr_u, fr_s, fr_v =  np.linalg.svd(fr_map_depth)\n",
    "depth_u, depth_s, depth_v =  np.linalg.svd(depth_probe)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.39182183"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.norm(en_s - de_s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.47894534"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.norm(fr_s - de_s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[16,9])\n",
    "plt.plot(en_s, label='en eigenvalues')\n",
    "plt.plot(de_s, label='de eigenvalues')\n",
    "plt.plot(fr_s, label='fr eigenvalues')\n",
    "plt.plot(depth_s, label='probe eigenvalues')\n",
    "#plt.ylim([0.8, 1.05])\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.1277322"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(np.max(en_v @ fr_v.transpose(), axis=-1) / np.max(en_u.transpose() @ fr_u, axis=0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.0066708 , 1.0039544 , 1.003847  , 1.0034826 , 1.0029308 ,\n",
       "       1.0027343 , 1.0025635 , 1.0023947 , 1.0022851 , 1.0021883 ,\n",
       "       1.0020903 , 1.0020072 , 1.0019116 , 1.0018849 , 1.0017798 ,\n",
       "       1.0017632 , 1.001684  , 1.0015615 , 1.0015225 , 1.0014782 ,\n",
       "       1.0014042 , 1.001388  , 1.001369  , 1.001313  , 1.0012624 ,\n",
       "       1.0012033 , 1.0011976 , 1.0011812 , 1.001149  , 1.0011042 ,\n",
       "       1.0010848 , 1.0010588 , 1.0010414 , 1.0010208 , 1.0010015 ,\n",
       "       1.0009574 , 1.0009307 , 1.0009037 , 1.00089   , 1.0008813 ,\n",
       "       1.0008382 , 1.0008117 , 1.0008018 , 1.0007958 , 1.0007665 ,\n",
       "       1.0007479 , 1.0007323 , 1.000711  , 1.0006855 , 1.0006747 ,\n",
       "       1.0006609 , 1.0006443 , 1.0006148 , 1.0006002 , 1.0005823 ,\n",
       "       1.0005679 , 1.0005579 , 1.0005282 , 1.0005099 , 1.0005066 ,\n",
       "       1.0004894 , 1.0004803 , 1.0004673 , 1.0004525 , 1.0004368 ,\n",
       "       1.0004282 , 1.0004176 , 1.0004134 , 1.0003892 , 1.0003856 ,\n",
       "       1.0003777 , 1.0003656 , 1.0003603 , 1.0003439 , 1.000335  ,\n",
       "       1.0003241 , 1.0003152 , 1.0003104 , 1.0002916 , 1.0002844 ,\n",
       "       1.0002781 , 1.0002723 , 1.0002589 , 1.0002513 , 1.0002446 ,\n",
       "       1.0002381 , 1.0002296 , 1.0002213 , 1.0002159 , 1.0002044 ,\n",
       "       1.0002027 , 1.0001976 , 1.0001876 , 1.0001823 , 1.0001738 ,\n",
       "       1.000167  , 1.0001637 , 1.0001582 , 1.0001566 , 1.0001522 ,\n",
       "       1.0001465 , 1.0001415 , 1.0001372 , 1.0001338 , 1.0001303 ,\n",
       "       1.0001279 , 1.0001245 , 1.0001202 , 1.0001156 , 1.0001135 ,\n",
       "       1.0001073 , 1.0001056 , 1.0001049 , 1.0000999 , 1.0000967 ,\n",
       "       1.0000957 , 1.0000906 , 1.00009   , 1.0000881 , 1.0000858 ,\n",
       "       1.000083  , 1.0000818 , 1.0000802 , 1.0000786 , 1.0000759 ,\n",
       "       1.0000745 , 1.0000734 , 1.0000718 , 1.0000707 , 1.0000684 ,\n",
       "       1.0000672 , 1.0000657 , 1.0000646 , 1.0000635 , 1.0000627 ,\n",
       "       1.0000608 , 1.0000596 , 1.000058  , 1.0000573 , 1.0000567 ,\n",
       "       1.0000559 , 1.0000547 , 1.0000536 , 1.0000526 , 1.0000513 ,\n",
       "       1.0000505 , 1.0000504 , 1.0000502 , 1.0000491 , 1.0000484 ,\n",
       "       1.0000482 , 1.0000477 , 1.0000467 , 1.000046  , 1.0000454 ,\n",
       "       1.0000451 , 1.0000442 , 1.0000435 , 1.000043  , 1.0000424 ,\n",
