The Same Numbers, Different Outcomes: How the Interface Becomes the Policy

In the spring of 2026, three research teams at the University of Tokyo ran what should have been a straightforward experiment. They took the same group of AI agents facing the same coordination problem, gave them the same information, and watched what happened. The only difference was how the agents' observations were formatted on the page. What they found upended a fundamental assumption about how language models process the world: the same numbers, the same data, presented differently caused one model to synchronize perfectly while another fell into disarray — and the reversal happened when they swapped which model got which format.

This is not a bug. It is a structural feature of how these systems work.

The Science

The researchers designed a minimal synchronization assay. Imagine 17 agents arranged in a circle, each aware only of where its neighbors stand relative to itself. At each step, every agent must choose one of three actions: advance, stay, or fall back. No communication, no memory, no goal stated. The only thing that changes between experimental conditions is how the description of the neighborhood gets written on the page.

The team, led by Takahiro Ezaki, Naoto Imura, and Katsuhiro Nishinari, encoded the same underlying data three ways. The first was a set of circular moments — statistical summaries that compress the field into its mean direction and concentration across three harmonic orders. The second was a 24-bin histogram labeled by bin center. The third was the identical histogram but labeled by bin interval to six decimal places. All three encode the same 24-bin measurement of the same field; they differ only in how that information is presented. (See

for the matched intervention design.)

The physical dynamics were identical across conditions. A deterministic engine applied the coupling based on whatever action each model chose. The language model saw only the encoded description, returned −1, 0, or +1, and the engine advanced phases accordingly. No learning within a run, no goal to synchronize, no identity or history — just a stateless response to an encoded field.

They tested gpt-4o-mini, claude-haiku-4-5-20251001, and gemini-3.5-flash, keeping costs manageable while preserving the core architecture of frontier systems.

What They Found

The results were stark. In GPT, the moment encoding produced full population synchronization in every trial: 6 out of 6 seeds locked at both K=0.08 and K=0.15 coupling strength. Both histogram encodings produced nearly nothing — centers locked in 0 out of 6, intervals in 0 out of 6. The polar order parameter, which runs from 0 (random phases) to 1 (perfect alignment), averaged 0.999 for moments but only 0.710 for centers and 0.382 for intervals at the stronger coupling.

GPT Synchronization by Encoding

Label	Value
Moments	0.999
Centers	0.71
Intervals	0.382

Data from Figure 1. K=0.15 coupling strength. n=6 physical seeds per encoding.

But here's the part that makes the result unreducible to a simple encoding superiority: when the same experiment ran in Claude, the relationship flipped entirely. Moments locked in 0 out of 6 seeds. Centers locked in 2 out of 6 at weak coupling and 6 out of 6 at strong coupling. Intervals reached 5 out of 6 and 6 out of 6. The observation map effect replicated — but in the opposite direction.

Claude Reversal: Histograms Lock, Moments Don't

Label	Value
Moments	0
Centers	6
Intervals	6

Data from Figure 4. K=0.15 coupling strength. n=6 confirmatory seeds per encoding.

The reversal is the paper's central finding. "The simple reading of the GPT experiment, that moment compression is intrinsically synchronization-promoting, is falsified by Claude under the same design," the authors write. "The outcome depends on the model and observation-map pair, not on a superior encoding."

To isolate whether the effect came from the encoding itself or from different trajectories feeding back different fields, the team ran an identical-field replay experiment. They took 48 fields that actually arose during the collective runs, froze them, and re-presented each one under all three encodings in alternating blocks. The same physical field, shown three ways, elicited measurably different action distributions.

The mean pairwise total-variation distance — a measure of how far apart two probability distributions are, on a scale where 0 is identical and 1 is no overlap — was 0.344. That sounds modest until you compare it to the test-retest floor: when the same encoding sees the same field twice in different blocks, the variation is only 0.092. The encoding effect was 3.76 times the within-encoding noise. Permuting the encoding labels within each field, none of 5,000 random reassignments produced a separation this large (p=0.0002).

