machine learning model developers

Abstract: We introduce matrix $Φ$-ribbons, extending the scalar $Φ$-ribbons to the matrix case. For $Φ$ in the subadditivity class, we establish data processing and tensorization properties of matrix $Φ$-ribbons. We establish scalar and matrix $Φ$-entropy inequalities and use them to show that both $Φ$-ribbons characterize the corresponding $Φ$-strong data processing inequality (SDPI) constants. We obtain exact evaluations of the SDPI constants for several sources. We provide examples showing that the matrix $Φ$-SDPI constant can exceed the scalar counterpart. Finally, we derive inner bounds for $Φ$-ribbons from prescribed independence structures and prove that these bounds are optimal when $Φ(t)=t\log t$.

Abstract: Language models are frequently aligned to human preferences via imperfect evaluators whose errors can be exploited during optimization. We train policies to search for comparisons on which an evaluator may reverse the underlying preference, providing candidates for additional supervision. Since human preferences are unavailable during policy training, we use disagreement among an ensemble of preference models as a proxy for prediction error. We formulate this search as a zero-sum Stackelberg game between two opposing policies, a Leader which tries to minimize disagreement, and a Follower which maximizes it. For a general class of finite contextual Stackelberg games, we establish equilibrium existence and, under regularization, uniqueness and a closed-form characterization. We introduce Stackelberg Mirror Descent-Ascent (SMIDA), a two-timescale algorithm with linear last-iterate convergence in the tabular setting, and develop a neural policy-gradient analogue. Experiments with a synthetic oracle support disagreement as an informative proxy for prediction error. On held out data the trained policies outperform reference policies and increase the fraction of comparisons that exceed a disagreement threshold and reverse the oracle's preference.

Abstract: We study the optimization landscape of low-tubal-rank tensor sensing through a balanced factorization. Under a tubal restricted isometry condition, we establish a quantitative strict-saddle landscape with no spurious local minima for arbitrary Fourier multi-rank profiles. We further show that the local geometry depends on the Fourier-slice ranks rather than the tubal rank alone. Uniform ranks yield quadratic growth transverse to the solution orbit, whereas nonuniform ranks produce quartically flat directions through hidden frequency-wise overparameterization, even when the factor width equals the exact tubal rank. Numerical experiments illustrate the global optimization behavior and the contrasting local geometries.

Abstract: The last decade has seen the development of powerful methods for learning complex structure from high-dimensional data. These advances have brought to the foreground fundamental connections between subdisciplines of physics, applied mathematics, and machine learning. In this review, we bring together some of these ideas, often expressed in different languages, to highlight a conceptual thread that links five distinct fields: control theory, optimal transport, probabilistic inference, non-equilibrium thermodynamics, and machine learning. A common theme is the optimization of free-energy-like functionals under dynamical or statistical constraints. We offer a guided tour through this thread and present selected applications in reinforcement learning, variational inference, and generative modeling. The review does not assume prior familiarity with these topics, and begins with principles originating from physics.