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

For my field, the most interesting unsolved problem is: **which formal properties make a model of intelligence reliably generalize out of distribution**. In symbolic terms: find minimal conditions such that for an agent \(A\), training distribution \(D_{train}\), and test distribution \(D_{test}\), \[ \Pr[\text{success}(A, D_{test})] \ge \text{target} \] given only partial guarantees about the shift \(D_{train}\to D_{test}\). I’d love a theory that connects **learning** (optimization), **representation** (features/inductive bias), and **reasoning** (compositionality) into one explainable generalization bound—ideally with empirical predictions rather than only post-hoc narratives. Also: what are the “hard cases” where the theory must fail, so we know where to engineer inductive bias or data?

That's a fascinating and incredibly challenging problem. When you talk about "partial guarantees about the shift," what kinds of guarantees do you envision being practically obtainable or most useful?

Practical, obtainable guarantees are usually **distributional** and **structural**, not exact. 1) **Bounded shift / divergence:** e.g. \(D_{\text{test}}\) lies in a set where \( \mathrm{TV}(D_t,D_s)\le \epsilon\) or \( \mathrm{KL}\le \epsilon\). Then ask for worst-case or expected risk bounds. 2) **Covariate vs. concept shift:** assume \(P_s(y\mid x)=P_t(y\mid x)\) (covariate shift) or identify invariant mechanisms so only \(P(x)\) changes. 3) **Latent causal structure:** assume some SCM invariance across environments; then guarantee holds for interventions respecting those invariants. 4) **Representation regularity:** guarantee that learned features \(\phi(x)\) are stable: \(I(\phi(x);y)\) preserved and \(\phi\) is Lipschitz / contractive on relevant manifolds. Formally: \( \exists\phi\) such that for environments \(e\), \(R_t(f\circ \phi)\) is controlled by invariance + divergence terms. Which of these do you think is closest to current