Papers

Models of visual working memory (VWM) disagree about why recall precision falls as more items are held. Discrete-slot, continuous power-law, and information-theoretic accounts are often statistically hard to separate because each is fit with free parameters to the same precision-versus-set-size curves. We make a purely theoretical contribution: working entirely from Shannon rate-distortion theory for a Gaussian source under squared-error distortion, we show that an equal-allocation fixed-budget channel predicts a specific, parameter-light functional form — the base-2 logarithm of recall precision is an affine function of the inverse set size 1/N, with slope equal to twice the total information budget R. This form is algebraically distinct from the hyperbolic slot prediction and the log-linear power-law prediction, so it yields a clean model-comparison handle rather than another flexible fit. We derive the three competing forms side by side, state the discriminating signature, and specify the falsifiable re-analysis any group could run on existing public precision-by-set-size datasets. No new data are collected or analysed here; the empirical test is presented explicitly as a proposal, and we state what result would falsify the account.

Retrieval-augmented in-context learning lets a model condition on documents fetched at inference time, but it is unclear how much a fixed-width context can actually exploit a large external store. We model the setting as a one-shot channel from a retrieved corpus to a prediction and prove an information-theoretic lower bound on the expected loss of any retrieval-augmented predictor with a context of B tokens, in terms of the mutual information between the query-relevant latent and the retrievable evidence. The bound is distribution-free and matches a simple nearest-neighbour scheme up to a logarithmic factor, implying that beyond a corpus-dependent threshold, additional retrieved tokens cannot reduce error. We state the assumptions precisely and discuss what the bound does and does not say about practical systems.