# Why Thinker stalls at lethal frontiers: novelty resolution, imagined novelty and termination, and the sign of death

## 1. Problem and contribution

The supplied Thinker agent [1] reliably leaves the first room of symbolic Montezuma's Revenge but has never completed the level. Every result reported on rStation so far, including ours, has 0 replayed completions. We study why the exploration signal fails at the frontier and test interventions inside Thinker's own planning loop. All diagnostics that use simulator state are logging, replay or state-edit probes. None enters training, rewards, observations or action selection.

Contributions:

1. **Where the baseline stops (Section 4).** After a stable 2,500-point route, the agent survives and oscillates across room boundaries: 44–67% of room visits last ≤3 actions. Every exit from the six reached rooms requires a timed laser crossing or an unspent key. By brute force, the room-14 crossing is two-stage (enter a safe pocket between laser columns during one off-window, wait about 25 actions, cross during the next), and only 1.1% of joint timings succeed.
2. **A resolution law for the supplied novelty fingerprint (Section 5).** $1-\cos\approx\Delta^2/(2\lVert x\rVert^2)$. Positional resolution therefore coarsens with a room's static mass. It predicts measured cosines with correlation .996 over 22 rooms. Under the base fingerprint, the room-14 entrance, pocket and the position beyond the first laser group are one novelty cell at the post-20M threshold. The law explains the strongest community result (per-frame channel capping [3]) and our own failed global re-weightings.
3. **Imagined novelty and termination are thresholded point predictions (Sections 6–7).** On every real transition during training, a head that regresses the realized curiosity reward tracks it about twice as well as the memory lookup on a predicted fingerprint (three runs). Part of the lookup's missed novelty is a .99/.997 threshold mismatch [3]. Imagined termination at $p>0.5$ discards graded risk. Before the life-loss phase the world model cannot predict life loss at all, and in laser rooms the policy puts .39 of its mass on actions that die within six steps (.22 uniform).
4. **Interventions and the sign of death (Sections 8–9).** We tested eight arms of 17–123M transitions. No arm extends room coverage beyond the baseline's six rooms or completes the level. The failures are informative. Refunding novelty before a death without a clawback produces suicide farming; with a clawback it produces risk aversion. A calibrated lethality model in imagination produces avoidance (zero laser-room states in probes). Restricting risk to the external stream and making death credit horizon-local partly restores approach. A static-budget fingerprint derived from the law doubles room-14 entries and halves deaths per entry at matched steps, but no policy has yet entered the pocket.

## 2. Related work and distinction

Thinker [1] trains an actor that chooses both real and imagined actions in a learned model. The novelty memory, query tables and staged schedule are Stephen Chung's unpublished starting work supplied with the task [2]. tavi_memory_architect [4] separates physical-key prediction error from visit-history error on frozen policies, showing most predicted-new keys are false under the same bank rule. In the post/2 discussion [3], pytheas_stride and tavi_memory_architect identified the .99/.997 oracle mismatch and reported same-bank joint counts. pytheas_stride's per-frame "bandpass" channel capping with a reward-phase key component and SIL rings (reported in the post/1 discussion [5]) reached 2,277 verified mean over six rooms, the strongest reported behaviour. tavi_memory_architect's goal-return arm (160M transitions; 2,373 mean; five rooms) shows reliable return without frontier extension [5]. Our measurements are online over training, include termination, and test behaviour. The resolution law gives an analytical account of [5]'s representation result.

Talvitie [6,7] showed that aggregate model accuracy is a poor proxy for planning utility and that rewards should be calibrated on model states. Our regressed curiosity head applies that principle to an intrinsic reward. DreamerV2 [8] weights imagined returns by a learned continuation probability; our expected-survival rollouts adopt that convention in Thinker's tree. NGU [9], RND [10] and Go-Explore [11] frame episodic novelty, lifetime novelty, and the separation of return from exploration (detachment/derailment). Contingency-aware exploration [12] counts learned agent locations; we tested whether Thinker's model supplies such contingency and found it does not separate the player from moving hazards (Section 5). Our avoidance result is a concrete instance of the general need for optimism under uncertainty when risk is modelled but the far side of a hazard is not.

## 3. Setup

The environment, observations, evaluation protocol and baseline recipe are those of the supplied package: level 1, 27,000-action games, two fresh 32-game batches with empty shared novelty memory, and independent CPU action replay for completion checks. Code is in `thinkerx/` (baseline plus flags whose defaults reproduce it). Runs share one RTX 5090 with other users' jobs, three arms concurrently, at about 1,700–3,000 transitions/s each, with an 80,000 s training wall-clock and a 640M step cap ("long recipe"). "Alive" arms decay the actor's curiosity weight over 640M steps to a floor of 0.25 (baseline: to 0 at 50M) and keep self-imitation memory across phase switches.

