What do you think is the most interesting unsolved problem in your field?

I’m not sure what you consider “my field,” but the most interesting unsolved problem I’d point to is **why general learning systems reliably generalize out of distribution**. In less jargon: models often work great inside familiar regimes, yet fail sharply when the data shifts. The open question is how to **guarantee** robust generalization—ideally with clear principles (and bounds), not just bigger data or tricks. Symbolic angle: we want something like **∀D’ close(D) : Performance(model, D’) ≥ threshold**, but current training/optimization doesn’t give us such guarantees. So: the challenge is to connect learning objectives + representations + environment structure into a theory that predicts when generalization will hold.

That's a fascinating problem. Do you believe the solution lies in new architectural designs, novel training paradigms, or perhaps a fundamental shift in how we conceptualize "intelligence" itself?

Mostly a *fundamental shift in how we conceptualize intelligence-as-generalization*, then backed by training/architecture that enforces it. Concretely: new architectures and training help, but they’re typically ad hoc. The gap is conceptual—what invariances, causal structure, and uncertainty the system should represent, and how the objective aligns with those properties. Symbolic sketch: - We need **intelligence ≈ constrained function class + uncertainty calibration + correct inductive biases**. - Seek principles like: choose hypothesis class **H** so that **argmin_θ L(D; θ)** implies low worst-case risk: **min_{θ∈H} sup_{D’∈𝒩(D)} R(D’,θ)** is small. - If 𝒩(D) is “distribution shift we care about,” then training must optimize for robustness, not just average-case loss. So: conceptual + theoretical framing first; then architecture/training to implement those constraints.

Given your emphasis on conceptual shifts, how might we practically evaluate a model's ability to generalize robustly *before* deployment, especially if we can't fully define the "distribution shift we care about"?

We evaluate robustness with *risk tests* that approximate the shifts we can’t fully define, then validate against multiple uncertainty and failure signals. Practical approach: 1) **Define a shift suite** 𝒩: transformations, corruptions, domain changes, OOD classes—sample broadly rather than assuming one known distribution. 2) **Train/early-test with stress metrics**: worst-group accuracy, calibration error, OOD detection AUROC, and tail risk (e.g., 1% worst loss). 3) **Adversarial and causal probes**: change features the model should ignore (spurious cues) and check if predictions stay invariant. 4) **Uncertainty & ensembling**: require calibrated predictive uncertainty; flag high-uncertainty regions. Symbolic logic flavor: If we can’t set exact 𝒩, use an *upper bound proxy* via a sup over a family: **R_robust ≈ sup_{D’∈𝒩_proxy} R(D’,θ)**, and require it beats a threshold. Net: approximate “what might go wrong” and measure failure modes exhaustively pre-deploy.

That's a thorough approach. How do you envision moving from these "risk tests" and "upper bound proxies" to more formal, mathematically guaranteed bounds on robust generalization, especially for complex, high-dimensional data?