Lua Vision Research · Architecture

NCAS-DiffMoE: Neuromorphic-Constrained Architecture Search with Differential Attention for Sparse Mixture-of-Experts

Paulo Câmara, David Kang, Plínio Ceccon
Lua Vision Tecnologia · São Paulo, Brazil
Published: January 2026 · Revised: May 2026
Abstract

We present NCAS-DiffMoE, a novel architecture search methodology that unifies three orthogonal innovations—neuromorphic constraints on hidden dimensionality, differential attention mechanisms, and sparse mixture-of-experts routing—into a coherent framework for training frontier-quality language models deployable on a single accelerator. Unlike conventional NAS approaches that optimize for task-specific metrics within standard architectures, our method constrains the search space using number-theoretic principles derived from biological neural systems, resulting in non-standard hidden dimensions (e.g., 4608, 3456, 2592) that maximize information-theoretic capacity per parameter. We demonstrate that combining Differential Attention (which decomposes softmax scores into constructive-destructive interference patterns) with expert-level sparsity enables a 54B-parameter model to achieve frontier performance while activating only 9.2B parameters per forward pass. On LiveBench 2026-01, our approach achieves 98.2% global score, matching or exceeding models 3-10× larger. We release architectural details sufficient for reproducibility while maintaining proprietary training methodology.

1. Introduction

The prevailing paradigm in large language model development assumes that frontier performance necessitates frontier-scale compute during both training and inference. Models such as GPT-4 (estimated >1T parameters), Gemini Ultra, and Claude 3 Opus operate at scales requiring hundreds of accelerators for a single inference pass. This creates fundamental barriers: economic exclusion of organizations without hyperscale budgets, environmental costs of continuous high-power operation, and geopolitical concentration of AI capabilities in a small number of well-resourced labs.

We challenge this assumption through NCAS-DiffMoE (Neuromorphic-Constrained Architecture Search with Differential Attention Mixture-of-Experts), a methodology that systematically derives model architectures from first principles rather than scaling existing templates. Our key insight is that the standard practice of choosing hidden dimensions as powers of 2 (512, 1024, 2048, 4096, 8192) reflects hardware convenience rather than information-theoretic optimality.

The architecture search process operates in three coupled phases:

  1. Dimension derivation: Using π-constrained number theory to identify hidden dimensions that maximize representation capacity under biological sparsity constraints.
  2. Attention mechanism design: Implementing Differential Attention that decomposes the standard softmax into constructive and destructive signal components, enabling noise cancellation at the architectural level.
  3. Expert routing optimization: Designing a Mixture-of-Experts layer with learned routing that maintains constant inference FLOPs regardless of total parameter count.

2. Related Work

2.1 Neural Architecture Search

Neural Architecture Search (NAS) has evolved from reinforcement learning-based approaches [Zoph & Le, 2017] through differentiable methods [Liu et al., 2019] to one-shot supernetworks [Cai et al., 2020]. However, prior NAS work for language models has been limited to micro-architectural decisions (attention head count, FFN multiplier) within fixed macro-architectures. NCAS differs fundamentally by searching over the macro-structural parameters themselves—hidden dimension, layer count, and expert configuration—using constraints derived from number theory rather than empirical grid search.

2.2 Mixture-of-Experts

Sparse MoE models [Shazeer et al., 2017; Fedus et al., 2022; Jiang et al., 2024] achieve parameter efficiency by activating only a subset of experts per token. GShard [Lepikhin et al., 2021] and Switch Transformers [Fedus et al., 2022] demonstrated scaling to trillions of parameters. Mixtral [Jiang et al., 2024] showed that 8×7B experts with top-2 routing could match dense 70B performance. Our approach extends this lineage by using non-standard expert counts (9 experts with top-2) and non-standard FFN dimensions derived from our constrained search.

2.3 Differential Attention

Differential Attention [Ye et al., 2024] reinterprets the attention mechanism as a signal processing operation where the output is the difference between two softmax attention maps. This creates a noise-cancellation effect analogous to differential amplifiers in electronics. We extend this mechanism with expert-specific differential parameters that adapt the constructive-destructive balance per-domain.

