We present a machine learning framework for testing general relativity (GR) with gravitational wave signals from binary black hole mergers. Using the source parameters of 173 BBH events from the GWTC catalog as a realistic astrophysical population, we generate simulated GR waveforms and construct beyond GR (BGR) waveforms by applying controlled phase deformations. We introduce a response function formalism that provides a systematic framework for quantifying how any observable responds to modifications of GR. We train convolutional neural networks (CNNs) on two input representations: whitened waveforms and a response function type observable derived from the waveform mismatch, which isolates the effect of phase deviations from the bulk signal. Using response functions as the CNN input improves the classification sensitivity by a factor of approximately 33 compared to whitened waveforms, demonstrating that the choice of observable representation is as important as the classifier architecture. We study the fundamental limits of this classification through Bayes optimal error analysis, averaging methods that reveal coherent patterns hidden in noise, and a comparison between CNN accuracy and a single feature classifier as a proxy for human performance. At all deformation scales, the CNN outperforms the best single feature approach. We extend the framework to physically motivated theories using the parameterized post Einsteinian (ppE) formalism and apply it to massive gravity, where the classifier detects deviations for graviton masses of order $m_g \sim 10^{-23}\;\mathrm{eV}/c^2$ with aLIGO design sensitivity.

On the construction of almost uniformly convergent random variables with given weakly convergent image laws.

Active seriation aims at recovering an unknown ordering of $n$ items by adaptively querying pairwise similarities. The observations are noisy measurements of entries of an underlying $n$ x $n$ permuted Robinson matrix, whose permutation encodes the latent ordering. The framework allows the algorithm to start with partial information on the latent ordering, including seriation from scratch as a special case. We propose an active seriation algorithm that provably recovers the latent ordering with high probability. Under a uniform separation condition on the similarity matrix, optimal performance guarantees are established, both in terms of the probability of error and the number of observations required for successful recovery.

Emerging ethical approaches have attempted to filter pretraining material, but such approaches have been ad hoc and failed to take context into account. We offer an approach to filtering grounded in law, which has directly addressed the tradeoffs in filtering material.

The23 proposed SSCM does coverthe case of non-zero variance, but currently the identifiability proof is only shown in a24 specific case. Inour simulations under non-zero variance settings, we neverobserved that the procedure converged25 to wrong solutions, suggesting that the non-zero-variance case is also identifiable. For the fMRI and cellular data, the null hypothesis was rejected at significance level 0.01. Regarding causal28 structure variation, for fMRI data, it is well-known that neural connectivities may change across different external29 stimuliorintrinsicstates. Forcellular32 data, causal structure may be different across conditions/interventions.(0)Theyare different.

We thank the reviewers for the thorough feedbacks. Based on those, we have made numerous improvements. Original code is for decrete actions.) IM baseline with the random object. The plot is similar to "tool" in Figure 1 and we omit it due to space constraints. Rev. #1 suggested that the environments could be solved by classic planning methods.

Details of the layers can be found in the supplement Table S.2. We will add another, larger figure illustrating the18 U-shape and thethree parts ofthearchitecture. Thesleepstage23 scores indeed show human interpretable patterns even on short timescales. We regard it as a big41 advantage thatwedidnotextensivelytune ourarchitec-42 ture to the tasks. Wewill improvethe colour palette as suggested.