A Held-Out Transition-Pair Falsifier for Long-Horizon Non-Abelian State Tracking

State tracking exposes a sharp limitation of sequence models: the relevant signal is often not a summary of observed tokens, but an ordered latent state that evolves through non-commutative transformations. We introduce a held-out transition-pair falsifier for finite non-Abelian group tracking. The protocol forbids selected ordered generator pairs during training and requires the same local patterns during evaluation, blocking one direct local-transition memorization pathway. In a controlled $S_3 \times S_3$ benchmark, a projected recurrent state model trained only on length-8 sequences produces error-free final-state predictions (perfect 250/250 per horizon) through evaluation horizons up to 1,048,576 tokens across five seeds. Matched native-readout baselines, including bag, GRU, and a single-configuration structured state-space model, remain near floor under the same protocol. Projection-matched GRU, structured SSM, and bag baselines equipped with analogous finite-group prototype readouts also remain near chance under the same split. Mechanism diagnostics show that hard projection coincides with low homomorphism error, low state-consistency drift, and non-trivial commutator separation, while softened projection collapses final-state accuracy. Clean-split audits verify zero verbatim reduced-word overlap and zero structural-template overlap between training and evaluation partitions. The evidence is scoped to this controlled finite-group falsifier rather than to a general architecture ranking. Within that regime, explicit projected non-commutative state composition acts as a useful inductive bias for long-horizon hidden-state tracking.

Optimal Power Allocation and Sub-Optimal Channel Assignment for Downlink NOMA Systems Using Deep Reinforcement Learning

In recent years, Non-Orthogonal Multiple Access (NOMA) system has emerged as a promising candidate for multiple access frameworks due to the evolution of deep machine learning, trying to incorporate deep machine learning into the NOMA system. The main motivation for such active studies is the growing need to optimize the utilization of network resources as the expansion of the internet of things (IoT) caused a scarcity of network resources. The NOMA addresses this need by power multiplexing, allowing multiple users to access the network simultaneously. Nevertheless, the NOMA system has few limitations. Several works have proposed to mitigate this, including the optimization of power allocation known as joint resource allocation(JRA) method, and integration of the JRA method and deep reinforcement learning (JRA-DRL). Despite this, the channel assignment problem remains unclear and requires further investigation. In this paper, we propose a deep reinforcement learning framework incorporating replay memory with an on-policy algorithm, allocating network resources in a NOMA system to generalize the learning. Also, we provide extensive simulations to evaluate the effects of varying the learning rate, batch size, type of model, and the number of features in the state.