SnakeBatch v6: Economics of Binary Divide and Conquer

Charles Dana · Monce SAS · April 2026

snakebatch.aws.monce.ai · /paper · /architecture

1. Cost Model

1.1 Lambda Pricing (eu-west-3)

v6 uses ONE Lambda type: v6-worker at 10GB.

v6-worker (10GB, ~6 vCPUs):
  invoke:  $0.0000002 per request
  compute: 10GB × duration × $0.0000166667/GB-s

  Leaf node (~200ms):    $0.000033
  Internal node (~100ms): $0.000017
  Total per worker:      ~$0.000025 avg

1.2 Workers Per Training Run

W(n, L) = L_layers × (2 × n/b − 1)

Binary tree: 2×leaves − 1 nodes per layer. All layers run in parallel.

Scale	Layers	Workers/layer	Total workers	Wall clock	Cost
250	5L	~7	~35	2.0s	$0.001
1K	5L	~25	~125	2.4s	$0.003
5K	15L	~130	~1,950	5.3s	$0.05
15K	5L	~400	~2,000	7.3s	$0.05
150K	5L	~4,000	~20,000	19.8s	$0.50
1M	5L	~27,000	~135,000	~30s (est)	$3.40

1.3 v5 vs v6 Cost Comparison

Scale	v5 cost	v5 wall	v6 cost	v6 wall	Speedup
1K (5L)	$0.002	~5s	$0.003	2.4s	2.1×
5K (15L)	$0.02	46s	$0.05	5.3s	8.7×
15K (5L)	$0.02	20s	$0.05	7.3s	2.7×
150K (5L)	$0.14	270s	$0.50	19.8s	13.6×

v6 costs 2–3x more per training (10GB workers vs 2GB) but runs 3–14x faster. The cost-per-second is dramatically better. For time-sensitive workloads, v6 dominates.

2. Why 10GB Workers

v6 workers need 10GB not for memory but for CPU. At 10GB, Lambda provides ~6 vCPUs. The worker does:

Decompress + parse population (~50ms at 10GB, ~200ms at 2GB)
oppose() + apply_literal scan (~2x faster at 10GB vs 2GB)
Snake(local_pop) for leaf SAT (~2x faster)

Downgrading to 2GB would halve cost but triple wall clock. Not worth it for the binary recursion pattern where each hop adds ~100ms.

3. Scaling Projections

3.1 With 10K Concurrent Limit

Scale	Layers	Peak concurrent	Within 10K?
5K	15L	~200	✓
15K	15L	~1,500	✓
30K	15L	~3,000	✓
150K	5L	~4,000	✓
150K	15L	~12,000	✗ (queue)

3.2 With 100K Concurrent (pending approval)

Scale	Layers	Peak concurrent	Within 100K?
150K	15L	~12,000	✓
150K	50L	~40,000	✓
1M	5L	~27,000	✓
1M	15L	~80,000	✓
1M	25L	~135,000	✗

4. Fixed vs Variable Costs

Component	Monthly	Type
EC2 t4g.micro (proxy)	$3	Fixed
S3 storage	~$0.50	Fixed
Route53 + CloudWatch	~$1.50	Fixed
Total fixed	$5/mo
Lambda compute	$0.003–$3.40/train	Variable

Zero traffic = $5/mo. Same as v5. The binary recursion is purely variable.
No provisioned capacity, no always-on workers, no orchestrator Lambda.

5. Business Model Impact

5.1 Speed as a Feature

v6’s 3–10x speed improvement enables new use cases:

Interactive classification. 5K rows classified in 4.7s — fast enough for browser-based /csv demo with real-time feedback.
CI/CD integration. Train + test on every commit. 15K rows in 6s fits in a pre-commit hook.
Real-time retraining. Customer uploads new data, model retrains in seconds. No batch job, no waiting.

5.2 Cost Per Classification

Scale	v6 cost	Per row	Comparable to
1K	$0.003	$0.000003	Free tier
15K	$0.05	$0.0000033	Cheaper than SageMaker inference
150K	$0.50	$0.0000033	Same per-row at scale
1M	$3.40	$0.0000034	Linear scaling

$3.40 per million classifications. Flat per-row cost at any scale. No bulk discount
needed because the baseline is already near-zero. Explainable SAT audit traces included.

6. Summary

2–14x faster than v5 at the same scale
1 Lambda type instead of 3 — simpler to deploy, monitor, debug
$0.001–$3.40 per training run, linear in n
$5/mo fixed — scales to zero
Self-recursive — no conductor bottleneck, no thread pool saturation
100% perfect fit 250–150K rows (all gates pass, Snake v5.4.5 datatypes enforcement)

Charles Dana · Monce SAS · snakebatch.aws.monce.ai · April 2026
Co-Authored-By: Claude (Anthropic)