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    "---\n",
    "title: \"Neuron Interpretability, Polysemanticity, and Superposition\"\n",
    "subtitle: \"A mathematical reading of Goodfire’s ‘Neural Networks Are Already Clean’\"\n",
    "date: 2026-10-15\n",
    "jupyter: python3\n",
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    "---\n",
    "\n",
    "::: {.content-visible when-format=\"html\"}\n",
    "[PDF](neuron-interpretability.pdf) · [Quarto source](notes.qmd) ·\n",
    "[Executed notebook](notes.ipynb) · [Source bundle](neuron-interpretability-source.zip)\n",
    ":::\n",
    "\n",
    "## What is the contribution?\n",
    "\n",
    "Nick Cammarata’s [*Neural Networks Are Already Clean*](https://already-clean.goodfire.com/)\n",
    "is a research essay presenting experiments, neuron studies, and a working\n",
    "hypothesis. The version inspected on 15 October 2026 describes a technical\n",
    "language-model companion paper as forthcoming.\n",
    "\n",
    "Its strongest contribution is **an empirical reassessment of how much can be\n",
    "understood directly from a network’s existing neurons**. Several apparently\n",
    "incoherent activation patterns become intelligible after changing the analysis:\n",
    "inspect both signs, condition on the activation’s computational regime, look\n",
    "beyond the highest-activating examples, and test explanations on new inputs.\n",
    "Some resulting explanations also predict the effects of intervening on neurons.\n",
    "\n",
    "The advance has three components:\n",
    "\n",
    "1. **Corrections to influential examples.** A neuron associated with cats and\n",
    "   cars is reinterpreted as detecting a shared shape. Other examples change\n",
    "   interpretation after examining the circuit that produces the activation.\n",
    "2. **A more demanding measurement procedure.** The essay combines activation\n",
    "   inspection with generated positive and near-miss examples, training\n",
    "   trajectories, and interventions on native units. It documents specific\n",
    "   failures of common visualization and labeling procedures.\n",
    "3. **A developmental hypothesis.** “Recursive generalization” proposes that\n",
    "   neurons acquire related uses successively during training. The accumulated\n",
    "   response set can look heterogeneous when described using an unsuitable\n",
    "   taxonomy.\n",
    "\n",
    "The practical conclusion is that **native-neuron analysis deserves a strong\n",
    "baseline in interpretability research**. The evidence for a general claim that\n",
    "large networks have little superposition is substantially weaker. That claim\n",
    "depends on the definition of a feature, the definition of superposition, and\n",
    "how the inspected cases represent the rest of the network.\n",
    "\n",
    "The novelty is chiefly in the reanalyses and empirical demonstrations. The\n",
    "underlying ideas of sparse coding, conjoined features, and causal ablation have\n",
    "substantial prior work.\n",
    "\n",
    "The equations below formalize these distinctions. The operational definitions\n",
    "and formalization of recursive generalization are introduced for this analysis.\n",
    "Reported neural-network results are attributed to the essay; the small\n",
    "coding example in Section 4 is an independent mathematical illustration.\n",
    "\n",
    "## Define the object being interpreted\n",
    "\n",
    "Fix a trained network $F_\\theta$ and an input distribution $X\\sim P$. Write\n",
    "$r_\\ell(X)\\in\\mathbb R^d$ for a layer representation, and $h_j(X)$ for a\n",
    "specified scalar hidden-unit activation. For a language model, the input\n",
    "includes the context and the token position at which the unit is measured.\n",
    "\n",
    "Three objects need separate definitions:\n",
    "\n",
    "- A **feature** is an input property $z_k(X)$, such as curvature, a grammatical\n",
    "  relation, or the presence of a particular entity. A feature can be continuous.\n",
    "- A **neuron** is a scalar variable in the implemented computation. Its\n",
    "  relationship to features is an empirical question.\n",
    "- A **circuit** is a selected set of variables and computational dependencies\n",
    "  proposed to account for an output behavior. Describing its units individually\n",
    "  supplies only part of a circuit explanation.\n",
    "\n",
    "The hidden coordinates of a coordinatewise nonlinear MLP have an architectural\n",
    "role that arbitrary coordinates of an embedding need not have. Rotating hidden\n",
    "activations generally changes their relationship to the nonlinearities.\n",
    "Consequently, a useful native-neuron interpretation can coexist with a different,\n",
    "distributed description of the residual representation.\n",
    "\n",
    "### Polysemanticity needs an ontology and a distribution\n",
    "\n",
    "Informally, a polysemantic neuron responds to several unrelated properties.\n",
    "The word “unrelated” carries the main difficulty.\n",
    "\n",
    "Here is one explicit operational definition. Fix a partition of test inputs\n",
    "into semantic categories $C_1,\\ldots,C_K$, and an independently specified\n",
    "semantic distance $d_{\\mathcal C}(k,m)$. For a positive activation threshold\n",
    "$\\tau$, define\n",
    "\n",
    "$$\n",
    "A_j^+(\\tau)=\\{x:h_j(x)>\\tau\\},\\qquad\n",
    "A_j^-(\\tau)=\\{x:h_j(x)<-\\tau\\}.\n",
    "$$\n",
    "\n",
    "Analyze either event $A_j$ separately. Assuming $P(A_j)>0$ and $P(C_k)>0$,\n",
    "define activation lift and the composition of the activation set:\n",
    "\n",
    "$$\n",
    "L_{jk}=\\frac{P(A_j\\mid X\\in C_k)}{P(A_j)},\\qquad\n",
    "p_{jk}=P(X\\in C_k\\mid A_j).\n",
    "$$\n",
    "\n",
    "For declared constants $\\lambda>1$, $\\epsilon>0$, and $\\delta>0$, call the\n",
    "unit **polysemantic relative to this measurement specification** if there\n",
    "exist categories $k\\ne m$ such that\n",
    "\n",
    "$$\n",
    "\\min(L_{jk},L_{jm})\\ge\\lambda,\\qquad\n",
    "\\min(p_{jk},p_{jm})\\ge\\epsilon,\\qquad\n",
    "d_{\\mathcal C}(k,m)>\\delta.\n",
    "$$\n",
    "\n",
    "The lift condition rules out a unit that fires indiscriminately. The mass\n",
    "condition requires both categories to account for a non-negligible share of\n",
    "activations. The distance condition encodes the chosen meaning of “unrelated.”\n",
    "The definition applies separately to each activation sign and, where relevant,\n",
    "each gating regime.\n",
    "\n",
    "For a single prespecified binary property $C$, a simple monosemanticity\n",
    "criterion would instead be $P(A_j\\mathbin{\\triangle}C)\\le\\epsilon$, with\n",