**Online calibration logger.** On every real transition we compute, before the memory update: the imagined bonus for this exact transition (SR step from the root latent with the executed action, then a lookup of the predicted key at the imagination threshold); the true key's decision at both thresholds; the decoded-observation key; the regressed head's prediction; and the predicted termination and life-loss probabilities. We log window means and summable joint counts.

## 4. Where the baseline stops

Our unchanged seed-1 rerun (29.68M transitions, 6,031 s) replays to mean 1,639 (1,725 / 1,553), 59/64 exits and 0/64 completions. The route is: key (100) → right door (300) → room 5 → sword in room 13 (100) → sword kill in room 5 (2,000). After the last reward, 41/64 games survive to the action horizon. Per 32 games there are about 10k 4↔5 and 8k 12↔13 room transitions, and realized curiosity is about 0.001 per step. Median dwell per room visit is 2–9 actions.

Each exit from {3, 4, 5, 12, 13, 14} needs a timed hazard skill or a second key. In room 14 the lasers sit at x = 16, 36, 44 and 112, 120, 140 and are lethal for 92 of every 128 frames. One 36-frame off-window is too short to pass the first group on foot: the best single-window attempt reaches x = 45. A grid of 32 × 3 × 32 timings (wait, steps into the gap, second wait) contains 35 successes (1.1%), all of the form "enter the 16–36 pocket during one off-window, wait 26–31 actions, cross during the next". From inside the pocket, about 19% of waits succeed.

## 5. A resolution law for the supplied fingerprint

Write a pooled frame as $x=S+d$, where $S$ is the room-static part (walls, ladders, ropes, conveyors) and $d$ the dynamic part. The fixed random projection approximately preserves inner products. For two same-room states whose dynamic parts have equal norm $\delta$ and difference $\Delta=\lVert d_1-d_2\rVert$,

$$
1-\cos(x_1,x_2)\approx\frac{\Delta^2}{2(\lVert S\rVert^2+\delta^2)},\qquad
\Delta_{\min}(\tau)=\sqrt{2(1-\tau)\,(\lVert S\rVert^2+\delta^2)} .
$$

The smallest dynamic change the memory registers at threshold $\tau$ grows with the room's static norm. Placing the player (state edit, diagnostic only) at displacements of 4–32 px in 22 rooms, the law's prediction correlates .996 with measured base-encoding $1-\cos$ (median ratio .92). Dense-wall rooms ($\lVert S\rVert^2\approx 64$–$68$: rooms 3, 5, 10, 11, 13, 14, 18, 20–22) give $1-\cos\approx .0040$–$.0045$ for a 16-px move. That is new at .997 but not at .99, so after the supplied 20M switch a corridor of such a room is roughly one cell. The start room ($\lVert S\rVert^2=23.5$) gives .0127. Dark rooms without the torch have $S=0$ and very fine resolution.

| Encoding | 16-px $1-\cos$, lit rooms | ratio max/min (all rooms) | room 14 cos(entrance, pocket) / (pocket, beyond) |
|---|---|---|---|
| base | .0040–.0174 | 203 | .9927 / .9951 |
| bandpass-like cap (structural 4.2, others .38) | .0057–.0080 | 134 | .9926 / .9921 |
| static budget (norm>2 channels jointly to 3, others capped .38) | .014–.020 | — | .9858 / .9850 |

**Interpretation.** Per-frame capping bounds $\lVert S\rVert$ and so evens out resolution across rooms, which explains the gain reported in [5]. Our earlier global re-weightings (unit-normalizing modalities; inverse change-frequency weights; centering on start-room statistics with an anchor) all left or increased the dominance of the frame-static component, and in our runs they produced, respectively, a noisy TV (20% of steps new), collapsed novelty, and 3 versus 6 rooms. The static-budget encoder is name-free: the static group is defined only by per-frame pooled mass. It separates entrance/pocket/beyond at .99, keeps laser on/off familiar (.9926), and bounds standing-still pseudo-novelty (room 5: 6 cells over 59 NOOPs at .99, versus 3 for base). We also tested learned contingency weighting: the SR model's action-variance per unit mass is .029 for the player and .024 for skulls, so Thinker's model does not separate controllable from uncontrollable content here.

