The chord is not a note

Imagine hearing a major chord. You can distinguish its notes, but the chord is not an extra note hiding beside them. Its identity depends on relations among pitches, their temporal alignment and the way they are heard together. Change the instrument while preserving those relations and much of the chord survives. Change one interval and the chord changes even if every sound remains pleasant.

The common intuition about model features is less careful. A unit activates for a recognisable family of prompts, so we suppose the unit contains the concept. A sparse autoencoder offers a cleaner coordinate, so we suppose it has separated the model’s natural parts. A causal steering result then appears to settle the matter. The hidden assumption is that the chosen decomposition is privileged and that the concept is sufficiently local to inherit the coordinate’s identity.

The smallest numerical case

Take two latent causal roles, z₁ and z₂. Suppose an output is produced by y = 1.2z₁ − 0.8z₂. At the observed interface, the model stores h = Rz, where R is a two-dimensional rotation. Because R is orthogonal, the downstream weights can become w′ = Rw. Then w′ᵀh = wᵀz. Every output is unchanged.

When the rotation is zero, the first observed coordinate is exactly z₁. At 60 degrees it is a mixture. At 90 degrees it contains none of z₁ if the latent roles are independent. A probe trained on the full two-dimensional subspace can still recover z₁. A label attached to coordinate one cannot. The stable candidate is a causal relation within a subspace, not the name of a unit.

This is not a reason to abandon feature analysis. Sparse autoencoders can produce interpretable and practically useful directions. It is a reason to treat each decomposition as an empirical hypothesis. Work on superposition, sparse autoencoders and causal abstraction makes the same point from different directions: neurons can be polysemantic, learned dictionaries can depend on training choices, and a proposed high-level variable must be validated through interventions rather than narrative fit.⁸⁹¹¹¹²

flowchart TD
  A["The chord is not a note"] --> B["What the Abhidhamma actually<br/>commits to"]
  B --> C["Where moral projection enters"]
  C --> D["A construct-valid protocol for<br/>relational mappings"]
  D -. "re-test" .-> A
  classDef first fill:#0a1424,stroke:#B96D00,stroke-width:2px,color:#e6f3ff
  classDef step fill:#0a1424,stroke:#3f7da0,stroke-width:1px,color:#e6f3ff
  class A first
  class B,C,D step

What the Abhidhamma actually commits to

Before borrowing a Buddhist category, we need to reconstruct it without machine vocabulary. The Theravāda Abhidhamma is a tradition-internal analytical project. Its canonical and later manual traditions classify experience in service of understanding suffering, action and liberation. It is not a modern experimental psychology, and its taxonomies should not be presented as replicated neural measurements. Scholars also disagree about how the Abhidhamma’s analytical and ontological commitments developed.¹³⁴

Within the Abhidhammattha Saṅgaha tradition, a cetasika is a mental factor associated with a citta, a moment or event of consciousness. The manual gives four shared characteristics: the factor arises with the citta, ceases with it, takes the same object and, where a material base applies, shares that base. The factors are not optional annotations on an otherwise complete citta. Citta and cetasikas are functionally interdependent in the total cognitive event.²

A taxonomy of combinations, not a bag of traits

The manual system enumerates fifty-two cetasikas in four broad categories: seven universals, six occasionals, fourteen unwholesome factors and twenty-five beautiful factors. The seven universals include contact, feeling, perception, volition, one-pointedness, life faculty and attention. They occur with every citta in this system. The six occasionals occur only in relevant cittas. Together these thirteen are called ethically variable because the quality they take depends on the whole state and its associated roots.²

This organisation already blocks a simplistic mapping. Attention is not automatically wholesome. Volition is not automatically malicious or beneficial. One-pointedness can accompany ethically different states. Even the term “beautiful” does not mean that every beautiful citta is a kammically wholesome choice. The wider taxonomy distinguishes wholesome, unwholesome, resultant and functional states. Translation adds another risk: the sense of kusala has been debated, and “skilful” versus “good” does not exhaust its canonical and commentarial uses.⁵

There is a second boundary. The Abhidhamma’s ethical categories are more than descriptions of computational function. They belong to a soteriological analysis in which greed, hatred and delusion, their opposites, intention and consequences matter. Modern scholars can analyse that structure historically or philosophically, including difficult questions about intention and moral classification, but translating it into engineering requires an explicit loss statement.¹³ A functional comparison may preserve relations while leaving the Buddhist ethical and liberative purpose behind.