    "precision and recall reported separately when $C$ is rare. Continuous features\n",
    "require an analogous predictive-error criterion.\n",
    "\n",
    "**None of these is an ontology-free property of a scalar function.** Under an\n",
    "object-label taxonomy, cats and cars are distant. Under a shape description,\n",
    "both can contain a V-shaped contour. Cammarata’s reanalysis of InceptionV1\n",
    "unit 4e:55 proposes the latter property and tests additional objects with that\n",
    "shape ([source](https://already-clean.goodfire.com/#cars-and-animals)).\n",
    "\n",
    "A shared-property model can be written\n",
    "\n",
    "$$\n",
    "h_j(X)=f_j(s(X))+u_j(X),\\qquad\n",
    "\\mathbb E[u_j(X)^2]\\ \\text{small},\n",
    "$$\n",
    "\n",
    "where $s$ is a specified, low-complexity property and $f_j$ belongs to a\n",
    "restricted function class. New objects sharing $s$ should activate the neuron;\n",
    "objects preserving the category label while removing $s$ should respond less.\n",
    "Allowing $s$ to be any post hoc union of activating examples makes the claim\n",
    "vacuous. Its content comes from complexity restrictions and successful held-out\n",
    "predictions, preferably including controlled changes to $s$.\n",
    "\n",
    "## Superposition is a different claim\n",
    "\n",
    "The standard linear-feature formulation is\n",
    "\n",
    "$$\n",
    "r(X)=D z(X)+e(X),\\qquad\n",
    "D=[d_1,\\ldots,d_K]\\in\\mathbb R^{d\\times K},\n",
    "$$\n",
    "\n",
    "where $z(X)$ contains meaningful latent feature intensities, $D$ contains their\n",
    "encoding directions, and $e$ is approximation error. The feature system must\n",
    "have substantive restrictions: arbitrary relabelings of the same property\n",
    "cannot be counted as additional independently meaningful features.\n",
    "\n",
    "In [*Toy Models of Superposition*](https://transformer-circuits.pub/2022/toy_model/index.html),\n",
    "superposition concerns representing features whose encoding directions are\n",
    "linearly dependent: $\\operatorname{rank}(D)<K$, in particular when $K>d$.\n",
    "The toy experiments specify the features through the data-generating process,\n",
    "which makes this claim measurable.\n",
    "\n",
    "For unit-norm columns, a matched-filter readout gives\n",
    "\n",
    "$$\n",
    "D^\\top r=z+(D^\\top D-I)z+D^\\top e.\n",
    "$$\n",
    "\n",
    "The second term is interference. Sparse $z$, suitable encoding directions,\n",
    "and nonlinear decoding can make interference tolerable. This connects the\n",
    "problem to sparse coding and compressed sensing. Merely distributing one\n",
    "feature across several coordinates establishes neither linear dependence nor\n",
    "overcompleteness.\n",
    "\n",
    "**Cammarata uses a narrower, causal description:** neurons acquire unrelated\n",
    "uses because those uses rarely interfere. His\n",
    "[terminology appendix](https://already-clean.goodfire.com/#superposition-note)\n",
    "explicitly distinguishes this from counting more features than dimensions.\n",
    "That changes the hypothesis being assessed. It adds a claim about *why the\n",
    "representation developed* to a claim about its final structure.\n",
    "\n",
    "The distinctions matter:\n",
    "\n",
    "- A coherent description of a neuron does not determine the number of latent\n",
    "  factors represented by the network.\n",
    "- A representation with $K>d$ does not identify the training mechanism that\n",
    "  produced it.\n",
    "- A neuron can generalize across related inputs while also participating in\n",
    "  an overcomplete code for other features.\n",
    "\n",
    "Composition and superposition can coexist. The earlier\n",
    "[Olah (2023) note](https://transformer-circuits.pub/2023/superposition-composition/index.html)\n",
    "already discusses this coexistence and the constraints imposed by how often\n",
    "features occur together. Thus some disagreement here concerns empirical\n",
    "prevalence and explanatory emphasis; some concerns terminology.\n",
    "\n",
    "### The econometric identification issue\n",
    "\n",
    "From observations of $r(X)$ alone, the factorization $Dz(X)$ generally lacks\n",
    "uniqueness. For example, for any invertible $A\\in\\mathbb R^{K\\times K}$,\n",
    "\n",
    "$$\n",
    "Dz(X)=(DA)(A^{-1}z(X)).\n",
    "$$\n",
    "\n",
    "Restrictions on sparsity, support, dependence, dictionaries, and\n",
    "measurement functions can improve identification. Assigning natural-language\n",
    "labels to one fitted decomposition supplies additional hypotheses to test.\n",
    "This equivalence concerns descriptive factorizations; the actual network’s\n",
    "nonlinearities and weights still constrain interventions on its native units.\n",
    "\n",
    "The developmental claim is still less identified. Several training histories\n",
    "can produce similar final response functions. Discriminating explanations\n",
    "requires training-time observations or interventions on the learning problem.\n",
    "This is the familiar distinction between fitting a latent-variable measurement\n",
    "model and identifying the mechanism that generated it.\n",
    "\n",
    "## An exact example: three features in two coordinates\n",
    "\n",
    "Take three independently meaningful binary features $z_k$ and encode them using\n",
    "three unit vectors separated by $120^\\circ$:\n",
    "\n",
    "$$\n",
    "D=\\begin{pmatrix}\n",
    "1&-1/2&-1/2\\\\\n",
    "0&\\sqrt{3}/2&-\\sqrt{3}/2\n",
    "\\end{pmatrix},\\qquad\n",
    "r=Dz,\\qquad\n",
    "\\widehat z=\\operatorname{ReLU}(D^\\top r).\n",
    "$$\n",
    "\n",
    "If at most one feature is present, $\\widehat z=z$ exactly. Each feature has an\n",
    "explicit direction and an exact detector on that restricted support, although\n",
    "three directions occupy two coordinates. If two features are present, this\n",
    "particular decoder returns $1/2$ for each. If all three are present, $r=0$:\n",
    "that state is indistinguishable from the state with no features.\n",
    "\n",
    "For independent $z_k\\sim\\operatorname{Bernoulli}(p)$, the decoder’s mean squared\n",
    "error per feature is\n",
    "\n",
    "$$\n",
    "R(p)=\\frac13\\mathbb E\\sum_{k=1}^3(\\widehat z_k-z_k)^2\n",
    "=\\frac13\\left[3p^2(1-p)\\frac12+3p^3\\right]\n",
    "=\\frac12p^2(1+p).\n",
    "$$\n",
    "\n",
    "For comparison, assigning the two coordinates to two features and always\n",
    "predicting zero for the third gives risk $p/3$. This is a specified\n",
    "dedicated-coordinate baseline; optimizing all possible encoders and decoders\n",
    "would be a separate problem. The construction makes the sparsity advantage\n",
    "precise without a training experiment."