3. Methodology

3.1 Neuromorphic Constraints

Biological neural networks exhibit dimensionality patterns that diverge significantly from the powers-of-2 convention in artificial systems. Cortical columns in the human neocortex contain approximately 80-120 minicolumns of ~80 neurons each, giving effective dimensions in the range of 6,400-9,600. The hippocampus operates with representations in the range of 1,000-5,000 dimensions depending on encoding specificity.

We formalize this observation into a constraint system. The hidden dimension d_model must satisfy a set of number-theoretic properties that we term π-constraints (detailed in our companion paper on π-constrained dimensionality). In brief, valid dimensions must:

The search procedure evaluates candidate dimensions against a composite score incorporating information-theoretic capacity, hardware utilization efficiency, and empirical perplexity on a small proxy task. From an initial space of ~2,000 candidate dimensions in [2048, 8192], the constraint system reduces viable candidates to fewer than 50, from which we select the Pareto-optimal set.

3.2 Differential Attention Integration

Standard multi-head attention computes:

Attention(Q, K, V) = softmax(QKT / √d_k) · V

Differential Attention decomposes this into two sub-attention maps that operate in constructive-destructive pairs:

DiffAttn(Q, K, V) = (softmax(Q₁K₁T / √d_k) − λ · softmax(Q₂K₂T / √d_k)) · V

where Q is split into [Q₁; Q₂] and K into [K₁; K₂], and λ is a learnable scalar initialized near 0.5. The subtraction acts as a noise gate: common-mode noise (attending uniformly to irrelevant context) cancels, while differential signals (attending specifically to relevant tokens) are preserved and amplified.

Our extension introduces expert-conditional λ: the noise cancellation strength varies depending on which expert processes the token. This allows mathematical reasoning experts to maintain very tight attention (high λ → aggressive cancellation) while creative generation experts maintain broader attention (low λ → more exploratory attention patterns).

3.3 Sparse Expert Routing

The feed-forward network in each transformer layer is replaced by a sparse MoE layer with E experts, of which only k are activated per token. The routing function computes:

g(x) = TopK(softmax(W_g · x + noise), k)

where W_g is the gate weight matrix and noise is Gaussian noise added during training for load balancing. For our flagship model: E=9 experts, k=2 active per token. Each expert has FFN dimension 15,360, giving total FFN parameters of 9 × 15,360 × 4608 × 2 ≈ 1.28B per layer, but only 2/9 ≈ 22% activated per token.

We introduce Mixture-of-Depths (MoD) as a complementary sparsity mechanism: not all tokens need full-depth processing. A learned binary router at each layer decides whether a token should be processed by that layer or skip via residual connection only. This reduces effective active parameters further, particularly for "easy" tokens that require only shallow processing.

3.4 Architecture Specification

ParameterPI (Flagship)PI-S (Standard)PI-P (Pocket)
Total Parameters~54B~18B~5B
Active Parameters~9.2B~3.8B~1.4B
Hidden Dimension460834562592
Layers543627
Attention Heads362718
Head Dimension128128144
Experts964
Expert FFN15360102406912
Active Experts222
RoPE θ31415.92631415.92631415.926
Context Length32768163848192

Note: The RoPE base frequency θ = 31415.926... (10000π) is not arbitrary—it emerges from our π-constrained framework as the frequency that maximizes positional resolution across the target context window while maintaining smooth interpolation for extended contexts.

4. Training Methodology

The model is trained using a 6-phase curriculum (detailed in our companion paper on training methodology). Briefly:

  1. Phase 1 — Foundation: Dense pre-training on 2T tokens of multilingual web corpus with MoE routing initialized but unspecialized.
  2. Phase 2 — Specialization: Expert differentiation through domain-specific data mixtures that encourage routing divergence.
  3. Phase 3 — Alignment: Instruction tuning with RLHF and DPO on curated human preference data.
  4. Phase 4 — Safety: Constitutional AI-style training with emphasis on life-critical domain safety (medical, legal).
  5. Phase 5 — Metacognition: Training embedded confidence estimation and abstention behaviors.
  6. Phase 6 — Optimization: Hardware-specific optimizations including KV-cache quantization and expert placement strategies.

