arXiv:2601.08998v1 Announce Type: new Abstract: Flaky tests are a common problem in software testing. They produce inconsistent results when executed multiple times on the same code, invalidating the assumption that a test failure indicates a software defect. Recent work on LLM-based test generation has identified flakiness as a potential problem with generated tests. However, its prevalence and underlying causes are unclear. We examined the flakiness of LLM-generated tests in the context of four relational database management systems: SAP […]

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arXiv:2601.07989v1 Announce Type: new Abstract: This paper identifies the Stein-exponent of distributed detection when the sensor communicates to the decision center over a discrete memoryless channel (DMC) subject to one of three stringent communication constraints: 1) The number of channel uses of the DMC grows sublinearly in the number of source observations n; 2) The number of channel uses is n but a block-input cost constraint is imposed almost surely, which grows sublinearly in n; 3) The block-input […]

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Deep neural networks constructed from linear maps and positively homogeneous nonlinearities (e.g., ReLU) possess a fundamental gauge symmetry: the network function is invariant to node-wise diagonal rescalings. However, standard gradient descent is not equivariant to this symmetry, causing optimization trajectories to depend heavily on arbitrary parameterizations. Prior work has proposed rescaling-invariant optimization schemes for positively homogeneous networks (e.g., path-based or path-space updates). Our contribution is complementary: we formulate the invariance requirement at the level of the backward adjoint/optimization […]

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arXiv:2602.00969v1 Announce Type: new Abstract: Training Large Language Models (LLMs) at ultra-low precision is critically impeded by instability rooted in the conflict between discrete quantization constraints and the intrinsic heavy-tailed spectral nature of linguistic data. By formalizing the connection between Zipfian statistics and random matrix theory, we prove that the power-law decay in the singular value spectra of embeddings is a fundamental requisite for semantic encoding. We derive theoretical bounds showing that uniform quantization introduces a noise floor […]

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arXiv:2211.11368v5 Announce Type: replace-cross Abstract: In a mixed generalized linear model, the goal is to learn multiple signals from unlabeled observations: each sample comes from exactly one signal, but it is not known which one. We consider the prototypical problem of estimating two statistically independent signals in a mixed generalized linear model with Gaussian covariates. Spectral methods are a popular class of estimators which output the top two eigenvectors of a suitable data-dependent matrix. However, despite the wide […]

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Shiba Inu has generated about 150,000X returns since its launch in August 2020 and PEPE has paid out more than 46,000X to first entrants since April 2023. Both the tokens presently trade at multi-billion dollars valuations that deny them any similar percentage gains to the present value. SHIB has a market cap of over $5B, and PEPE has approximately $2.7B which puts them in mathematical limits regarding the possibility of massive future growth. Cryptocurrency whale wallets have distinctive […]

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Quantum generative modeling, where the Born rule naturally defines probability distributions through measurement of parameterized quantum states, is a promising near-term application of quantum computing. We propose a Quantum Scrambling Born Machine in which a fixed entangling unitary — acting as a scrambling reservoir — provides multi-qubit entanglement, while only single-qubit rotations are optimized. We consider three entangling unitaries — a Haar random unitary and two physically realizable approximations, a finite-depth brickwork random circuit and analog time evolution […]

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Clark Packard Last week, Disney+ released a restored version of The Beatles Anthology, the landmark 1995 ABC eight-part documentary series that remains the closest thing to a definitive account of the band’s extraordinary journey. I binge-watched the updated Anthology over the Thanksgiving holiday weekend, which brought back memories of watching the original with my parents 30 years ago. Now I’m the parent, though my wife and four-year-old son were less enthusiastic about the marathon viewing sessions. Last year, I […]

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