       "       1.0000416 , 1.0000414 , 1.0000404 , 1.0000402 , 1.0000397 ,\n",
       "       1.0000396 , 1.0000389 , 1.0000385 , 1.0000377 , 1.0000373 ,\n",
       "       1.0000365 , 1.000036  , 1.0000358 , 1.0000356 , 1.000035  ,\n",
       "       1.0000347 , 1.0000346 , 1.0000342 , 1.0000339 , 1.000033  ,\n",
       "       1.0000325 , 1.0000324 , 1.0000322 , 1.0000321 , 1.0000315 ,\n",
       "       1.000031  , 1.0000308 , 1.0000305 , 1.0000303 , 1.00003   ,\n",
       "       1.0000296 , 1.0000292 , 1.0000287 , 1.0000286 , 1.0000283 ,\n",
       "       1.0000279 , 1.0000275 , 1.0000272 , 1.0000271 , 1.0000268 ,\n",
       "       1.0000262 , 1.0000262 , 1.0000261 , 1.0000257 , 1.0000256 ,\n",
       "       1.0000254 , 1.000025  , 1.0000247 , 1.0000246 , 1.0000244 ,\n",
       "       1.0000242 , 1.0000238 , 1.0000236 , 1.0000234 , 1.000023  ,\n",
       "       1.0000228 , 1.0000225 , 1.0000223 , 1.0000223 , 1.0000218 ,\n",
       "       1.0000217 , 1.0000216 , 1.0000212 , 1.000021  , 1.0000206 ,\n",
       "       1.0000204 , 1.0000203 , 1.00002   , 1.0000198 , 1.0000197 ,\n",
       "       1.0000194 , 1.0000192 , 1.0000191 , 1.000019  , 1.0000184 ,\n",
       "       1.0000181 , 1.000018  , 1.0000176 , 1.0000176 , 1.0000175 ,\n",
       "       1.0000173 , 1.0000172 , 1.000017  , 1.0000169 , 1.0000166 ,\n",
       "       1.0000165 , 1.0000162 , 1.0000161 , 1.0000159 , 1.0000156 ,\n",
       "       1.0000155 , 1.0000154 , 1.0000151 , 1.000015  , 1.0000149 ,\n",
       "       1.0000148 , 1.0000147 , 1.0000144 , 1.0000143 , 1.0000141 ,\n",
       "       1.000014  , 1.0000137 , 1.0000136 , 1.0000134 , 1.0000132 ,\n",
       "       1.0000131 , 1.0000129 , 1.0000128 , 1.0000128 , 1.0000124 ,\n",
       "       1.0000122 , 1.000012  , 1.0000118 , 1.0000117 , 1.0000116 ,\n",
       "       1.0000114 , 1.0000113 , 1.0000112 , 1.000011  , 1.0000108 ,\n",
       "       1.0000107 , 1.0000105 , 1.0000104 , 1.0000104 , 1.0000101 ,\n",
       "       1.00001   , 1.0000099 , 1.0000098 , 1.0000095 , 1.0000094 ,\n",
       "       1.0000093 , 1.0000093 , 1.0000091 , 1.000009  , 1.0000087 ,\n",
       "       1.0000086 , 1.0000085 , 1.0000082 , 1.0000082 , 1.0000081 ,\n",
       "       1.0000079 , 1.0000077 , 1.0000076 , 1.0000075 , 1.0000074 ,\n",
       "       1.0000072 , 1.0000072 , 1.000007  , 1.000007  , 1.0000067 ,\n",
       "       1.0000066 , 1.0000064 , 1.0000063 , 1.0000062 , 1.0000061 ,\n",
       "       1.000006  , 1.0000058 , 1.0000057 , 1.0000057 , 1.0000055 ,\n",
       "       1.0000054 , 1.0000052 , 1.0000052 , 1.000005  , 1.0000049 ,\n",
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       "       1.0000033 , 1.0000032 , 1.0000031 , 1.000003  , 1.0000029 ,\n",
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       "       1.0000002 , 1.0000001 , 1.0000001 , 1.        , 0.99999994,\n",
       "       0.9999998 , 0.99999964, 0.9999996 , 0.99999946, 0.99999934,\n",
       "       0.9999993 , 0.99999917, 0.999999  , 0.99999887, 0.99999875,\n",
       "       0.9999986 , 0.99999845, 0.99999845, 0.9999984 , 0.99999803,\n",
       "       0.9999979 , 0.9999978 , 0.9999977 , 0.99999756, 0.99999744,\n",
       "       0.9999974 , 0.9999973 , 0.99999714, 0.999997  , 0.99999696,\n",
       "       0.99999684, 0.9999967 , 0.99999654, 0.9999964 , 0.9999963 ,\n",
       "       0.9999961 , 0.999996  , 0.9999959 , 0.9999958 , 0.99999577,\n",