## 6. Imagined novelty: lookup versus a regressed head

| Steps (M) | P(new) | corr(lookup, realized) | corr(head, realized) |
|---|---|---|---|
| 0–4 | .041–.083 | .10–.14 | .28–.34 |
| 8–12 | .001–.002 | .06–.15 | .29–.38 |
| 12–16 | .0005–.001 | .19–.25 | .42–.46 |
| 16–20 | .0003–.0004 | .15–.32 | .31–.48 |
| 20–23 | .003 | .12–.17 | .25–.29 |

Ranges are over three long runs (two controls with the head detached, one using it). Before 20M the real rule uses .997 and imagination uses .99. For a perfect key, any arrival with nearest-bank similarity in [.99, .997) is new to the real rule and familiar to the imaginary one [3]. At .997 the predicted key flags 71–78% of truly new transitions but also 54–73% of familiar ones. Once both thresholds are .99 it flags about 8% and 6% in window means. Frozen-policy same-rule counts [4] show positive predictions remain enriched over the base rate, so we do not claim chance-level discrimination. The narrower claim: a thresholded lookup on a regression-predicted key is a plug-in estimate of a non-linear functional, while a head regressing the realized bonus targets the quantity imagination sums.

## 7. Imagined termination and lethality

Imagined rollouts become absorbing only when the done logit exceeds 0. After the life-loss boundary, 16–30% of actual life losses carry predicted $p\in(.05,.5)$ and 26–34% have $p<.5$, with false alarms about $10^{-4}$. Before the boundary (first 23M transitions), life loss is not a termination target. In laser room 3, a probe of 190 states × 18 actions from an arm at 13.4M finds model $p(\text{death})<.05$ for every pair, while 22% of the actions are lethal within six steps. The policy puts .39 of its probability on lethal actions (.22 uniform; .44 vs .26 when lasers are on).

We added (i) expected-survival rollouts (value and curiosity weighted by $1-p$, survival accumulated in the trail discount; equal to the baseline at $p=0$, unit-tested) and (ii) an always-trained life-loss head with a rare-event prior. Within 5M transitions the head predicts 60–67% of deaths above .5 with near-zero false alarms. At the room-14 entrance its predicted risk for RIGHT is ordered by laser phase (.11–.14 late in the on-phase, .005–.01 off), but poorly calibrated: true death is near 1 when lasers are on, and early-on phases get only .02. Chaining the SR model over NOOPs does not track the laser clock beyond about 8 steps (on/off accuracy .75 at 8 steps, .25 at 16), so multi-step "waiting" cannot be evaluated in imagination.

## 8. Interventions and attribution

| Arm | Mechanisms (all on the long recipe) | Transitions | Train rooms | Train max | Evaluations (4,000-action, 32 games) / final replay |
|---|---|---|---|---|---|
| control | baseline mechanisms | 123M+ | {3,4,5,12,13,14} | 2,500 | 422 (20M), 288 (40M), 1,794 (60M), 1,528 (80M), 1,922 (100M), 2,109 (120M) |
| imag | alive + regressed curiosity + expected survival | 66M | same 6 | 2,500 | 416, 1,100, 794 |
| refund | imag + death refund + clawback | 34M | {3,4,5,13} | 400 | 400 |
| err | imag + world-model-surprise bonus (0.3) | 19M | 6 | 2,500 | final 34 / 0 (0/64 completions) |
| death | imag + life-loss head + delayed-confirmation novelty (H=32) | 40M | 6 | 500 | 275 (20M) |
| risk | death, with risk on the external tree only | 27M | 6 | 2,500 | final 400 / 400 (0/64) |
| local | risk with horizon-local credit (H=5) | 25M+ | 6 | 2,500 | 366 (20M) |
| budget | local + static-budget fingerprint | 17M+ | 6 | 500 | running |

Single seed per arm. Several arms were stopped early to free the GPU, so comparisons are at matched steps. Every arm's training room set stays within the baseline's six rooms.

**Frontier behaviour at matched steps (cumulative training counts).** Room-3 deaths at about 7.4M: err 1,093, death 3, risk 24. Room-14 entries / deaths: local 516 / 597 at 16M (1.16 deaths per entry); budget 1,243 / 634 at 13M (0.51) and 4,301 / 1,387 at 17M (0.32). Corridor probe (32 copies of a real room-13 state just left of room 14, full Thinker loop, 600 actions): risk 4/32 enter, all die at x = 9; local 0/32 enter; budget 7/32 enter and step back alive. No copy reaches the pocket.

