Undergraduate computer science (CS) students often struggle in theoretical, proof-based courses, which require formal proof and rigorous reasoning skills. Despite ongoing efforts to improve these courses, challenges remain due to the complex nature of the material and CS students' perception that it has limited practical relevance. In this work, we take a human-centered approach to investigate the challenges and needs of both instructors and students in such courses. Through semi-structured interviews with 16 instructors and 20 students followed by a thematic analysis of the resulting data, we develop the CNPE framework, which captures the Challenges and Needs in Proof Education. While rooted in our local experience, the CNPE framework can be adapted for broader application, underscoring the value of understanding stakeholder challenges and needs before designing educational interventions.

We propose a new method for the problem of controlling linear dynamical systems under partial observation and adversarial disturbances. Our new algorithm, Double Spectral Control (DSC), matches the best known regret guarantees while exponentially improving runtime complexity over previous approaches in its dependence on the system's stability margin. Our key innovation is a two-level spectral approximation strategy, leveraging double convolution with a universal basis of spectral filters, enabling efficient and accurate learning of the best linear dynamical controllers.

We present the first provable method for identifying symmetric linear dynamical systems (LDS) with accuracy guarantees that are independent of the system’s state dimension or effective memory. Our approach builds upon recent work that represents symmetric LDSs as convolutions learnable via fixed spectral transformations. We show how to invert this representation—recovering an LDS model from its spectral transform—yielding an end-to-end convex optimization procedure. This distillation preserves predictive accuracy while enabling constant-time and constant-space inference per token, independent of sequence length. We evaluate our method, SpectraLDS, as a component in sequence prediction architectures and demonstrate that accuracy is preserved while inference efficiency is improved on tasks such as language modeling.