Per Ardua
Research Program
Structural Compression Theory — 25 papers across neural network geometry, multi-agent coordination, organizational physics, market mechanisms, and applied analysis
Activation Geometry
Neural network training dynamics and model composition through activation-space analysis
Training Trajectory Structure: Regime Detection, Cross-Seed Convergence, and Speculative Weight Prediction
Consolidated paper. Three-regime taxonomy via activation fingerprints generalizes across 124M-7B. Cross-seed convergence: CV 0.41-2.43%, phase boundaries synchronized to +/-50 steps. Linear prediction achieves 60-90% strict acceptance at 7B in stable regimes. Universal momentum catastrophe: 100-10,000x loss inflation at all scales. Supersedes Leap+Verify and Ensemble Collapse.
Constellation-Indexed Model Composition
Dynamic specialist composition via activation fingerprints. Generalist-space indexing: 20.6% to 98.1% win rate. Stochastic resonance at sigma=0.020.
The Shape of the Problem: Domain-Invariant Structural Signatures
INLP erases domain signal to near-chance while shape classification holds at 95.6%+. Clean double dissociation of domain and structure.
Capability Manifold Surveillance: Topological Detection of Model Distillation
Activation fingerprint geometry as security primitive. AUC 1.000 on systematic attacks at 1.5B+. Economic deterrence via temporal accumulation and coverage-clustering tradeoff.
GenAI Is Socially Awkward: RLHF Instruction Tuning Damages Social Cognition at Small Scale by Suppressing Pragmatic Inference
RLHF hurts social cognition at 7B (-18 points) but helps at 72B (+6). The deficit is processing mode: compliance training suppresses fuzzy pattern matching social reasoning requires.
The Geometry of Failure: Terminal Measurement, Concentration Barriers, and the Limits of Linear Intervention in Neural Networks
Consolidated paper. Shaped noise breaks 100% of repetition loops but cross-domain selectivity fails. Layer-resolved mapping, spectral analysis, concentration barrier theorem (selectivity bounded by k/d_eff), and SR channel capacity (~2 bits) converge on one result: classification and intervention operate under different constraints. The forward pass is an isotropic amplifier; no fixed subspace can isolate domain-specific computation.
Causal Basis Discovery for Domain-Selective Noise Injection
INLP is the only basis with positive selectivity (+0.618). All causal bases (patching, contrastive, gradient) are anti-selective. Classification-intervention dissociation established.
The Inter-Instance Compression Barrier: Domain-Specific Information Loss at the Natural Language Interface
NL interface is a uniform lossy channel dropping ~80% proportionally across domain-specific and domain-agnostic subspaces. The concentration barrier is the sole constraint.
The Dissociation of Geometry and Function: Why Activation-Level State Transfer Cannot Compete with Text
Consolidated paper. Four experiments on activation-level state transfer converge: geometric similarity does not imply functional equivalence. Text preserves 63.7% of reasoning trajectory; activation injection adds 1.2%. Priming selection (activation-guided input) closes 48.9% of the expert gap, outperforming injection by 5.4x. Domain reversal: text preserves legal best, activations preserve science best. Supersedes Projection Transmission, Bandwidth-Fidelity, Continuation Perplexity, and Ensemble Gravity.
Context Management in Autoregressive Language Models
Consolidated paper. Ritual shape, shepherd agents, context fences, and hop scaling unified. 15 tokens capture 98.8% of benefit. Adaptive priming is harmful. Mode switching, not garbage collection. Chain degradation saturates logarithmically by hop 5. Cross-domain handoffs outperform within-domain.
Universal Entanglement in Transformer Activation Space
Consolidated paper. SVD directions can be concept-pure for classification yet carry all concepts in activations. Random Gaussian projections reproduce learned entanglement intensity (EI=1.50). Superlinear amplification confirmed. Entanglement is geometric, not learned.
The Entanglement Theorem: Structural Concept Coupling as a Geometric Consequence of High-Dimensional Encoding
Proves structural entanglement is a mathematical theorem via concentration of measure. Specialist bound: compositional architecture is geometric necessity. Alignment implication: surgical concept editing is geometrically limited.
