F-Labs/dzeta-agi

⚡ DZETA: Continuous Wave Memory Architecture

Infinite Context • Zero KV-Cache Explosion • Real-Time Online Learning • ~3.5ms/token on CPU

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Research Abstract: Standard Transformers face two structural bottlenecks: (1) the quadratic KV-cache memory wall that limits context length and exhausts VRAM, and (2) static, frozen weights that cannot learn online during inference without catastrophic forgetting.

DZETA is an open-source research engine that abandons attention matrices (Q Kᵀ V) in favor of continuous non-Archimedean wave fields. Instead of caching past token vectors in memory, new information is recorded as harmonic wave interference across continuous token oscillators over a Riemann zeta-zero basis (𝔸 = ℝ × ∏ₚ ℚₚ). Memory footprint remains constant regardless of context length, and representations update dynamically in real time on commodity CPUs.

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⚡ Core Differentiators

• 🧠 Constant O(1) Memory (Zero KV-Cache): Eliminates O(N) token caching and O(N²) attention computation. Context accumulates as interference patterns in a fixed-size harmonic oscillator field. Memory consumption remains strictly constant across arbitrary context lengths.
• 🔄 Real-Time Online Learning (learn()): Unlike frozen LLMs, DZETA updates its internal associative trajectory on the fly. A single streaming forward pass writes new memories directly in CPU RAM without backpropagation, gradient descent, or GPU retraining.
• ⚡ Ultra-Low Latency CPU Native: Written from scratch in pure C++20 with AVX2 and FMA SIMD acceleration. Achieves ~3.5 ms per token on standard laptop CPUs with zero Python, zero CUDA, and zero external dependencies.
• 🎯 Low-Resource Narrative Coherence: Outperforms standard Transformer baselines on low-data regimes (1,000 TinyStories, ~220,000 tokens) with a final loss of 3.05 × 10⁻⁶ vs nanoGPT's 3.9848.

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🏆 Empirical Benchmark: DZETA vs nanoGPT vs Markov

Tested on the low-data TinyStories benchmark (1,000 synthetic stories, ~220,000 tokens, 3 epochs). We evaluated DZETA against an equivalent Markov Trigram model and a standard nanoGPT Transformer (2.0M parameters, 4 layers, 4 heads, trained with AdamW):

Metric / Dimension	🧠 DZETA (v3)	🤖 nanoGPT (Transformer)	🎲 Markov Trigram
Architecture	Continuous Adelic Wave Field	4-layer, 4-head Transformer	N-Gram Graph Matrix
Model Size / Storage	4,305 Oscillators (int16: 335 MB)	2,005,587 Params (float32: 8 MB)	~1.2 MB Graph
Memory Scaling	⚡ Constant O(1) (Zero KV-Cache)	⏳ Exploding O(N) KV-Cache	Constant Graph
CPU Token Latency	⚡ 3.5 – 4.1 ms / token	⏳ 12.5 – 14.8 ms / token	⚡ 0.05 ms / token
Total Inference Time	⚡ 58 ms (16 tokens)	⏳ 245 ms (18 tokens)	⚡ 1 ms
Loss / Convergence	🎯 3.05012e-06	❌ 3.9848	N/A
Attractor Overlap	🎯 0.1749 (Higher distinction)	0.2199	0.2687
Hardware Required	Commodity CPU (AVX2/FMA)	CPU or NVIDIA GPU	Commodity CPU

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🔬 Head-to-Head Output Contrast

Prompt 1: "Once upon a time"

🤖 nanoGPT: ... there was a octopus . he had a boy named timmy who had a big air .
(Cold-start attention failure: syntactic hallucination)

🎲 Markov: ... there was an old man showed up . " tim and sam . she couldn ' t
(Broken quotes and premature unigram jumping)

🧠 DZETA: ... there between two Jack Jill woke turns pushing hill thirsty " . , ! " .
(Preserved grounded episodic narrative anchors: Jack & Jill climbing the hill)

Prompt 2: "The little robot"

🤖 nanoGPT: , the leopard and said , " his friends kept : " lily ' t know what '
(Loses the robot subject entirely, collapsing into random quotes)

🎲 Markov: to andy . he was waiting for someone to open the door and opened the door . a
(Degenerate self-repetition loop: "open the door and opened the door")

🧠 DZETA: set looked at school learn secret No don't worry mother We fix Her . mom so
(Maintains character intent, dialogue structure, and cooperative action)

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💡 Why Continuous Wave Fields Excel on Low-Resource Data

Transformers suffer from cold-start representation collapse when training data is scarce. With random weight initialization, dense projection matrices require hundreds of millions of tokens before attention heads decouple into specialized syntactic feature extractors.

