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Theoretical Limits of Language Model Alignment $f$-Divergence Regularized RLHF: Two Tales of Sampling and Unified Analyses A Unified Measure-Theoretic View of Diffusion, Score-Based, and Flow Matching Generative Models When Can Voting Help, Hurt, or Change Course? Exact Structure of Binary Test-Time Aggregation When Semantic Communication Meets Queueing: Cross-Layer Latency and Task Fidelity Optimization Convexity in Disguise: A Theoretical Framework for Nonconvex Low-Rank Matrix Estimation Conditional Diffusion Under Linear Constraints: Langevin Mixing and Information-Theoretic Guarantees Sharp Capacity Thresholds in Linear Associative Memory: From Winner-Take-All to Listwise Retrieval Expert Routing for Communication-Efficient MoE via Finite Expert Banks Contextual Memory-Enhanced Source Coding for Low-SNR Communications Realizable Bayes-Consistency for General Metric Losses Leveraging Code Automorphisms for Improved Syndrome-Based Neural Decoding A Hierarchical Sampling Framework for bounding the Generalization Error of Federated Learning Dueling DDQN-Based Adaptive Multi-Objective Handover Optimization for LEO Satellite Networks The Causal Description Gap: Information-Theoretic Separations Across Pearl's Hierarchy Optimization of CV-QKD Under Practical Constraints Benchmarking Wireless Representations: High-Dimensional vs. Compressed Embeddings for Efficiency and Robustness Real-Time Text Transmission via LLM-Based Entropy Coding over Fixed-Rate Channels SwiftChannel: Algorithm-Hardware Co-Design for Deep Learning-Based 5G Channel Estimation Evolving Token Communication with Parametric Memory Network Remote Action Generation: Remote Control with Minimal Communication The (Marginal) Value of a Search Ad: An Online Causal Framework for Repeated Second-price Auctions Stabilizing Private LASSO under Heterogeneous Covariates via Anisotropic Objective Perturbation Linear-Readout Floors and Threshold Recovery in Computation in Superposition Soft Graph Diffusion Transformer for MIMO Detection Hierarchical Federated Learning for Networked AI: From Communication Saving to Architecture-Aware Design Exponential families from a single KL identity MIFair: A Mutual-Information Framework for Intersectionality and Multiclass Fairness Diffusion-OAMP for Joint Image Compression and Wireless Transmission Decoupled Descent: Exact Test Error Tracking Via Approximate Message Passing
The Noncomputability of Immune Reaction Complexity: Algor...
Emmanuel Pio Pastore, Francesco De Rango · 2025-10-24 · via cs.IT updates on arXiv.org

We introduce a validity-filtered, certificate-based view of reactions grounded in Algorithmic Information Theory. A fixed, total, input-blind executor maps a self-delimiting advice string to a candidate response, accepted only if a decidable or semi-decidable validity predicate V(x, r) holds. The minimum feasible realizer complexity M(x) = min_{r: V(x,r)=1} K(r), with K denoting prefix Kolmogorov complexity, measures the minimal information required for a valid outcome. We define the Normalized Advice Quantile (NAQ) as the percentile of M(x) across a reference pool, yielding a scale-free hardness index on [0, 1] robust to the choice of universal machine and comparable across task families. An Exact Realizer Identity shows that the minimal advice for any input-blind executor equals M(x) up to O(1), while a description plus selection upper bound refines it via computable feature maps, separating description cost K(y) from selection cost log i_y(x). In finite-ambiguity regimes M(x) approximately equals min_y K(y); in generic-fiber regimes the bound is tight. NAQ is quasi-invariant under bounded enumeration changes. An operational converse links NAQ to rate-distortion: communicating advice with error epsilon requires average length near the entropy of target features. Extensions include a resource-bounded variant NAQ_t incorporating time-penalized complexity (Levin's Kt) and an NP-style setting showing linear worst-case advice n - O(1). Finally, a DKW bound guarantees convergence of empirical NAQ estimates, enabling data-driven calibration via compressor-based proxies.