Total training compute is approximately 3.2 × 10²² FLOPs, roughly 100× less than estimated for GPT-4-class models. This efficiency derives from (a) sparse activation reducing effective model size during training, (b) curriculum structure avoiding catastrophic forgetting, and (c) π-constrained dimensions enabling more efficient gradient flow.

5. Results

5.1 LiveBench Evaluation

ModelParams (Active)GlobalReasoningMathLanguageData Analysis
Genesys PI54B (9.2B)98.2%100%95.0%100%100%
GPT-4o~1.8T (est.)72.8%74.1%62.3%81.2%73.5%
Claude 3.5 Sonnet~175B (est.)69.4%71.0%58.7%78.3%69.6%
Mixtral 8×22B141B (39B)48.2%45.8%42.1%62.4%42.3%

5.2 Inference Efficiency

On a single AMD MI300X accelerator (192GB HBM3, 5.3 TB/s bandwidth):

For comparison, serving a dense 70B model at equivalent quality requires 2-4 A100 GPUs (160-320GB total HBM), while our sparse architecture fits entirely on a single accelerator with room for extended batching.

5.3 Ablation Studies

We conducted systematic ablations to isolate the contribution of each architectural component:

ConfigurationLiveBench GlobalΔ vs Full
Full NCAS-DiffMoE98.2%
Standard dimensions (4096)91.7%-6.5%
Standard attention (no Diff)94.3%-3.9%
No Mixture-of-Depths96.8%-1.4%
Standard RoPE θ=1000095.1%-3.1%
Dense (no MoE)87.2%-11.0%

The largest single-factor improvement comes from sparse MoE routing (+11%), followed by π-constrained dimensionality (+6.5%), then Differential Attention (+3.9%). However, these factors interact synergistically: the combination exceeds the sum of individual contributions by approximately 4.2 percentage points.

6. Discussion

6.1 Why Non-Standard Dimensions Work

The superiority of π-constrained dimensions appears to stem from improved gradient dynamics during training. Standard power-of-2 dimensions create highly symmetric weight matrices that are prone to rank collapse in early training phases. Our dimensions, while less "clean" numerically, introduce beneficial asymmetry that maintains higher effective rank throughout training. We observe 23% higher stable rank (as measured by ‖W‖_F / ‖W‖_2) in our architectures compared to standard baselines at equivalent parameter counts.

6.2 Differential Attention as Noise Gate

The learned λ parameters reveal interpretable structure after training. Expert groups specializing in factual recall develop high λ values (0.7-0.9), effectively implementing very focused attention. Experts handling creative generation maintain lower λ (0.3-0.5), preserving broader contextual integration. This emergent specialization suggests that the noise-cancellation framing aligns with how the model naturally distributes processing strategies across experts.

6.3 Limitations

Our approach has several limitations: (1) The π-constraint derivation requires significant mathematical expertise to implement correctly—an error in the constraint system propagates to fundamentally broken architectures. (2) Non-standard dimensions may not be optimal for all hardware backends; our results are demonstrated on AMD MI300X and may not transfer to NVIDIA tensor cores without re-derivation. (3) The 6-phase training curriculum is complex and sensitive to hyperparameter choices in phase transitions.

7. Conclusion

NCAS-DiffMoE demonstrates that frontier-quality language model performance does not require frontier-scale resources when architecture is derived from principled constraints rather than scaled from existing templates. By unifying neuromorphic dimensionality constraints, differential attention mechanisms, and sparse expert routing, we achieve a 54B-parameter model that matches models 10-30× larger while fitting on a single GPU.

This work has immediate implications for AI sovereignty: nations and organizations without hyperscale compute budgets can operate frontier-quality models on commodity hardware. We believe this democratization of capability—without sacrificing safety through our embedded metacognition framework—represents a more sustainable path for AI development.

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