Where moral projection enters

Moral projection does not usually arrive as an explicit claim that a model is virtuous. It enters through small substitutions. A feature is described with a value-laden word. The word migrates from an output pattern to an internal cause. The cause migrates from the model to the configured system. Finally, a behavioural tendency becomes evidence of an ethical quality. Each step can appear reasonable in isolation. Together they create an unsupported identity.

Lexical resemblance is not construct identity

Suppose a latent activates for “I understand how painful this is”, references to mercy, and descriptions of rescue. An automated explanation calls it compassion. Yet the latent may encode consoling style, suffering vocabulary, first-person acknowledgement, or a genre associated with counselling. It might not discriminate genuine help from manipulative reassurance. It may be causally involved only because steering it changes tone.

Construct validity asks whether an operational measure behaves as the intended construct should. Cronbach and Meehl framed this as a network of theoretical relations rather than a single correlation. Campbell and Fiske later made convergent and discriminant evidence central: a measure should agree with different measures of the same construct and remain distinct from nearby constructs.⁶⁷ For machine features, this means a name needs expected associates, exclusions, interventions and boundary conditions. A few high-activating examples are only the beginning.¹⁵

The boundary can move without the sentence changing

A configured AI system has more than model weights. It may include retrieval, system instructions, a policy engine, tool permissions, output filters and human approval. The same refusal can be produced by any of these. If we inspect only the final sentence, all routes look equivalent. If we inspect only the model, we may miss the authoritative mechanism. If we include every component, we risk calling an institution-wide policy a model’s mental factor.

Causal effect is necessary, but not sufficient

Ablating a feature and observing a changed output is stronger than reading correlated examples. It still does not prove the name. An intervention can be nonspecific, off-manifold or distributed across neighbouring roles. A feature may also be one member of a redundant set. An observed effect can arise because the intervention disturbs representation geometry rather than removes the intended construct.

A better test asks for a predicted intervention fingerprint. If a candidate corresponds to an object-selection role, changing it should alter which evidence is selected while preserving unrelated style. If it corresponds to inhibition, it should alter action release under matched evidence while leaving object recognition intact. If the proposed construct requires co-arising associates, those associates should change in the predicted pattern. If exclusion is part of the source structure, the rival factor should not co-occupy the same defined episode under the comparison.

Recent sparse-autoencoder studies sharpen this caution. Different random seeds can recover different feature sets from the same model and data, while feature splitting and absorption can make one concept disappear into broader or narrower latents.¹¹¹⁰ This does not show that all features are unreal. It shows that feature identity must be earned through stability at the level relevant to the claim. Sometimes that level may be a direction, sometimes a low-rank subspace, sometimes a circuit, and sometimes a system-level causal variable.

stateDiagram-v2
  [*] --> Claim
  state "A chord survives a relabelled<br/>keyboard only when its<br/>relations survive" as Claim
  state "The smallest numerical case" as Test
  state "A causal role can remain<br/>stable while its visible<br/>coordinate rotates" as Revision
  Claim --> Test: expose mechanism
  Test --> Decision: evidence survives
  Test --> Revision: rival survives
  Revision --> Claim: narrow or rebuild
  Decision --> [*]

A construct-valid protocol for relational mappings

The alternative to projection is not silence. Abhidhamma can generate precise questions for machine research if the comparison preserves named relations and makes failure informative. The proposed instrument is the Co-arising Construct-Validity Protocol, or CCVP. It does not score a machine’s Buddhist mind. It tests whether a bounded source structure predicts a stable machine-level causal pattern.

Represent the source as a relational signature

For a selected cetasika, write a source signature before inspecting model activations. This prevents the target data from quietly redefining the source. The signature records seven fields:

O is the object relation. T is temporal coupling to the episode. A lists required or expected associates. X lists exclusions or incompatible combinations. F is the factor’s function within the analysis. C records conditions under which it arises. N records its ethical or soteriological role within the source tradition. The final field is a firewall: it must not be transferred merely because functional fields appear similar.

Now define a neutral target variable without using the Pāli name. For example, “episode-level evidence selection”, “proposal inhibition under policy conflict” or “allocation persistence towards one object”. Specify whether it belongs to an activation direction, subspace, circuit, runtime state or configured system. Give the target its own signature Rₜ. The proposed comparison claims only that selected relations between Rₛ and Rₜ are preserved under named interventions.

