Hallucination Basins: A Dynamic Framework for Understanding and Controlling LLM Hallucinations

Large language models (LLMs) hallucinate: they produce fluent outputs that are factually incorrect. We present a geometric dynamical systems framework in which hallucinations arise from task-dependent basin structure in latent space. Using autoregressive hidden-state trajectories across multiple open-source models and benchmarks, we find that separability is strongly task-dependent rather than universal: factoid settings can show clearer basin separation, whereas summarization and misconception-heavy settings are typically less stable and often overlap. We formalize this behavior with task-complexity and multi-basin theorems, characterize basin emergence in L-layer transformers, and show that geometry-aware steering can reduce hallucination probability without retraining.

Learning Pareto-Optimal Rewards from Noisy Preferences: A Framework for Multi-Objective Inverse Reinforcement Learning

As generative agents become increasingly capable, alignment of their behavior with complex human values remains a fundamental challenge. Existing approaches often simplify human intent through reduction to a scalar reward, overlooking the multi-faceted nature of human feedback. In this work, we introduce a theoretical framework for preference-based Multi-Objective Inverse Reinforcement Learning (MO-IRL), where human preferences are modeled as latent vector-valued reward functions. We formalize the problem of recovering a Pareto-optimal reward representation from noisy preference queries and establish conditions for identifying the underlying multi-objective structure. We derive tight sample complexity bounds for recovering $\epsilon$-approximations of the Pareto front and introduce a regret formulation to quantify suboptimality in this multi-objective setting. Furthermore, we propose a provably convergent algorithm for policy optimization using preference-inferred reward cones. Our results bridge the gap between practical alignment techniques and theoretical guarantees, providing a principled foundation for learning aligned behaviors in a high-dimension and value-pluralistic environment.

Q-Policy: Quantum-Enhanced Policy Evaluation for Scalable Reinforcement Learning

We propose Q-Policy, a hybrid quantum-classical reinforcement learning (RL) framework that mathematically accelerates policy evaluation and optimization by exploiting quantum computing primitives. Q-Policy encodes value functions in quantum superposition, enabling simultaneous evaluation of multiple state-action pairs via amplitude encoding and quantum parallelism. We introduce a quantum-enhanced policy iteration algorithm with provable polynomial reductions in sample complexity for the evaluation step, under standard assumptions. To demonstrate the technical feasibility and theoretical soundness of our approach, we validate Q-Policy on classical emulations of small discrete control tasks. Due to current hardware and simulation limitations, our experiments focus on showcasing proof-of-concept behavior rather than large-scale empirical evaluation. Our results support the potential of Q-Policy as a theoretical foundation for scalable RL on future quantum devices, addressing RL scalability challenges beyond classical approaches.

Low-Rank Matrix Approximation for Neural Network Compression

Deep Neural Networks (DNNs) are often constrained by their large memories and computational restrictions. In this paper, we introduce a novel adaptive-rank Singular Value Decomposition (ARSVD) that dynamically chooses the rank increase of the fully connected layers below a certain threshold in energy expenditure. Unlike conventional SVD compression methods that apply a fixed rank reduction in all layers, our ARSVD method uses energy distribution to adaptively select rank per layer while retaining accuracy. This is done for each layer in an effort to use as much energy as possible while maintaining the lowest accuracy loss. Such accuracy-adaptive approaches outperform traditional static rank reduction methods by providing an improved balance between compression and model performance. We first train a simple Multi-Layer Perceptron (MLP) on the MNIST, CIFAR-10, and CIFAR-100 dataset and evaluate its performance using accuracy and F1-score. After applying ARSVD, our results demonstrate that the technique can achieve substantial model compression without compromising classification accuracy. These results illustrate the usefulness of ARSVD in computing scenarios where both computational and memory resources are scarce.