{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "27bab5c5",
   "metadata": {},
   "source": [
    "# Visual intuition atlas\n",
    "\n",
    "This notebook is a visual companion to the chronological research notes. The examples are deliberately small and synthetic; I use them to isolate one mechanism at a time and make some of the less intuitive parts of the research easier to see.\n",
    "\n",
    "Unless a figure is explicitly labeled **historical result**, its values are illustrative. These plots explain ideas behind the experiments; they aren't evidence from the research program.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2572c1ad",
   "metadata": {},
   "source": [
    "## 1. Representation can change coordinates without losing information\n",
    "\n",
    "Related milestone: [001 — What if text were a signal?](001_text_as_signal.ipynb)\n",
    "\n",
    "A Fourier transform can preserve all of the information in a signal while making different structure visible. The waveform and its frequency representation below describe the same synthetic signal, but they make different properties easy to inspect.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "c868dd43",
   "metadata": {
    "publication": {
     "outputAlt": [
      "Synthetic signal combining 5 Hz and 17 Hz sine waves over one second.",
      "Fourier magnitude of the synthetic signal, with peaks at 5 Hz and 17 Hz."
     ]
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x300 with 1 Axes>"
      ]
     },
     "metadata": {
      "publication": {
       "alt": "Synthetic signal combining 5 Hz and 17 Hz sine waves over one second."
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x300 with 1 Axes>"
      ]
     },
     "metadata": {
      "publication": {
       "alt": "Fourier magnitude of the synthetic signal, with peaks at 5 Hz and 17 Hz."
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "t = np.linspace(0, 1, 256, endpoint=False)\n",
    "x = np.sin(2*np.pi*5*t) + 0.45*np.sin(2*np.pi*17*t)\n",
    "freq = np.fft.rfftfreq(len(t), d=t[1]-t[0])\n",
    "mag = np.abs(np.fft.rfft(x))\n",
    "\n",
    "plt.figure(figsize=(7,3))\n",
    "plt.plot(t, x)\n",
    "plt.xlabel('Position')\n",
    "plt.ylabel('Signal value')\n",
    "plt.title('The same information in the original coordinates')\n",
    "plt.show()\n",
    "\n",
    "plt.figure(figsize=(7,3))\n",
    "plt.plot(freq, mag)\n",
    "plt.xlim(0, 30)\n",
    "plt.xlabel('Frequency')\n",
    "plt.ylabel('Magnitude')\n",
    "plt.title('A coordinate change exposes different structure')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f929b6ae",
   "metadata": {},
   "source": [
    "> **Sticky note — coordinate system:** an invertible change of coordinates can preserve all of the information in a state while changing how difficult that information is for a particular downstream operation to use.\n",
    "\n",
    "The visible frequency peaks don't imply that a spectral language model should perform better. They illustrate the distinction that started this research sequence: **information being preserved and information being easy for a particular consumer to use are different questions.**\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "12276a4d",
   "metadata": {},
   "source": [
    "## 2. Phase-aware similarity responds directly to phase difference\n",
    "\n",
    "Related milestones: [003](003_coordinates_and_matched_operations.ipynb) and [004](004_isolating_phase_attention.ipynb)\n",
    "\n",
    "For unit-length complex values, the normalized real-Hermitian similarity used in the phase-aware attention experiment reduces to `cos(Δθ)`. Relative phase therefore affects similarity in a predictable circular way.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "034136b3",
   "metadata": {
    "publication": {
     "outputAlt": [
      "Cosine similarity is 1 at zero phase difference, 0 at a quarter turn, and minus 1 at a half turn."
     ]
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x300 with 1 Axes>"
      ]
     },
     "metadata": {
      "publication": {
       "alt": "Cosine similarity is 1 at zero phase difference, 0 at a quarter turn, and minus 1 at a half turn."
