Can LLMs recover true joint distributions from marginal census data?
This explores whether LLMs can reconstruct how traits co-occur in a real population (the joint distribution — e.g. age and income and location together) when they're only given each trait's separate breakdown (the marginals, like what census tables actually publish).
This explores whether LLMs can reconstruct how traits co-occur in a real population when they're only handed each trait's separate breakdown — the gap between marginal data (what census tables publish) and the joint distribution (who actually has which combination of traits). The corpus is blunt on the headline: no, not reliably. Work on population-scale persona generation finds that LLM-built personas produce systematic, downstream-distorting biases in tasks like election forecasting precisely because the methods are heuristic stand-ins that cannot recover true joint distributions from marginal data How do we generate realistic personas at population scale?. Getting the marginals right (X% are this age, Y% earn this much) doesn't pin down how those attributes cluster in real people, and the model fills that gap with plausible-but-wrong correlations.
Why this is hard becomes clearer when you look at what LLMs do instead of genuine inference. Several notes show they pattern-match rather than compute: they recognize an optimization problem as template-similar and emit confident, incorrect values rather than actually running the procedure Do large language models actually perform iterative optimization?, and they plateau around 55–60% on constraint-satisfaction tasks regardless of size or reasoning training Do larger language models solve constrained optimization better?. Recovering a joint distribution from marginals is exactly that kind of constrained inference problem — and the corpus suggests scale won't rescue it.
There's a sampling subtlety worth knowing too: even when an LLM gives you a 'distribution' of personas, each one is a draw from the model's learned probabilities, not from the real population. Pinning temperature to zero just replays the same draw — consistency that masquerades as reliability without making the underlying sample any more representative Does setting temperature to zero actually make LLM outputs reliable?. And because models internalize skewed training corpora — flattening low-resource cultures into proxies of dominant ones, for instance Do LLMs represent low-resource cultures through dominant cultural proxies? — the implied joint structure tends to drift toward whatever was overrepresented in pretraining, not toward your target population.
The interesting tension is that LLMs are genuinely good at a neighboring trick. They can stitch together scattered, never-explicitly-stated facts across the training distribution — inferring a censored city's identity from distance relationships alone Can LLMs reconstruct censored knowledge from scattered training hints?. That's reconstruction from partial signal, which sounds like recovering joints from marginals. The difference: that works when the true relationships are latent in the data the model already absorbed. It does not conjure the correct correlations for a specific external population you hand it as marginals. So the honest answer the corpus points to is calibration, not faith — treating persona generation as a measurement discipline that needs benchmarks, ground-truth joint datasets, and ImageNet-style infrastructure before the numbers can be trusted How do we generate realistic personas at population scale?.
Sources 6 notes
LLM persona generation produces systematic biases in downstream tasks like election forecasting because it relies on heuristic techniques that cannot recover true joint distributions from marginal data. Solving this requires benchmarks, training datasets, and structured frameworks analogous to ImageNet.
Research shows LLMs cannot perform iterative procedures in latent space. They recognize optimization problems as template-similar and emit plausible-looking but incorrect values, a failure mode that persists across model scale and training approaches.
Across constrained-optimization tasks, LLMs converge to ~55–60% constraint satisfaction independent of architecture, parameter count, or training regime. Reasoning models do not systematically outperform standard models, suggesting a fundamental ceiling rather than a scaling gap.
Fixed seeds and zero temperature replicate the same output repeatedly, but that output remains one draw from the model's probability distribution. McDonald's omega testing across 100 repetitions reveals that consistency does not equal reliability.
Mechanistic interpretability analysis reveals that low-resource cultures like Ethiopia and Algeria are structurally represented through high-resource cultural proxies in internal model states, not just output. This architectural bias persists even when models can produce correct surface-level answers.
Language models perform out-of-context reasoning across the full training distribution, reconstructing information never explicitly stated in any single document. Experiments show models can infer city identities from scattered distance relationships and apply them downstream without in-context learning.