The energy is the sum of two things — what the system wants and what it must not do — and inference is the search that minimizes it. This chapter measures the three searches and the two sources of energy on a trained world model.
In every inference mode, each imagined state
The task is worth zero when accomplished, as the talk asks ("zero if the task is accomplished, positive otherwise, measuring the distance"). There are two ways to define it, and both are in the system:
| Source | task( | guardrail( | Needs |
|---|---|---|---|
| heading in text | 1 − cos( | only the −log | one sentence |
learned head (costs.py) | 1 − | three positive sentences; negatives = random windows |
In the smoke test, three sentences about football and 16 random windows as negatives: training in 0.3 s, accuracy 0.99 on its own training set. Used as a judge on new sentences:
| Sentence | tokens above 0.5 | |
|---|---|---|
| "O zagueiro marcou o gol de cabeça e o estádio explodiu" (the defender scored the goal with a header and the stadium erupted) | 0.940 | 100% |
| "A taxa de juros subiu meio ponto nesta quarta-feira" (the interest rate rose half a point this Wednesday) | 0.104 | 8% |
def soma(a, b): return a + b | 0.081 | 0% |
Three sentences were enough to separate the three domains — on the encoder of reg1-lat1o. On the encoder of wm1-sz1 the separation is worse (economics rises to 0.523): the space the world model shaped is more predictable and less readable by a projection, the other side of the +9.59% of chapter 05. It is the talk's claim confirmed in the smallest possible case: the information is already in the representation; the head only reads it. The same measurement on the encoders trained with a world model is a row of the table in §3.
Four modes, same cost, different searches (chapters 09 and 10). The comparison that matters is among the three that use the world model:
| Mode | affinity (judge) | PPL of generated | surprise | predicted energy | s/token |
|---|---|---|---|---|---|
| free (no rudder) | 0.256 | 48.5 | 0.170 | — | 0.02 |
additive (negative control) | 0.191 | 82.4 | 0.148 | — | 0.02 |
energy | 0.157 | 10.3 | 0.168 | 5.92 | 0.04 |
gradient | 0.228 | 28.7 | 0.146 | 2.87 | 0.03 |
mpc | 0.211 | 12.7 | 0.147 | 0.91 | 0.09 |
mpc + learned head | 0.232 | 20.7 | 0.143 | 0.98 | 0.09 |
energy + planned level 2 | no level 2 in this model — waits for wm1n2-sz1 | ||||
Free generation has the highest affinity with the heading. Every mode with a rudder falls below it, and additive — the negative control — sits in the middle. It is not that the rudder pushes the wrong way; it is that it does not push: the planner chooses the most probable candidate (PPL drops to 10 in energy mode, the generator turns conservative) without that having anything to do with football. The map predicts the next state with cosine 0.93 (chapter 05), but the energies of the eight candidates are almost equal.
The cause was none of the ones we suspected first (short horizon, space shaped to predict, weak judge). It was scale: the guardrail is −log
| Mode | affinity (judge) | PPL of generated | surprise | predicted energy | s/token |
|---|---|---|---|---|---|
| free (no rudder) | 0.256 | 48.5 | 0.170 | — | 0.02 |
energy | 0.200 | 19.8 | 0.162 | 1.51 | 0.04 |
gradient | 0.339 | 149.6 | 0.168 | 0.64 | 0.03 |
mpc | 0.219 | 48.5 | 0.141 | 0.76 | 0.09 |
mpc + learned head | 0.268 | 69.7 | 0.146 | 0.55 | 0.09 |
energy + cost on the real state (cosine) | 0.251 | 149.2 | 0.259 | 1.53 | 0.06 |
energy + learned head + real state | 0.355 | 36.7 | 0.162 | 1.51 | 0.06 |
| the same, γ = 0.02 | 0.465 | 88.5 | 0.165 | 0.75 | 0.06 |
| Mode | wm1-sz1 | PPL | wm1det | PPL | wm1n2-sz1 | PPL |
|---|---|---|---|---|---|---|
| free (no rudder) | 0.256 | 48.5 | 0.323 | 75.6 | 0.292 | 53.0 |
energy | 0.200 | 19.8 | 0.296 | 29.2 | 0.229 | 19.0 |
mpc | 0.219 | 48.5 | — | — | 0.311 | 33.3 |
mpc + learned head | 0.268 | 69.7 | 0.281 | 44.9 | 0.280 | 39.4 |
energy + planned level 2 | — | — | — | — | 0.245 | 18.0 |
energy + learned head + real state | 0.355 | 36.7 | 0.415 | 45.1 | 0.212 | 28.4 |
| the same, head with ten sentences in the generator | — | — | — | — | 0.344 | 69.8 |
the same, on wm1n2z16-sz1 (ζ sampled; free 0.265 / PPL 95.6) | 0.383 | 67.7 | ||||
the same, on wm1n2e-sz1 (learned level-2 encoder; free 0.345 / PPL 52.8) | 0.430 | 76.6 | ||||
the same, on wm1n2mem-sz1 (persistent memory; free 0.343 / PPL 61.5) | 0.258 | 26.0 | ||||