Entanglement Under Fine-Tuning: Architecture-Dependent Collapse, Scale Thresholds, and Entanglement-Optimal Adaptation
Consolidated paper. B3 drives EI to zero in Qwen-32B (8 seeds, phase transition by step 3500) but not in four other architectures. Scale ladder: -32% at 7B, -93% at 14B, -100% at 32B. Block-diagonal LoRA adapters that respect entanglement geometry outperform concept-isolating adapters (48.2% vs 36.6% HumanEval+). CSR preserves structure.
Bridge Theory
Unifying frameworks connecting neural and organizational phenomena
Organizational Theory
Structural forces, information dynamics, and governance in organizations
Multi-Agent AI: Substrate-Independent Dysfunction
Token governance overhead scales with links (25.5% at n=3 to 69.4% at n=15), not capability (CV=0.0000).
Ambient Structure Discovery via Stigmergic Mesh
22,500 Monte Carlo runs. Coordination failure TPR 0.82 at FPR<0.15. Patent filed USPTO #63/981,369.
Emergence: A Programming Paradigm for Constraint-Shaped Agency
WF1-WF4 well-formedness definitions. Q-dynamics contraction. Tessera as existence proof.
Contraction Dynamics: Constraint Typing and Gaussian Fixed-Point Convergence
Pure mathematics. Gaussian Contraction Theorem. Constraint type system. Five open problems.
The Strategic Rate-Distortion-Perception Tradeoff
Info-theoretic bridge. RLHF mapping: sycophancy as generative distortion. Conformity pressure = 27.4% of distortion at bias=0.1.
Applied Analysis
Empirical investigations of organizational mechanisms
Tournament-Based Performance Evaluation and Systematic Misallocation
54,000 MC trials. Error rate 0.494. $10M pool → $11.76M total cost. BTL supplement: 22% reduction.
Structural Immunity: Platform Dominance and Corporate Impunity
Six-filter multiplicative pipeline. Consumer finance: 0.00075% survival rate.
The Inversion of Doubt: Skepticism Inverts Epistemic Warrant
Cross-domain metascience synthesis. Three structural mechanisms. Composite threshold from RR divergence, calibration gap, and falsifiability timescale.
The Topology of Influence: Latent Structure and Resilience in Online Populations
1.4B Reddit comments, 44,837 subreddits. 12-dimensional latent space. Influence wave propagation (ρ=0.27). Simpson's paradox in leadership (18.5x per-dimension, 1.0x global). Topology predicts resilience (ρ=0.56).
Entropy-Bounded Decomposition for Time Series Forecasting
1,200 lines of NumPy vs 200M-param transformer. Fourier + wavelet + AR with max-entropy stopping. ETTh1: 0.131 vs TimesFM 0.375 (+65%). ETTm1: 0.088 vs 0.320 (+73%). Residual AC(1) predicts which basis to use.
Decentralized Drone Swarm Coordination via Broadcast-as-Shared-State and Hierarchical PCA-Tree Bisection
One primitive (broadcast-as-shared-state with PCA-tree-keyed local computation), four provable layers (assignment, recovery, priority, localization). 1.43% gap from Hungarian at N=10,000. 14× fewer messages than CBBA at 3.0% gap. Slot-disjointness composition theorem. Witness-alarm byzantine defense. v1.1 adds comms-layer empirical validation: inverted EN_ROUTE+ETA quiescence holds 0% missed-deadline through p=0.7 packet loss; ETA-spoofing attack closed by per-drone sanity bound. Bootstrap CIs throughout.
Welfare-Optimal Matching in Hiring Markets via Min-Cost Flow
MCF-Tiered: 95.3% vs greedy 24.5% company satisfaction. Adaptive β=0.7σ(S). 3 datasets, scorer-independent. p<10⁻²⁰.
Academic Monograph
The unified theoretical framework
Structural Compression Theory: A Unified Information-Theoretic Account of Organizational Dysfunction, Creativity, and Substrate-Independent Selection Dynamics
Academic monograph unifying 24 papers into a single formal framework. Proves that compression under selection produces systematic drift from reality toward internal fit — and that the mechanism is substrate-independent across cognition, organizations, and AI. Three theorems, one lemma, five sufficient conditions, and the inseparability corollary: dysfunction and creativity share a single channel, distinguished only by selection regime. 17 chapters across five parts, 17 appendices (including the Entanglement Theorem), validated across 500 computational configurations with zero counterexamples. Derives the Hallucination Corollary: you cannot eliminate hallucination without eliminating generalization.
In Progress
Active research awaiting formal publication