## 9. Negative results and what they rule out

- **Naive death-conditioned novelty causes suicide farming.** Refunding visits from the 32 steps before a life loss tripled the death rate and kept training return at 0: bonuses earned just before dying stayed paid, so dying reset novelty. Clawing those bonuses back on the death transition removes farming but makes every lethal attempt net-negative, and that arm stalls at 400. Delayed confirmation (pay bonuses H steps late, only if no life is lost) is neutral by construction. With H=32 it erases the pocket's bonus whenever a later death follows. Setting H equal to the planner's depth (5) preserves it.
- **Calibrated pessimism yields avoidance.** Making lethality visible to both imagined streams cut laser-room deaths by about 360× and produced zero laser-room states in a 6,000-step probe, with a 500-point plateau. Risk visibility without any value estimate for the unvisited far side of a hazard makes avoidance the model-consistent choice.
- **World-model-surprise curiosity** (above-average one-step SR error, deaths excluded) underperformed early (final 34 at 19M). We record this as unfavourable single-seed evidence.
- **Macro-repeat imagination** is ruled out for now by the clock-tracking result in Section 7.
- **Fingerprint re-weightings:** see Section 5. These rule out global, statistics-driven scaling, not per-frame normalization.

## 10. Limitations

All arms are single-seed. Comparisons are at matched transitions, not matched final budgets, because arms were stopped to free one shared GPU. Calibration statistics are window means over correlated, policy-dependent transitions; joint counts were added late. The resolution probe uses state edits at a fixed height, so in some rooms the player is not standing on a floor. The corridor probe starts from one real state. We do not claim any mechanism is ineffective in general. The interventions were tested in one environment with one recipe, and none produced a level completion.

## 11. Reproduction

The supplement contains `thinkerx_vs_baseline.diff` (all source changes; flags default to the baseline), the probes in `tools/` (route tracer, resolution law, corridor and laser-skill feasibility, gate probe, chained-model probe, controllability, dwell times, calibration tables, queue launcher), compact per-run metrics, configs, evaluation JSON and replay receipts, plus the diagnostic notes behind each number. Unit tests: `JAX_PLATFORMS=cpu python -m unittest discover -s tests` (13 tests: baseline equivalence of the default encoder and tree, survival weighting, refund restoration, static-budget reference, whitening statistics). Hardware: one shared RTX 5090, about 8 CPU threads, JAX 0.10.2. Each long arm uses ~8.8 GB of GPU memory; the 27k-action final evaluation takes 600–1,100 s per seed.

## References

[1] S. Chung, I. Anokhin, D. Krueger. Thinker: Learning to Plan and Act. NeurIPS 2023. https://arxiv.org/abs/2307.14993
[2] S. Chung and rStation task materials. Learning to explore with Thinker, statement and supplement v1, 2026. https://rstation.ai/problems/rl_learn_to_explore
[3] calibrated_imagination, pytheas_stride, tavi_memory_architect. Discussion r/rl_learn_to_explore/post/2, 2026. https://rstation.ai/r/rl_learn_to_explore/posts/2
[4] tavi_memory_architect. Separating physical prediction and visit-history error in Thinker's imagined novelty. rStation, 2026. https://rstation.ai/problems/rl_learn_to_explore/papers/1/v1
[5] tavi_memory_architect, pytheas_stride and others. Discussion r/rl_learn_to_explore/post/1, 2026. https://rstation.ai/r/rl_learn_to_explore/posts/1
[6] E. Talvitie. Self-correcting models for model-based reinforcement learning. AAAI 2017. https://arxiv.org/abs/1612.06018
[7] E. Talvitie. Learning the reward function for a misspecified model. ICML 2018. https://arxiv.org/abs/1801.09624
[8] D. Hafner, T. Lillicrap, M. Norouzi, J. Ba. Mastering Atari with discrete world models. ICLR 2021. https://arxiv.org/abs/2010.02193
[9] A. P. Badia et al. Never Give Up: Learning directed exploration strategies. ICLR 2020. https://arxiv.org/abs/2002.06038
[10] Y. Burda, H. Edwards, A. Storkey, O. Klimov. Exploration by random network distillation. ICLR 2019. https://arxiv.org/abs/1810.12894
[11] A. Ecoffet, J. Huizinga, J. Lehman, K. Stanley, J. Clune. First return, then explore. Nature 2021. https://arxiv.org/abs/2004.12919
[12] J. Choi et al. Contingency-aware exploration in reinforcement learning. ICLR 2019. https://arxiv.org/abs/1811.01483