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MAIS Math for AI Safety

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92 problems. Tags (MAIS-O…) are permanent and never change, even if a title does.

TagTitleAgendaFieldsDiff.Status
MAIS-O1Quantitative bounded LöbAgenda: A1Fields: logic, complexity theoryA1logic, complexity theory★★★open
MAIS-O2Recovering world-models from behaviorAgenda: A2Fields: statistics, probability, complexity theoryA2statistics, probability, complexity theory★★☆open
MAIS-O3The geometry and identifiability of superpositionAgenda: A3Fields: statistics, optimization, probabilityA3statistics, optimization, probability★★★open
MAIS-O4Training for interpretabilityAgenda: A4Fields: optimization, convex geometry, probabilityA4optimization, convex geometry, probability★★★open
MAIS-O5Representation theory of learned circuitsAgenda: A5Fields: dynamical systems, probability, representation theoryA5dynamical systems, probability, representation theory★★★open
MAIS-O6Does geometric simplicity force a legible mechanism?Agenda: A6Fields: algebraic geometry, harmonic analysisA6algebraic geometry, harmonic analysis★★★open
MAIS-O7Opposing staircasesAgenda: A7Fields: algebraic geometryA7algebraic geometry★★☆open
MAIS-O8A predictive theory of out-of-distribution generalizationAgenda: A8Fields: probability, optimization, dynamical systemsA8probability, optimization, dynamical systems★★★open
MAIS-O9Steering Conway's Life from a small seedAgenda: –Fields: probability, dynamical systems, complexity theory–probability, dynamical systems, complexity theory★★★open
MAIS-O10Polynomial overhead for Löb's theoremAgenda: A1Fields: logic, complexity theoryA1logic, complexity theory★★☆open
MAIS-O11Does Löb's rule shorten proofs?Agenda: A1Fields: logic, complexity theoryA1logic, complexity theory★★★open
MAIS-O12Expansion and diagonalization costs in Peano arithmeticAgenda: A1Fields: logic, complexity theoryA1logic, complexity theory★★☆open
MAIS-O13Provable comparisons between exp-log terms in arithmeticAgenda: A1Fields: logicA1logic★★☆open
MAIS-O14Bounded Löb at logarithmic proof budgetsAgenda: A1Fields: logicA1logic★★★open
MAIS-O15Explicit thresholds in parametric bounded LöbAgenda: A1Fields: logic, complexity theoryA1logic, complexity theory★★☆open
MAIS-O16The FairBot cooperation thresholdAgenda: A1Fields: logic, computationalA1logic, computational★★☆open
MAIS-O17Cooperation thresholds over families of bounded agentsAgenda: A1Fields: logic, complexity theoryA1logic, complexity theory★★☆open
MAIS-O18Admissible budgets for a bounded Löb axiomAgenda: A1Fields: logicA1logic★★★open
MAIS-O19Soundness of Gödel–Löb logic under polynomial budgetsAgenda: A1Fields: logicA1logic★★★open
MAIS-O20A bounded Payor lemma and its cooperation thresholdAgenda: A1Fields: logicA1logic★★☆open
MAIS-O21Is the Löb overhead invariant under polynomial simulation?Agenda: A1Fields: logic, complexity theoryA1logic, complexity theory★★☆open
MAIS-O22A bounded analogue of Solovay's completeness theoremAgenda: A1Fields: logicA1logic★★★open
MAIS-O23Do margins imply behavioral identifiability of causal models?Agenda: A2Fields: algebraic geometry, probabilityA2algebraic geometry, probability★★★open
MAIS-O24Explicit polynomial margins replacing generic causal identifiabilityAgenda: A2Fields: algebraic geometry, probability, complexity theoryA2algebraic geometry, probability, complexity theory★★☆open
MAIS-O25Query complexity of causal model extraction from optimal policiesAgenda: A2Fields: complexity theory, statisticsA2complexity theory, statistics★★☆open
MAIS-O26Bisection attains optimal query complexity for causal model extractionAgenda: A2Fields: complexity theory, statisticsA2complexity theory, statistics★★☆open
MAIS-O27How agent regret limits causal model identifiabilityAgenda: A2Fields: statistics, probabilityA2statistics, probability★★★open
MAIS-O28Causal model identifiability under average-case regretAgenda: A2Fields: probability, statisticsA2probability, statistics★★☆open
MAIS-O29Estimation rates and query design for Boltzmann agentsAgenda: A2Fields: statistics, optimizationA2statistics, optimization★★☆open
MAIS-O30Which interventions identify which parts of the causal graph?Agenda: A2Fields: combinatorics, probabilityA2combinatorics, probability★★★open
MAIS-O31What one intervenable variable reveals about a causal chainAgenda: A2Fields: probabilityA2probability★★☆open
MAIS-O32Tightness of the 1/n rate for depth-n goal agentsAgenda: A2Fields: probability, combinatoricsA2probability, combinatorics★★☆open
MAIS-O33Tolerable corruption fraction for goal-based model extractionAgenda: A2Fields: complexity theory, combinatorics, probabilityA2complexity theory, combinatorics, probability★★★open