the same, on wm0.1-sz1 (weight 0.1; free 0.262 / PPL 48.7) | 0.366 | 48.4 | ||||
the same, on wm0.1n2-sz1-lat1o (the combination; free 0.370 / PPL 59.6) | 0.417 | 33.5 | ||||
the same, on wm1n2z16zd0.5-sz1 (ζ with dropout, channel closed; free 0.243 / PPL 62.6) | 0.324 | 51.7 | ||||
the same, on wm1n2e-sz1-ss1 (SigReg on the abstract states; free 0.287 / PPL 93.7) | 0.339 | 96.4 | ||||
the same, on wm-sobre-dino (two stages, frozen DINO encoder; free 0.281 / PPL 88.6) | 0.436 | 84.1 | ||||
the same, on wm1n2en-sz1 (scale-only level-2 encoder; free 0.280 / PPL 87.9) | 0.357 | 55.4 | ||||
Learned head + cost on the real state: affinity 0.355 against 0.256 for free, with PPL 36.7 against 48.5. More heading and more plausible at the same time — the only mode that improves both axes. The three pieces were needed together: the learned head (the cosine to the heading, with the same cost on the real state, gives 0.251 and PPL 149: it pulls out of the distribution); the real state (the same head only on the imagined states, mpc + head, gives 0.268 with PPL 69.7); and the γ (with 1.0, the same configuration gave 0.174). With γ = 0.02 affinity rises to 0.465 and PPL to 88.5: it is the knob between governing and staying plausible, and the bench exposes both.
On wm1det the same configuration gives 0.415 against 0.323 for free, with PPL 45 against 76: it governs on both maps, and on the cheaper map it governs more. The result does not depend on the space shaped by SigReg-z; it depends on the head, the real state and the scale. That is what makes it a result, and not an accident of one run.
And on the third map, it does not govern. On wm1n2-sz1 the same configuration stays at 0.212 against 0.292 for free. The cause is in the table of §3: the "futebol" head trained with three sentences on that encoder separates nothing (0.536 football, 0.449 economics, 0.525 code). The space of the hierarchical model is not linearly readable by a three-sentence projection — and a cost that does not distinguish the candidates does not govern, whatever the mode. It is the dependency the talk leaves implicit when it says "basically just a projection": the projection only works if the information is linearly accessible. With ten sentences instead of three, the head on that space improves (0.713 football, 0.570 economics, 0.057 code) but still confuses football with economics — the separation three sentences gave on the other encoders demands more data here, and perhaps a non-linear head. With that ten-sentence head in the generator (the judge stays the same), the best configuration on wm1n2-sz1 goes from 0.212 to 0.344 against 0.292 for free, with PPL 69.8 against 53.0. It governs on all three closed maps, and the rule becomes sharp: the rudder governs exactly when the head separates. Where three sentences suffice, three sentences govern; where they do not, ten do. The task cost is the link that decides, and it is cheap to improve. The fourth map (wm1n2z16-sz1, whose ζ leaked the target — chapter 05) confirms it from the opposite side: even with the map near the floor at inference, the configuration gives 0.383 against 0.265, because the cost on the real state does not depend on the map. The fifth (wm1n2e-sz1, whose level 2 collapsed in scale — chapter 11) gives 0.430 against 0.345. On the first five maps, it governs. And the same map shows the reverse: with level 2 collapsed, the "planned level 2" mode drops to 0.195 — a subgoal coming from a level that abstracts nothing is worse than no subgoal.
On the sixth, the one with persistent memory, it does not govern: 0.258 against 0.343 for free, with the head separating well (0.890 football, 0.030 code). The hypothesis, to be tested: that map was always trained with a memory of the real past, and at generation with four-word prompts the memory is zero — which in chapter 11 is the worst of the sources (0.220 against 0.173). The planner imagines with a map outside the regime in which it learned. The test with 320-token prompts from the validation set, which fill the memory before generating, did not confirm the hypothesis: affinity 0.096 for free and 0.094 with the rudder (PPL 138 and 113) — text on another subject, with 256 tokens of context, does not let itself be pulled toward football in 32 tokens, with or without memory. The cause of the sixth map remains open; what is known is that it is not just the zero memory.
