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The Evaluation Blind Spot: A Stereological Theory of Benchmark Coverage for Large Language Models
arXiv:2606.05169v1 Announce Type: new Abstract: We give a stereological theory of LLM benchmark coverage. For any suite with effective dimensionality d_eff, the visible Hausdorff distance between two convex capability profiles consistent with the same scores is bounded by epsilon + C R m^(-1/(d_eff-1)), with matching Lipschitz lower bound. Empirically, three independent leaderboards (Open LLM v2, an extended 12-benchmark suite, LiveBench) all have d_eff in [2.86, 4.80] on their competitive...
Collision Resistance of Single-Layer Neural Nets
arXiv:2606.03807v1 Announce Type: new Abstract: We initiate the study of the algorithmic complexity of finding collisions in single-layer binary neural networks. Given a random matrix $\mathbf{A} \in \mathbb{R}^{m\times n}$, an input $\mathbf{x} \in \{-1,1\}^n$ is mapped to a binary output vector $\varphi(\mathbf{A}\mathbf{x})\in \{-1,1\}^m$, where $\varphi$ is an activation function with constant behavior on $[\kappa, \infty)$ for some threshold $\kappa \geq 0$. We identify the threshold...
Listing Even Cycles Faster than the Submodular-Width Barrier
arXiv:2605.30564v1 Announce Type: new Abstract: A classic result of Alon, Yuster, and Zwick (AYZ, Algorithmica 1997) shows that all $2k$-cycles in an $m$-edge graph can be listed in $\tilde O(m^{2-1/k}+t)$ time, where $t$ is the output size. This bound underlies the {\em submodular width} of Marx (JACM 2013) and the PANDA framework of Abo Khamis, Ngo, and Suciu (PODS 2017), which extend AYZ to arbitrary conjunctive queries with degree constraints. A central open question is whether...
$\mathbb{R}^{2k}$ is Theoretically Large Enough for Embedding-based Top-$k$ Retrieval
Announce Type: replace Abstract: This paper studies the Minimal Embeddable Dimension (MED): the least dimension in which there exists a configuration of $m$ object vectors so that every subset of size at most $k$ is exactly retrieved by score comparison. Our result shows MED is $\Theta(k)$, independent of $m$, for inner product, Euclidean distance, and cosine similarity. We then consider Robust MED (RMED), where all vectors are unit normed and an $\epsilon$ gap of scores is required.
Construction of cyclic codes with large minimum distance from power functions over odd characteristic finite fields
Announce Type: new Abstract: Cyclic codes with dimensions exceeding half of the code length and minimum distance greater than the square root of the code length are of significant interest due to their high transmission efficiency and strong error-correcting capability. Such codes are well suited for demanding applications, including communication and storage systems, post-quantum cryptography, radar and sonar systems, wireless sensor networks, and space communications. Motivated by the work...
Reed-Muller Codes for Joint Random and Stuck-At Error Correction
arXiv:2605.21727v2 Announce Type: replace Abstract: Block codes are considered for improving the reliability of messages stored in a computer memory with both stuck-at defects and random errors. It is assumed that the side information about the state of the defects is available to the encoder, but not to the decoder. A novel recursive construction of a set of masks is developed such that it can satisfy any $s$ stuck-at errors in a $2^m$ binary sequence, when $s \leq m$. We prove that the...
Decoupling heat and electricity: A thermal invisible gateway
Announce Type: replace Abstract: The Wiedemann-Franz law couples electrical and thermal conductivity, making high electrical conduction with low thermal conduction a major challenge. To overcome this, we designed an active thermal metasurface (ATMS) - based thermal invisible gateway that decouples thermal and electrical paths. Built on a copper substrate with a dumbbell-shaped bridge, the structure suppresses heat flow via directional compensation while allowing unimpeded electrical conduction.
Efficient Mean Curvature Computation on High-Dimensional Data Manifolds
Announce Type: new Abstract: Estimating local mean curvature at each point of a high-dimensional dataset is a key ingredient of geometry-aware machine learning algorithms, such as the Mean Curvature Boundary Points (MCBP) method. The naive implementation of this computation, based on a local shape operator approximated from k-nearest neighbor patches, involves an explicit construction of a matrix $H$ whose trace form yields an $O(m^4)$ cost per point, rendering the approach intractable for...
Belmont Stakes 2026 at Saratoga Race Course: Best bets, exotics, 'Pick 5' for the Grade 1 stakes races
This will be the final of three consecutive years that the Belmont Stakes will run at the mecca of horse racing: the Saratoga Race Course. Traditionally held at Belmont Park, the third jewel of horse racing’s Triple Crown has been held in Saratoga during Belmont's renovations and will return to its original home next year. As you probably already know, we won’t get a Triple Crown winner.
21cmEMUv3: a hybrid diffusion-LSTM emulator of 21cmFAST summary observables
arXiv:2606.00219v1 Announce Type: cross Abstract: We are witnessing a surge in observations of the cosmic dawn (CD) and epoch of reionisation (EoR), driving an increasing demand for fast and robust theoretical interpretation frameworks. In response, machine learning (ML), and emulation in particular, has emerged as a powerful approach to accelerate and enhance inference pipelines. In this work, we present 21cmEMUv3, an emulator trained on 21cmFASTv3 simulations that model both atomically and...