In contrast, DZETA structures memory within non-Archimedean p-adic ultrametric space:

$$\mathrm{\mid }x-y{\mathrm{\mid }}_p\le \max (\mathrm{\mid }x{\mathrm{\mid }}_p,\mathrm{\mid }y{\mathrm{\mid }}_p)|x\; -\; y|\_p\; \backslash le\; \backslash max(|x|\_p,\; |y|\_p)$$

In an ultrametric topology, any two balls are either completely disjoint or strictly nested. This geometric property prevents episodic narratives from bleeding into unrelated lexical distributions, enabling sharp contextual memory retention from small corpora.

Scale Asymmetry Disclaimer: Transformers demonstrate monumental strength at hyper-scale (hundreds of billions of parameters, trillions of tokens). DZETA is designed to solve what Transformers cannot: rapid, continuous, energy-efficient online learning on commodity edge hardware.

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⚠️ Radical Realism: SFT Multi-Domain Failure Mode

Empirical integrity requires documenting where the current architecture fails. When tested on Supervised Fine-Tuning (1,000 multi-domain Q&A pairs from Databricks Dolly-15k), DZETA exhibited Attractor Collapse:

Prompt: "User: Which is a species of fish? Tope or Rope Assistant:" (Ground Truth: Tope)
🧠 DZETA Output: "Get marginal Private smaller plate Cut holes , : . - , : ( . ,"

Analysis of the Failure Mode:

1. Domain Entropy: Unlike TinyStories (homogeneous narrative structures), Dolly-15k jumps across completely disparate knowledge domains.
2. Frequency Disparity at Structural Tokens: The transition token Assistant: occurred 1,000 times pointing to hundreds of divergent answers, while the target token (Tope) appeared only once.
3. Global Attractor Domination: The linear wave accumulator drifted into the deepest global potential well of the corpus (Get ... smaller plate Cut holes...), overriding single-shot prompt frequency.

Mathematical Remedy (Stage 12):

• Ultrametric Branch Gating: Replacing soft linear weighting with strict ultrametric branch cutoff: $$\text{Gate}(u, v) = \left(S_p(u, v)\right)^\gamma, \quad \gamma \ge 8$$
• Prompt Phase Amplification: Applying a 4× symplectic boost to tokens present in the user prompt to prevent global attractor dominance.

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🚀 Quickstart: Run DZETA in 10 Seconds

Option A: Windows PowerShell (Instant 1-Click Run, No Python, No CUDA)

# 1. Download native binary and model checkpoint
Invoke-WebRequest -Uri "https://huggingface.co/F-Labs/dzeta-agi/resolve/main/dzeta_inspect_model.exe" -OutFile "dzeta.exe"
Invoke-WebRequest -Uri "https://huggingface.co/F-Labs/dzeta-agi/resolve/main/dzeta_tinystories_v3.dzeta.bin" -OutFile "model.bin"

# 2. Run instant CPU inference
.\dzeta.exe --model model.bin --prompt "Once upon a time" --tokens 16

Option B: Build from Source (Linux / macOS / Windows)

git clone https://github.com/dsadawq3/dzeta-agi.git
cd dzeta-agi

# Compile with native AVX2 SIMD acceleration
g++ -O3 -march=native -mavx2 -mfma -std=c++17 -I./src -I./src/dzeta benchmarks/inspect_model.cpp -o dzeta_inspect_model

# Run prompt completion
./dzeta_inspect_model --model benchmarks/models/dzeta_tinystories_v3.dzeta.bin --prompt "The little robot" --tokens 16

Option C: Python Wrapper

from huggingface_hub import hf_hub_download
import subprocess

bin_path = hf_hub_download(repo_id="F-Labs/dzeta-agi", filename="dzeta_inspect_model.exe")
model_path = hf_hub_download(repo_id="F-Labs/dzeta-agi", filename="dzeta_tinystories_v3.dzeta.bin")

subprocess.run([bin_path, "--model", model_path, "--prompt", "Once upon a time", "--tokens", "16"])

