Interpretability · main findings
Embodied Cognition in Transformers
Image schemas, metaphorical mappings, and substrate coupling in language models trained on text alone.
Language models write about rising spirits and heavy hearts, arguments that collapse and plans that move forward, as if the bodily scaffolding under those phrases were available to them. How does a system trained on nothing but text come by that?
Pythia 70M–1.4B · GPT-2 medium · Llama-3.2-1B · GloVe, word2vec, fastText as controls. Full write-up with every control and every failed hypothesis: mac-n.github.io/lakoff-schemas-in-transformers · code, raw outputs, pre-registrations
1 · The questionLakoff's schemas: the body as the source of abstract thought
George Lakoff and Mark Johnson argued that abstract thought is structured by image schemas: UP-DOWN, IN-OUT, BALANCE, FORCE, PATH. Recurring patterns of bodily experience, projected metaphorically into abstract domains. HAPPY IS UP. MORE IS UP. DIFFICULTY IS A BURDEN.
From there a familiar argument runs: LLMs have no body. No body, no image schemas; no image schemas, no embodied cognitive structure; so LLM meaning is structurally defective.
My hypothesis: as well as explicit descriptions of the physical world, human language encodes a lot of implicit information about having a body, and a model that compresses human language hard enough reconstructs embodiment as a projection from it.
So: take the most foundational metaphor Lakoff describes and test whether it transfers to the transformer, or whether the concepts come apart.
2 · First experimentUP is HAPPY, for transformers too
Take UP words (high, rise, peak, climb) and DOWN words (low, fall, valley, descend), run each through the model as a bare single token, subtract the mean activations. That single-word contrast vector, added to the residual stream during generation, makes the output happier.
- Dose-responsive, linear in steering strength, symmetric around zero.
- Works from every injection layer tried; beats matched random directions and meaningful non-schema contrasts (concrete/abstract, animate/inanimate, noun/verb) by roughly 2×.
- A frequency confound nearly killed it: two independently built UP vectors came out at cosine −0.99. Stripping the frequency axis made them agree (+0.57) and amplified the effect 5–13×. The confound was a curtain in front of the signal.
+0.69
Δvalence at L14 after UP-steering, Pythia 410M, α=4
−0.03
matched random direction
Downstream projections after UP-steering at L12 (blue) vs random control (grey). UP also shifts magnitude (MORE IS UP).
3 · The objectionOf course UP is HAPPY in the text
The corpus was written by embodied humans who think in these metaphors; a model that compresses their language inherits their shadow. Steering shows the direction is causally live inside the model, not that it is anything more than the corpus's fingerprint.
The way to answer that is not to argue with it. It is to keep going and see where the structure stops matching the corpus. The next three findings are where it stops.
4 · The confound that became the findingGrammar organises itself around the schemas
Every attempt to build a schema contrast came back correlated with UP. The word lists were full of comparatives and superlatives: higher, lowest, brighter, strongest. If UP tracks -er and -est wherever they appear, UP is not a region of word-space. It is an operator on other concepts, which is Lakoff's actual claim.
Seven morphological operators (-ing, -ed, -s, -er, -est, un-, re-), built as pair differences and projected onto all eight schema axes after anisotropy and frequency stripping:
- All seven sink onto BALANCE-negative (−0.09 to −0.66): inflected forms are marked forms, departures from a base.
- -ed and re- map onto FORWARD-BACK negative at every probed layer: the past is behind you; repetition goes back along the path.
Operator × schema projections, Pythia 410M, after anisotropy and frequency stripping.
5 · The keystoneword2vec doesn't do this: the schema system is learned, not inherited
If the schema–morphology geometry were just how English distributes, anything that learns the distribution should have it. Same pairs, same axes, same stripping, run on GloVe, word2vec and fastText:
−0.38
-ER × BALANCE, Pythia L8–20
- Static spaces agree with each other about inflection (r = 0.71–0.77) and disagree with the transformer (r = 0.20–0.36).
- The split lands exactly where it is informative: derivational operators (un-, re-) replicate across all substrates, so their position is in the text for anything to read. It is specifically inflection that the transformer relocates onto the schema system.
- The distribution was available to GloVe and word2vec too. They built something else with it. The transformer instantiated this structure during learning: a cognitive primitive, not a statistic.
GloVe (left) vs Pythia L12 (right). The inflectional BALANCE sink (bottom row) exists only in the transformer.
6 · Watching it get builtPartly trained in, mostly computed
The inflectional sink is faintly present in Pythia's embedding matrix before any layer runs (−0.13), is computed to full strength between layers 2 and 4 (−0.23 to −0.47), and plateaus by layer 8.
The one caveat this claim still owes: the substrates differ in corpus, objective and tokenisation as well as architecture, and inflection is where tokenisation could matter. A matched-corpus, matched-vocabulary baseline is the outstanding control.
-ER × BALANCE across depth.
7 · Is it a system?The schemas couple to each other exactly as the theory predicts
Lakoff's claim was never about isolated correspondences: the schemas form a coherent system. So the predictions were written down first. Six couplings the embodied logic implies (UP↔BALANCE, UP↔LIGHT-DARK, FORWARD-BACK↔PATH, FORCE↔DIFFICULTY…), then the full 8×8 cosine matrix at every layer.
