Focus: Biological Engram Sparse Memory Allocation & Hopfield Energy Geometry
Continuing the codebase extraction. This volume addresses KAI's memory storage. Traditional AI stores "memory" either inside fixed network weights (which require fine-tuning) or inside a dense vector database (RAG). KAI employs a biologically-plausible *Sparse Engram Allocation System*, mimicking human memory formation where a memory is structurally encoded as a tiny, active subset of cells within an energy landscape.
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In biological brains, an "engram" is a physical trace of a memory encoded by the synchronous firing of roughly 2% to 6% of neurons in a specific region. KAI physically implements this.
src/cognition/engram.rs
/// Target sparsity: what fraction of the lattice should be recruited per memory
/// The transcript says 2-6% for biological engrams. We use 5% as a default.
pub const ENGRAM_SPARSITY: f32 = 0.05;
/// Allocate a sparse engram for a new memory
/// Biological principle: only 2-6% of cells are recruited per memory.
/// Competitive allocation: cells with highest excitability win.
pub fn allocate_engram(&mut self, universe: &mut Universe, label: &str, vec: &SparseVec) -> Engram {
// Target number of cells to recruit (5%)
let target_count = ((cell_count as f32) * ENGRAM_SPARSITY).max(1.0).min(50.0) as usize;
// Score all cells by: excitability + cosine similarity to input
let mut scored: Vec<(usize, f32)> = (0..cell_count)
.map(|i| {
let cell = &universe.get_cells()[i];
let sim = vec.cosine(&cell.claim.vec);
let score = self.states[i].excitability + sim;
(i, score)
})
.collect();
// Sort by score descending (competitive selection)
scored.sort_by(|a, b| b.1.partial_cmp(&a.1).unwrap_or(std::cmp::Ordering::Equal));
Proof Analysis: When KAI stores an experience, it does not create a completely new, isolated vector. It executes a *Competitive Allocation*. It calculates the geometric resonance (sim) between the new memory and the existing cells, adds in the cells' biological excitability (how recently they fired), and recruits the top 5% of the lattice. This physical subset of pre-existing cells *becomes* the engram.
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Human memories experienced close together in time physically share neurons. KAI implements this via TEMPORAL_LINK_WINDOW_SECS.
src/cognition/engram.rs
// Check temporal linking: if close in time to previous engram, share some cells
let mut selected = HashSet::new();
let time_since_last = now.saturating_sub(self.last_engram_time);
if time_since_last < TEMPORAL_LINK_WINDOW_SECS && !self.engrams.is_empty() {
// Force overlap with the most recent engram (temporal linking)
let last_engram = self.engrams.last().unwrap();
let overlap_count = (target_count / 4).max(1); // 25% overlap
for idx in last_engram.cell_indices.iter().take(overlap_count) {
if *idx < cell_count {
selected.insert(*idx);
}
}
}
Proof Analysis: If KAI creates two memories within an hour (3600 seconds), it forcibly overlaps 25% of the physical cells between the two engrams. This ensures that recalling one memory geometrically pulls on the physical structure of the other memory. This is the exact mechanism of episodic continuity—how humans remember events in a timeline rather than as isolated facts.
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KAI ensures memory stability not through static data fields, but through an energy potential function modeled after continuous Hopfield Networks.
src/cognition/engram.rs
/// Calculate energy of an engram: lower energy = more stable memory
/// Energy = -sum(cosine similarity between engram vector and each cell vector)
/// - sum(connection weights between selected cells)
pub fn calculate_engram_energy(&self, universe: &Universe, cell_indices: &[usize], vec: &SparseVec) -> f32 {
let cells = universe.get_cells();
let mut energy = 0.0f32;
// Field energy: how well the engram vector aligns with selected cells
for idx in cell_indices {
if let Some(cell) = cells.get(*idx) {
let sim = vec.cosine(&cell.claim.vec);
energy -= sim; // Lower energy when aligned
}
}
// Connection energy: penalize if selected cells don't reinforce each other
for i in 0..cell_indices.len() {
for j in (i + 1)..cell_indices.len() {
if let (Some(cell_i), Some(cell_j)) = (cells.get(cell_indices[i]), cells.get(cell_indices[j])) {
let connection = cell_i.claim.vec.cosine(&cell_j.claim.vec);
energy -= connection * 0.5; // Lower energy when cells are connected
}
}
}
energy
}
Proof Analysis: Memories in KAI seek a state of lowest physical energy. The memory's stability is verified by mathematically computing the internal constructive interference (energy -= connection * 0.5) between the 5% of cells recruited. If the cells geometrically contradict each other, the engram has high energy and is unstable (causing cognitive dissonance). If they align, the memory settles into a deep, stable basin of attraction in the 16,384-dimensional topography.