SGM

Survivorship Amplification in Parameter-Locked Evolutionary Systems

A geometric neuroplasticity substrate for continual learning. Lock what converges. Survivors get exponentially stronger.

The Finding

Binary parameter locking with evolutionary optimization produces exponential per-parameter amplification -- a phenomenon we call survivorship plasticity. As parameters lock (stabilize), the remaining free parameters become exponentially more productive per dimension.

This is how the brain works. Synaptic pruning makes survivors stronger. We measured the rate.

1,313x amplification at 99% locked. R^2 = 0.984. dim = 500,000.

Key Results

Survivorship Amplification (Novel Finding)

The per-dimension learning improvement follows an exponential law as lock percentage increases. This has never been reported in the machine learning literature.

Dimension	Alpha	R^2	Ratio at 99%
10,000	0.018	0.808	9.8x
50,000	0.022	0.825	16.2x
100,000	0.025	0.861	22.4x
500,000	0.068	0.984	1,313x

LLM Knowledge Preservation (Qwen2.5-0.5B)

SGM preserves 95% of a 494M-parameter LLM's general knowledge during aggressive domain fine-tuning. Without protection, the model retains 0%.

Epoch	SGM (30% locked)	Naive	Perplexity (SGM)	Perplexity (Naive)
0	98% retained	18%	10.7	334
2	95% retained	1%	11.0	2,393
4	95% retained	0%	12.6	112,036

Continual Learning Benchmarks

Multi-Head Split-MNIST (5 binary tasks, separate output per task, 3 seeds):

Method	Avg Accuracy	Backward Transfer
Naive	90.8%	-11.2%
EWC	90.8%	-11.3%
SGM	99.4%	-0.2%

Multi-Head Split-CIFAR-10 (5 binary tasks, CNN backbone, 3 seeds):

Method	Avg Accuracy	Backward Transfer
Naive	81.1%	-12.9%
EWC	85.5%	-4.9%
SGM Evo+Coalition	86.1%	-3.0%
SGM Coalition	87.2%	-3.0%

Permuted-MNIST (20 sequential tasks):

SGM retains 28% of Task 0 after 20 tasks. Naive retains 12%.

Boolean Space (NAND GateMesh)

Survivorship amplification is substrate-independent. It emerges in discrete Boolean circuits (5 bytes/gate) with the same exponential shape as continuous parameters.

Substrate	Alpha	R^2	Ratio at 95%
Continuous (500K dims)	0.068	0.984	1,313x
Boolean (8,192 NAND gates)	0.026	0.794	16.7x

The Primitive

Three lines of code:

if locked:
    delta = 0  # This dimension cannot change

Combined with:

• Evolutionary optimization: Fixed mutation count creates selective pressure
• Convergence-based locking: Stable dimensions lock organically (like synaptic pruning)
• Coalition detection: Groups of individually-weak parameters tested for collective importance

No replay buffers. No regularization. No adapters. No architectural changes. The geometry does the work.

How It Connects

The brain: Prunes ~40% of childhood synapses. Adults are smarter because survivors carry more signal.

SGM: Locks converged parameters. Remaining free parameters exhibit exponential amplification (alpha per percentage locked).

MIT Platonic Representation Hypothesis (Huh et al., 2024): All AI models converge to the same geometric representation of reality. SGM extends this: explicitly locking converged representations produces exponential amplification of the remaining parameters.

What SGM Is Not

SGM is not:

• A neural network optimization technique
• PackNet, EWC, or any existing continual learning method
• Weight freezing "with extra steps"
• A replacement for transformers

SGM is a missing primitive -- a substrate layer that sits underneath training methods and gives them neuroplasticity. The survivorship amplification constant is a newly discovered property of parameter-locked evolutionary systems.

Repository Structure

sgm/
  core.py            # The primitive: SGMSystem (evolutionary) + SGMGradientLock (LLM)
  gates.py           # NAND GateMesh (5 bytes/gate, evolvable Boolean circuits)
experiments/
  survivorship.py    # Alpha measurement across dimensions (GPU, CuPy)
  benchmarks.py      # Split-MNIST + Permuted-MNIST + survivorship curves
  llm_knowledge.py   # Qwen2.5-0.5B knowledge preservation (SGM only)
  nand_survivorship.py # Boolean space amplification
figures/             # Publication-ready charts

Quick Start

git clone https://github.com/ACD421/sgm.git
cd sgm
pip install -r requirements.txt

# Run survivorship measurement (requires CUDA + CuPy)
python experiments/survivorship.py

# Run LLM knowledge preservation (requires ~8GB VRAM)
python experiments/llm_knowledge.py

# Run Split-MNIST + Permuted-MNIST benchmarks
python experiments/benchmarks.py

Requirements

numpy>=1.24.0
scipy>=1.10.0
torch>=2.0.0
cupy-cuda12x>=13.0.0
transformers>=4.40.0
torchvision>=0.15.0
matplotlib>=3.7.0

Prior Art

SGM's survivorship amplification has no prior art. Four targeted literature searches across pruning, continual learning, and parameter efficiency found zero publications reporting exponential per-parameter improvement as a function of lock percentage.

Related work that SGM extends:

• Platonic Representation Hypothesis (Huh et al., ICML 2024): All models converge to geometry. SGM shows what happens after convergence.
• Loss of Plasticity (Lyle et al., Nature 2024): Networks lose plasticity. SGM shows controlled locking INCREASES it.
• Lottery Ticket Hypothesis (Frankle & Carlin, 2019): 90% of parameters are redundant. SGM shows locking 90% makes the 10% each 28x better.

Author

Andrew Dorman -- Independent AI researcher

• GitHub: ACD421
• Research: Geometric primitives for intelligence without neural scaling

License

Proprietary. See LICENSE for terms.