MAIS-O34Exact identified set for two-variable causal modelsAgenda: A2Fields: algebraic geometry, computationalA2algebraic geometry, computational★☆☆open
MAIS-O35Finite-sample recovery of two-variable causal modelsAgenda: A2Fields: statistics, probabilityA2statistics, probability★☆☆open
MAIS-O36Global ℓ¹ dictionary recovery under independent supportsAgenda: A3Fields: probability, optimization, statisticsA3probability, optimization, statistics★★★open
MAIS-O37Two smeared features: recover, merge, or splitAgenda: A3Fields: optimization, probability, convex geometryA3optimization, probability, convex geometry★★★open
MAIS-O38Polynomial sample complexity for dictionary uniqueness with growing sparsityAgenda: A3Fields: combinatorics, statisticsA3combinatorics, statistics★★★open
MAIS-O39Does the amortized encoder change the learned dictionary?Agenda: A3Fields: optimization, statisticsA3optimization, statistics★★★open
MAIS-O40Regular pentagon as global minimizer of a ReLU autoencoderAgenda: A3Fields: optimization, harmonic analysisA3optimization, harmonic analysis★★★open
MAIS-O41Two-feature phase diagram for ℓ¹ dictionary learningAgenda: A3Fields: optimization, convex geometryA3optimization, convex geometry★☆☆open
MAIS-O42Pentagon optimality for a pure ReLU packing energyAgenda: A3Fields: optimization, harmonic analysisA3optimization, harmonic analysis★★☆open
MAIS-O43Measure the sparse-autoencoder recovery–merging phase diagramAgenda: A3Fields: computational, statisticsA3computational, statistics★☆☆open
MAIS-O44Does penalizing average interference lower coherence?Agenda: A4Fields: optimization, harmonic analysis, probabilityA4optimization, harmonic analysis, probability★★☆open
MAIS-O45Does penalizing interference make features recoverable by dictionary learning?Agenda: A4Fields: statistics, optimization, probabilityA4statistics, optimization, probability★★☆open
MAIS-O46Does lower coherence imply better dictionary recovery?Agenda: A4Fields: statistics, harmonic analysisA4statistics, harmonic analysis★★☆open
MAIS-O47Uniqueness of ReLU toy-model minimizers up to symmetryAgenda: A4Fields: optimization, convex geometryA4optimization, convex geometry★★★open
MAIS-O48Loss frontier for neuron-feature alignment under a bottleneckAgenda: A4Fields: optimization, probabilityA4optimization, probability★★☆open
MAIS-O49Exact cost of weight sparsity in the ReLU toy modelAgenda: A4Fields: optimization, probability, combinatoricsA4optimization, probability, combinatorics★★☆open
MAIS-O50Which minima does gradient flow select from random initialization?Agenda: A4Fields: dynamical systems, probability, optimizationA4dynamical systems, probability, optimization★★★open
MAIS-O51The regularized phase diagram of the smallest modelAgenda: A4Fields: optimization, probabilityA4optimization, probability★☆☆open
MAIS-O52How many Fourier frequencies do modular-addition networks use?Agenda: A5Fields: probability, dynamical systems, harmonic analysisA5probability, dynamical systems, harmonic analysis★★★open
MAIS-O53Law of large numbers for neuron representation multiplicitiesAgenda: A5Fields: probability, representation theory, dynamical systemsA5probability, representation theory, dynamical systems★★★open
MAIS-O54Are selection probabilities proportional to squared representation dimension?Agenda: A5Fields: representation theory, probabilityA5representation theory, probability★★★open
MAIS-O55Neuron purity and representation selection for S_3 networksAgenda: A5Fields: dynamical systems, representation theory, probabilityA5dynamical systems, representation theory, probability★★★open
MAIS-O56Vanishing weight decay selects both S_3 representationsAgenda: A5Fields: dynamical systems, representation theory, optimizationA5dynamical systems, representation theory, optimization★★★open
MAIS-O57Does gradient flow on S_5 select randomly among representation sets?Agenda: A5Fields: probability, dynamical systems, representation theoryA5probability, dynamical systems, representation theory★★★open
MAIS-O58Exchangeability of learned frequencies beyond multiplicative symmetryAgenda: A5Fields: probability, harmonic analysis, dynamical systemsA5probability, harmonic analysis, dynamical systems★★★open
MAIS-O59Two neurons learning mod-5 addition: which frequencies win?Agenda: A5Fields: dynamical systems, probability, harmonic analysisA5dynamical systems, probability, harmonic analysis★★☆open
MAIS-O60Does a single ReLU neuron align to one frequency?Agenda: A5Fields: dynamical systems, probability, harmonic analysisA5dynamical systems, probability, harmonic analysis★★☆resolved
MAIS-O61Pilot measurement of representation selection in small trained networksAgenda: A5Fields: computational, statisticsA5computational, statistics★☆☆open