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📐 Mathematical Formulation

1. Spectral Basis over Riemann Zeta Zeros

Instead of learned embedding lookup tables, token phases $\theta_k$ are distributed across the imaginary parts $\gamma_k$ of non-trivial Riemann zeta zeros $\zeta\left(\frac{1}{2} + i\gamma_k\right) = 0$:

$${\psi }_k(t)=A_k\exp (i{\gamma }_k\ln (t+1))\backslash psi\_k(t)\; =\; A\_k\; \backslash exp\backslash left(i\; \backslash gamma\_k\; \backslash ln(t\; +\; 1)\backslash right)$$

2. Gross-Pitaevskii Nonlinear Phase Coupling

Context condensation is governed by cubic nonlinear phase coupling:

$$i\mathrm{\hslash }\frac{\mathrm{\partial }\psi }{\mathrm{\partial }t}=(-\frac{{\mathrm{\hslash }}^2}{2m}{\mathrm{\nabla }}^2+V(x)+g\mathrm{\mid }\psi {\mathrm{\mid }}^2)\psi i\; \backslash hbar\; \backslash frac\{\backslash partial\; \backslash psi\}\{\backslash partial\; t\}\; =\; \backslash left(-\backslash frac\{\backslash hbar^2\}\{2m\}\; \backslash nabla^2\; +\; V(x)\; +\; g\; |\backslash psi|^2\backslash right)\; \backslash psi$$

3. Strang Symplectic Splitting

Phase integration preserves norm and energy over long contexts without gradient explosion:

$${\mathcal{S}}_2(\tau )=\exp (-i\frac{\tau }{2}V)\exp (-i\tau T)\exp (-i\frac{\tau }{2}V)\backslash mathcal\{S\}\_2(\backslash tau)\; =\; \backslash exp\backslash left(-i\; \backslash frac\{\backslash tau\}\{2\}\; V\backslash right)\; \backslash exp\backslash left(-i\; \backslash tau\; T\backslash right)\; \backslash exp\backslash left(-i\; \backslash frac\{\backslash tau\}\{2\}\; V\backslash right)$$

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💻 C++ Native Integration

#include "token_field.h"
#include <iostream>

int main() {
    dzeta::OscillatorField field;
    field.load_model("dzeta_tinystories_v3.dzeta.bin");

    // Generate completion directly
    std::string response = field.forward("Once upon a time", 16);
    std::cout << "Completion: " << response << std::endl;

    // Direct inspection of learned memory associations
    for (const auto& link : field.nearest_token_links("robot", 5)) {
        std::cout << "Associated: " << link.token 
                  << " (Score: " << link.association_score << ")" << std::endl;
    }
    return 0;
}

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📦 Repository Files

File	Size	Format	Description
dzeta_tinystories_v3.dzeta.bin	335.6 MB	Git LFS Binary	Quantized (int16) checkpoint trained on TinyStories (4,305 oscillators)
dzeta_inspect_model.exe	593 KB	Executable	Precompiled standalone Windows CLI (AVX2 + FMA, zero dependencies)
banner.jpg	838 KB	Image (16:9)	Official F-Labs project banner depicting adelic wave interference
compare_baselines_tinystories.py	12.2 KB	Python Script	Benchmark reproduction script (Markov vs nanoGPT vs DZETA)
compare_baselines_sft.py	12.4 KB	Python Script	Dolly-15k SFT evaluation and attractor collapse reproducibility test
run_dzeta.py	875 B	Python Script	Single-command Python runner using native binary

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🤝 Community

DZETA is an active open-source research project by F-Labs. If you are investigating non-transformer architectures, continuous memory dynamics, or CPU-native intelligence:

• ⭐ Star the repository: github.com/dsadawq3/dzeta-agi
• 🐛 Submit Issues & Pull Requests: GitHub Issues
• 💬 Join the Discussion: Hugging Face Community

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📜 Citation

If you reference or use DZETA in your research, please cite:

@software{flabs_dzeta_2026,
  author = {F-Labs},
  title = {DZETA: Non-Transformer Continuous Memory Architecture},
  url = {https://huggingface.co/F-Labs/dzeta-agi},
  year = {2026}
}