{
  "id": "oai:papers.qnfo.org:subliminal-learning-as-architecture-specific-latent-space-steganography-a-channe",
  "slug": "subliminal-learning-as-architecture-specific-latent-space-steganography-a-channe",
  "title": "Subliminal Learning as Architecture-Specific Latent-Space Steganography: A Channel Model for Trait Transfer Under Distillation",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Subliminal learning — the transfer of a teacher model's behavioral traits to a student trained on semantically unrelated outputs such as number sequences — is documented empirically but lacks a quantitative channel model that explains why transfer succeeds within a model family and fails across families. This gap blocks any principled design of filters, training recipes, or audits for the increasingly common practice of training on model-generated data. We formalize subliminal learning as steganographic modulation of the teacher's output distribution: a trait is encoded as a low-amplitude perturbation along a teacher-specific direction in function space, budgeted by a per-token KL divergence D. We derive a covert capacity C = D/ln 2 bits per token, a steganalytic detection threshold n gtrsim ln(1/α)/D tokens, and an architecture-specificity condition in which per-sample trait information scales with the squared representational overlap ρ² between teacher and student directions. At $D = 0.05$ nats the model gives $C = 0.072134$ bits per token, detection at $92.10$ tokens for a known-reference detector at 10^-2 false-alarm tolerance, and a cross-family sample-complexity penalty of a factor of $9$ at ρ_cross = 0.3 versus ρ_same = 0.9 (factor $81$ at ρ_cross = 0.1). The model predicts that content filtering preserves the channel whenever the trait direction is orthogonal to the filtered semantic subspace, and it converts empirical observations of brittleness and context dependence into testable quantitative conditions.",
  "abstract_markdown": "Subliminal learning — the transfer of a teacher model's behavioral traits to a student trained on semantically unrelated outputs such as number sequences — is documented empirically but lacks a quantitative channel model that explains why transfer succeeds within a model family and fails across families. This gap blocks any principled design of filters, training recipes, or audits for the increasingly common practice of training on model-generated data. We formalize subliminal learning as steganographic modulation of the teacher's output distribution: a trait is encoded as a low-amplitude perturbation along a teacher-specific direction in function space, budgeted by a per-token KL divergence $D$. We derive a covert capacity $C = D/\\ln 2$ bits per token, a steganalytic detection threshold $n \\gtrsim \\ln(1/\\alpha)/D$ tokens, and an architecture-specificity condition in which per-sample trait information scales with the squared representational overlap $\\rho^2$ between teacher and student directions. At $D = 0.05$ nats the model gives $C = 0.072134$ bits per token, detection at $92.10$ tokens for a known-reference detector at $10^{-2}$ false-alarm tolerance, and a cross-family sample-complexity penalty of a factor of $9$ at $\\rho_{\\mathrm{cross}} = 0.3$ versus $\\rho_{\\mathrm{same}} = 0.9$ (factor $81$ at $\\rho_{\\mathrm{cross}} = 0.1$). The model predicts that content filtering preserves the channel whenever the trait direction is orthogonal to the filtered semantic subspace, and it converts empirical observations of brittleness and context dependence into testable quantitative conditions.",
  "date": "2026-11-03",
  "first_published": "2026-11-03",
  "last_revised": "2026-11-03T00:00:00Z",
  "modified": "2026-11-03T00:00:00Z",
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  "url": "https://papers.qnfo.org/papers/subliminal-learning-as-architecture-specific-latent-space-steganography-a-channe",
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  "version_url": "https://papers.qnfo.org/papers/subliminal-learning-as-architecture-specific-latent-space-steganography-a-channe/v/1.0.0",
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    "creators": [
      {
        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
      {
        "title": "Subliminal Learning as Architecture-Specific Latent-Space Steganography: A Channel Model for Trait Transfer Under Distillation"
      }
    ],
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    "publicationYear": "2026",
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        "description": "Subliminal learning — the transfer of a teacher model's behavioral traits to a student trained on semantically unrelated outputs such as number sequences — is documented empirically but lacks a quantitative channel model that explains why transfer succeeds within a model family and fails across families. This gap blocks any principled design of filters, training recipes, or audits for the increasingly common practice of training on model-generated data. We formalize subliminal learning as steganographic modulation of the teacher's output distribution: a trait is encoded as a low-amplitude perturbation along a teacher-specific direction in function space, budgeted by a per-token KL divergence D. We derive a covert capacity C = D/ln 2 bits per token, a steganalytic detection threshold n gtrsim ln(1/α)/D tokens, and an architecture-specificity condition in which per-sample trait information scales with the squared representational overlap ρ² between teacher and student directions. At $D = 0.05$ nats the model gives $C = 0.072134$ bits per token, detection at $92.10$ tokens for a known-reference detector at 10^-2 false-alarm tolerance, and a cross-family sample-complexity penalty of a factor of $9$ at ρ_cross = 0.3 versus ρ_same = 0.9 (factor $81$ at ρ_cross = 0.1). The model predicts that content filtering preserves the channel whenever the trait direction is orthogonal to the filtered semantic subspace, and it converts empirical observations of brittleness and context dependence into testable quantitative conditions.",
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