       "       0.99999565, 0.9999955 , 0.99999535, 0.99999523, 0.9999951 ,\n",
       "       0.999995  , 0.999995  , 0.99999475, 0.99999464, 0.99999434,\n",
       "       0.99999416, 0.99999404, 0.999994  , 0.9999939 , 0.99999386,\n",
       "       0.99999374, 0.99999356, 0.9999935 , 0.9999932 , 0.99999315,\n",
       "       0.9999931 , 0.9999929 , 0.9999928 , 0.99999267, 0.99999255,\n",
       "       0.9999925 , 0.9999923 , 0.9999922 , 0.999992  , 0.999992  ,\n",
       "       0.9999919 , 0.9999918 , 0.9999917 , 0.99999154, 0.99999136,\n",
       "       0.9999913 , 0.9999912 , 0.999991  , 0.9999909 , 0.9999908 ,\n",
       "       0.99999064, 0.9999904 , 0.9999903 , 0.9999902 , 0.99999005,\n",
       "       0.99998987, 0.9999898 , 0.9999897 , 0.9999896 , 0.99998933,\n",
       "       0.99998915, 0.9999891 , 0.999989  , 0.9999888 , 0.99998873,\n",
       "       0.99998844, 0.9999884 , 0.99998826, 0.9999882 , 0.99998814,\n",
       "       0.99998796, 0.99998784, 0.9999877 , 0.99998766, 0.9999874 ,\n",
       "       0.99998724, 0.999987  , 0.99998695, 0.99998677, 0.9999867 ,\n",
       "       0.99998665, 0.9999865 , 0.9999863 , 0.9999861 , 0.999986  ,\n",
       "       0.9999859 , 0.9999856 , 0.99998546, 0.9999853 , 0.9999852 ,\n",
       "       0.9999851 , 0.99998486, 0.99998474, 0.99998444, 0.9999843 ,\n",
       "       0.9999842 , 0.999984  , 0.99998397, 0.99998385, 0.9999837 ,\n",
       "       0.9999836 , 0.9999832 , 0.9999831 , 0.99998295, 0.9999829 ,\n",
       "       0.99998266, 0.9999823 , 0.99998224, 0.99998206, 0.9999819 ,\n",
       "       0.99998164, 0.9999815 , 0.9999814 , 0.9999813 , 0.9999811 ,\n",
       "       0.999981  , 0.9999807 , 0.99998045, 0.9999804 , 0.9999803 ,\n",
       "       0.99998015, 0.99998   , 0.99997973, 0.99997956, 0.99997944,\n",
       "       0.99997926, 0.9999791 , 0.99997896, 0.9999788 , 0.99997866,\n",
       "       0.9999783 , 0.9999782 , 0.9999781 , 0.99997795, 0.9999777 ,\n",
       "       0.9999775 , 0.99997723, 0.99997705, 0.99997675, 0.9999766 ,\n",
       "       0.99997646, 0.99997604, 0.9999759 , 0.99997586, 0.9999757 ,\n",
       "       0.99997514, 0.9999751 , 0.99997467, 0.9999746 , 0.9999744 ,\n",
       "       0.9999742 , 0.999974  , 0.99997383, 0.9999737 , 0.9999733 ,\n",
       "       0.99997306, 0.99997276, 0.9999726 , 0.9999722 , 0.9999721 ,\n",
       "       0.99997187, 0.9999717 , 0.99997145, 0.99997115, 0.99997103,\n",
       "       0.99997044, 0.9999699 , 0.99996984, 0.9999696 , 0.9999694 ,\n",
       "       0.99996924, 0.999969  , 0.9999686 , 0.99996835, 0.9999682 ,\n",
       "       0.99996775, 0.9999676 , 0.9999674 , 0.99996716, 0.99996674,\n",
       "       0.99996656, 0.9999664 , 0.9999659 , 0.9999656 , 0.99996513,\n",
       "       0.9999645 , 0.99996424, 0.9999637 , 0.99996346, 0.9999633 ,\n",
       "       0.99996257, 0.9999619 , 0.99996173, 0.9999614 , 0.99996084,\n",
       "       0.99996066, 0.99996054, 0.99996006, 0.9999596 , 0.9999594 ,\n",
       "       0.99995935, 0.99995893, 0.9999587 , 0.99995786, 0.9999569 ,\n",
       "       0.9999563 , 0.9999557 , 0.9999553 , 0.9999546 , 0.9999541 ,\n",
       "       0.9999538 , 0.99995375, 0.9999531 , 0.9999521 , 0.99995124,\n",
       "       0.9999507 , 0.9999498 , 0.9999496 , 0.99994874, 0.9999485 ,\n",
       "       0.9999481 , 0.9999475 , 0.99994713, 0.99994564, 0.9999448 ,\n",
