Link from X

Murphys Laws of AI Alignment: Why the Gap Always Wins

• We prove a formal impossibility result for reinforcement learning from human feedback (RLHF). In misspecified environments with bounded query budgets, any RLHF-style learner suffers an irreducible performance gap Omega(gamma) unless it has access to a calibration oracle. We give tight lower bounds via an information-theoretic proof and show that a minimal calibration oracle suffices to eliminate the gap. Small-scale empirical illustrations and a catalogue of alignment regularities (Murphy’s Laws) indicate that many observed alignment failures are consistent with this structural mechanism. Our results position Murphys Gap as both a diagnostic limit of RLHF and a guide for future work on calibration and causal preference checks.

Neural Thermodynamics I: Entropic Forces in Deep and Universal Representation Learning

• With the rapid discovery of emergent phenomena in deep learning and large language models, explaining and understanding their cause has become an urgent need. Here, we propose a rigorous entropic-force theory for understanding the learning dynamics of neural networks trained with stochastic gradient descent (SGD) and its variants. Building on the theory of parameter symmetries and an entropic loss landscape, we show that representation learning is crucially governed by emergent entropic forces arising from stochasticity and discrete-time updates. These forces systematically break continuous parameter symmetries and preserve discrete ones, leading to a series of gradient balance phenomena that resemble the equipartition property of thermal systems. These phenomena, in turn, (a) explain the universal alignment of neural representations between AI models and lead to a proof of the Platonic Representation Hypothesis, and (b) reconcile the seemingly contradictory observations of sharpness- and flatness-seeking behavior of deep learning optimization. Our theory and experiments demonstrate that a combination of entropic forces and symmetry breaking is key to understanding emergent phenomena in deep learning.