Fields
Problems by the mathematics they use. A problem can appear under several fields.
Probability 47 problems
- MAIS-O2 Recovering world-models from behavior
- MAIS-O3 The geometry and identifiability of superposition
- MAIS-O4 Training for interpretability
- MAIS-O5 Representation theory of learned circuits
- MAIS-O8 A predictive theory of out-of-distribution generalization
- MAIS-O9 Steering Conway's Life from a small seed
- MAIS-O23 Do margins imply behavioral identifiability of causal models?
- MAIS-O24 Explicit polynomial margins replacing generic causal identifiability
- MAIS-O27 How agent regret limits causal model identifiability
- MAIS-O28 Causal model identifiability under average-case regret
- MAIS-O30 Which interventions identify which parts of the causal graph?
- MAIS-O31 What one intervenable variable reveals about a causal chain
- MAIS-O32 Tightness of the 1/n rate for depth-n goal agents
- MAIS-O33 Tolerable corruption fraction for goal-based model extraction
- MAIS-O35 Finite-sample recovery of two-variable causal models
- MAIS-O36 Global ℓ¹ dictionary recovery under independent supports
- MAIS-O37 Two smeared features: recover, merge, or split
- MAIS-O44 Does penalizing average interference lower coherence?
- MAIS-O45 Does penalizing interference make features recoverable by dictionary learning?
- MAIS-O48 Loss frontier for neuron-feature alignment under a bottleneck
- MAIS-O49 Exact cost of weight sparsity in the ReLU toy model
- MAIS-O50 Which minima does gradient flow select from random initialization?
- MAIS-O51 The regularized phase diagram of the smallest model
- MAIS-O52 How many Fourier frequencies do modular-addition networks use?
- MAIS-O53 Law of large numbers for neuron representation multiplicities
- MAIS-O54 Are selection probabilities proportional to squared representation dimension?
- MAIS-O55 Neuron purity and representation selection for S_3 networks
- MAIS-O57 Does gradient flow on S_5 select randomly among representation sets?
- MAIS-O58 Exchangeability of learned frequencies beyond multiplicative symmetry
- MAIS-O59 Two neurons learning mod-5 addition: which frequencies win?
- MAIS-O60 Does a single ReLU neuron align to one frequency?
- MAIS-O69 When does the localized posterior estimate the local learning coefficient?
- MAIS-O71 Free energy asymptotics for continuous-input ReLU networks
- MAIS-O73 Eyring–Kramers law for singular wells
- MAIS-O74 Eyring–Kramers prefactor for a singular well and Morse gate
- MAIS-O75 Entropic selection between two flat strata on the torus
- MAIS-O76 SGD limit diffusions on a singular set of minimizers
- MAIS-O78 A time-sample correspondence for the deep linear network
- MAIS-O82 Wide networks select the proxy policy with probability one
- MAIS-O83 Does some finite-width network favor the intended goal?
- MAIS-O84 The crossover time and its asymptotics
- MAIS-O86 Does gradient descent match the Gaussian process posterior?
- MAIS-O87 Does policy gradient stay misgeneralized despite training diversity?
- MAIS-O88 Misgeneralization versus diversity for reinforcement learning
- MAIS-O90 Does finite-width training inherit the kernel flow's selection?
- MAIS-O91 Numerical atlas of misgeneralization across widths and diversity
- MAIS-O92 The outcome law of one rectifier neuron
Statistics 27 problems
- MAIS-O2 Recovering world-models from behavior
- MAIS-O3 The geometry and identifiability of superposition
- MAIS-O25 Query complexity of causal model extraction from optimal policies
- MAIS-O26 Bisection attains optimal query complexity for causal model extraction
- MAIS-O27 How agent regret limits causal model identifiability
- MAIS-O28 Causal model identifiability under average-case regret
- MAIS-O29 Estimation rates and query design for Boltzmann agents
- MAIS-O35 Finite-sample recovery of two-variable causal models
- MAIS-O36 Global ℓ¹ dictionary recovery under independent supports
- MAIS-O38 Polynomial sample complexity for dictionary uniqueness with growing sparsity
- MAIS-O39 Does the amortized encoder change the learned dictionary?
- MAIS-O43 Measure the sparse-autoencoder recovery–merging phase diagram
- MAIS-O45 Does penalizing interference make features recoverable by dictionary learning?
- MAIS-O46 Does lower coherence imply better dictionary recovery?
- MAIS-O61 Pilot measurement of representation selection in small trained networks
- MAIS-O63 Learning coefficients of modular addition
- MAIS-O64 Marginal cost of width for modular-addition networks
- MAIS-O65 Learning coefficients of modular addition under cross-entropy
- MAIS-O66 Generic constancy of learning coefficients over attention teachers
- MAIS-O67 Learning coefficients of one-head softmax attention
- MAIS-O68 Learning coefficients of linear attention
- MAIS-O69 When does the localized posterior estimate the local learning coefficient?
