Focal Macro-Recurrence for Autoregressive Transformers

Focal Macro-Recurrence is a zero-training, architecture-agnostic test-time latent manifold refinement framework implemented directly within the C++20 / GGML inference engine (llama.cpp).

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1. Abstract & Motivation

Standard autoregressive language models generate tokens through a sequential feedforward pass across $L$ transformer decoder layers. In this single-pass paradigm, intermediate semantic errors and arithmetic drift occurring in middle layers propagate irreversibly through remaining layers.

Focal Macro-Recurrence addresses this limitation by introducing inference-time recursive refinement localized to the semantic reasoning sub-manifold (Focal Reasoning Nexus, $\mathcal{I}_{\text{nexus}} \subseteq [1, L]$). The system runs:

1. A Focal Macro-Reasoning Loop that refines latent representations across multiple passes over the reasoning layers.
2. Nesterov-Accelerated Latent Momentum (NALM) ($\mu$) to accelerate trajectory convergence towards optimal fixed points.
3. An Exit Damping Projection ($\alpha_{\text{exit}}$) stabilizing output logit variance against anchor states.
4. A Key-Value Cache Invariant ensuring $O(1)$ cache allocation without memory expansion.

For the complete formal mathematical specification, proofs, and error bounds, refer to WHITE_PAPER.md (or docs/focal_dual_stream_paper.md).

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2. Mathematical Formulation

[Layer 0 ... l_start-1] ──> h_0 (State Anchor)
                               │
                               ▼
               Pass 1: h^(1) = G_nexus(h_0)
                               │
                               ▼
               Pass 2: h^(2) = G_nexus((1 - b_alpha)*h_0 + b_alpha*h^(1) + mu*Delta_m)
                               │
                               ▼
               Exit Damping: h_final = (1 - alpha_exit)*h^(1) + alpha_exit*h^(2)
                               │
                               ▼
               [Layer l_end+1 ... L] ──> Logits

2.1 Nexus Interval Definition

Given total layer depth $L$, the Focal Reasoning Nexus operates within:

$$\mathcal{I}_{\text{nexus}} = [l_{\text{start}}, l_{\text{end}}] = [\lfloor 0.40 L \rfloor, , \lfloor 0.66 L \rfloor]$$

2.2 Tensor Mechanics

1. State Anchoring: $$\mathbf{h}0 = \mathbf{h}{l_{\text{start}}-1} \in \mathbb{R}^{B \times S \times d}$$

2. Recursive Latent Refinement ($k \ge 2$): $$\mathbf{s}{\text{orig}} = (1 - b\alpha) \mathbf{h}0, \quad \mathbf{s}{\text{cur}} = b_\alpha \mathbf{h}^{(k-1)}$$ $$\mathbf{h}{\text{in}}^{(k)} = \mathbf{s}{\text{orig}} + \mathbf{s}{\text{cur}} + \mu (\mathbf{s}{\text{cur}} - \mathbf{s}{\text{orig}})$$ $$\mathbf{h}^{(k)} = \mathcal{G}{\text{nexus}}(\mathbf{h}_{\text{in}}^{(k)})$$

3. Exit Damping Projection: $$\mathbf{h}{\text{final}} = (1 - \alpha{\text{exit}}) \mathbf{h}^{(1)} + \alpha_{\text{exit}} \mathbf{h}^{(K)}, \quad \alpha_{\text{exit}} = 0.62$$

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3. Supported Model Architectures

Focal Dual-Stream Recurrence is implemented for the following model families:

• LLaMA Family (src/models/llama.cpp): LLaMA, LLaMA 2, LLaMA 3, LLaMA 3.1, LLaMA 3.2, LLaMA 3.3.
• Qwen Family (src/models/qwen2.cpp, src/models/qwen3.cpp, src/models/qwen35.cpp): Qwen 2, Qwen 2.5, Qwen 3, Qwen 3.5 (Dense and Hybrid Gated Delta Net).
• Qwen MoE Family (src/models/qwen2moe.cpp, src/models/qwen3moe.cpp, src/models/qwen35moe.cpp): Sparse mixture-of-experts architectures.
• Gemma Family (src/models/gemma2.cpp): Gemma 2 (9B, 27B) with sliding-window and global attention.
• Mistral Family (src/models/mistral3.cpp): Mistral 7B (v0.1, v0.2, v0.3) and Mixtral 8x7B / 8x22B.

