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Benign Loss Landscapes Can Coexist with Worst-Case Hardness

arXiv · AI, language, vision and robotics · article · Sep 11, 2026 · UTC

Deep neural networks are expressive enough to contain worst-case targets that can be evaluated in polynomial time but cannot be learned in polynomial time by gradient descent. For practical tasks they nonetheless learn well, raising the question of what non-generic structure of real-world targets enables this. Existing surrogate models cannot pose this question because they either lack hard-to-learn targets entirely (deep linear networks) or cannot evaluate such targets efficiently (kernel methods, infinite-width limits). We study tree tensor networks (TTNs), a model class that generalizes dee

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