Generative models’ competence is jagged: local reliability gaps can block blind adoption but reward users who learn where the model works; increasing scale raises average quality yet can leave sharp local failures and, without better local signals, render improvements invisible.

Main Finding

Generative-AI systems can be systematically "jagged": performance varies sharply across nearby tasks because model knowledge is spatially uneven and users cannot observe local reliability. When knowledge is modelled as scattered support points and truth as a rough process, the user-facing uncertainty (posterior variance) between support points has closed-form structure; longer gaps dominate experienced error (the inspection paradox). As a result, average benchmark scores can understate experienced risk, adoption depends on discoverability as well as scale, and investments in calibration, interface design, and user mastery can be economically complementary to model scaling.

Key Points

• Artificial Jagged Intelligence (AJI): uneven, local model performance—pockets of competence and holes of high error—plus opacity about where those pockets are.
• Parsimonious formalisation:
  • Truth Y(x) is a Brownian motion along a task dimension (rough, locally correlated).
  • Knowledge/support points {xi} follow a homogeneous Poisson point process with intensity λ (coverage density).
  • The AI interpolates between neighbouring knowledge points; posterior variance at x is the irreducible local uncertainty.
• Posterior variance (Brownian bridge) for x in gap [xi, xi+1]:
  • σ^2(x) = (x − xi)(xi+1 − x) / (xi+1 − xi).
• Inspection paradox (length bias): a uniformly drawn task is more likely to fall in longer gaps. Gap containing a random task X* ∼ Gamma(2, λ) with mean 2/λ (double the mean gap 1/λ).
• Expected experienced posterior variance:
  • E[σ^2] = E[X*]/6 = (2/λ)/6 = 1/(3λ). (Contrast: naive use of mean gap gives 1/(6λ).)
• Economic consequences:
  • Blind adoption: a user who cannot observe local σ^2(x) uses the tool only if stakes parameter q is large enough to tolerate expected error; inspection paradox raises the required q.
  • Scaling (increasing λ) reduces average error but preserves relative jaggedness — long gaps still dominate experienced exposure.
  • Calibration (observing/estimating local uncertainty) can unlock positive expected value even when blind adoption would be irrational: users can selectively use the model where it’s reliable.
  • Mastery (learning the reliability map) is not instantaneous: modelled as Gaussian process regression over the latent reliability function, learning rates are bounded by information gain; in high-dimensional or rough landscapes, discovering where the model works can be slow and subject to an "abstention trap".
  • Complementarities/Substitutability: below the blind-adoption threshold, scaling and calibration are complements (both needed); above it they are substitutes (marginal calibration value smaller).
• Interface and governance tools (similarity cues, uncertainty estimates, abstention mechanisms, provenance) are strategic complements to model improvements and can be decisive for adoption and productivity.

Data & Methods

• Analytical, tractable economic model of task-level reliability:
  • Task space: one-dimensional domain Z (for closed-form results; higher-d generalisations discussed).
  • Truth process: driftless Brownian motion (captures roughness; yields Brownian-bridge conditional distributions).
  • Knowledge/support points: homogeneous Poisson point process with intensity λ (represents knowledge/coverage density; interpretable as scale).
  • AI prediction: posterior mean interpolation between neighbouring support points; posterior variance given by Brownian-bridge formula (equation above).
• Key derived objects:
  • Length-biased gap distribution for task-uniform sampling: f_X*(x) = λ^2 x e^{−λx} (Gamma(2,λ)).
  • Conditional expected variance in a gap of length X: E[σ^2 | X] = X/6.
  • Expected experienced variance E[σ^2] = 1/(3λ).
• Learning/mastery model:
  • Users attempting to learn the reliability map are modelled via Gaussian process regression tools; learning-rate bounds are derived that scale with information gain (links to Gaussian process bandit literature).
• Conceptual/analytical techniques: combination of spatial Poisson processes, Brownian bridge variance calculations, Bayesian posterior variance as local error measure, and Gaussian-process learning theory (Rasmussen & Williams; Srinivas et al.) to bound mastery rates.

Implications for AI Economics

• Evaluation and Benchmarks:
  • Headline/benchmark averages can mislead: they do not reflect length-biased exposure to gaps. Regulators, evaluators and purchasers should weight task distributions and consider measures of local worst-case/variance, not only mean accuracy.
• Adoption and Productivity:
  • Opacity about local reliability can suppress adoption even when average performance is good (blind-adoption threshold). Organisations may underuse otherwise valuable models if rare but severe local failures are hard to detect.
  • Experienced error is amplified by the inspection paradox; policy and procurement should account for exposure-weighted risk.
• Product & Interface Design:
  • Signals that improve discoverability (uncertainty estimates, similarity cues, provenance, abstention options) are high-return investments; they can convert jagged capability into usable value without changing base model scale.
  • Calibration tools and user training (mastery) interact with scaling: below certain thresholds both are needed; above them one can substitute the other. Optimal deployment mixes depend on stakes and λ.
• Model Scaling & Research Priorities:
  • Increasing training/coverage density (λ) reduces overall error but does not eliminate jaggedness; scaling alone may leave surprising failures intact.
  • Opacity can hide gains from scaling: if users cannot discover where reliability improved, scale benefits may not be harvested.
  • Research that increases regularity (smoother interpolation), retrieval/coverage strategies that reduce long gaps, or methods that make local uncertainty observable can be as valuable as raw parameter scaling.
• Policy and Governance:
  • Regulation that focuses solely on average performance is insufficient. Policies should require (or incentivise) disclosure of uncertainty, provenance, and tools enabling discoverability, especially for high-stakes domains where users cannot absorb rare catastrophic errors.
  • Certification and procurement could condition on exposure-weighted risk metrics or on the existence of reliable calibration/abstention mechanisms.
• Research implications:
  • Empirical work should measure task-uniform exposure to errors, not only benchmark averages.
  • Further theoretical and empirical work to quantify learning costs (mastery) in real workflows and high-dimensional task spaces is important for understanding adoption dynamics.

Summary: AJI reframes adoption and evaluation of generative-AI systems as an information problem about where a model is locally reliable. Simple stochastic geometry (Poisson support + rough truth) produces closed-form insights (inspection paradox; experienced variance = 1/(3λ)) that change how we should think about scaling, calibration, interfaces, and policy.