Nat Friedman

Iron-Rhodium's AFM-FM Coupling Enables Robust Antiferromagnetic Memory at Room Temperature

This paper demonstrates a working antiferromagnetic (AFM) magnetic memory scheme using patterned iron-rhodium (FeRh) thin films, imaged under ambient conditions via quantum diamond microscopes (QDMs). The key mechanistic finding is that pinned uncompensated magnetic moments (UMMs) in the FeRh structure create a deterministic coupling between the ferromagnetic (FM) magnetization vector and the antiferromagnetic Néel vector, meaning magnetic orientation is preserved as the material cycles between phases. This provides the foundational mechanism for practical HAMR-compatible AFM memory, with FeRh's sharper phase transition and lower write temperature offering engineering advantages over competing materials.

LLM Mathematical Reasoning Benchmark: 98/100 Research-Level Problems Solved with Repeated Sampling

A group of 49 mathematicians created a curated benchmark of 100 research-level math problems with known answers, evaluated across three stages of LLM testing. A single-attempt pass left 41 problems unsolved; repeated sampling (20 runs/model) reduced that to 16; and "heavy-thinking" models in a final stage left only 2 unsolved. The results suggest that with sufficient sampling budget and advanced reasoning models, frontier LLMs are approaching near-complete coverage of research-grade mathematical benchmarks, raising questions about benchmark saturation in this domain.

Weyl Semimetal/Topological Insulator Heterostructures Restore Topological Transport via Interface Hybridization

A Mn₃₊ₓSn₁₋ₓ/Bi₀.₈₅Sb₀.₁₅ heterostructure demonstrates that a hybridized topological state at the WSM/TI interface can restore Weyl node magnetotransport suppressed by ferromagnetic defect phases in the WSM layer. Ferromagnetic disorder in Mn₃₊ₓSn₁₋ₓ films eliminates the anomalous Hall effect signature of topological Weyl node conduction, but deposition of a Bi₀.₈₅Sb₀.₁₅ topological insulator overlayer recovers this signal — an effect not replicated by non-topological heavy metal overlayers. This interface-specific recovery is attributed to hybridization between the WSM Fermi arc states and TI surface states, offering a materials pathway to engineer robust topological transport in polycrystalline, sputter-grown systems.

From O(n⁷r) to O(nr²): Near-Optimal Algorithms for Network Facility Interdiction on Trees and Bounded Treewidth Graphs

This paper presents a dynamic programming algorithm for the r-edge interdiction covering problem (REIC) — removing up to r edges to maximally disconnect customers from facilities — achieving O(nr²) time on trees, a dramatic improvement over the prior O(n⁷r) algorithm by Fröhlich and Ruzika. The algorithm extends to graphs of bounded treewidth with the same O(nr²) runtime. The authors also introduce RFIC (r-facility interdiction), prove it NP-complete via reduction to the minimum p-union problem, and give an O(nr²) tree algorithm for it, yielding an O(n³) algorithm for the small set bipartite vertex expansion (SSBVE) problem on trees. Empirical benchmarks against Gurobi and the Fröhlich-Ruzika baseline confirm the new algorithm is significantly faster and less sensitive to network topology and size.

Flash-MaxSim: Eliminating the Materialization Bottleneck in Late-Interaction Retrieval via IO-Aware Fused Kernels

Late-interaction models like ColBERT and ColPali compute relevance via the MaxSim operator, which naively requires materializing a full query-token × document-token similarity tensor — reaching 21 GB in FP16 for just 10K ColPali documents, exhausting GPU memory. Flash-MaxSim resolves this by fusing the similarity computation and row-maximum reduction into a single tiled SRAM-resident pass, never writing the intermediate tensor to HBM. The approach extends to the backward pass, INT8 quantization, and variable-length (padding-free) scoring, yielding up to 4.7× speedup and ~28× training memory reduction with exact ranking preservation.

Polarization structure of gravitational waves in extended relativity

A Foundation for the Core Mathematician

Resilient AI Supercomputer Networking using MRC and SRv6