MAIS-O62Minimal network width for exact modular additionAgenda: A6Fields: complexity theory, algebraic geometry, harmonic analysisA6complexity theory, algebraic geometry, harmonic analysis★★☆open
MAIS-O63Learning coefficients of modular additionAgenda: A6Fields: algebraic geometry, statisticsA6algebraic geometry, statistics★★★open
MAIS-O64Marginal cost of width for modular-addition networksAgenda: A6Fields: algebraic geometry, statisticsA6algebraic geometry, statistics★★★open
MAIS-O65Learning coefficients of modular addition under cross-entropyAgenda: A6Fields: algebraic geometry, statisticsA6algebraic geometry, statistics★★★open
MAIS-O66Generic constancy of learning coefficients over attention teachersAgenda: A6Fields: algebraic geometry, statisticsA6algebraic geometry, statistics★★★open
MAIS-O67Learning coefficients of one-head softmax attentionAgenda: A6Fields: algebraic geometry, statisticsA6algebraic geometry, statistics★★★open
MAIS-O68Learning coefficients of linear attentionAgenda: A6Fields: algebraic geometry, statistics, computationalA6algebraic geometry, statistics, computational★★☆open
MAIS-O69When does the localized posterior estimate the local learning coefficient?Agenda: A6Fields: statistics, probabilityA6statistics, probability★★☆open
MAIS-O70Local learning coefficients of reduced-rank regressionAgenda: A6Fields: algebraic geometry, statisticsA6algebraic geometry, statistics★★☆open
MAIS-O71Free energy asymptotics for continuous-input ReLU networksAgenda: A6Fields: algebraic geometry, probability, statisticsA6algebraic geometry, probability, statistics★★★open
MAIS-O72Finiteness and frontier condition for learning-coefficient strataAgenda: A7Fields: algebraic geometryA7algebraic geometry★★★open
MAIS-O73Eyring–Kramers law for singular wellsAgenda: A7Fields: probability, algebraic geometryA7probability, algebraic geometry★★★open
MAIS-O74Eyring–Kramers prefactor for a singular well and Morse gateAgenda: A7Fields: probability, algebraic geometryA7probability, algebraic geometry★★☆open
MAIS-O75Entropic selection between two flat strata on the torusAgenda: A7Fields: probabilityA7probability★★☆open
MAIS-O76SGD limit diffusions on a singular set of minimizersAgenda: A7Fields: probability, algebraic geometryA7probability, algebraic geometry★★★open
MAIS-O77Learning coefficients on the matrix factorization fiber and saddlesAgenda: A7Fields: algebraic geometryA7algebraic geometry★★☆open
MAIS-O78A time-sample correspondence for the deep linear networkAgenda: A7Fields: statistics, probabilityA7statistics, probability★★★open
MAIS-O79Saddles as effective minima under coarse-grainingAgenda: A7Fields: dynamical systems, algebraic geometryA7dynamical systems, algebraic geometry★★★open
MAIS-O80Is leap complexity determined by singularity data?Agenda: A7Fields: algebraic geometry, combinatoricsA7algebraic geometry, combinatorics★★★open
MAIS-O81Does a saddle have a well-defined free energy?Agenda: A7Fields: statistics, algebraic geometryA7statistics, algebraic geometry★★★open
MAIS-O82Wide networks select the proxy policy with probability oneAgenda: A8Fields: probability, optimizationA8probability, optimization★★★open
MAIS-O83Does some finite-width network favor the intended goal?Agenda: A8Fields: probability, optimizationA8probability, optimization★★★open
MAIS-O84The crossover time and its asymptoticsAgenda: A8Fields: dynamical systems, optimization, probabilityA8dynamical systems, optimization, probability★★★open
MAIS-O85Which feature maps make the max-margin classifier misgeneralize?Agenda: A8Fields: convex geometry, optimizationA8convex geometry, optimization★★☆open
MAIS-O86Does gradient descent match the Gaussian process posterior?Agenda: A8Fields: probability, statisticsA8probability, statistics★★★open
MAIS-O87Does policy gradient stay misgeneralized despite training diversity?Agenda: A8Fields: dynamical systems, probabilityA8dynamical systems, probability★★☆open
MAIS-O88Misgeneralization versus diversity for reinforcement learningAgenda: A8Fields: probability, dynamical systemsA8probability, dynamical systems★★★open
MAIS-O89Boundary-state residual of max-margin gradient descentAgenda: A8Fields: optimization, dynamical systemsA8optimization, dynamical systems★☆☆open
MAIS-O90Does finite-width training inherit the kernel flow's selection?Agenda: A8Fields: probability, optimizationA8probability, optimization★★☆open
MAIS-O91Numerical atlas of misgeneralization across widths and diversityAgenda: A8Fields: computational, probabilityA8computational, probability★☆☆open
MAIS-O92The outcome law of one rectifier neuronAgenda: A5Fields: dynamical systems, probability, harmonic analysisA5dynamical systems, probability, harmonic analysis★★★open