Research preview · October 2026
Replicating Qamar et al. 2013 with an AI research agent
In 2013, Qamar, Cotton, George, Beck, Prezhdo, Laudano, Tolias and Ma reported in PNAS that humans and monkeys move their decision boundaries from trial to trial with their own sensory uncertainty, and that a neural network with quadratic operations and divisive normalization can approximate the optimal computation. The original work took a team about a year around 2010. Here an October-2026 AI agent (Claude, orchestrating subagents) rebuilt the analysis from the archived data and code, checked every published number, audited the code, corrected what was wrong, and is now extending the work. This site reports what it found, including its own mistakes.
Replication
The likelihood at the archived parameters matches for 69 of 70 fits to 10−6 (the 70th to 1.1×10−6). Tables, RMSEs, the ANOVA and all three network information losses reproduce.
Behaviour and network →Corrections that matter
A gradient bug hid better Lin-σ fits (Monkey A + log-likelihood). The boundary ANOVA weakens from p = 4×10−6 to p = after a sphericity correction. The published LIN/QUAD network losses (41.7% / 21.0%) were optimiser artefacts: / when converged.
What changed and what did not →New finding
show strong trial-history effects (p < 0.001), which had been hidden because the stored trial order interleaved sections of each block. Monkey L perseverates; Monkey A does not.
History effects →Agent time so far
of main-agent working time, plus of summed subagent time, over a session. The 2010 effort took about a year.
The meta-task →What the paper claimed
Observers sorted a grating's orientation into one of two categories: both centred on horizontal, one narrow (), one wide (; for Monkey L). Contrast changed at random from trial to trial, which changes how noisy the observer's measurement is. The best decision boundary moves outward as noise grows, so an observer who ignores its own uncertainty is measurably worse off. Five models were compared: the optimal observer (Opt), Opt with a free prior (Opt-P), two heuristics whose boundary is a linear or quadratic function of noise (Lin-σ, Quad-σ), and a fixed boundary (Fixed). Fixed always lost, and the winner differed between subjects. A small network with divisive normalization came close to the optimal posterior; linear and quadratic networks did not.
What we found
- The main conclusions hold. No model winner changes after the corrections. Fixed is never the best model and stays outside the "within " set for every main-experiment subject and both monkeys.
- The archived optimiser had a bug in one gradient term (Lin-σ and Quad-σ). It missed much better optima for both monkeys. Monkey A still prefers Quad-σ and Monkey L still prefers Lin-σ.
- Several claims need qualifying. In the control experiment Fixed is within for one subject. The boundary ANOVA survives the sphericity correction only at p ≈ 0.016. The independent-σ check is strong across contrasts but inconclusive across six subjects.
- The network story is weaker than published. QDN is still near-optimal (0.22%), but LIN and QUAD were undertrained, and divisive normalization did not "emerge automatically" through learning: it was built into the architecture and its initialization.
- New: half the human subjects show strong trial-history effects, but modelling them changes no model comparison. Noise added to the optimal observer does not explain the data; a Bayesian observer that over-weights its own uncertainty matches the best heuristic in Monkey A; in humans it is clearly better for no one, and where recovery shows it could be identified it is rejected. Divisive normalization helps networks generalise across contrast when it divides by roughly uniform total activity (Phase 3).
Sections
The meta-task
How the agent worked, how long it took, speed-ups, and the mistakes it caught.
Context
An interactive map of 115 papers placing Qamar 2013 in the Bayesian-observer research programme.
Replication: behaviour
Model fits, the code audit, corrected vs published tables, and what changed.
Replication: network
QDN, LIN and QUAD networks, the reconstructed missing script, and whether normalization "emerges".
Extensions
History effects, near-Bayesian and noise models, model recovery, and neural extensions including contrast generalisation.
Games
A playable prototype of the 2013 task, and three new games aimed at open questions in the field (in development).
Prompt
The project lead's first 15 chat messages, consolidated into the single brief they could have written up front.
Status: Phase 1 (replication with corrections) is complete and gate-reviewed; Phases 2 and 3 are complete. Numbers on this site are generated from the
project's results/ files. This is a preview, not a peer-reviewed publication.