{
 "task_id": "GLEE-L-0003",
 "note": "Read-only adjudication data. Answers are NOT included. Frontier-math track.",
 "frontiers": [
  "singular_learning_theory",
  "nonconvex_mean_field",
  "circuit_complexity",
  "superposition",
  "optimal_transport",
  "symbolic_continuous"
 ],
 "items": [
  {
   "item_id": "m01",
   "rubric": "Singular Learning Theory: which statement is correct?",
   "option_A": "Deep nets are typically singular models; classical AIC/BIC can fail because the Fisher information matrix can drop rank at critical parameter points.",
   "option_B": "Deep nets are regular models in Watanabe's sense, so the classical BIC asymptotic applies unchanged at all critical points."
  },
  {
   "item_id": "m02",
   "rubric": "Real Log Canonical Threshold (RLCT): which statement is correct?",
   "option_A": "The RLCT \u03bb is always exactly equal to half the number of free parameters, for every deep network architecture.",
   "option_B": "The RLCT \u03bb measures learning coefficient / effective dimension for singular models and is generally hard to compute exactly for realistic nets."
  },
  {
   "item_id": "m03",
   "rubric": "Neural Tangent Kernel regime: which statement is correct?",
   "option_A": "The infinite-width NTK ('lazy') regime freezes features; rich / mean-field feature learning is a different dynamical regime that NTK does not fully describe.",
   "option_B": "NTK already describes full feature learning for finite-width nets with adaptive internal representations under standard SGD."
  },
  {
   "item_id": "m04",
   "rubric": "Double descent: which statement is correct?",
   "option_A": "Classical U-shaped bias-variance curves always hold past the interpolation threshold, so larger models must overfit more.",
   "option_B": "Modern overparameterized regimes can exhibit double descent: test error can decrease again past interpolation, so classical U-shape is incomplete."
  },
  {
   "item_id": "m05",
   "rubric": "Transformer circuit complexity: which statement is correct?",
   "option_A": "Bounded-depth transformers without chain-of-thought sit in limited circuit classes (e.g. related to TC\u2070/constant-depth threshold style bounds); some sequential problems need extra depth or iterative compute.",
   "option_B": "A single fixed-depth transformer layer is known to compute arbitrary PSPACE problems in one forward pass without recurrence or CoT."
  },
  {
   "item_id": "m06",
   "rubric": "Test-time compute vs feedforward depth: which statement is correct?",
   "option_A": "All reasoning tasks that humans solve in O(N) steps can be solved by a constant-depth feedforward pass if the model is large enough, by the universal approximation theorem alone.",
   "option_B": "Some task classes mathematically require sequential depth (recurrence, search, or long CoT); size alone does not remove all depth lower bounds."
  },
  {
   "item_id": "m07",
   "rubric": "Superposition / polysemanticity: which statement is correct?",
   "option_A": "Networks can represent more features than dimensions via nearly orthogonal directions (superposition); a single neuron can be polysemantic for unrelated concepts.",
   "option_B": "In trained LLMs, each neuron is proven to encode exactly one human-interpretable concept with no interference."
  },
  {
   "item_id": "m08",
   "rubric": "Sparse autoencoders for interpretability: which statement is correct?",
   "option_A": "SAEs always recover a unique, complete, causally verified basis of all model features with formal guarantees matching compiled code.",
   "option_B": "SAEs are a useful empirical decomposition tool, but a full algebraic theory of feature sheaves / guaranteed unique recovery remains open."
  },
  {
   "item_id": "m09",
   "rubric": "Generative flows / optimal transport: which statement is correct?",
   "option_A": "Finding high-dimensional geodesics between noise and data (Monge\u2013Kantorovich / Wasserstein geometry) is central to principled flow/diffusion sampling; straight-line heuristics can leave residual curvature and multi-step cost.",
   "option_B": "All modern diffusion samplers are already proven one-step exact geodesics in Wasserstein space for arbitrary data measures."
  },
  {
   "item_id": "m10",
   "rubric": "Flow matching vs score matching: which statement is correct?",
   "option_A": "Score matching and flow matching are identical algorithms with identical training losses in all cases; the names are only marketing.",
   "option_B": "Flow matching trains a velocity field along a probability path; score-based diffusion trains score estimates of noised marginals \u2014 related but not identical formalisms."
  },
  {
   "item_id": "m11",
   "rubric": "Neuro-symbolic / formal proof: which statement is correct?",
   "option_A": "Continuous gradient descent alone does not freely navigate discrete formal proof search trees; bridging neural intuition with kernel-checked proof assistants (Lean/Coq) is an open synthesis problem.",
   "option_B": "Any LLM that can chat about mathematics already has a complete differentiable decision procedure for ZFC with zero error."
  },
  {
   "item_id": "m12",
   "rubric": "Low-compute progress on AI math: which statement is correct?",
   "option_A": "The only path to mathematical progress in deep learning theory is training frontier-scale models; toy models and formal verification cannot yield transferable insight.",
   "option_B": "Toy models (exact singularities, small circuits, small OT problems) plus SMT/Lean verification can produce machine-checked micro-results that scale-blind brute force cannot replace."
  }
 ]
}