- MAIS-O70 Local learning coefficients of reduced-rank regression
- MAIS-O71 Free energy asymptotics for continuous-input ReLU networks
- MAIS-O78 A time-sample correspondence for the deep linear network
- MAIS-O81 Does a saddle have a well-defined free energy?
- MAIS-O86 Does gradient descent match the Gaussian process posterior?
Optimization 24 problems
- MAIS-O3 The geometry and identifiability of superposition
- MAIS-O4 Training for interpretability
- MAIS-O8 A predictive theory of out-of-distribution generalization
- MAIS-O29 Estimation rates and query design for Boltzmann agents
- MAIS-O36 Global ℓ¹ dictionary recovery under independent supports
- MAIS-O37 Two smeared features: recover, merge, or split
- MAIS-O39 Does the amortized encoder change the learned dictionary?
- MAIS-O40 Regular pentagon as global minimizer of a ReLU autoencoder
- MAIS-O41 Two-feature phase diagram for ℓ¹ dictionary learning
- MAIS-O42 Pentagon optimality for a pure ReLU packing energy
- MAIS-O44 Does penalizing average interference lower coherence?
- MAIS-O45 Does penalizing interference make features recoverable by dictionary learning?
- MAIS-O47 Uniqueness of ReLU toy-model minimizers up to symmetry
- MAIS-O48 Loss frontier for neuron-feature alignment under a bottleneck
- MAIS-O49 Exact cost of weight sparsity in the ReLU toy model
- MAIS-O50 Which minima does gradient flow select from random initialization?
- MAIS-O51 The regularized phase diagram of the smallest model
- MAIS-O56 Vanishing weight decay selects both S_3 representations
- MAIS-O82 Wide networks select the proxy policy with probability one
- MAIS-O83 Does some finite-width network favor the intended goal?
- MAIS-O84 The crossover time and its asymptotics
- MAIS-O85 Which feature maps make the max-margin classifier misgeneralize?
- MAIS-O89 Boundary-state residual of max-margin gradient descent
- MAIS-O90 Does finite-width training inherit the kernel flow's selection?
Algebraic geometry 22 problems
- MAIS-O6 Does geometric simplicity force a legible mechanism?
- MAIS-O7 Opposing staircases
- MAIS-O23 Do margins imply behavioral identifiability of causal models?
- MAIS-O24 Explicit polynomial margins replacing generic causal identifiability
- MAIS-O34 Exact identified set for two-variable causal models
- MAIS-O62 Minimal network width for exact modular addition
- MAIS-O63 Learning coefficients of modular addition
- MAIS-O64 Marginal cost of width for modular-addition networks
- MAIS-O65 Learning coefficients of modular addition under cross-entropy
- MAIS-O66 Generic constancy of learning coefficients over attention teachers
- MAIS-O67 Learning coefficients of one-head softmax attention
- MAIS-O68 Learning coefficients of linear attention
- MAIS-O70 Local learning coefficients of reduced-rank regression
- MAIS-O71 Free energy asymptotics for continuous-input ReLU networks
- MAIS-O72 Finiteness and frontier condition for learning-coefficient strata
- MAIS-O73 Eyring–Kramers law for singular wells
- MAIS-O74 Eyring–Kramers prefactor for a singular well and Morse gate
- MAIS-O76 SGD limit diffusions on a singular set of minimizers
- MAIS-O77 Learning coefficients on the matrix factorization fiber and saddles
- MAIS-O79 Saddles as effective minima under coarse-graining
- MAIS-O80 Is leap complexity determined by singularity data?
- MAIS-O81 Does a saddle have a well-defined free energy?
Dynamical systems 18 problems
- MAIS-O5 Representation theory of learned circuits
- MAIS-O8 A predictive theory of out-of-distribution generalization
- MAIS-O9 Steering Conway's Life from a small seed
- MAIS-O50 Which minima does gradient flow select from random initialization?
- MAIS-O52 How many Fourier frequencies do modular-addition networks use?
- MAIS-O53 Law of large numbers for neuron representation multiplicities
- MAIS-O55 Neuron purity and representation selection for S_3 networks
- MAIS-O56 Vanishing weight decay selects both S_3 representations
- MAIS-O57 Does gradient flow on S_5 select randomly among representation sets?
- MAIS-O58 Exchangeability of learned frequencies beyond multiplicative symmetry
- MAIS-O59 Two neurons learning mod-5 addition: which frequencies win?