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "delta = np.linspace(-np.pi, np.pi, 400)\n",
    "similarity = np.cos(delta)\n",
    "plt.figure(figsize=(7,3))\n",
    "plt.plot(delta, similarity)\n",
    "plt.axhline(0, linewidth=1)\n",
    "plt.xlabel('Phase difference Δθ (radians)')\n",
    "plt.ylabel('Normalized real-Hermitian similarity')\n",
    "plt.title('Phase-aware similarity is circular')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "78e2f619",
   "metadata": {},
   "source": [
    "Two values with aligned phase receive positive similarity, a quarter-turn difference produces a score near zero, and opposing phases produce negative similarity. The point isn't that this is the only useful way to compare phase-valued features; it's that the operation directly reflects the structure we chose to represent.\n",
    "\n",
    "That was the distinction behind the coordinate-control experiments. Expressing information in phase-aware coordinates may help on its own, while applying operations that explicitly respect relative phase is a separate intervention.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e0b85271",
   "metadata": {},
   "source": [
    "## 3. A frozen endpoint can reverse a trajectory story\n",
    "\n",
    "Related milestones: [005](005_unit_hypersphere_anomaly.ipynb) and [006](006_endpoint_can_mislead.ipynb).\n",
    "\n",
    "The curves below are illustrative.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "babde455",
   "metadata": {
    "publication": {
     "outputAlt": [
      "Invented training curves illustrating that the best observed checkpoint and the final checkpoint can give different rankings."
     ]
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x300 with 1 Axes>"
      ]
     },
     "metadata": {
      "publication": {
       "alt": "Invented training curves illustrating that the best observed checkpoint and the final checkpoint can give different rankings."
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "steps = np.array([0,16,32,64,96,128,192,288])\n",
    "shared = np.array([5.4,3.7,2.95,3.02,3.18,3.38,3.55,3.72])\n",
    "unit = np.array([5.5,4.5,4.05,3.85,3.72,3.60,3.42,3.30])\n",
    "plt.figure(figsize=(7,3))\n",
    "plt.plot(steps, shared, marker='o', label='Shared recurrent control')\n",
    "plt.plot(steps, unit, marker='o', label='Unit-hypersphere model')\n",
    "plt.xlabel('Training update')\n",
    "plt.ylabel('Illustrative validation NLL')\n",
    "plt.title('Ranking depends on the checkpoint-selection question')\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0a26cd71",
   "metadata": {},
   "source": [
    "A fixed endpoint asks which model is better at one specified training budget. The best checkpoint observed anywhere along each curve asks a different question, and a stopping policy frozen before seeing the outcome asks another one.\n",
    "\n",
    "The same pair of learning curves can therefore support different rankings without any of the measurements being numerically wrong. This is why the unit-hypersphere anomaly eventually required a fair checkpoint-selection experiment rather than another comparison at a convenient endpoint.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7d4448eb",
   "metadata": {},
   "source": [
    "## 4. Normalization removes radial motion and rescales tangent motion\n",
    "\n",
    "Related milestone: [007 — Derive before training](007_derive_before_training.ipynb).\n",
    "\n",
    "For\n",
    "\n",
    "`N(x) = x / ||x||`\n",
    "\n",
    "the first-order gain of a radial perturbation is zero, while the gain of a tangent perturbation is `1 / ||x||`.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "53dd5b3d",
   "metadata": {
    "publication": {
     "outputAlt": [
      "Normalization derivative gain: radial gain stays zero while tangent gain decreases as one divided by radius."
     ]
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x300 with 1 Axes>"
      ]
     },
     "metadata": {
      "publication": {
       "alt": "Normalization derivative gain: radial gain stays zero while tangent gain decreases as one divided by radius."
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "r = np.linspace(0.2, 4.0, 300)\n",
    "plt.figure(figsize=(7,3))\n",
    "plt.plot(r, 1/r, label='Tangent gain 1/r')\n",
    "plt.plot(r, np.zeros_like(r), label='Radial gain 0')\n",
    "plt.axvline(1.0, linestyle='--', linewidth=1)\n",
    "plt.xlabel('Input radius ||x||')\n",
    "plt.ylabel('First-order gain')\n",
    "plt.title('Normalization is exactly anisotropic')\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3cc7b4f9",
   "metadata": {},
   "source": [
    "At unit radius, tangent perturbations are preserved to first order. At larger radius they are attenuated, while close to zero they are strongly amplified. That last behavior is one reason the theorem explicitly requires a nonzero input.\n",
    "\n",
    "✓ **Formal checkpoint:** this derivative is machine-checked in the public [Theorem Library normalization proof](https://github.com/pH34r-pH/theorem-library/blob/2c90ec3d482a64a5bce5787f48c5828429c50305/TheoremLibrary/Geometry/Sphere/Normalization.lean).\n",
    "\n",
    "The figure shows the mathematical behavior of normalization. It doesn't assign meaning to either direction; deciding whether radial or tangent variation matters for a task remains empirical.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "06390311",
   "metadata": {},
   "source": [
    "## 5. Small per-step differences can compound across recurrence\n",
    "\n",
    "Related milestone: [008 — What does the sphere actually do?](008_frozen_mechanism_tests.ipynb).\n",
    "\n",
    "For the simplest possible scalar example, if one recurrent step scales a perturbation by `g`, then repeating the same operation for `T` steps scales it by `g^T`.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "02dde5a0",
   "metadata": {
    "publication": {
     "outputAlt": [
      "Repeated scalar gains of 0.98, 0.9, and 0.7 compound with depth; smaller gains decay faster."
