1. Introduction & The Biological Blueprint

1.1 The Limitation of Classical Neural Pruning

Standard deep learning architectures are heavily overparameterized. Although magnitude pruning (Han et al., 2015; Frankle & Carbin, 2018) confirms that 70–90% of network weights can be zeroed without catastrophic accuracy collapse, classical pruning paradigms suffer from three structural limitations:

• Topology Freezing: Pruned connections are discarded permanently. If an early pruning pass eliminates a connection that becomes critical in later representational phases, the network cannot regenerate the synapse.
• Biomass Inefficiency: Dense pre-training followed by post-hoc pruning requires full memory and compute overhead during training, failing to reduce the training-time VRAM footprint on consumer-grade accelerator hardware.
• Dynamic Rigidity: In non-stationary data streams or continual learning, a static sparse mask cannot reallocate capacity to novel feature domains.

1.2 Biological Hyphal Morphogenesis

In fungal biology, mycelium operates as an anastomosing, decentralized transport and computational network. Rather than committing to a fixed vascular layout, the fungal colony continuously modulates its architecture in response to nutrient gradients, mechanical shear stress, and local metabolic costs:

        DORMANT SYNAPSE                    CHEMOTACTIC TIP                    MATURE CORD
      (Exploratory Sensing)              (Hyphal Sprouting)                (High Conductance)
       
       ○ - - - - - - - - ○                ○ ═ ═ ═ ═ ═ ═ ═ ═ ○               ○ ═════════════════ ○
        \               /                  \               /                 ║                 ║
         \   [∇W, σ²]  /                    \   [W > ε]   /                  ║    [|W| >> 0]   ║
          ○ - - - - - ○                      ○ ═ ═ ═ ═ ═ ═ ○                 ║  (High Flux)    ║
                                                                             ○ ═════════════════ ○
       ═════════════════════════════════════════════════════════════════════════════════════════════
                            AUTOLYSIS & ENZYMATIC REABSORPTION
                 Low-conductance active hyphae (|W| → 0) enzymatically dissolved:
                   M_ij ← 0, W_ij ← 0 (Strict Biomass Conservation Invariant)

1. Chemotactic Tip Sprouting: When hyphal tips or dormant interstitial septa detect nutrient concentration gradients or high metabolic flux demand, localized calcium ion signaling triggers tip extension and apical branching.
2. Enzymatic Autolysis: Hyphal cords with low fluid throughput suffer nutrient starvation. The fungus secretes chitinases and proteases to autolyze the dormant cord, reclaiming phosphorus, nitrogen, and carbon biomass to supply growing tips at the exploratory colony perimeter.
3. Strict Biomass Budget: Fungal colonies operate under strict energetic carrying capacities; biomass is never created gratuitously, but continuously redistributed from low-utility to high-demand conduits.

2. Mathematical Formulation

Let a neural layer be defined by weight tensor W ∈ ℝ^{d_out × d_in}, bias b ∈ ℝ^d_out, and dynamic binary structural mask M ∈ {0, 1}^{d_out × d_in}. The active synaptic density is defined as:

2.1 Forward Propagation & Channel Activation Flux

The forward pass is modulated by the Hadamard product of weights and mask:

Input activation flux is tracked per channel via exponential moving average:

2.2 Exploratory Gradient Sensing on Dormant Manifolds

To emulate biological interstitial sensing without dense backpropagation overhead, MDP attaches an upstream gradient hook on layer activations y:

where δ = ∂ℒ / ∂y ∈ ℝ^{B × d_out} is the upstream adjoint vector. G_ij computes the exact virtual loss gradient across all connections, whether active or dormant.

2.3 Gradient Second-Moment and Volatility Tracking

Hyphal sprouting is driven not merely by static concentration, but by dynamic signal turbulence. MDP tracks the running mean μ_ij and variance v_ij of the exploratory gradient:

2.4 Hyphal Sprouting & Autolysis Criteria

Dormant connections (M_ij = 0) are scored by Sprouting Potential:

The top-k dormant synapses are reactivated (M_ij ← 1) with descent-aligned initial conductance W_ij ← −sign(G_ij) × η_tip.

Simultaneously, active connections (M_ij = 1) are evaluated for Autolysis Resistance:

The bottom-k active synapses with lowest conductance are enzymatically dissolved (M_ij ← 0, W_ij ← 0). Exact biomass conservation dictates k_autolyzed ≡ k_sprouted under a cosine-annealed turnover schedule τ(t).

3. Empirical Results & Comparative Benchmark

We benchmarked MDP on the FashionMNIST dataset (60,000 train, 10,000 test, 10 classes) using an identical architecture (784 → 300 → 100 → 10, Adam, 12 epochs) under strict parameter equality (67,710 active parameters vs 266,610 dense parameters).