Latent Time-Adaptive Drift-Diffusion Model
The drift-diffusion model (DDM) is a well-validated computational account of binary decision-making: evidence accumulates noisily toward one of two thresholds, and the speed-accuracy tradeoff emerges naturally from the threshold setting. Dr. François Rivest's Time-Adaptive DDM (TDDM) extended this by making the drift rate — the average rate of evidence accumulation — learnable from experience rather than fixed, allowing the model to account for how decision-making behaviour changes as an animal learns the timing of events in its environment.
The LTDDM is a deep extension of the TDDM. Where the TDDM maintains a single latent representation of the current task, the LTDDM stacks multiple layers, composing representations hierarchically. This allows the model to capture qualitative shifts in behaviour — the kind observed in animal learning experiments where a subject's strategy changes structurally between task phases, not just parametrically. The model learns from few observations, which is necessary for modelling individual subjects rather than population averages.
Comparison with LSTM on sparse temporal prediction tasks showed the practical consequence of the architectural difference. On a heartbeat prediction dataset, LSTM recall was 0.03; LTDDM recall was 0.31. The difference reflects a fundamental property: LSTM learns by gradient descent over long sequences and struggles with the timescale invariance property of animal timing behaviour. The LTDDM's inductive bias is designed around that property. It converges orders of magnitude faster on tasks where events are rare and intervals are variable.
The implementation predates my PhD and was written from first principles — the model is recurrent and unconventional enough that autodiff frameworks added friction rather than removing it. This is a recurring pattern in my AI implementation work: the constraint that made standard tools impractical produced a deeper understanding of what the algorithm is actually doing.
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