     ]
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x300 with 1 Axes>"
      ]
     },
     "metadata": {
      "publication": {
       "alt": "Repeated scalar gains of 0.98, 0.9, and 0.7 compound with depth; smaller gains decay faster."
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "depth = np.arange(0, 21)\n",
    "plt.figure(figsize=(7,3))\n",
    "for g in [0.98,0.9,0.7]:\n",
    "    plt.plot(depth, g**depth, marker='o', label=f'g={g}')\n",
    "plt.xlabel('Recurrent depth')\n",
    "plt.ylabel('Perturbation gain')\n",
    "plt.title('Mild one-step contraction can become strong finite-horizon contraction')\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dde4d52e",
   "metadata": {},
   "source": [
    "Even mild contraction can therefore become substantial after enough recurrent steps.\n",
    "\n",
    "Real neural networks are more complicated because the directions being amplified or contracted can rotate between steps. Multiplying the actual Jacobians along the trajectory captures that interaction; independently inspecting the singular values of each step generally does not.\n",
    "\n",
    "This is why the mechanism campaign moved from one-step derivatives to finite-horizon Jacobian products.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7c0ccf95",
   "metadata": {},
   "source": [
    "## 6. Radius and angle are coupled in ordinary Euclidean polar geometry\n",
    "\n",
    "Related milestone: [011 — Geometry should follow invariance](011_geometry_from_invariance.ipynb).\n",
    "\n",
    "For two vectors separated by a fixed angle `θ`, their ordinary inner product is\n",
    "\n",
    "`r_q r_k cos(θ)`.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "82e33dde",
   "metadata": {
    "publication": {
     "outputAlt": [
      "Heatmap of radius product times the cosine of a fixed angle: increasing either radius increases the inner product."
     ]
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x400 with 2 Axes>"
      ]
     },
     "metadata": {
      "publication": {
       "alt": "Heatmap of radius product times the cosine of a fixed angle: increasing either radius increases the inner product."
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rq = np.linspace(0.5,3.0,80); rk = np.linspace(0.5,3.0,80)\n",
    "RQ,RK = np.meshgrid(rq,rk)\n",
    "S = RQ*RK*np.cos(np.pi/3)\n",
    "plt.figure(figsize=(6,4))\n",
    "plt.imshow(S, origin='lower', aspect='auto', extent=[rq.min(),rq.max(),rk.min(),rk.max()])\n",
    "plt.colorbar(label='Raw inner product')\n",
    "plt.xlabel('Query radius'); plt.ylabel('Key radius')\n",
    "plt.title('At fixed angle, Euclidean similarity still changes with radius')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0769b7e8",
   "metadata": {},
   "source": [
    "The angle is fixed throughout the figure, but changing either radius still changes the similarity.\n",
    "\n",
    "If semantic similarity is supposed to ignore radius, this is a mismatch between the desired invariance and the operation being used. If radius is supposed to modulate similarity, the same coupling may be useful. The equation doesn't choose the interpretation; the task requirement does.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f07c9b4e",
   "metadata": {},
   "source": [
    "## 7. Longer contexts trade repeated support for specificity\n",
    "\n",
    "Related milestone: [012 — Natural-source task distinctions](012_natural_source_distinctions.ipynb).\n",
    "\n",
    "The following counts are illustrative rather than historical benchmark measurements.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "e24b6ad1",
   "metadata": {
    "publication": {
     "outputAlt": [
      "Illustrative counts of repeated contexts and branch contexts decrease as exact context length grows."
     ]
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x300 with 1 Axes>"
      ]
     },
     "metadata": {
      "publication": {
       "alt": "Illustrative counts of repeated contexts and branch contexts decrease as exact context length grows."