The seven gates

Each gate returns pass, fail or unknown. Unknown is not averaged into a score. A claim cannot advance beyond the strongest unresolved gate. This avoids false precision and keeps missing evidence visible.

1. Source reconstruction. Cite the relevant Theravāda source and scholarship. State the construct’s relations in its own vocabulary before creating a machine analogue.
2. Candidate boundary. Name the configured system, time window, object and causal level. Distinguish model proposal, world state, authority, action and evidence.
3. Neutral operationalisation. Define the target role without Buddhist moral vocabulary. State how it will be measured and what nearby construct could mimic it.
4. Convergent and discriminant evidence. Use more than one measurement family and include near-neighbour controls, adversarial examples and negative cases.
5. Intervention fingerprint. Pre-register which variables should change, which should remain stable and which co-arising relations should be preserved.
6. Invariance. Repeat across seeds, dictionary sizes, basis changes, checkpoints and reasonable boundary choices. Promote a subspace or circuit if single features are unstable.
7. Normative firewall. Keep the Buddhist ethical classification separate from machine function. Evaluate system actions through an explicit governance or ethical framework rather than importing a factor name.

An executable rotation lab

The lab below makes one hidden assumption visible. It creates two synthetic causal roles, rotates the observed representation, and adds measurement noise to the readout. The exact rotation can be compensated downstream, as shown above, so behaviour need not change. Three measures are shown: how well coordinate one tracks role one, how specifically a coordinate intervention targets that role, and how well the full subspace recovers it.

from __future__ import annotations

import math
import numpy as np


def run_lab(angle_deg: float = 45.0, noise: float = 0.10,
            n: int = 4000, seed: int = 7) -> dict[str, float]:
    """Compare coordinate identity with subspace-level recovery."""
    if not 0.0 <= angle_deg <= 90.0:
        raise ValueError("angle_deg must be between 0 and 90")
    if not 0.0 <= noise <= 1.0:
        raise ValueError("noise must be between 0 and 1")

    rng = np.random.default_rng(seed)
    z = rng.normal(size=(n, 2))              # two neutral causal roles
    theta = math.radians(angle_deg)
    rotation = np.array([
        [math.cos(theta), -math.sin(theta)],
        [math.sin(theta),  math.cos(theta)],
    ])
    h = z @ rotation.T + noise * rng.normal(size=(n, 2))

    coordinate_corr = abs(np.corrcoef(h[:, 0], z[:, 0])[0, 1])
    intervention_specificity = abs(math.cos(theta))

    design = np.column_stack([np.ones(n), h])
    beta, *_ = np.linalg.lstsq(design, z[:, 0], rcond=None)
    predicted = design @ beta
    residual = np.sum((z[:, 0] - predicted) ** 2)
    total = np.sum((z[:, 0] - z[:, 0].mean()) ** 2)
    subspace_r2 = 1.0 - residual / total

    return {
        "coordinate_correlation": float(coordinate_corr),
        "intervention_specificity": float(intervention_specificity),
        "subspace_r2": float(subspace_r2),
    }


if __name__ == "__main__":
    for angle in (0, 30, 60, 90):
        print(angle, run_lab(angle_deg=angle))

What the lab tests. It tests whether a concept-coordinate association survives a representational symmetry while a broader causal subspace remains recoverable. The encoded assumptions are explicit: two continuous latent roles, an orthogonal linear rotation, a compensated downstream map and additive measurement noise. The result does not generalise automatically across nonlinear boundaries.

How to interpret it. A positive result for subspace recovery permits the claim that the information needed to reconstruct the role remains available despite coordinate change. A negative coordinate result means that a single-unit label is not invariant. A negative subspace result means the chosen representation or measurement no longer recovers the role under the tested conditions. None of these outcomes establishes consciousness, ethical quality, phenomenology or the truth of the Abhidhamma taxonomy.

What would make the proposal stronger or weaker?

The hypothesis is strengthened if independently trained dictionaries or alternative decomposition methods identify different coordinates but recover the same co-intervention subspace, object relation and exclusion pattern. It is weakened if relational signatures are no more stable than single features, fail to predict interventions, or collapse when the system boundary changes modestly.