       "       0.99994344, 0.99994314, 0.9999419 , 0.9999417 , 0.99994123,\n",
       "       0.99994045, 0.9999387 , 0.9999385 , 0.99993783, 0.99993724,\n",
       "       0.9999366 , 0.99993587, 0.9999343 , 0.9999333 , 0.99993306,\n",
       "       0.99993235, 0.99993074, 0.9999303 , 0.99992937, 0.9999281 ,\n",
       "       0.9999267 , 0.9999256 , 0.9999245 , 0.9999232 , 0.99992204,\n",
       "       0.99992144, 0.99992007, 0.99991935, 0.9999167 , 0.99991363,\n",
       "       0.99991184, 0.99991095, 0.9999078 , 0.99990654, 0.999905  ,\n",
       "       0.99990237, 0.99990165, 0.9998995 , 0.9998957 , 0.99989414,\n",
       "       0.9998916 , 0.99989   , 0.9998872 , 0.99988425, 0.9998816 ,\n",
       "       0.9998802 , 0.9998729 , 0.9998676 , 0.9998663 , 0.9998661 ,\n",
       "       0.9998581 , 0.9998573 , 0.99984926, 0.9998482 , 0.9998466 ,\n",
       "       0.9998377 , 0.99983406, 0.99983007, 0.9998244 , 0.9998207 ,\n",
       "       0.999814  , 0.99980915, 0.99980336, 0.9997955 , 0.9997943 ,\n",
       "       0.99978894, 0.9997853 , 0.9997822 , 0.9997754 , 0.9997701 ,\n",
       "       0.99975985, 0.99975437, 0.9997434 , 0.99973327, 0.99972254,\n",
       "       0.9997179 , 0.9996961 , 0.9996915 , 0.9996891 , 0.9996751 ,\n",
       "       0.9996671 , 0.99965644, 0.99964744, 0.9996406 , 0.9996336 ,\n",
       "       0.9996131 , 0.9995997 , 0.99959075, 0.99958664, 0.9995687 ,\n",
       "       0.99955267, 0.9995356 , 0.99953043, 0.9995221 , 0.9995087 ,\n",
       "       0.9994943 , 0.999488  , 0.9994634 , 0.9994607 , 0.9994448 ,\n",
       "       0.9994361 , 0.9994221 , 0.9994157 , 0.99938476, 0.99937016,\n",
       "       0.9993571 , 0.9993478 , 0.9993173 , 0.99928635, 0.99927235,\n",
       "       0.999254  , 0.9992374 , 0.9992186 , 0.999209  , 0.999188  ,\n",
       "       0.9991818 , 0.99916124, 0.9991244 , 0.99911356, 0.9990794 ,\n",
       "       0.99904835, 0.99900407, 0.99896747, 0.9989572 , 0.9989215 ,\n",
       "       0.9988953 , 0.9988551 , 0.9988353 , 0.9988186 , 0.9987879 ,\n",
       "       0.99873275, 0.99869144, 0.9986376 , 0.9985898 , 0.99856836,\n",
       "       0.99850446, 0.99849826, 0.99839616, 0.9983789 , 0.9982786 ,\n",
       "       0.99811757, 0.99805534, 0.998016  , 0.9979232 , 0.99772245,\n",
       "       0.99765104, 0.997373  , 0.9972173 , 0.9966095 , 0.99587   ,\n",
       "       0.9950729 , 0.99028087, 0.10127254], dtype=float32)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "de_s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
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       "       0.9998934 , 0.9998933 , 0.9998868 , 0.9998851 , 0.99988323,\n",
       "       0.99988055, 0.999879  , 0.99987376, 0.99987096, 0.99986786,\n",
       "       0.9998661 , 0.9998646 , 0.99985886, 0.9998559 , 0.99985236,\n",
       "       0.9998461 , 0.99984366, 0.99983656, 0.99983436, 0.9998317 ,\n",
       "       0.9998246 , 0.9998146 , 0.9998063 , 0.99980456, 0.9997999 ,\n",
       "       0.99979967, 0.9997975 , 0.99978554, 0.99978113, 0.9997788 ,\n",
       "       0.99977183, 0.99976134, 0.9997597 , 0.99975246, 0.99974674,\n",
       "       0.9997353 , 0.9997314 , 0.99972624, 0.99972063, 0.999709  ,\n",
       "       0.99970466, 0.9996897 , 0.99968714, 0.99967563, 0.99966145,\n",
       "       0.9996528 , 0.99963784, 0.99963313, 0.9996307 , 0.9996196 ,\n",
       "       0.9996078 , 0.9996055 , 0.9995917 , 0.9995776 , 0.99956363,\n",
