atmaram.

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associative tree memory for asynchronous retrieval & attention mapping

VRAM: 64.46 MB (O(1) Flat) NVMe: 132 Pages Latency: 2.18–2.39 ms Recall: 200/200 Top-3

Interactive 3D ATMARAM Neural Tree Engine

Top-down branch pruning, bottom-up learned aggregation, and off-chip NVMe subword page blocks.

ATMARAM Tier Key 3D Interactive

L3/L2 VRAM Hot

L1 Staging

L0 NVMe 4KB

MaxSim Route

Drag to rotate · Scroll to zoom · Tap node to inspect

Status: Orbiting

Node Telemetry

L3 Global Root

Node ID: L3_Root_0

Dimension $d$: 8192 (spec) / 192 (build)

Residency: HOT — VRAM / RAM

Page Offset: 0x0000 (Root Slot)

MaxSim Score: 1.000 (Active Root)

Architectural Function

The L3 Global Root anchors highest-abstraction linear sequence memory in VRAM. It coordinates top-down branch pruning and routes multi-block queries directly to L2 sections without full-sequence $O(N^2)$ quadratic cost.

Subword Payload State

[CLS] ATMARAM Temporal Memory Root

Leaves: 12 Chunk $S$: 16 tok Slots $k$: 8

Incremental Multi-Block Streaming Loop

Simulate sequence generation step-by-step ($t = 0 \dots 2048$). Watch VRAM stay flat while NVMe cold storage scales.

Token Step $t$: 128 / 2048 NVMe Chunks: 8 Hot Window $W$: 32 tok VRAM Usage: 64.46 MB (FLAT)

Live Token Stream & Sliding Window ($W = 32$)

ATMARAM Footprint O(1) Flat Overhead

N = 128 ... 2048 64.46 MB

ATMARAM freezes attention state into $k=8$ strided RAW slots stored in off-chip NVMe cold storage. Active VRAM memory remains strictly constant $O(1)$.

Standard KV Baseline O(N) Linear / Quadratic

N = 128 68.8 MB

Standard quadratic attention scales linearly/quadratically with token sequence length $N$, leading to VRAM OOM exhaustion past $N = 2048$ on 4GB hardware.

H3-k8 Late Interaction MaxSim Matrix

Computes query-token to chunk-slot late interaction to guarantee 100% factual recall without mean-pooling collapse.

NVMe Chunk:

MaxSim Scoring Rule: S(q, C) = ∑_i=1..Q max_k (q_i · s_k) / √d

Calculated MaxSim Score: 14.82

Query \ Slot	s₁	s₂	s₃ (Max)	s₄	s₅	s₆	s₇	s₈	max_k

Why H3-k8 MaxSim Prevents Loss

Standard sentence embeddings average token vectors before retrieval, discarding fine-grained facts and causing recall to drop to ~0.19.

ATMARAM retains $k=8$ strided raw token slots per chunk, computing token-level dot products to achieve 100% (200/200) target recall.

Empirical Hardware Benchmarks

Measured on baseline RTX 3050 Laptop GPU (4GB VRAM), NVMe SSD, full-book Wilde dataset.

Full-Book Perplexity (PPL) Decomposition

Lower is better. ATMARAM achieves 151.2 PPL comparable to unconstrained 4L full attention (142.0) while running in flat 64.46 MB VRAM.

Planting Rate ($plant\_p$) Sweep & Recall Cliff

PPL stays flat across all planting rates while recall exhibits a sharp cliff below $plant\_p = 0.125$.

Measured Hardware Verification Log

Architecture Mechanism	Measured Result	Status
Phase 0 — H2D Positional Recall	1.000 vs 0.234 baseline	PASS
Stage 1 — H2D Subword Recall	1.000x3 vs 0.163 baseline	PASS
H3-k8 Content Late Interaction	0.978 (baseline 0.568)	PASS
Phase 5 — Triton Kernel SDPA (fp32)	maxdiff 4.77e-07 (T=8192)	PASS

Mathematical Foundations & Formal Specification

Formal definitions for 2D Positional Embeddings, Learned Pooling, MaxSim Late Interaction, and Online Softmax.

1. Hierarchical 2D Rotary Encoding (H2D-RoPE)

Splits dimension into halves, applying 1D RoPE per half using tree depth $D_i$ and sibling offset $P_i$:

$$e_i = x_i + \text{RoPE}_{2D}(D_i, P_i)$$

2. Learned Bottom-Up Pooling

Query-free softmax pooling over sibling nodes $s_j$ with up-projection $W_{\text{up}}$ and LayerNorm:

$$\alpha_j = \text{softmax}(w_a \cdot s_j) \quad \cdot \quad p = \text{LN}\left( W_{\text{up}} \sum_j \alpha_j s_j \right)$$

3. H3-k8 Late Interaction (MaxSim)

Token-level interaction between $Q=8$ query states and $k=8$ strided raw slots per chunk:

$$S(q, C) = \sum_{i=1}^{Q} \frac{\max_k (q_i \cdot s_k)}{\sqrt{d}}$$

4. Tree-FlashAttention Online Softmax

Per $K/V$ tile $i$ (32x32 block, SRAM budget ~24.6 KB):

$$m_i = \max(m_{i-1}, \text{rowmax}(S_i)) \quad \cdot \quad l_i = l_{i-1}e^{m_{i-1}-m_i} + \text{rowsum}(e^{S_i-m_i})$$