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "L = np.array([8,16,32,64,128])\n",
    "repeated = np.array([1200,760,410,125,18])\n",
    "branches = np.array([310,245,180,62,9])\n",
    "plt.figure(figsize=(7,3))\n",
    "plt.plot(L,repeated,marker='o',label='Repeated exact contexts')\n",
    "plt.plot(L,branches,marker='o',label='Contexts with distinct continuations')\n",
    "plt.xscale('log',base=2)\n",
    "plt.xlabel('Exact context length L (bytes)')\n",
    "plt.ylabel('Illustrative support count')\n",
    "plt.title('Specificity and repeated support trade off')\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b5dab684",
   "metadata": {},
   "source": [
    "Longer exact contexts identify increasingly specific situations, but naturally occurring text repeats those exact situations less often. Eventually there may be too little repeated support to estimate a useful conditional distinction.\n",
    "\n",
    "The natural-source benchmark qualified at `L=32`. Context length was frozen before favorable model outcomes were inspected because choosing it afterward would turn benchmark construction into another form of outcome-dependent tuning.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7a824e68",
   "metadata": {},
   "source": [
    "## 8. Probe recoverability changes continuously with signal strength\n",
    "\n",
    "Related milestone: [013 — Accessible does not imply used](013_accessible_not_used.ipynb).\n",
    "\n",
    "This synthetic experiment changes only the strength of a linearly accessible class signal embedded in otherwise noisy states.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "c5fc5a4c",
   "metadata": {
    "publication": {
     "outputAlt": [
      "Held-out accuracy of a logistic probe on synthetic random states rises as the injected class signal strengthens."
     ]
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x300 with 1 Axes>"
      ]
     },
     "metadata": {
      "publication": {
       "alt": "Held-out accuracy of a logistic probe on synthetic random states rises as the injected class signal strengthens."
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.model_selection import train_test_split\n",
    "rng=np.random.default_rng(12); strengths=np.linspace(0,1.5,13); scores=[]\n",
    "for strength in strengths:\n",
    "    n,d=3000,24; y=rng.integers(0,2,n); h=rng.normal(size=(n,d))\n",
    "    v=rng.normal(size=d); v/=np.linalg.norm(v)\n",
    "    h+=(2*y[:,None]-1)*strength*v\n",
    "    Xt,Xe,yt,ye=train_test_split(h,y,test_size=.3,random_state=5,stratify=y)\n",
    "    scores.append(LogisticRegression(max_iter=1000).fit(Xt,yt).score(Xe,ye))\n",
    "plt.figure(figsize=(7,3))\n",
    "plt.plot(strengths,scores,marker='o')\n",
    "plt.axhline(.5,linestyle='--',linewidth=1)\n",
    "plt.xlabel('Injected linearly accessible signal strength')\n",
    "plt.ylabel('Held-out affine-probe accuracy')\n",
    "plt.title('Accessible information is not a binary property')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91fae2b6",
   "metadata": {},
   "source": [
    "As the accessible signal becomes stronger, a simple affine probe recovers it more reliably. There isn't a universal point where information suddenly changes from “absent” to “present”; recoverability depends on signal strength, sample size, the consumer being tested, and the evaluation protocol.\n",
    "\n",
    "A strong probe result therefore establishes accessibility only for the tested probe family and task. It doesn't establish native causal use. A weak result is similarly ambiguous: the signal may be weak, the dataset may be too small, the probe family may be mismatched, or the optimization/protocol may have failed.\n",
    "\n",
    "## How to use this atlas\n",
    "\n",
    "Each section is designed so that one assumption or parameter can be changed without rebuilding the whole experiment. Before rerunning a cell, predict what should happen and why.\n",
    "\n",
    "The questions I find most useful are the same ones that eventually shaped the research program: **what is fixed, what changed, what else could produce the same result, and what observation would make me change the next experiment?**\n",
    "\n",
    "The figures are here to build intuition around those questions. The milestone notebooks and their underlying research artifacts carry the evidence.\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "name": "python",
   "version": "3"
  },
  "publication": {
   "exampleKind": "illustrative",
   "outputEnvironment": {
    "matplotlib": "3.11.2",
    "numpy": "2.5.3",
    "scikit-learn": "1.9.1"
   },
   "question": "What do coordinate changes, normalization, recurrence, and probing look like in small controlled examples?"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