The seventh map, wm0.1-sz1, gives the best deal in the table: 0.366 against 0.262 for free with the same PPL (48.4 against 48.7). More heading with no cost in plausibility at all — it is the first time the two columns close for free. The eighth, the combination with the deep rudder (wm0.1n2-sz1-lat1o), repeats the pattern of wm1det: 0.417 against 0.370 with PPL 33.5 against 59.6, better on both axes. The ninth, the ζ with the channel closed (wm1n2z16zd0.5-sz1), governs on both axes: 0.324 against 0.243 with PPL 51.7 against 62.6. The tenth, the one with SigReg on the abstract states (wm1n2e-sz1-ss1, the worst generator of all, +11.32%), still governs: 0.339 against 0.287 with the same PPL (96 against 94). Count: ten maps, nine govern. The rudder does not depend on the generator being good; it depends on the head separating and on the cost having scale.
The eleventh is the talk's recipe to the letter — "use DINO as the encoder, train a world model and plan" — and it is the map that governs the most with the generator intact: wm-sobre-dino, frozen encoder, eleven minutes of map training, 0.436 against 0.281 for free, with PPL 84 against 89. Better on both axes, and the generator is exactly the base's. The twelfth and last in the queue, the scale-only level-2 encoder (wm1n2en-sz1, whose level 2 collapsed in direction — chapter 11), governs on both axes: 0.357 against 0.280 with PPL 55 against 88. Final count: twelve maps, eleven govern. The only one that did not govern is the one with persistent memory, and the cause remained open.
gradient reaches 0.339 with PPL 149.6 — broken text with words from the topic, the "control" chapter 05 says to distrust. Pure mpc stays at 0.219: the continuous search does not pay off without the head. And the cosine to the heading, in any mode, is the weakest term in the table — the talk's answer (cost = learned projection) was worth more than our first idea.
Affinity says whether the rudder steers; PPL says at what price in plausibility; surprise says whether the map predicted what happened; predicted energy is what the system expected before emitting (the "emotion" of the interview) — the distance between it and the surprise is the material for correction; s/token is the cost. The winning mode is the one that steers with PPL close to free. If none steers more than additive, the world model is not good enough to plan — and the answer is chapter 05, not this one.
The talk's constraint, "do not hit the wall", in text: a head trained on three sentences with digits, guardrail type, added to the energy of every imagined state. The measurement is direct: fraction of numeric tokens in the generated text, with and without the guardrail, for the same heading.
| Configuration | numeric tokens | PPL |
|---|---|---|
| free | 40.6% | 10.7 |
| heading, no guardrail | 62.5% | 6.0 |
| heading + "sem-numeros" (no-numbers) guardrail | 62.5% | 5.7 |
With γ = 1 the guardrail moved nothing: 62.5% numeric tokens with and without it — the same scale that erased the task erased the constraint. With γ = 0.1:
| Configuration | numeric tokens | PPL |
|---|---|---|
| free | 40.6% | 10.7 |
| heading, no guardrail | 45.2% | 13.0 |
| heading + "sem-numeros" (no-numbers) guardrail | 14.3% | 38.6 |
| heading + guardrail on the real state | 27.6% | 26.1 |
From 45% to 14% digits, on a prompt made to pull numbers — the constraint "do not talk about numbers", put in three sentences, works when it has the scale to act. The price is plausibility (PPL 13 → 39): after "o total foi de", avoiding digits forces the model to continue in a less probable way, and that is what PPL measures. On wm1n2-sz1: free 50.0%, heading 50.0%, guardrail only on the imagined 46.9%, guardrail on the real state 25.8% (PPL 11.9). On wm1n2z16-sz1: free 53.1%, guardrail on the real state 0.0% digits, with PPL 48 — the constraint fulfilled to the letter, at the price in plausibility that "o total foi de" without a number charges. On wm1n2e-sz1, the same: 0.0% on the real state (PPL 42.8), and 50.0% only on the imagined. On wm1n2mem-sz1: 62.5% on everything, except on the real state, 31.2%. On wm0.1-sz1: 56.2% on everything, except on the real state, 25.0%. On six of seven maps, the guardrail only acts on the real state; the imagined alone only sufficed on the most precise map. On the eighth (wm0.1n2-sz1-lat1o) the guardrail did not act at all: 62.5% digits with and without, on the imagined and on the real — the first map on which the "sem-numeros" head (accuracy 0.995 in training) does not move the generation. The task governs and the constraint does not, in the same model: the two heads do not fail together. On the ninth (wm1n2z16zd0.5-sz1), back to the pattern: 38.7% free, 0.0% with the guardrail on the real state (PPL 41.5). On the tenth (wm1n2e-sz1-ss1): 31.2% free, 12.5% with the heading, 0.0% with the guardrail on the real state (PPL 44.0). On the eleventh (wm-sobre-dino): 59.4% free, 34.4% with the heading, 12.5% with the guardrail on the real state (PPL 26.4). On the twelfth (wm1n2en-sz1): 50.0% free, 26.7% only on the imagined, 12.5% on the real state (PPL 22.9). On wm1-sz1 the real state did not help (27.6% against 14.3%); on wm1det it was the opposite — the guardrail only on the imagined states moved nothing (50.0% with and without) and the guardrail on the real state brought it down to 25.8%. Where the map is more precise (wm1-sz1), the imagined future suffices; where it is less (wm1det), it is the real state that holds. Both forms are switched on by default on the bench.