       "       0.99955714, 0.99954367, 0.99953324, 0.9995155 , 0.9995094 ,\n",
       "       0.99949944, 0.9994905 , 0.99947596, 0.9994679 , 0.99944997,\n",
       "       0.999446  , 0.9994145 , 0.9993995 , 0.9993916 , 0.99937373,\n",
       "       0.99935675, 0.999336  , 0.9993298 , 0.9993261 , 0.9992943 ,\n",
       "       0.9992905 , 0.99927306, 0.9992577 , 0.99923784, 0.99923384,\n",
       "       0.99920565, 0.999186  , 0.9991638 , 0.9991573 , 0.9991451 ,\n",
       "       0.9991251 , 0.99908686, 0.9990279 , 0.99899924, 0.9989639 ,\n",
       "       0.9989478 , 0.9989228 , 0.9988841 , 0.9988539 , 0.9987874 ,\n",
       "       0.9987776 , 0.9987669 , 0.9987365 , 0.99870265, 0.9986211 ,\n",
       "       0.99857235, 0.9985467 , 0.9984167 , 0.998363  , 0.9982997 ,\n",
       "       0.99807763, 0.9980439 , 0.99796146, 0.99789274, 0.99764985,\n",
       "       0.9966565 , 0.9954244 , 0.57876605], dtype=float32)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fr_s"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# DISTANCE MATRICES with ORTHOGONALITY CONSTRAINT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'experiments/train_en_de_fr_ortho/task_distance-layer_6-trainl_en_de_fr_ortho_1._dso/params/ckpt-20'"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_dim = 768\n",
    "probe_rank = 768\n",
    "\n",
    "languages = ['en', 'fr', 'de']\n",
    "out_dir = 'experiments/train_en_de_fr_ortho/task_distance-layer_6-trainl_en_de_fr_ortho_1._dso/'\n",
    "\n",
    "\n",
    "DistanceProbe = tf.Variable(tf.random_uniform_initializer(minval=-0.05, maxval=0.05, seed=42)\n",
    "                             ((probe_rank, model_dim)),\n",
    "                             trainable=True, name='distance_probe', dtype=tf.float32)\n",
    "\n",
    "DepthProbe = tf.Variable(tf.random_uniform_initializer(minval=-0.05, maxval=0.05, seed=42)\n",
    "                             ((probe_rank, model_dim)),\n",
    "                             trainable=True, name='depth_probe', dtype=tf.float32)\n",
    "\n",
    "optimizer=tf.optimizers.Adam()\n",
    "\n",
    "LanguageMaps = {lang: tf.Variable(tf.initializers.Identity(gain=1.0)((model_dim, model_dim)),\n",
    "                                               trainable=False, name='{}_map'.format(lang))\n",
    "                             for lang in languages}\n",
    "ckpt = tf.train.Checkpoint(optimizer=optimizer, depth_probe=DepthProbe, distance_probe=DistanceProbe, **LanguageMaps)\n",
    "\n",
    "checkpoint_manger = tf.train.CheckpointManager(ckpt, os.path.join(out_dir, 'params'), max_to_keep=1)\n",
    "\n",
    "checkpoint_manger.restore_or_initialize()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "en_map_distance = ckpt.en.numpy()\n",
    "fr_map_distance = ckpt.fr.numpy()\n",
    "de_map_distance  = ckpt.de.numpy()\n",
    "distance_probe = ckpt.distance_probe.numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.9462458136817424e-05"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "orthogonality_check(en_map_distance)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.9471124160947498e-05"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "orthogonality_check(fr_map_distance)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "27.48387829288227"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "orthogonality_check(distance_probe)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "en_u, en_s, en_v =  np.linalg.svd(en_map_distance)\n",