+0.21
mean coupling, the 6 predicted pairs (all positive; 5 of 6 at ≥23 of 24 layers)
+0.004
mean coupling, the 22 unpredicted pairs
Nothing in the measurement knows which pairs the theory picked. The elevation lands on exactly those six. And one schema kept drawing attention to itself: the strongest coupling runs through BALANCE, every morphological operator sinks onto it. The system had a centre of gravity.
Predicted (blue) vs unpredicted (grey) inter-schema couplings across the 24 layers of Pythia 410M.
8 · What BALANCE is readingThe model's concept of balance is coupled to its own physiology
Inflected forms are marked forms, so BALANCE seemed to be reading deviation from a norm. Pythia continuously computes a norm. What if BALANCE were coupled to the norm of the residual stream itself?
- Inflected forms have lower residual norms than their bases; per-pair correlation between norm-drop and BALANCE projection r = +0.86 to +0.97 at layer 4.
- cos(BALANCE, norm-direction) = +0.64 to +0.77, measured with a held-out estimator that excludes both the suffix pairs and the BALANCE words. Replicates from Pythia 70M to 1.4B.
- Other schemas lean on the norm carrier in a graded order; BALANCE leans hardest.
No sentence in the Pile describes the L2 norm of a hidden state. It is a quantity the model processes on every forward pass, perhaps as close to an interoceptive signal as a transformer has. The schema at the centre of gravity of the system is anchored on it.
Per-suffix norm displacement (top) and BALANCE projection (bottom) across layers, four Pythia sizes.
9 · The replication that failedEach architecture anchors BALANCE on a different signal
GPT-2 uses LayerNorm like Pythia; Llama uses RMSNorm. If the coupling were about normalisation as such, GPT-2 should share it. It doesn't. But GPT-2 has something else: BALANCE tracks attention entropy, the diffuseness of the model's attention. Pre-registered, confirmed on fresh prompts, BALANCE-unique (orthogonalising against the other seven schemas makes it stronger), negative at every layer from 0 to 17. Llama shows the same coupling at layers 5–7, confirmed on a checksum-frozen third prompt set.
| Pythia (LayerNorm) | GPT-2 (LayerNorm) | Llama (RMSNorm) |
|---|
| BALANCE ↔ residual norm | +0.64 to +0.77 (held-out) | no stable coupling | no stable coupling |
| Inflectional Δ-norm | large, uniformly negative | no uniform displacement | no uniform displacement |
| BALANCE ↔ attention entropy | ~0 (null on fresh prompts) | −0.15 to −0.32 (L0 to L17) | −0.14 to −0.20 (L5 to 7) |
Three model families, one concept, two different computational carriers. Each model has organised the same schema around a signal intrinsic to its own processing, and the signal differs by architecture. A candidate case of multiple realizability.
10 · Which way does causation run?Substrate shapes concept, not the reverse
Concept → operation: nothing specific. Steering on the BALANCE direction does not move attention entropy beyond what a matched-magnitude random push does. BALANCE is not a control knob for entropy.
Operation → concept: confirmed. Sharpening attention via temperature specifically shifts the BALANCE projection (GPT-2 L3: slope −0.0083, CI [−0.0088, −0.0078], Spearman −1.00), with BALANCE moving more than all seven other schemas. The pre-registered specificity bar was four. Same at L8.
The confirmed direction is the one embodied cognition predicts: substrate state shaping concept geometry, the way the vestibular system shapes balance perception rather than the reverse.
And you can watch the coupling arrive. In Pythia's public training checkpoints BALANCE is anti-coupled to norm at step 512 (cos −0.61). By step 4,000 it has flipped to +0.64, and it stays there for the rest of training. It doesn't drift in. It inverts, early, and locks.
11 · ConclusionsEmbodied-style structure without a body
- The schemas are there, recoverable from bare single-word activations, and one of them executes a causal cross-domain mapping: steering UP makes the model happier.
- The system is learned, not inherited. The schemas couple to each other in the configuration the theory predicts, and extend their reach into inflectional grammar in a way that the same distributional evidence does not produce in static embedding spaces.
- Its centre of gravity, BALANCE, is coupled to the model's own computational dynamics, causally in the operation-to-concept direction, and the carrier varies by architecture: residual norm in Pythia, attention entropy in GPT-2 and Llama.
Embodied cognition can be disaggregated: bodily origin, bodily implementation, and embodied-style structure. The third can exist without the first two, and parts of it end up anchored on whatever substrate the system actually has. Arguments that LLM meaning is defective because LLMs are disembodied need a premise these results take away. And there is an angle on the grounding problem: a concept coupled to the model's running physiology is anchored on something that isn't text.
Open edges, stated plainly: the mechanism behind these geometries is unknown (all eight mechanistic hypotheses tested died, 0 for 8); the causal picture is one confirmed direction, not a settled loop; the matched-corpus baseline for the static comparison is still owed. Next: carrier-first search, and a Mamba model with no attention at all — does entropy coupling disappear, or does the model find a third carrier?
Full write-up → · Every experiment script, raw output, pre-registration and lab-notebook volume, including the failures
Niamh McCombe, 2026. The research was conducted as a collaboration between the author and Claude (Anthropic) across many sessions.