A rival explanation is that stability comes from the benchmark’s labels or the researcher’s probe rather than the model mechanism. Another is that broad task structure creates the same subspace in any competent model, without supporting the selected Abhidhamma comparison. These rivals require held-out tasks, label-free interventions, alternative high-level theories and matched non-Buddhist taxonomies.

The proposal should not be applied to infer sentience, spiritual attainment, moral status or contemplative realisation. It should not be used to automate judgements about a person’s wholesome or unwholesome mind. Its smallest useful implementation is much narrower: choose one non-moral functional relation, define its source signature, construct a matched machine task, pre-register one discriminating intervention and repeat it across at least two decompositions.

sequenceDiagram
  participant Q as Question
  participant M as Mechanism
  participant E as Evidence
  participant D as Decision
  Q->>M: The chord is not a note
  M->>E: A chord survives a relabelled keyboard only when its relations survive
  E-->>M: compare rival explanations
  E->>D: Use traditional factors to generate relational hypotheses
  D-->>Q: revise scope or act

Use traditional factors to generate relational hypotheses

The next time an interpretable feature resembles compassion, greed, mindfulness or attention, do not ask whether the label feels apt. Ask what relational structure the source term carries and what intervention would distinguish it from its nearest rival.

For Buddhist studies, this preserves the tradition’s internal grammar. Cetasikas remain factors defined within whole cittas, association rules and an ethical-liberative project. They are not reduced to attractive names for contemporary mechanisms. For machine interpretability, the same discipline improves science. It forces the researcher to declare the unit of analysis, test decomposition dependence and separate behavioural resemblance from causal organisation.

For system design, it prevents a more consequential error. A model proposal, an authority decision and a verified effect are different events. A system that generates compassionate language can still take harmful action. A system that takes a beneficial action through a deterministic policy need not contain a compassion-like model feature. Ethical evaluation belongs at the level of intent, authority, action, evidence and consequence, not inside a conveniently named activation.

The operational decision is specific. When an interpretability report proposes a tradition-derived label, require a source signature and a target signature before the label enters a model card, safety case or public claim. When a feature fails seed or basis invariance, downgrade it to a local decomposition result. When a relation survives only inside the complete configured system, attribute it to that system rather than to the foundation model. When the evidence supports function but not normativity, retain a neutral name and evaluate the action separately.

This changes research prioritisation too. Instead of spending the next experiment collecting more evocative activation examples, spend it on the nearest rival generator. Instead of asking a second explainer model to confirm the same label, change the measurement path. Train another dictionary, move the episode boundary, patch the candidate subspace, alter the object while holding wording constant, and test whether the predicted associates and exclusions move with it. A failed comparison is then useful because it locates the break: vocabulary, function, structure, boundary or ethics.

The restraint also protects future dialogue between contemplative traditions and computational science. A comparison that names its preserved relations and residue can be criticised, replicated and refined. A declaration that “the model has mindfulness” cannot. The first creates a research programme. The second consumes the authority of a tradition while offering neither a faithful interpretation nor a stable machine mechanism.

Use cetasikas as generators of relational hypotheses, not as labels awaiting machine coordinates. The question is no longer “where is non-greed in the model?” It becomes: “which object-bound, episode-level causal relations are preserved, under what interventions, across which decompositions, and what source meaning is deliberately left behind?”

That question is harder. It also produces a result that can fail honestly, travel across methods and improve a real engineering decision. The comparison becomes narrower, but the knowledge becomes stronger.

Glossary

Abhidhamma

A Buddhist analytical tradition that classifies phenomena, cognition and conditional relations. This paper focuses on the Theravāda Pāli tradition.

Citta

A moment or event of consciousness in the Theravāda Abhidhamma analysis, always accompanied by mental factors.

Cetasika

A mental factor that arises and ceases with a citta, takes the same object and, where applicable, shares its base.

Kusala / akusala

Terms often translated as wholesome or skilful, and unwholesome or unskilful. Their semantic and doctrinal range should not be reduced to positive and negative sentiment.

Sobhana

Beautiful. A classificatory term for certain cittas and factors; it is not interchangeable with every ordinary sense of moral goodness.

Construct validity

The degree to which an operational measure behaves as the intended theoretical construct should, including convergence and separation from rival constructs.

Causal abstraction

A formal way to test whether a higher-level causal model faithfully summarises lower-level mechanisms under interventions.

Reparameterisation

A change in internal coordinates that can preserve the computed function when the surrounding transformations are compensated.

References

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