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// Copyright 2024-2026 WritersLogic Contributors
// SPDX-License-Identifier: Apache-2.0
//! Counting holographic membership store.
//!
//! A variant of [`super::bloom_memory::HolographicBloomMemory`] that keeps a
//! per-index HIT COUNT instead of a one-bit OR union. The binary union saturates
//! to all-ones as items accumulate, at which point non-members become
//! indistinguishable from members and discrimination collapses to chance. The
//! count preserves the signal the union throws away -- each member adds +1 to each
//! of its k active indices -- and a Poisson z-score readout recovers that shift far
//! past the binary wall.
//!
//! Measured (D=16384, k=64, 20 seeds, member-vs-non-member AUC): the binary
//! readout walls at AUC<0.95 by ~1000 items and is at chance by ~2000; the counting
//! readout holds AUC>0.95 to ~4000 and degrades gracefully (0.84 at 8000). A ~4x
//! usable-capacity gain at matched dimension. See `docs/PREREGISTRATION-binding-
//! readout.md` §19 and `src/bin/bloom-wall.rs`.
//!
//! Cost: one `u32` per index rather than one bit -- this trades a Bloom filter's
//! bit-compactness for capacity. It remains a deterministic integer fold of its
//! inserts, so the store is an exact, replay-verifiable function of what was added.
use crate::core::entangled::EntangledHVec;
/// A z-score threshold of 3.0 bounds the per-query non-member false-positive rate
/// to roughly 0.1% under the Poisson null (the summed statistic is ~N(0,1) for a
/// non-member), independent of load.
pub const DEFAULT_Z_THRESHOLD: f64 = 3.0;
pub struct CountingBloomMemory {
dim: usize,
counts: Vec<u32>,
/// Σ over inserted items of their active-index count -- the Poisson null rate
/// is λ = active_insertions / dim.
active_insertions: u64,
item_count: usize,
}
impl CountingBloomMemory {
pub fn new(dim: usize) -> Self {
Self {
dim,
counts: vec![0; dim],
active_insertions: 0,
item_count: 0,
}
}
/// Add one item, incrementing the count at each of its active indices.
pub fn insert(&mut self, item: &EntangledHVec) {
for &i in item.indices() {
// Indices are < dim by construction; the bounds check guards against a
// mismatched-dimension item rather than trusting the caller.
if let Some(c) = self.counts.get_mut(i as usize) {
*c = c.saturating_add(1);
self.active_insertions += 1;
}
}
self.item_count += 1;
}
pub fn insert_batch(&mut self, items: &[EntangledHVec]) {
for item in items {
self.insert(item);
}
}
/// Poisson z-score membership statistic.
///
/// Under the non-member null each queried index has count ~ Poisson(λ), so the
/// summed excess `Σ(count_i − λ)` over the query's k indices is ~N(0, kλ). A
/// member shifted every one of its indices up by +1, moving the sum by +k. The
/// returned standardized value `Σ(count_i − λ) / √(kλ)` is therefore ~0 for a
/// non-member and ~√(k/λ) for a member. (Ranking is invariant to the √(kλ)
/// scale at fixed k; the normalization is what makes the value an interpretable
/// z-score for thresholding.)
pub fn membership_score(&self, item: &EntangledHVec) -> f64 {
let ix = item.indices();
if ix.is_empty() {
return 0.0;
}
let lambda = self.active_insertions as f64 / self.dim.max(1) as f64;
let excess: f64 = ix
.iter()
.map(|&i| self.counts.get(i as usize).copied().unwrap_or(0) as f64 - lambda)
.sum();
let std = (ix.len() as f64 * lambda).sqrt();
if std <= f64::EPSILON {
// Empty or near-empty store: any present index is unambiguous signal.
return if excess > 0.0 { f64::INFINITY } else { 0.0 };
}
excess / std
}
/// Whether `item` is a member at the given z-score threshold.
pub fn contains(&self, item: &EntangledHVec, z_threshold: f64) -> bool {
self.membership_score(item) >= z_threshold
}
/// Candidate indices whose membership z-score meets `z_threshold`, with scores.