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   "source": [
    "import itertools\n",
    "import numpy as np\n",
    "\n",
    "D = np.array([[1, -.5, -.5], [0, np.sqrt(3)/2, -np.sqrt(3)/2]])\n",
    "states = np.array(list(itertools.product([0., 1.], repeat=3)))\n",
    "decoded = np.maximum(states @ D.T @ D, 0)\n",
    "loss = ((decoded - states)**2).mean(axis=1)\n",
    "count = states.sum(axis=1)\n",
    "p = np.linspace(0.001, 1, 300)\n",
    "mass = p[:, None]**count * (1 - p[:, None])**(3 - count)\n",
    "risk = mass @ loss\n",
    "\n",
    "np.testing.assert_allclose(decoded[count <= 1], states[count <= 1], atol=1e-15)\n",
    "np.testing.assert_allclose(risk, .5 * p**2 * (1 + p), atol=1e-15)"
   ]
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   "id": "fig-superposition",
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xptlfV111VZKCY9qaxNe5oDfD7tO1ppyvFk32wIEe0+uvv97ls1oA8FZw0dpR3mhB031Z67h5S3O4g2PJOR4aZLbOI72hd6e1Tt335+GHH/aaDq1NZy2jhcFwH9NgJedcD2f6w3mOa81m93Va58Bvv/1mltfCrrcgsa7HKhRbL60RqBUErPmhCI5p4dF+vupx8Pa7pWnfs2eP1/V5e/ioD4P0muitsog+fPFWi05r9Gre2K8D9jyzv6ZOnerxeS3Ae7sm6LHwdoy1YOHt2nfs2DGXlt/WS9Ol093zhuAYAIQvONaoUSNHhQoVPK7r9lra1ksrKdotX77c/GZYv5360nt1b78r3u43tTzh7fdA0+/tt1LvG3zdR9r3SVsm2R+q6b2Q7pOVFq3oYb23t5CyL2O97K0nIpVe6yGdtnLXexX37eu9gK97Av3t9sUevNEeWNx/k71VhtHWNr7oPbbWxHf/jL70nsu9opCv4Fio9zNY69at81pW0rS7fx9uvPHGRAXH3J876Has42sFELRiolYuct++fqf0Xt79GYGeb76CD9oyyFpOe07wRu/T7OvTbXjrxUGfXVjL9OrVy2WeBlC85ZneF3q7p0tOcCyl9ilQcEwrm+lxs19n9Rzxdt3T1lW+gmPu3zlfz7b0+qq9LSSXe+DQeuk10Nt33VtwLJTnaFJ5C/Do+abHwH37+v+ff/7Z7/q0RwxvlUOs67D79cYeHNOec6xjbe/pyNu5oK2KExMo0udiVllZzw1/lQ6tY6M9b1jp3L59e1jyLpz7bG8B5y2Iq+ep/Tfbeunx0wr2vljLaZrsLfKs7663bWnLZKRtBMeQboNj1ktr62iBwnr4pxdC7a7L/sOlN0/Brk9rYvz1119eHybquq0H6/rS1l5ai8PeTFwLLFrL3r6cXnS9CfX6grVhwwaX/NFm1NOnT3d2Jaa1/HSb9u4jQhkcs17aTYg+dPXVnZ/WSrWW1RttPY7anYB1bPRBq6bHflOmy/lqtq834Pbt6+e09pU9QKI3m4sXLzYPtDXw4Y3VmiSY5t/BBsf0Bka7E7M/7NaWffYbUT1u7rUmb7vtNp/bdC+46Q326NGjXfJHgxX2GyPdp3379nmsq1q1as5ltBuRP/74w2U/9MZo27ZtplWM5rP7zX+og2PJOR4a7La2r91tuPv444+d863awNqs3hutNWtt271GUTiOabBCca6HOv0pcY7rDa0GcrULHG/0QZ57gUav9xb9nHZ/5P7AJlTBMeul3Sfaf2f03BkzZozLdp988kmv69MHm506dTK/c9rqWINL1no0j/U7rTUF7ZUHvv/+e595qN1qWsvp/gRDH4Dau3LU674WmOzdqWq3vNpdqz3oqf/3d0y0tq7+Buo+uXfFqq3LtHb2/fffH1QaAQCJD45ZL73v+/HHH01ra+v3Ra/Deu9ur8Dirbxkv9fT7o+CoWUQvdeyPqdlEL0fs7cg198Ybclv3XtZARVvafC2T3ovrt0EeuuW0KKBDV+tPFJbeocMGeJcVu8f9H5DAzrWw3/9qw/97YEYLf/p/Xqg4I1VptJ7G/s+6We1gqp9Od2mN/YH//pq3ry5qTxnnVPWg2i9p9BuGrXclxL7GSwNFFvr0wewer9kb5GgD2zd77eDDY5Z69R7Tm/lLqXdfNuX18qlet9u7be2eNB7Rw1CWMvow3tv98DaAs5aRrvnc6fHxLpvtLeEtN8jW7QrOWu+tjzyVflWA7z6PMFeyU3v6fR80ucC+hzGV68bwUipfQoUHPPXjXog7t8RfWnFAb2/t64TGgTR76H9vl7zOTn0e2jfph4r3W9rSA3r+qWtiPUc03Kkt8rmoTxHk0orsGqAUrsa1IqF9rKulq/0Gmwvf+p11V/Xe+4BI/3//PnznV3r6Wf1WYoOTfLYY4+Zbge9sSpd6u9vsAIFirRMHOg8tGi5P9DvcKjzLhz7rNcMe4VfvbZrN/z2c1WfJ7kHl3VICV/cv3Na/tTyqL38qeu0P2PU71+4ugZFyiA4hnQdHHv11Vd9Lqt9SlvL+RoLyH19jz76qN/t2x8i6o+/r3GVrAfP9oCIt8JoqNcXrP79+zvXowU2Xy0z9Gbd/UY+VMEx7bbMX+FUf5CsZbWmmb/x4/RH2j5GlP5g+qsRpi8thCVVOIJjGpy0p08fSPiiabfXwLL3de0rcKCBMV/9lGt67IUGbzdb1oNwvXkO1Oe4P3rjZa9BpDfdyZXY46HdAlj7qrXm3FldQ2hA2moxpzWg3G+ItJBgrUcL0ClxTIMRqnM91OkP9zmuDxn0QYW/64S9Nry3LqEsGuix19QMZXDs2Wef9ZlGe2BWH0Amh+avvfVYKINj9m4ptQWaP0uXLnUW6LXwYVXC8Nblh78gHgAgZYJj+jDMVxdC+kDK3jLEWyWnpATH7ON+aRnBX6txTVudOnX8BrHc90nHW9FATCDBBscinV6tWGT9turx1QCTP/Yyrz4M9cZe5tOKLdq1ozd672Tv0k7vI9zpfZt9qALdZlLG1g3HfgZDA8H2+1Bvlel8BTiCCY5puUqDO75cvnzZjClrLa/dpPsqf2kgxf4d93bfr/deVgsLb89f7M9ntGtvqwWIt3tbLetby+ozAF/fn0AtdJIrpfYpJYNjOrauL/YAXrDXVV/fX3tgX6/3SWmJFupzNJw0sKXBeWv7vr7P9oCrvjR4nVThCBTp2G9W2rRnJ3/slcy1fBnuvAvXPusY2ta29Tvsq3cipcFKa1ldn6+x0uzHWHsK27Fjh89rjL2CeLDfa6ROBMeQboNj2lWav5oL2hrJah2lDza9LWtfnzY71h95f6zWW3pDG8ygnlpbyl/rtVCvLxh602Lv8spXCx+L9nsejuCYtjzy56GHHkrUD7oWIK3Ck7cm2/aAYHK75QpHcMzeV7fWfAl0DO03td76kHYPHGiLMX90vrXsoEGDfN7s6DkbzECnKSmxx0ML2ta+6hhVvtanNY7sA9m6P7i3fze8tfIJxzENRqjO9VCnP9znuL+gkxWksZbVGoz+ultQevxDHRzTVrr+Hg7pTbhVeNTzOdBvUiA6bpv1kMtXgTWxwTGtiW0P4AXzsMv+sERrlNppZQb7wwsAQGSDY95aVtjZK6R56848KcExvXe3PqMPUgOxlyu0zBBon/yNQZ2U4Fik02vvUi6YB7jaIsB+Lx8oeBOonKkt2vzd0+l9sf3he1Ir1oVjP4OhXWgFCnbZnznYx9EOJjgWqIsu+/MSDUYHCuzaAyfaojNQxSb3CpOPP/64ma7BJn0YbgVzO3bs6LKc3pda15NixYr5fbYS6BlDKKTEPqVUcMzb8ws7LbdYAWd9lpNUeh9ubVOfnXjrbi8Y4ThHw0lbf1nbf/755wP+tmkvHckRrlZUeo5agSJfQ61ohXurEouWYZM7ZEMweReufdZxAq1t24e68Uafsdm7xNRzzhv7b+3YsWP9rlMD1tayGnxD2hUtQDp18803S1RUlM/52bNnl0qVKpn3ly5dkrNnz/pdX8+ePSVz5sw+5+/atcu81NVXXy05cuSQY8eOmdfRo0fN68iRI87X4cOHpWrVqs7P//3332FdX7DWr18vZ86cMe/Lli0rrVu39rv8TTfdJHny5JFQKl++vDRq1MjvMr/99pvzfatWrTzyxp4/mjdxcXFSuXJls/yqVau0YoDL+hYsWOB8P2TIEEltli5d6nw/YMAAv8tmypRJ+vfv7/Wz/r4v/tSuXdv5/vjx4x7zr7/+evNXz1ldl55/7nmcVpQqVcp5bVixYoXLtWHDhg3mfFL63dB8KViwoMc56f5/b9+jcB9TX0J1roc6/eHOj969e/udv2zZMuf7Hj16BLyu9evXT0JNr6fR0b5vzbJkyeK8zsfHx8vJkyeDWq9+F/W6rufuoUOHnK9y5cqZ+efPn5cdO3aEZB/s532HDh0kNjbW57XZuj5fddVVPn+7rGuLevDBB+Wbb75x/kYBAFJWxYoVpV69esm6Z0ysU6dOOX8btIxQokSJgGUi654/mDJR3rx5pWPHjslOZ2pKr/23+LrrrgtYTtI0W7/Fei9/4sQJv+u/5ZZbknUO2O