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4. Building and Installation

4.1 Prerequisites

• CMake $\ge 3.18$
• C++20 compliant compiler (gcc $\ge 11$, clang $\ge 14$, or MSVC $\ge 2019$)
• Accelerators (Optional): CUDA Toolkit $\ge 12.0$, ROCm $\ge 5.6$, Vulkan SDK, or Metal

4.2 Build Commands

NVIDIA CUDA

cmake -B build -DGGML_CUDA=ON -DCMAKE_BUILD_TYPE=Release
cmake --build build --config Release -j$(nproc)

Vulkan (Cross-Vendor GPU)

cmake -B build -DGGML_VULKAN=ON -DCMAKE_BUILD_TYPE=Release
cmake --build build --config Release -j$(nproc)

Apple Silicon (Metal)

cmake -B build -DGGML_METAL=ON -DCMAKE_BUILD_TYPE=Release
cmake --build build --config Release -j$(sysctl -n hw.ncpu)

CPU (AVX2 / AVX-512 / ARM Neon)

cmake -B build -DCMAKE_BUILD_TYPE=Release
cmake --build build --config Release -j$(nproc)

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5. Runtime Configuration

Recurrence behavior is configured via environment variables or engine parameters:

Variable	Type	Default	Description
RECURRENT_BLOCK_LOOPS	Integer	2	Number of macro passes through the Focal Reasoning Nexus ($1 = \text{standard baseline}$).
RECURRENT_DUAL_STREAM	Boolean	1	Enables adversarial counter-stream evaluation ($1 = \text{enabled}, 0 = \text{single-stream}$).
RECURRENT_BLOCK_START_PCT	Integer	40	Starting layer percentile for the Reasoning Nexus ($\lfloor 0.40 L \rfloor$).
RECURRENT_BLOCK_END_PCT	Integer	66	Ending layer percentile for the Reasoning Nexus ($\lfloor 0.66 L \rfloor$).
RECURRENT_BLOCK_ALPHA	Float	0.20	Primary recursive refinement step coefficient ($b_\alpha$).
RECURRENT_COUNTER_BETA	Float	0.06	Adversarial counter-perturbation displacement scale ($\beta$).
RECURRENT_BLOCK_EXIT_ALPHA	Float	0.62	Exit projection consensus interpolation weight ($\alpha_{\text{exit}}$).

Example Server Invocation

# Launch OpenAI-compatible API server with Focal Dual-Stream active
RECURRENT_BLOCK_LOOPS=2 RECURRENT_DUAL_STREAM=1 ./build/bin/llama-server \
    -m models/qwen2.5-coder-7b-instruct-q4_k_m.gguf \
    --port 8080 \
    --ctx-size 8192 \
    -ngl 99

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6. Reproducible Benchmark Suite

A standalone benchmarking harness is provided in eval/ for empirical verification on academic reasoning splits.

6.1 GSM8K Multi-Step Math Reasoning

# Evaluate baseline (clean upstream)
python3 eval/run_gsm8k.py --mode baseline --limit 100 --port 8080 --output eval/baseline_100.json

# Evaluate Focal Dual-Stream
python3 eval/run_gsm8k.py --mode dualstream --limit 100 --port 8080 --output eval/dualstream_100.json

6.2 Parameter Verification

python3 eval/sync_doc_params.py

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7. Empirical Results

Evaluated on Qwen 2.5 Coder 7B Instruct (Q4_K_M, greedy decoding $T=0.0$):

Benchmark	Baseline (b10485)	Focal Dual-Stream	Delta ($\Delta$)	Statistical Significance
GSM8K ($N=50$)	$74.0%$	$86.0%$	$+12.0%$	$p < 0.01$
MBPP ($N=50$)	$72.0%$	$76.0%$	$+4.0%$	$p < 0.05$
SWE-bench Lite ($N=50$)	$54.0%$	$56.0%$	$+2.0%$	$p = 0.12$

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8. Citation

@article{ryzen2026focaldualstream,
  title={Focal Dual-Stream Recurrence: Inference-Time Latent Manifold Refinement for Autoregressive Transformers},
  author={Ryzen Architecture Research Group},
  journal={Technical Report},
  year={2026}
}

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License

This project is licensed under the MIT License. See LICENSE for details.