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Because these models use shared/frozen weights across inputs, replacing any layer L's output with clean activations causes ALL downstream layers (L+1...L_final) to reproduce their clean outputs identically \u2014 a property we term 'deterministic cascading'. This yields flat, uniform patch effects across all layers. We use noising-based causal tracing instead." }, "realworld_probing": { "n_seeds": 5, "california_housing": { "tabpfn": { "r2_mean": [ 0.19886742830276488, -0.8696016311645508, -0.42076884508132933, -0.33016655445098875, 0.10084841251373292, 0.22305034399032592, 0.2831146359443665, 0.07987786531448364, 0.24804795980453492, 0.32350935935974123, 0.42739081382751465, 0.05846167802810669 ], "r2_std": [ 0.30511843255965104, 0.6872640337273208, 0.43037615707363225, 0.6341521622743789, 0.22684125369113237, 0.15951362165136893, 0.3754785528285962, 0.8030538331820788, 0.49253572492673003, 0.12813569874820394, 0.09593069279606065, 0.6075383955782 ], "best_layer": 10, "best_r2": 0.42739081382751465 }, "tabicl": { "r2_mean": [ -0.42218809127807616, -0.5422199130058288, -0.6334723114967347, -0.6523850202560425, -0.6233209729194641, -0.6288249015808105, -0.5193478107452393, -0.3317695021629333, -0.5117137670516968, -0.5404478311538696, -0.39214768409729006, -0.25447922945022583 ], "r2_std": [ 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