pub fn query_candidates(
&self,
candidates: &[EntangledHVec],
z_threshold: f64,
) -> Vec<(usize, f64)> {
candidates
.iter()
.enumerate()
.map(|(i, item)| (i, self.membership_score(item)))
.filter(|&(_, z)| z >= z_threshold)
.collect()
}
pub fn item_count(&self) -> usize {
self.item_count
}
pub fn dim(&self) -> usize {
self.dim
}
/// Poisson null rate λ = Σk / dim (mean count per index).
pub fn mean_count(&self) -> f64 {
self.active_insertions as f64 / self.dim.max(1) as f64
}
}
#[cfg(test)]
mod tests {
use super::*;
fn store(dim: usize, n: u64) -> CountingBloomMemory {
let mut mem = CountingBloomMemory::new(dim);
let items: Vec<EntangledHVec> = (0..n)
.map(|i| EntangledHVec::new_deterministic(dim, i * 100))
.collect();
mem.insert_batch(&items);
mem
}
fn mean(v: &[f64]) -> f64 {
v.iter().sum::<f64>() / v.len() as f64
}
#[test]
fn single_member_scores_high_nonmember_near_zero() {
let dim = 16384;
let mut mem = CountingBloomMemory::new(dim);
let item = EntangledHVec::new_deterministic(dim, 42);
mem.insert(&item);
let member = mem.membership_score(&item);
assert!(member > 20.0, "lone member must stand out, got {member:.2}");
// At near-empty load the null variance √(kλ) is tiny, so an individual
// non-member sharing an index or two is noisy; the null MEAN over a sample
// still sits near zero, and the member dwarfs any individual non-member.
let nms: Vec<f64> = (0..50)
.map(|j| mem.membership_score(&EntangledHVec::new_deterministic(dim, 900_000 + j)))
.collect();
assert!(
mean(&nms).abs() < 1.0,
"non-member mean should sit near the null"
);
let nm_max = nms.iter().cloned().fold(f64::NEG_INFINITY, f64::max);
assert!(
member > 5.0 * nm_max.max(1.0),
"member must dwarf non-members"
);
}
#[test]
fn empty_query_is_zero() {
let mem = store(16384, 100);
let empty = EntangledHVec::from_indices(Vec::new(), 16384);
assert_eq!(mem.membership_score(&empty), 0.0);
}
#[test]
fn discriminates_at_1000_items() {
// Where the binary readout is already collapsing (AUC~0.87), counting is
// near-perfect. Assert a comfortable, theory-predicted margin.
let dim = 16384;
let mem = store(dim, 1000);
let members: Vec<f64> = (0..1000)
.map(|i| mem.membership_score(&EntangledHVec::new_deterministic(dim, i * 100)))
.collect();
let nonmembers: Vec<f64> = (0..200)
.map(|j| mem.membership_score(&EntangledHVec::new_deterministic(dim, 5_000_000 + j)))
.collect();
let m = mean(&members);
let nm = mean(&nonmembers);
assert!(m > 3.0, "member mean z should clear 3, got {m:.2}");
assert!(
nm.abs() < 1.0,
"non-member mean z should sit near 0, got {nm:.2}"
);
let fpr = nonmembers.iter().filter(|&&z| z >= 3.0).count() as f64 / nonmembers.len() as f64;
assert!(
fpr < 0.05,
"non-member FPR@z>3 should be small, got {fpr:.3}"
);
}
#[test]
fn still_discriminates_where_binary_is_dead() {
// At 2000 items the binary OR-union readout is at chance (AUC~0.51);
// counting still separates the means by a clear margin (~4x capacity).
let dim = 16384;
let mem = store(dim, 2000);
let members: Vec<f64> = (0..400)
.map(|i| mem.membership_score(&EntangledHVec::new_deterministic(dim, i * 100)))
.collect();
let nonmembers: Vec<f64> = (0..400)
.map(|j| mem.membership_score(&EntangledHVec::new_deterministic(dim, 6_000_000 + j)))
.collect();
assert!(
mean(&members) - mean(&nonmembers) > 2.0,
"counting must still separate at 2000 items: members {:.2} vs non {:.2}",
mean(&members),
mean(&nonmembers)
);
}
}