- MAIS-O60 Does a single ReLU neuron align to one frequency?
- MAIS-O79 Saddles as effective minima under coarse-graining
- MAIS-O84 The crossover time and its asymptotics
- MAIS-O87 Does policy gradient stay misgeneralized despite training diversity?
- MAIS-O88 Misgeneralization versus diversity for reinforcement learning
- MAIS-O89 Boundary-state residual of max-margin gradient descent
- MAIS-O92 The outcome law of one rectifier neuron
Logic 14 problems
- MAIS-O1 Quantitative bounded Löb
- MAIS-O10 Polynomial overhead for Löb's theorem
- MAIS-O11 Does Löb's rule shorten proofs?
- MAIS-O12 Expansion and diagonalization costs in Peano arithmetic
- MAIS-O13 Provable comparisons between exp-log terms in arithmetic
- MAIS-O14 Bounded Löb at logarithmic proof budgets
- MAIS-O15 Explicit thresholds in parametric bounded Löb
- MAIS-O16 The FairBot cooperation threshold
- MAIS-O17 Cooperation thresholds over families of bounded agents
- MAIS-O18 Admissible budgets for a bounded Löb axiom
- MAIS-O19 Soundness of Gödel–Löb logic under polynomial budgets
- MAIS-O20 A bounded Payor lemma and its cooperation threshold
- MAIS-O21 Is the Löb overhead invariant under polynomial simulation?
- MAIS-O22 A bounded analogue of Solovay's completeness theorem
Complexity theory 14 problems
- MAIS-O1 Quantitative bounded Löb
- MAIS-O2 Recovering world-models from behavior
- MAIS-O9 Steering Conway's Life from a small seed
- MAIS-O10 Polynomial overhead for Löb's theorem
- MAIS-O11 Does Löb's rule shorten proofs?
- MAIS-O12 Expansion and diagonalization costs in Peano arithmetic
- MAIS-O15 Explicit thresholds in parametric bounded Löb
- MAIS-O17 Cooperation thresholds over families of bounded agents
- MAIS-O21 Is the Löb overhead invariant under polynomial simulation?
- MAIS-O24 Explicit polynomial margins replacing generic causal identifiability
- MAIS-O25 Query complexity of causal model extraction from optimal policies
- MAIS-O26 Bisection attains optimal query complexity for causal model extraction
- MAIS-O33 Tolerable corruption fraction for goal-based model extraction
- MAIS-O62 Minimal network width for exact modular addition
Harmonic analysis 11 problems
- MAIS-O6 Does geometric simplicity force a legible mechanism?
- MAIS-O40 Regular pentagon as global minimizer of a ReLU autoencoder
- MAIS-O42 Pentagon optimality for a pure ReLU packing energy
- MAIS-O44 Does penalizing average interference lower coherence?
- MAIS-O46 Does lower coherence imply better dictionary recovery?
- MAIS-O52 How many Fourier frequencies do modular-addition networks use?
- MAIS-O58 Exchangeability of learned frequencies beyond multiplicative symmetry
- MAIS-O59 Two neurons learning mod-5 addition: which frequencies win?
- MAIS-O60 Does a single ReLU neuron align to one frequency?
- MAIS-O62 Minimal network width for exact modular addition
- MAIS-O92 The outcome law of one rectifier neuron
Representation theory 6 problems
- MAIS-O5 Representation theory of learned circuits
- MAIS-O53 Law of large numbers for neuron representation multiplicities
- MAIS-O54 Are selection probabilities proportional to squared representation dimension?
- MAIS-O55 Neuron purity and representation selection for S_3 networks
- MAIS-O56 Vanishing weight decay selects both S_3 representations
- MAIS-O57 Does gradient flow on S_5 select randomly among representation sets?
Computational 6 problems
- MAIS-O16 The FairBot cooperation threshold
- MAIS-O34 Exact identified set for two-variable causal models
- MAIS-O43 Measure the sparse-autoencoder recovery–merging phase diagram
- MAIS-O61 Pilot measurement of representation selection in small trained networks
- MAIS-O68 Learning coefficients of linear attention
- MAIS-O91 Numerical atlas of misgeneralization across widths and diversity
Combinatorics 6 problems
- MAIS-O30 Which interventions identify which parts of the causal graph?
- MAIS-O32 Tightness of the 1/n rate for depth-n goal agents
- MAIS-O33 Tolerable corruption fraction for goal-based model extraction
- MAIS-O38 Polynomial sample complexity for dictionary uniqueness with growing sparsity
- MAIS-O49 Exact cost of weight sparsity in the ReLU toy model
- MAIS-O80 Is leap complexity determined by singularity data?