Encoding Effect vs. Test-Retest Noise

Label	Value
Encoding effect	0.344
Test-retest floor	0.092

Data from Figure 3. Mean pairwise total-variation distance over 48 frozen fields.

Most striking: centers and intervals carry identical information — the same 24 bin masses under different labels. Their separation was 0.290, still 3.2 times the block noise. The serialization moves the operator with the retained information fixed.

The presentation control went further. The researchers took the exact same moment values and presented them three ways: as narrative text, as a reformatted table, and with task-irrelevant padding added. Even with identical numbers, presentation mattered. Reformatting as a table shifted the operator by 0.145 — about 2.1 times the block noise. Adding irrelevant context shifted it by 0.414, exceeding the 0.344 separation between different encodings. A secondary analysis found that response differences tracked coordinate binding — whether each bin's mass is written together with its coordinate — more closely than character-count differences. Length alone, it appears, is not the driver.

Why This Changes Things

The paper challenges a quiet assumption buried in how we build and evaluate multi-agent systems. When we design a language-model agent, we typically treat the observation map — the way physical state becomes text — as a neutral interface, an implementation detail. The paper's title names the stakes: the encoding is not interchangeable. It is part of the model-dependent effective interaction law.

This matters for a practical reason. Language models are increasingly assembled into populations that coordinate, trade, and shape collective outcomes. Populations form social conventions, amplify biases, steer markets toward concentration. If the observation map is part of the policy, then changing it need not preserve behavior — a lesson the field has learned piecemeal with prompt sensitivity, but has not yet absorbed into multi-agent design.

The reversal between GPT and Claude is the sharpest version of this lesson. There is no universally superior encoding. What synchronizes one model may paralyze another. Validation cannot transfer by analogy.

The identical-field replay adds another layer. The effect was not just that the encoding shaped trajectories over time; on the same frozen field, the encoding shaped the three probabilities an agent assigns to advancing, staying, and retarding. Since the sampled action is the only model output entering the deterministic engine, that action channel is exhaustive. The effect is real, localized, and causal.

And the presentation results suggest that even within a single encoding family, how numbers sit on the page — surrounding context, layout, the binding between values and labels — changes behavior. This is consistent with prior work on prompt formatting and order effects, but it gains weight in a closed-loop setting where small operator differences accumulate into macroscopic bifurcation.

What's Next

The paper is careful about its scope. The collective experiments used a minimal, stateless system with 17 agents and a fixed horizon. The findings are finite-system phenotypes, not claims about phase transitions or universal critical couplings. All three models tested were lower-cost offerings at a fixed temperature. Frontier-scale models, temperature dependence, richer action spaces, memory, and task environments remain open.

But the principle is clear, and the next experiments are suggested. A further collective replication in another model family would test whether the reversal recurs. Operator-swap experiments — replacing one model's response function with another's at fixed state sequences — could close the quantitative gap between the observed operator differences and the observed trajectory differences. And the principle should move into task-based multi-agent settings, where coordination architectures and message-passing interfaces are explicit design choices.

Practically, the observation serializer belongs in what an agent evaluation reports. It must be revalidated with the model, in the closed loop in which both will operate. "Treat the observation map as a versioned component, and treat its validation as inseparable from the model's," the authors imply without quite saying it.

What the experiment demonstrates is that language models do not see a neutral description of an environment. They see a description, and that description is part of what they are. The interface is not a window. It is a lens, and lenses bend light differently depending on what they are made of.

That has implications far beyond synchronization tasks. Anywhere language models are assembled into systems that shape the world — markets, negotiations, collective inference, multi-agent coordination — the encoding is a design choice with causal consequences. Choosing how to describe a state is choosing part of the policy. That is the finding, and it does not require a sophisticated reading to see its weight.