    "de_u, de_s, de_v =  np.linalg.svd(de_map_distance)\n",
    "fr_u, fr_s, fr_v =  np.linalg.svd(fr_map_distance)\n",
    "distance_u, distance_s, distance_v =  np.linalg.svd(distance_probe)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[16,9])\n",
    "plt.plot(en_s, label='en eigenvalues')\n",
    "plt.plot(de_s, label='de eigenvalues')\n",
    "plt.plot(fr_s, label='fr eigenvalues')\n",
    "plt.plot(distance_s, label='probe eigenvalues')\n",
    "#plt.ylim([0.8, 1.05])\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9595089391764223"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix_smpl_distance(en_map_depth, en_map_distance)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8214079999495911"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix_smpl_distance(en_map_depth, fr_map_depth)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9605946863860961"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix_smpl_distance(fr_map_distance, fr_map_depth)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9512517506629828"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix_smpl_distance(en_map_distance, fr_map_distance)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9819832071493951"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix_smpl_distance(en_map_depth, de_map_distance)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.7521539 ,  0.01371565,  0.02153927, ..., -0.01763755,\n",
       "         0.02950492,  0.06344136],\n",
       "       [-0.03690137,  0.69589615, -0.02401245, ..., -0.01475647,\n",
       "        -0.01752466, -0.01342426],\n",
       "       [-0.01676211, -0.00113208,  0.738546  , ..., -0.01658557,\n",
       "         0.00539953,  0.00673981],\n",
       "       ...,\n",
       "       [ 0.01096843, -0.02123662, -0.02205694, ...,  0.66213965,\n",
       "         0.00347736,  0.03425073],\n",
       "       [ 0.01229717,  0.01830409, -0.00958871, ...,  0.00933759,\n",
       "         0.6990686 , -0.01948741],\n",
       "       [-0.04965568, -0.02408411, -0.02114687, ...,  0.00368433,\n",
       "        -0.00885504,  0.58397526]], dtype=float32)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "en_map_distance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 7.0838064e-01, -3.3767927e-02, -2.0554403e-02, ...,\n",
       "        -2.2334931e-03,  1.5735434e-02,  1.5522198e-02],\n",
       "       [ 1.1787200e-02,  7.0018190e-01,  1.4714720e-02, ...,\n",
       "        -3.8528804e-02, -1.5454463e-02, -1.6481283e-03],\n",
       "       [ 4.6777703e-02, -2.6050841e-02,  7.4486256e-01, ...,\n",
       "        -1.0209412e-02,  4.9033392e-02,  1.7696686e-02],\n",
       "       ...,\n",
       "       [ 1.7284077e-02,  1.1983007e-02, -4.9201248e-04, ...,\n",
       "         6.6485858e-01, -1.9598693e-02, -2.9464060e-02],\n",
       "       [ 9.0703247e-03,  2.0430395e-03, -4.0280435e-02, ...,\n",
       "         1.2469566e-02,  7.0943373e-01,  2.0360809e-02],\n",
       "       [ 2.8636785e-02,  8.0670137e-03, -7.7706384e-03, ...,\n",
       "        -2.9801797e-02, -3.5127942e-02,  5.8171767e-01]], dtype=float32)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fr_map_distance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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