Abstract

Distributed vector representation — embedding items and retrieving them by approximate-nearest-neighbor (ANN) search [1] — is the established substrate for semantic retrieval. This note applies three psychophysical principles as the control law for selective, sparse activation over such a representation: Weber–Fechner compression [2], which spends effort in proportion to relative rather than absolute change; the just-noticeable difference (JND), which suppresses sub-threshold updates so computation concentrates on the changes that matter; and Signal Detection Theory (SDT) [3], which decides which nodes and paths to activate by separating signal from noise. These are measurable perceptual tools — Weber–Fechner scaling, the JND, and SDT's sensitivity (d′) and criterion (β) — applied directly to the activation decision, not figures of speech laid over it.

1. Distributed Vector Representation

Embedding items into a shared vector space and retrieving them by ANN search is a mature, GPU-accelerated technique consolidated in FAISS [1]. The cost that grows with the corpus is not the index lookup but the churn: recomputing, re-weighting, and propagating updates across entries whose state barely moved. The design here targets that churn. Over an ANN-indexed store, the operative question at every step is not what is the nearest neighbor but which entries have changed enough to be worth touching — and that is a perceptual decision with an established quantitative form.

2. Three Applied Psychophysical Principles

Weber–Fechner compression. Perception responds to proportional change: the increment needed to notice a difference scales with the magnitude already present [2]. Read as a control law, this says spend effort where the relative change is large and damp response to signals that are already strong. A vector entry with a large stable norm absorbs a small perturbation without a meaningful shift in its retrieval behavior; the compressive curve is what tells the system to skip it. This is the measurable Weber–Fechner relation governing where update effort is allocated.

The just-noticeable difference. The JND is the smallest change a detector resolves. Applied to a vector store, it is the activation threshold: an update whose effect falls below the JND changes no downstream retrieval and is suppressed, so computation concentrates on supra-threshold changes. Setting the threshold at the JND is the difference between propagating every micro-perturbation and propagating only the changes that alter an outcome. The threshold is a resolution limit, applied as one.

Signal Detection Theory. Deciding whether an observed change is meaningful signal or noise is a detection problem [3]. SDT gives it two independent, tunable knobs: sensitivity (d′), how separable a real change is from background noise, and criterion (β), how eagerly the system activates. The recall-versus-noise trade-off in deciding which nodes or paths to fire is a criterion shift along an ROC curve; the quality of the underlying representation is d′. This is where the activation decision meets a number.

3. Sparse Activation as a Composed Control Law

The three principles compose into one policy over the ANN store [1]: Weber–Fechner scaling sets how much a change counts relative to the signal already present; the JND sets the threshold below which a change is dropped; and SDT sets the decision — activate or not — with d′ and β as the tunable parameters. Each entry's update is gated through this policy, so per-step work tracks the set of supra-JND, above-criterion changes rather than the full corpus. The saving is a direct consequence of the gate: the representation stays large, but the activated subset stays small because the psychophysics decides what crosses the threshold.

Evidence & Scope

This is a design grounded in applied psychophysics, not a benchmark report. Weber–Fechner scaling [2], the JND, and Signal Detection Theory [3] are the measurable tools the activation policy is built from, and d′ and β are its tunable parameters. The architecture it defines — sparse, threshold-gated activation over an ANN-indexed vector store — stands to be measured against FAISS [1] on a shared corpus for retrieval quality and update cost. FAISS is the reference substrate; the psychophysical gate is the variable that decides how much of the corpus each step has to touch.

References

  1. Jeff Johnson et al. (2019). Billion-Scale Similarity Search with GPUs. IEEE Transactions on Big Data. arXiv:1702.08734. [FAISS.]
  2. Gustav Theodor Fechner (1860). Elemente der Psychophysik. Breitkopf und Härtel.
  3. David M. Green & John A. Swets (1966). Signal Detection Theory and Psychophysics. Wiley.