9FBw8ebO7rkiLc++nLH3/84Xx/1113+V1WnzkEKmcl9p7Vft+r96wFChTwu7zeV1v3lzt37pSDBw96LGMvq/gq0zRt2lSyZs3qXHbRokVy5coV53Jabjp37pzH+rzd091zzz3y448/mnvQcEmJfUopgb5zWm7RZzdK75P12UdS2L+b3bt3lwoVKiRpPeE4R0Pl8uXLpnxiLxNZ5Xm1bt26gHnz6KOPSmqj19HbbrvNWfbTMpM3U6ZMcT7f6NKli+TPnz/seRcu9vJ7oOcHMTEx5roT7PMDPR+1bJ6S9zuInJgIbhsIKy2MBJI7d27ne70xs//fnf3hna+gkmXlypVSuHBhSQy9kQ/n+oK1bds25/sGDRoEXF4DhnXr1pXff/9dQiVQXickJMjGjRud/7cHBYNhPVS2bgT0/9u3b3fOb9mypaQmeoO+d+9e814Dvo0bNw74mSZNmjjf2/fNm1y5cgU8v9y/K+6GDx9ubk727NljCjr6KlSokDRs2NA8RLn22mulRYsWpvCRFmjhR78LmvdaSLIeQrgXwvV4aHB20qRJ8uuvv7qsw1pWvyPNmjVL0WPqS6jO9VCnP9z5oTfD1atXD/rap+dtIHpe602zXo8i+bvli34fv/rqK3P+btmyJWAhWQs6oWD/7RoxYoR5Jee3S8+FRx55RN59911TUL7jjjvM8dRKI3oMdH67du1MUBsAEF6h/J0K1qZNm5y/tfrQNNRlopo1a/qtmJIW02v/LbbfLyUmDf4emAY6DwKdA5s3bw5JuSvc++mL/b6zfv36AZcPFFBObFnYXqEpmP3WfdTyslV+1s8XL17cZRl74EfLNPfdd595f/r0aWfAVss+1t+RI0eaB+waPLLSEKhioAbH+vbtK19++aUJTvbq1ctU/KpTp47JIw1UtWnTxiNtSZUS+5Sar70aSE+sUH03Q32OXrx4MWClwKJFi3qtHK/BzXHjxsm0adNkzZo1zoquiSkTaX7u27fPGYRq3ry5pEYarLfKXuPHj5enn37aYxmdbl/en1DkXbjod1UrPigtGwZzLU7M8wMN6Ab6DoX6fgeRQ8sxpFuJfQgfqJVLoAtjcmsKuF9MQ72+YGmNOkuRIkWC+kywywUrUF7rjVFyH0jb80drDVrHXwNF+kpN7LUaNW1aAzEQvTn09vlwfVdKly5tWuQ99thjzocAWuD86aef5JVXXjEPr4sVK2ZqWSU1cJuSfNU0tAJgVapUMTWB7ctqAOLAgQPmvd48W8EWDbTkzJkzRY+pL6E610Od/nDnh964+mtJnJRrn35vklLoDLTO5H4XtSW0BpD0AcNHH31kHhwFU3s0UOvpYIXjt0sfVkyePNlZoNFgqlYa+eSTT0wNwDJlypgg9fz585O1bQBAypavghHuMlGof8sjnV7N86TeJwabhsScB+7ngJbh7A+5kxoISYn99EbTb90zac8u+gp1WTnQMbbvd7DrDnTfrJVirXKBvYWMVoDVynX2Mo9WerRa+3krJ9mXdffFF1+YFi1WwFBbovz555/y4Ycfyp133mkqO7Vv3z5ZvWSk9D6lp2uvPbiRnCBlqM/RqVOnmvT4e3m79i5cuNC0zNXeJ+bOnRswuOOrTGTPFw3kpdYKv1p50Aqua0UNLS/ZaUuvX375xbzXFl/+WiGHKu/CxX6O6DHx18tXpJ6RIe2g5RgQpEA19OwXQ32wm9iuBu3NkcOxvqTsp3XTGIi964GUzmtdNrE1Mt23Ye/KI9h9TklJSZ99uaR2VZJYWrvmrbfekmHDhplAmXY5snz5cnNjpS3KtCCsD7m///57U0CxdyGT2rjXNLTOO6uFpFXL0NuyGpiwF6Tsy0b6mIbqXA91+sOdH8HUCE8N175Q0Fqx3rrR0AKDBmm1hq4VKNSasxcuXAjpDb19PfpwJ1u2bIn6vK8W3DfeeKN5aeuxJUuWmAcp1l89Dvrd1JcG45999tlk7wcAIHWw/67ow6p8+fIl6vOBygmhbDWWGtL7/+PKe30YGCythR8ueg+i923WPVRS70cjtZ+afn3ptpNyzxqMQMc4HPfNep+orWHmzJljWmNo92i1atVyBor0/szqVUafS1xzzTWmhZWWebR1ilbOsro400qTVhf13mjXb/rSyoSLFy923tPpg3xN57x580yFJ+01YNCgQZJUKblP6UVqLSsmhbY+0+CPtyC4Bk31+mxdA/T7bLVC8lYmSu3Pi+w0yPz44487W4nZW65OmDDBmf5bb73VZ0AplHkXLqnhHEP6QXAMCBHtQs4+zor25Zua1hcse9cSViuYQIJdLpRp1B8z/XHTH3TdfnIKtlpotdanD4q1f/qkBNzCRdNnFcL0BkWDTIEK2lazfxWoj+9Q07zUZu36euihh8w07briiSeeMDWV9Hhpaw/t7i210lZu2g2fdu2ggT7N8927dztrpNkDXjVq1DDLa00sLWxpcCxQFxyROqahOtdDnf7UcI4n9tqn/fmnZO24YGzdutV0fWHvKkNfWovQ/pti0a5t7MuHgn07r732mqltGEpaM1T7f7f6gNdz5fPPP5cnn3zStJB77rnnTGEusV0YAQBSJ/vvij7ITs33j6khvVom0vsiq6cG7SYt1K3jkkPv9zR91sNUvb8O1PV1atpPTb9uR1sdaPBE/wbqmjHU4yfZ73v3798f1GeCuW/WMosGkpSWZeyBJO0e3x5M1LKQBpK0hZe2/tJKkVaFq2BbWGkrMX1Ary+lx/Ljjz+W559/3rTQ07GR9TmI9tiRVCm9T2md/fql383Uco5qZfFAAXD350Gvv/66M7ijPb489dRTpttOHTtTKwvaaTneX0s5e8VzLXtoBcPEVl5PKbfffrspF+l3SINhb7/9tvM8D7ZLxVDmXbjYr7t6TDS9gVryRvIZGVI3ulUEQsTeN7jWfEpui4JQry9Y+qDfojeEgbarD4i1/+GUpDc+ViFKCyX2QZGTWsix57c2G0/u+kK9v/ZCgbbECsQ+BlxSCpyhpjXxpk+f7ryp1VqC4RxoNxTHwyoE6Y2l5qdVkLLGGbOz/m+1GLOW1VpV3vpZj9QxDdW5Hur0p4Zz3H7tC+ZBlp7Dqa37BHu3ghqA1sCXFmS8BcassVBC/f3Rhw6WUI5F6YsGUbW7Vi0EWn744YewbxcAkDSJ/V3R33irhrdWtkptFVNSY3pT+rc4sWrXrh2Sclek9tN+3xlM939alg+latWqJeqeWcf1te759Pvna7xu994wtCu5tWvXesyz/1+DR9q6KhRjc+n96jPPPOOsWKWV+XRc5+SI9D6F6/lAav9uhvoc7d69uwnC+Hu5Bzus7gN1fVpG0kq7+t11D+4EUybSz1j7pOU/bd2YWs8HDWZp+U9pJQQrrRs2bDCVfpWWu/2NsR3KvAvXPmvAtGzZss7nNVo2T2vPyJB6EBwDQkTHPLF+MLU1xtixYxP1efeHrKFeX7C0uwBtBWNtN9BDRk2XDpCa0nRAX3vNlsTwNl6ZjollefPNN03QLamsbsT0hj5UQU3tB90yatSogAOnfvrpp87/a624cAr2XNMbGHsAxF5zJ5ySejzcxx2zCkhaEHdvbWUtq4NLa8HLqmmngTFf3cpF6piG6lwPdfojfY7bB1aeMWOGKaT5M3r0aEltrFrYyuomxl8rs2Ae6NjP32Cu9TpOhFX40fEBtCCWnGtzsONL6mDuKX1tAQAkXmJ/V7R2vlXRSGuGa1driZHccYoTKzWk115OeuONNxK1zpTIL/u9qHa5rpUt09J+NmvWzPlex3cNdG+W3ACPv3vmmTNnBnw4bT8HtZKcr94ZtDKj1frOqhho5ZN7N/F632x1yWYvJ/kLJEXini7c+xSu616k2L+bGiBJamA3XOdoUspFek22B+u8CaYnDXve6DASwYzpHOh80HJ4OCpbateKFqu1mL3VmH1+SuRduPbZfp69//77fpfV1n7a20hKPSND2kJwDAghbfpvfx9MV4irV682DxO3b98e9vUFy97EWrer3VR4o/2Da7cHkaC1V6yb11mzZskjjzwS8AZFg326P94KMVpDzWpu/s8//5iu8QLduPrq29je7F4HQg0FbQViv1HVsb18pWnAgAHOB/t6E6L7Ek56rrVt29Z0Q+GPjjumNWj9NWXX9NtrgIUiuJjU46GtwayH/JrnVq03b2OI2afZvxP+ClKROqahOtdDnf5In+Ma9NQCtHXTrl1S+BqoXW++f/rpJ0lt7N0JaUHUV8FDB1Tu1atXUN+vxH5/dEwGq8tDvSZ37do14Of0IYX+vmnXOe769etngqVWtza+2H8f6SYDAFIvfehpdX+1bdu2oMYKsZeJXnzxRfniiy8CfkZ/e3SsykD3p+EQ6fT279/fOYantoDRe6xAv6PaLZV2TaxBpnDT9Ok4qEorlOl9gz649MfbeRKp/bQ/WNb7Le0K0Bu9n+zTp4+p1BVKTZs2dbZ60Hut3r17+8w/rfD13nvvueSZL9ri0XpgrN1FauDS6r7MHrBSevyslidaFrd6cilfvryzNYc77T5RK7dpl4W+6L2rVq4K1T1duPcpWOF4PhAO2pOGlustN998s7Olnb9j5h74DNc5mpRy0alTp/y2XtOAib3Spb/nT9Zvl46Pp93TB6pkGuh5kZbFkvPczpcePXo4r7H6fdK8t8ak1ucbgcrOoc67cO2z/fmBfmd9Bch0m3fffbd5vqQ0b/ScBJwcQCoze/ZsfZpnXiVLlkzUZwcPHuz87MSJEwMu36hRI+fyBw8eTPb6Ll++7GjSpInzM/pq166d4/PPP3esWrXKsWfPHsfWrVsdv//+u+PNN990WVanh3t9wdK8yJcvn3NdefPmdbzyyiuOv//+22xz+fLljieffNKRPXt2l7Tpa9GiRR7r27hxo3N+hw4dvG5z3rx5zmX69OkTVDpfeOEFl21XqVLF5MPixYsdO3bscOzatcvx119/OT799FNHr169HFmyZDHLjRw50uv6nnrqKZf1lStXzjF8+HCzv7t373Zs2LDB8csvvzhGjx7tuP766x2dO3f2up6+ffs619GqVStzfDTfNF/1deTIEY/PVKxY0fmZuLg4r+vt2rWrS/q6devmmDVrltlXPd4TJkxwNGjQwGUZPU6+ZM2a1SxTsGDBgHmt55u1zu7du7vM021b83T7w4YNM/u8bds2k7alS5c6XnrpJUexYsWcy1WqVMnrdnbu3OmS/n/++ceRXEk5HparrrrK4xyfOnWq12VLly7tsezChQv9pi3UxzRYoTrXQ53+SJ7jaubMmR7XlM8++8xcw/R6MnfuXMfNN9/scZx1O96MGjXKuYzmrzdPPPGEc5nx48cHTGPLli2dy+v3xU6v0fZ0tW/f3pyvmzZtMsd1yZIljueff97kh/s+6DXYm9WrVzuXyZEjh2Ps2LGOzZs3O78/+rpw4YLLZ7Zv3+4oUKCAS/7cfffdjsmTJ5u83Lt3rznH9Njq8dPzT5crW7asx/b13NN5+fPndwwcONDxww8/mOuCfoc1bXpO6O+ifV9mzJgRMB8BAP/KmTOn8/q5YsUKv/eAvu4H7D788EPn8npP6E21atWcywwYMMCxcuVKx/79+52/KydOnHBZPiEhwdGxY0eXa33z5s0dH3/8sfms/sbpfaeWAUaMGOFo3bq1c7lly5Yle58s/fr1c35Oy6y+pIb02u9BrN9YLc/pfbD+Tmsa9L7hyy+/dNxxxx3Oct0zzzzjdX1aLrfWFYj+zlvLNmvWzOsy77zzjkv6ihcv7nj11VdNuUHvufTe5ddffzV5pveDTZs2TZH9DNaNN97ost3bbrvN3Cdaaf/qq6+8liP0HEpu/qpJkyZ53Mvrd2/9+vVmn3X/7733XkemTJmcy2h58+zZs37X635c9HXDDTd4XfbZZ5/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      "text/plain": [
       "<Figure size 864x345.6 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
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    "#| label: fig-superposition\n",
    "#| fig-cap: 'An explicit overcomplete code. Left: feature directions and the encoded states with two active features. Right: exact reconstruction risk, summing over all eight binary states. This is an independently constructed example.'\n",
    "#| code-fold: true\n",
    "#| code-summary: Draw the encoding and exact risks\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.rcParams.update({\"font.size\": 10, \"axes.spines.top\": False,\n",
    "                     \"axes.spines.right\": False})\n",
    "fig, axes = plt.subplots(1, 2, figsize=(9, 3.6), layout=\"constrained\")\n",
    "colors = [\"#216d87\", \"#b34d35\", \"#725c93\"]\n",
    "for k, color in enumerate(colors):\n",
    "    x, y = D[:, k]\n",
    "    axes[0].arrow(0, 0, x, y, color=color, width=.012,\n",
    "                  length_includes_head=True, head_width=.09)\n",
    "    axes[0].text(1.13*x, 1.13*y, f\"$d_{k+1}$\", color=color,\n",
    "                 ha=\"center\", va=\"center\")\n",
    "pairs = states[count == 2] @ D.T\n",
    "axes[0].scatter(*pairs.T, marker=\"x\", color=\"#555555\", label=\"Two active features\")\n",
    "axes[0].scatter(0, 0, color=\"black\", s=18)\n",
    "axes[0].set(xlim=(-1.35, 1.35), ylim=(-1.3, 1.3), aspect=\"equal\",\n",
    "            xlabel=\"$r_1$\", ylabel=\"$r_2$\", title=\"Three directions; two coordinates\")\n",
    "axes[0].legend(loc=\"lower center\", fontsize=8, frameon=False)\n",
    "axes[1].plot(p, risk, color=colors[0], label=\"Overcomplete code + ReLU readout\")\n",
    "axes[1].plot(p, p/3, color=colors[1], linestyle=\"--\", label=\"Store two; omit the third\")\n",
    "axes[1].set(xlabel=\"Feature activation probability $p$\",\n",
    "            ylabel=\"MSE per feature\", title=\"Interference grows with co-activation\")\n",
    "axes[1].legend(fontsize=8, frameon=False)\n",
    "plt.show()"
   ]
  },
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   "source": [
    "Readable feature directions and sparse-data recovery therefore coexist with\n",
    "superposition in a fully specified example. The phenomenon’s prevalence in\n",
    "trained language models remains an empirical question.\n",
    "\n",
    "## “Recursive generalization” as a testable hypothesis\n",
    "\n",
    "Let $\\theta_t$ be a training checkpoint and\n",
    "$S_{j,t}(\\tau)=\\{x:h_j(x;\\theta_t)>\\tau\\}$ a response set. The essay proposes\n",
    "that a neuron’s response set often develops by extending existing uses to\n",
    "related cases. Iterated extensions can connect semantically distant endpoints.\n",
    "An example is expansion from a spelling fragment to “DIY” and then to\n",
    "“do it yourself.”\n",
    "\n",
    "A possible formalization requires a fixed external similarity metric\n",
    "$d_\\kappa$ on inputs and a declared threshold convention across checkpoints.\n",
    "Let $B_{j,t}=S_{j,t+1}\\setminus S_{j,t}$ be the newly acquired response set.\n",
    "A local-expansion hypothesis predicts, when $P(B_{j,t})>0$,\n",
    "\n",
    "$$\n",
    "P\\left(d_\\kappa(X,S_{j,t})>\\eta\n",
    "\\;\\middle|\\;X\\in B_{j,t}\\right)\\ \\text{is small}.\n",
    "$$\n",
    "\n",
    "This permits previously active inputs to drop out. It also requires tracking\n",
    "the same computational unit and accounting for activation rescaling. Choosing\n",
    "the metric after seeing the trajectory can make the hypothesis unfalsifiable.\n",
    "\n",
    "The essay supplies suggestive trajectories and related examples. A sharper\n",
    "mechanism test would remove intermediate “bridge” examples during training,\n",
    "vary co-occurrence while holding marginal frequencies fixed, and vary width\n",
    "at matched task quality. These manipulations yield predictions about what\n",
