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Abstract Large language models (LLMs) have demonstrated tremendous capabilities in solving complex tasks, from quantitative reasoning to understanding natural language. However, LLMs sometimes suffer from confabulations (or hallucinations), which can result in them making plausible but incorrect statements^1,2. This hinders the use of current large models in scientific discovery. Here we introduce FunSearch (short for searching in the function space), an evolutionary procedure based on pairing a pretrained LLM with a systematic evaluator. We demonstrate the effectiveness of this approach to surpass the best-known results in important problems, pushing the boundary of existing LLM-based approaches³. Applying FunSearch to a central problem in extremal combinatorics—the cap set problem—we discover new constructions of large cap sets going beyond the best-known ones, both in finite dimensional and asymptotic cases. This shows that it is possible to make discoveries for established open problems using LLMs. We showcase the generality of FunSearch by applying it to an algorithmic problem, online bin packing, finding new heuristics that improve on widely used baselines. In contrast to most computer search approaches, FunSearch searches for programs that describe how to solve a problem, rather than what the solution is. Beyond being an effective and scalable strategy, discovered programs tend to be more interpretable than raw solutions, enabling feedback loops between domain experts and FunSearch, and the deployment of such programs in real-world applications. 

We recently reported on the radio-frequency attenuation length of cold polar ice at Summit Station, Greenland, based on bistatic radar measurements of radio-frequency bedrock echo strengths taken during the summer of 2021. Those data also include echoes attributed to stratified impurities or dielectric discontinuities within the ice sheet (layers), which allow studies of a) estimation of the relative contribution of coherent (discrete layers, e.g.) vs. incoherent (bulk volumetric, e.g.) scattering, b) the magnitude of internal layer reflection coefficients, c) limits on the azimuthal asymmetry of reflections (birefringence), and d) limits on signal dispersion in-ice over a bandwidth of ~100 MHz. We find that i) after averaging 10000 echo triggers, reflected signal observable over the thermal floor (to depths of approximately 1500 m) are consistent with being entirely coherent, ii) internal layer reflection coefficients are measured at approximately -60 to -70 dB, iii) birefringent effects for vertically propagating signals are smaller by an order of magnitude relative to comparable studies performed at South Pole, and iv) within our experimental limits, glacial ice is non-dispersive over the frequency band relevant for neutrino detection experiments. 

Abstract The TAROGE-M radio observatory is a self-triggered antenna array on top of the ∼2700 m high Mt. Melbourne in Antarctica, designed to detect impulsive geomagnetic emission from extensive air showers induced by ultra-high energy (UHE) particles beyond 10 17 eV, including cosmic rays, Earth-skimming tau neutrinos, and particularly, the “ANITA anomalous events” (AAE) from near and below the horizon. The six AAE discovered by the ANITA experiment have signal features similar to tau neutrinos but that hypothesis is in tension either with the interaction length predicted by Standard Model or with the flux limits set by other experiments. Their origin remains uncertain, requiring more experimental inputs for clarification. The detection concept of TAROGE-M takes advantage of a high altitude with synoptic view toward the horizon as an efficient signal collector, and the radio quietness as well as strong and near vertical geomagnetic field in Antarctica, enhancing the relative radio signal strength. This approach has a low energy threshold, high duty cycle, and is easy to extend for quickly enlarging statistics. Here we report experimental results from the first TAROGE-M station deployed in January 2020, corresponding to approximately one month of livetime. The station consists of six receiving antennas operating at 180–450 MHz, and can reconstruct source directions of impulsive events with an angular resolution of ∼0.3°, calibrated in situ with a drone-borne pulser system. To demonstrate TAROGE-M's ability to detect UHE air showers, a search for cosmic ray signals in 25.3-days of data together with the detection simulation were conducted, resulting in seven identified candidates. The detected events have a mean reconstructed energy of 0.95 -0.31 +0.46 EeV and zenith angles ranging from 25° to 82°, with both distributions agreeing with the simulations, indicating an energy threshold at about 0.3 EeV. The estimated cosmic ray flux at that energy is 1.2 -0.9 +0.7 × 10 -16 eV -1 km -2 yr -1 sr -1 , also consistent with results of other experiments. The TAROGE-M sensitivity to AAEs is approximated by the tau neutrino exposure with simulations, which suggests comparable sensitivity as ANITA's at around 1 EeV energy with a few station-years of operation. These first results verified the station design and performance in a polar and high-altitude environment, and are promising for further discovery of tau neutrinos and AAEs after an extension in the near future.