SBLA-Cortical: Unifying 1.58-Bit Ternary Synapses, O(1) Dendritic Fast-Weight Memory, and Homeostatic Spiking Predictive Coding for Ultra-Efficient Foundation Models
Year: 2026
Type: preprint
Abstract: Contemporary autoregressive Foundation Models (such as GPT, Llama, and DeepSeek architectures) face a severe physical and computational ceiling driven by four foundational bottlenecks: (1) the Von Neumann memory wall caused by transferring 16-bit floating-point parameters between off-chip High-Bandwidth Memory (HBM) and arithmetic logic units, (2) quadratic O(T²) time complexity and linear O(T) Key-Value (KV) cache growth over sequence length T, (3) synchronous dense neuronal activation that expends identical computational energy on trivial and complex tokens alike, and (4) unconstrained Euclidean latent spaces that permit representation drift across recurrent reasoning steps. In contrast, the biological human neocortex processes continuous multimodal streams on approximately 20 Watts of metabolic power by utilizing co-located discrete synapses, fixed-volume continuous working memory, sparse event-driven spikes, and predictive habit consolidation. In this paper, we present SBLA-Cortical (Sparse-Binary Liquid-Associative Cortical Architecture), a physics-grounded neuromorphic foundation model architected from mathematical first principles by Sumit Shrivastava. SBLA-Cortical unifies four architectural pillars: Pillar I — Factorized 1.58-Bit Ternary Synaptic Algebra (W in {-1, 0, +1}): Compresses 81.1% of network parameters (15,361,856 core synapses) into 2-bit hardware-packed uint8 integers (4 synapses per byte, occupying just 3.64 MB of core weight RAM) paired with a continuous high-resolution sensory readout bridge. Pillar II — Zero-Quadratic O(1) Dual Cortical Working Memory: Combines a 3-Tap Causal Dendritic Delay Line with Decoupled-RoPE Fast-Weight Associative Memory and a Continuous-Time Liquid Time-Constant (LTC) Differential Equation to lock single-stream working memory at a strictly constant 72.0 KB across all sequence lengths (from 1K to 131K+ tokens). Pillar III — Homeostatic Ternary Leaky Integrate-and-Fire (T-LIF) Spiking & Cortical Habituation: Keeps 79.7% of cortical channels silent (0) while automatically reducing active Mixture-of-Experts (MoE) routing from 69.8% down to 18.3% as patterns transition from unfamiliar effort (System 2) to mastered habit (System 1). Pillar IV — Monotonic Two-Step Hierarchical Predictive Coding on an RMS-Preserving Riemannian Manifold: Contracts variational Free Energy by 6.0x (F: 0.5676 -> 0.0943) across two recurrent cortical passes. Key Empirical Benchmark Results (SBLA-Cortical-v0.9 vs. Standard Dense Transformer) In head-to-head empirical benchmarks on real English Byte-Pair Encoding (BPE) sequences (tiktoken GPT-2 vocabulary, V = 50,257), SBLA-Cortical-v0.9 (18.93M parameters) outperforms a matched Standard Dense Transformer (29.94M parameters): Final English Cross-Entropy Loss: 0.0057 (Perplexity 1.01) vs. 0.0080 for the Dense Transformer (28.7% lower loss with 36.8% fewer parameters). Deployed Weight RAM Footprint: 10.48 MB total (3.64 MB 2-bit packed ternary core) vs. 57.11 MB (5.4x less weight memory). Working Memory at 32,768 Tokens: 72.0 KB constant O(1) state vs. 128.0 MB KV-cache (1,820.4x less working RAM; 7,281.8x less at 131K tokens). Active Neuron Sparsity: 20.3% active ternary spikes (79.7% silent neurons) and 18.3% routed experts (81.7% bypassed after habituation). Official Code, Pretrained Weights & Author Links Official GitHub Repository & 9-Stage Ablation Suite (v0.1 to v0.9): https://github.com/sumitshrivastava-tech/SBLA-Cortical Pretrained 2-Bit Packed & FP32 Checkpoints (Hugging Face): https://huggingface.co/SumitShrivastava/SBLA-Cortical-19M Author Contact (Sumit Shrivastava — LinkedIn): https://www.linkedin.com/in/sumitshrivastava-tech
Author: Shrivastava, Sumit
Language: English
Subfield: Electrical and Electronic Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223022975
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