    "gets grouped together under generalization and capacity-sharing accounts.\n",
    "Both processes could respond to the same manipulation, so the predictions\n",
    "must be specified before fitting.\n",
    "\n",
    "The idea has an acknowledged antecedent in the “conjoined features” discussion\n",
    "of [Goh et al. (2021)](https://distill.pub/2021/multimodal-neurons/).\n",
    "Cammarata’s extension is its proposed importance across models and its use as\n",
    "a developmental explanation. A quantified model of representation learning\n",
    "would require a specified similarity structure, an update mechanism, and\n",
    "out-of-sample predictions for training trajectories.\n",
    "\n",
    "## What the experiments actually establish\n",
    "\n",
    "### Predicting activations from explanations\n",
    "\n",
    "The most informative explanation test is in\n",
    "[“Explanations That Could Lose”](https://already-clean.goodfire.com/#near-miss-test).\n",
    "An agent saw explanations of 200 random neurons from the gallery and generated\n",
    "five positive examples and five near misses for each, before activations were\n",
    "measured. The reported summary covers the **183 explanations describing the\n",
    "positive side**:\n",
    "\n",
    "- **76%** of positive examples exceeded the strong-response threshold.\n",
    "- **11%** of near misses exceeded it.\n",
    "- Strong meant at least **30% of that neuron’s strongest corpus activation**.\n",
    "\n",
    "These are estimates of\n",
    "\n",
    "$$\n",
    "P_{Q_+}(A_j),\\qquad P_{Q_-}(A_j),\n",
    "$$\n",
    "\n",
    "averaged over the selected neurons, where $Q_+$ and $Q_-$ are the agent’s\n",
    "explanation-conditioned example distributions. The contrast is useful evidence\n",
    "that explanations predict responses. It is not an estimate of precision or\n",
    "recall under the model’s ordinary input distribution $P$. Generated examples\n",
    "are clustered within neurons, which matters for any uncertainty calculation.\n",
    "\n",
    "The same procedure generated examples for a deliberately distant concept:\n",
    "about 1% activated strongly, with no such activation for 179 of 183 neurons.\n",
    "Five sampled examples of one distant concept per neuron leave most possible\n",
    "alternative meanings untested. The experiment establishes specificity against\n",
    "those controls; semantic exhaustiveness would require substantially broader\n",
    "coverage.\n",
    "\n",
    "### The principal quantitative claims\n",
    "\n",
    "| Experiment | Reported result | Scope of the inference |\n",
    "|:--|:--|:--|\n",
    "| Weak-activation deletion, medium ConvNeXt, all 18 blocks | Removing the weakest 75% changes top-1 accuracy from about 72% to 71%; roughly 10% of predictions change. Removing the strongest 7%, with matched total activation magnitude, reduces accuracy to about 4%. | Strong activations dominate this aggregate task metric. Residual bypasses remain intact. |\n",
    "| Retrained InceptionV1 bottleneck | Reducing mixed3b from 480 to 10 spatial channels, with no bypass, gives 58.35% top-1 accuracy on 50,000 ImageNet validation images. Units appear coarser. | Useful coarse representations survive a severe channel bottleneck. Spatial locations remain available. |\n",
    "| SAE on that squeezed representation | A 640-feature TopK SAE, with 2 active features per position, explains 82% of held-out activation variance. Substitution reduces top-1 accuracy from 58.8% to 43.0% on a separate 10,000-image evaluation. | Reconstruction variance explained is insufficient to guarantee preservation of the model’s function. |\n",
    "| Qwen3-32B “Santa” intervention | Removing 8 identified negative-pole neurons gives reported $P(\\mathrm{Santa})=0.059$; removing the same number of neurons from the same layers at random gives 0.997. | The selected neurons have a large causal effect on this prompt’s output under this ablation. |\n",
    "\n",
    "Sources: [weak activations](https://already-clean.goodfire.com/#do-weak-activations-matter),\n",
    "[measurement controls](https://already-clean.goodfire.com/#weak-activation-controls),\n",
    "[bottleneck and SAE](https://already-clean.goodfire.com/#image-models),\n",
    "[language-model circuits](https://already-clean.goodfire.com/#language-models).\n",
    "\n",
    "Three qualifications affect interpretation of these numbers.\n",
    "\n",
    "**Aggregate accuracy can conceal important changes.** Let $c(X)$ and\n",
    "$\\widetilde c(X)$ be predictions before and after an intervention. Then\n",
    "\n",
    "$$\n",
    "\\Delta\\mathrm{Acc}\n",
    "=P(\\widetilde c(X)=Y,\\ c(X)\\ne Y)\n",
    "-P(c(X)=Y,\\ \\widetilde c(X)\\ne Y).\n",
    "$$\n",
    "\n",
    "Improvements and deteriorations can offset. A one-point accuracy change,\n",
    "alongside 10% prediction disagreement, provides limited information about\n",