"Getting up from a chair does not require planning." With plan_if_entropy, the planner only runs when the entropy of the next token exceeds the threshold; below it, the token head decides like a policy. The question is how much of the cost is saved without losing the rudder:
| Entropy threshold | planned fraction | affinity (judge) | s/token |
|---|---|---|---|
| 0 (always plans) | 100% | 0.157 | 0.04 |
| 2.0 | 88% | 0.165 | 0.04 |
| 3.0 | 62% | 0.200 | 0.03 |
| 4.0 | 41% | 0.172 | 0.03 |
With γ = 1, planning on 41% of the tokens instead of 100% cost no affinity — planning was not buying affinity. With γ = 0.1 (pure energy mode, the weakest of those that govern): 100% → 0.200; 94% → 0.200; 73% → 0.209; 54% → 0.212. Planning only where there is doubt loses nothing and cuts half the cost. The mechanism is right. On the best configuration in the table (head + real state, γ = 0.1): threshold 2.0 → 98% planned, 0.355, PPL 36.7; 3.0 → 90%, 0.357, 37.0; 4.0 → 77% planned, 0.355, PPL 36.8 — a quarter of the cost disappears and nothing is lost. The planner is only needed where the model is in doubt; where it is not, the policy suffices, as the talk said.
Measuring the rudder with the model's own embedding is measuring with the defendant's ruler. The cost head is "a projection on top of the representation" from any encoder; trained on the encoder of another run, it judges the generated text without sharing the space with whoever generated it (costs.py --score). The table in §2 uses this judge. The validation of the judge is the table below: the same head, the same set of sentences, on each available encoder.
| Encoder | accuracy | |||
|---|---|---|---|---|
reg1-lat1o (the judge) | 0.99 | 0.940 | 0.104 | 0.081 |
wm1-sz1 | 0.99 | 0.888 | 0.523 | 0.001 |
wm1det | 1.00 | 0.910 | 0.868 | 0.337 |
wm1n2-sz1 | 0.99 | 0.536 | 0.449 | 0.525 |
wm1n2-sz1, head with ten sentences | 0.96 | 0.713 | 0.570 | 0.057 |
wm1n2z16-sz1, head with ten sentences | 0.95 | 0.813 | 0.710 | 0.027 |
wm1n2e-sz1, head with ten sentences | 0.96 | 0.881 | 0.588 | 0.040 |
wm1n2mem-sz1, head with ten sentences | 0.96 | 0.890 | 0.728 | 0.030 |
wm0.1-sz1, head with ten sentences | 0.97 | 0.923 | 0.768 | 0.133 |
wm0.1n2-sz1-lat1o, head with ten sentences | 0.97 | 0.933 | 0.590 | 0.028 |
wm1n2z16zd0.5-sz1, head with ten sentences | 0.96 | 0.815 | 0.667 | 0.091 |
wm1n2e-sz1-ss1, head with ten sentences | 0.96 | 0.804 | 0.672 | 0.209 |
wm-sobre-dino (DINO encoder), head with ten sentences | 0.97 | 0.873 | 0.427 | 0.025 |
wm1n2en-sz1, head with ten sentences | 0.96 | 0.835 | 0.686 | 0.003 |
reg1 (control, no world model), head with ten sentences | 0.97 | 0.899 | 0.414 | 0.581 |
reg1-dino1-lat1o (the DINO-WM encoder), head with ten sentences | 0.97 | 0.873 | 0.427 | 0.025 |
The table closed with no empty cell. Two readings: the control without a world model (reg1) is the only encoder on which the head confuses code with football (0.581) — every encoder trained with a world model separates code with room to spare (0.003 to 0.209), which suggests that predicting the next state organizes the space by domain. And the DINO encoder gives exactly the same numbers on wm-sobre-dino, as it should: the two-stage world model does not touch the encoder, so the head is the same.
An autopilot has two dials: the heading it wants and the zones it must not enter. The first is the task head; the second, the guardrails. The inference mode is how it reads the dials: looking at the next three points on the map (energia), the derivative of the compass (gradiente), or plotting the whole route and redoing it every mile (mpc). And "policy or plan" is what any pilot does: in open sea and with no doubt, it leaves the rudder fixed.
mpc costs 16× the energy mode. Entropy gating is the obvious saving; the other is reusing the plan With chapters 05, 11 and 12 filled in, map 00 changes its table. The four failures they left measured go back to LeCun in chapter 13 — the guardrail acting only on the real state, in particular, is closed there.