    "rare behaviors, subgroups, probability calibration, or robustness.\n",
    "\n",
    "**Ten spatial channels still yield many scalar variables.** A tensor with\n",
    "shape $10\\times H\\times W$ has $10HW$ entries. Retraining can also discard\n",
    "fine distinctions. The bottleneck experiment supports a coarsening account\n",
    "for the cases studied; it does not identify the total number of represented\n",
    "features. Failure of a particular SAE to recover a feature provides limited\n",
    "evidence of absence when substitution substantially degrades task performance.\n",
    "\n",
    "**“Cleanliness” percentages depend on the rubric.** The essay reports roughly\n",
    "90% of inspected language neurons as having one main job and describes\n",
    "near-complete readability in some modern vision models. The denominator,\n",
    "activation sign, corpus, explanation granularity, and judgment procedure\n",
    "determine what those percentages mean. Architecture, training, and analysis\n",
    "tools also change together in several comparisons. These are useful exploratory\n",
    "assessments, with limited identification of which change caused the improvement.\n",
    "\n",
    "## A concrete diagnostic: SwiGLU has two positive regimes\n",
    "\n",
    "One practically useful observation follows directly from the activation\n",
    "algebra. For a SwiGLU unit, write\n",
    "\n",
    "$$\n",
    "g_j=w_{g,j}^\\top r+b_{g,j},\\qquad\n",
    "v_j=w_{v,j}^\\top r+b_{v,j},\\qquad\n",
    "h_j=\\operatorname{SiLU}(g_j)v_j\n",
    "=g_j\\sigma(g_j)v_j.\n",
    "$$\n",
    "\n",
    "Bias terms may be absent in a particular architecture. Since\n",
    "$\\sigma(g_j)>0$, a positive product has two possible regimes:\n",
    "\n",
    "$$\n",
    "\\{h_j>0\\}\n",
    "=\\{g_j>0,v_j>0\\}\\ \\cup\\ \\{g_j<0,v_j<0\\}.\n",
    "$$\n",
    "\n",
    "A positive-activation ranking mixes them. An explanation fitted to the\n",
    "double-negative branch can misdescribe the unit’s large responses in the\n",
    "other branch or on its negative side. Cammarata documents examples where\n",
    "this changes an automatic label substantially, including a unit initially\n",
    "labeled by biblical references whose stronger negative responses concern\n",
    "Russian text ([source](https://already-clean.goodfire.com/#language-models)).\n",
    "\n",
    "The diagnostic is to examine response distributions conditional on\n",
    "$(\\operatorname{sign}g_j,\\operatorname{sign}v_j)$, along with their magnitudes\n",
    "and downstream effects. The algebra is elementary; its value here lies in\n",
    "identifying a measurement failure and demonstrating consequential examples.\n",
    "The sign of $h_j$ alone also does not determine whether it increases an\n",
    "output: downstream weights and nonlinear computations determine that effect.\n",
    "\n",
    "## From a readable unit to an identified mechanism\n",
    "\n",
    "### Predictability, causal effect, and explanatory coverage\n",
    "\n",
    "A probe showing that $z_k(X)$ is predictable from $h(X)$ establishes available\n",
    "information. To assess use, define an output functional $T$, such as a logit\n",
    "contrast, and an intervention replacing a set of activations $h_S$ by a\n",
    "specified baseline $b_S$. Its average effect is\n",
    "\n",
    "$$\n",
    "\\tau_S(P;b)\n",
    "=\\mathbb E_{X\\sim P}\\left[\n",
    "T(F_\\theta(X))-T(F_\\theta^{\\operatorname{do}(h_S\\leftarrow b_S)}(X))\n",
    "\\right].\n",
    "$$\n",
    "\n",
    "This estimand depends on the input distribution, selected variables, baseline,\n",
    "and output. A large effect supports a functional role under that intervention.\n",
    "It leaves open whether the proposed semantic description covers all uses of\n",
    "the unit. A small effect can reflect redundancy or compensation. Setting a\n",
    "unit to zero may produce activation combinations rarely seen during ordinary\n",
    "operation; matched-input activation replacement offers another estimand.\n",
    "\n",
    "The essay itself includes a useful distinction: three social-security-number\n",
    "detectors are predictive, while their ablation produces only a small average\n",
    "next-target log-probability change (about $-0.004$ nats in the reported test).\n",
    "See [the appendix](https://already-clean.goodfire.com/#social-security-appendix).\n",
    "This is evidence that detection and an effect on the tested output can differ.\n",
    "\n",
    "Likewise, a selected circuit can explain a particular response while leaving\n",
    "other pathways unaccounted for. The Santa intervention is stronger evidence\n",
    "than a plausible neuron label. Its one-prompt effect still requires replication\n",
    "over a defined prompt distribution before supporting a population claim.\n",
    "\n",
    "### What native circuits avoid, and what they still require\n",
    "\n",
    "A sparse autoencoder approximates activations by a learned representation:\n",
    "\n",
    "$$\n",
    "\\widehat r=D_{\\mathrm{SAE}} f_\\phi(r),\\qquad\n",
    "\\min_{D_{\\mathrm{SAE}},\\phi}\n",
    "\\mathbb E\\sum_{i=1}^d(r_i-\\widehat r_i)^2\n",
    "+\\lambda\\mathbb E\\sum_k|f_{\\phi,k}(r)|,\n",
    "$$\n",
    "\n",
    "with hard TopK sparsity as another formulation. Dictionary learning can expose\n",
    "useful features, as in [Bricken et al. (2023)](https://transformer-circuits.pub/2023/monosemantic-features/index.html).\n",
    "Its features depend on the reconstruction objective, dictionary size, and\n",
    "sparsity constraint. They require independent validation.\n",
    "\n",
    "Studying native units avoids inserting this learned approximation into the\n",
    "network. A circuit assembled from native units still needs tests of omitted\n",
    "paths, attribution approximations, and its semantic explanations. In either\n",
    "approach, **functional fidelity** can be measured on held-out inputs by\n",
    "\n",
    "$$\n",
    "\\mathcal F\n",
    "=\\mathbb E_{X\\sim P}\n",
    "\\operatorname{KL}\\left(p_\\theta(\\cdot\\mid X)\n",
    "\\,\\|\\,p_{\\mathrm{approx}}(\\cdot\\mid X)\\right),\n",
    "$$\n",
    "\n",
    "supplemented by agreement on interventions of interest. The reported SAE\n",
    "substitution loss illustrates why low activation reconstruction error alone\n",
    "is inadequate. Native-versus-transcoder examples drawn from different\n",
    "language models also leave the comparative method effect unidentified.\n",
    "\n",
    "## Assessment and the next decisive tests\n",
    "\n",
    "The work provides useful evidence for **better native-neuron measurement and\n",
    "case-specific causal explanations**. It also weakens some prominent examples\n",
    "previously used to motivate a particular account of polysemanticity.\n",
    "Recursive generalization is a plausible developmental hypothesis with a clear\n",
    "need for stronger operationalization.\n",
    "\n",
    "The broad conclusions require three further kinds of evidence:\n",
    "\n",
    "1. **A defined prevalence estimand.** Sample layers, neurons, signs, and inputs\n",
    "   using a published rule; fix the semantic rubric; report failures and\n",
    "   uncertainty. This would turn “most neurons are interpretable” into a\n",
    "   reproducible statistical statement.\n",
    "2. **Matched-model comparisons.** Compare native units, learned dictionaries,\n",
    "   and circuit approximations on the same network, input distribution,\n",
    "   functional-fidelity targets, intervention tasks, and analysis budget.\n",
    "3. **Training-time discrimination.** Prespecify how width, feature\n",
    "   co-occurrence, and bridge-example removal should change response sets under\n",
    "   competing developmental explanations, then test those predictions across\n",
    "   training seeds.\n",
    "\n",
    "For an ML or econometrics reader, the main lesson is a measurement one:\n",
    "**semantic coherence, representation rank, and causal explanatory coverage\n",
    "are distinct estimands**. Progress on the first two can make circuit analysis\n",
    "easier. Claims about comprehensive model understanding or safety require\n",
    "evidence about the third, including rare and shifted input distributions.\n",
    "\n",
    "## References and scope {.unnumbered}\n",
    "\n",
    "- Cammarata, N. (2026). [*Neural Networks Are Already Clean*](https://already-clean.goodfire.com/).\n",
    "  Primary source, inspected 15 October 2026. Section-specific links above\n",
    "  identify the reported experiments and the author’s qualifications.\n",
    "- Elhage, N., et al. (2022). [*Toy Models of Superposition*](https://transformer-circuits.pub/2022/toy_model/index.html).\n",
    "  Controlled examples with specified latent features and sparse inputs.\n",
    "- Olah, C. (2023). [*Distributed Representations: Composition & Superposition*](https://transformer-circuits.pub/2023/superposition-composition/index.html).\n",
    "  Distinguishes and combines the two coding strategies.\n",
    "- Goh, G., et al. (2021). [*Multimodal Neurons in Artificial Neural Networks*](https://distill.pub/2021/multimodal-neurons/).\n",
    "  Earlier observations of multimodal and conjoined features.\n",
    "- Bricken, T., et al. (2023). [*Towards Monosemanticity: Decomposing Language Models With Dictionary Learning*](https://transformer-circuits.pub/2023/monosemantic-features/index.html).\n",
    "  Sparse dictionary learning for language-model representations.\n",
    "\n",
    "The neural-network measurements above are source-reported results. Only the\n",
    "eight-state mathematical illustration is computed here; all of its code is\n",
    "contained in this document."
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