arXiv subjects

Yusuke Takahashi

Publications and source records attributed to Yusuke Takahashi.

4 recordsLinked to original sources

arXiv2026

RAG Deserves an Index: Why Ingest-Time Compilation Beats Query-Time Interpretation

Nearly every retrieval-augmented question-answering system in production ships with a hidden interpreter: on each query a language model re-derives the meaning of raw corpus text and then throws that work away. Cheaper models do not close the gap: per-token prices have fallen by orders of magnitude while inference spend has risen, because context volume grows faster than prices fall. This is the modern equivalent of the full-table scan, and the remedy is the one databases found fifty years ago: do the expensive work once, at write time, into a maintained structure that makes reads cheap. A corpus whose read pattern is known before it ever meets a user can and should be indexed too. We call the paradigm ingest-time semantic compilation (ISC): compile a corpus's meaning into a queryable substrate with two coupled layers - incrementally maintained embeddings, and atomic claims whose provenance is validated at compile time - and treat that substrate as a first-class database object with its own DDL, maintenance contract, migration contract, and cost model. Two existence proofs support it. Substrate upkeep scales with change rather than corpus size: incremental updates run 33.7x cheaper than reconstruction while tracking it to floating-point precision. And on a held-out sample of 500 broadcast-interview transcripts, compiled claims as the retrieval payload win all 32 budget-by-model cells: 85.2% correct from roughly 2.2k reader tokens against 72.5% from 16.3k for the best chunk configuration anywhere. The only baseline that keeps pace is a contextualized-chunk pipeline with hybrid retrieval and reranking, statistically indistinguishable from compiled claims at roughly twenty-one times the query-path tokens - and it reaches that parity, we argue, precisely because it has itself begun to compile. We close with the systems agenda this opens, from compilation planners to read planning.

cs.AI↗

arXiv2026

Cost Scales with Change, Not Corpus Size: Incrementally Maintaining an Evolving Semantic Substrate

Retrieval-augmented and agentic question-answering systems increasingly re-derive the meaning of a corpus at query time. Put plainly, instead of re-deriving what a corpus means on every question, the work is done once when a document arrives and is thereafter merely consulted -- a compiler, not an interpreter, of meaning. An alternative is to compile that meaning once, at ingest time, into a compact, queryable semantic substrate and maintain it as the corpus evolves. The central objection is maintenance cost: rebuilding a truncated singular value decomposition (SVD) on every change appears prohibitive, and a change of embedding model seems to force a full re-embedding. We argue and show empirically that maintenance cost scales with the amount of change, not corpus size. On a controlled synthetic pilot (dimension 256, rank 32, a corpus grown from 3,000 to 9,000 documents over 50 update events), incremental low-rank updates were 33.7 times cheaper per update than full re-SVD and 23.8 times cheaper cumulatively, while the incremental subspace tracked the full recomputation to within floating-point precision (maximum principal-angle drift below 1e-11 degrees; recall@10 = 1.0). An orthogonal Procrustes virtual axis update recovered 0.95 mean cosine to truly re-embedded vectors by re-embedding only about 10 percent of the corpus. The results support maintaining, rather than repeatedly reconstructing, a semantic substrate.

cs.AI↗

arXiv2022

Faces of Directed Edge Polytopes

Given a finite quiver (directed graph) without loops and multiedges, the convex hull of the column vector of the incidence matrix is called the directed edge polytope and is an interesting example of lattice polytopes. In this paper, we give a complete characterization of facets of the directed edge polytope of an arbitrary finite quiver without loops and multiedges in terms of the connectivity and the existence of a rank function. Our result can be regarded as an extension of the result of Higashitani et al. on facets of symmetric edge polytopes to directed edge polytopes. When the quiver in question has a rank function, we obtain a characterization of faces of arbitrary dimensions.

math.CO↗

arXiv2019

Convolutional Neural Network-based Topology Optimization (CNN-TO) By Estimating Sensitivity of Compliance from Material Distribution

This paper proposes a new topology optimization method that applies a convolutional neural network (CNN), which is one deep learning technique for topology optimization problems. Using this method, we acquire a structure with a little higher performance that could not be obtained by the previous topology optimization method. In particular, in this paper, we solve a topology optimization problem aimed at maximizing stiffness with a mass constraint, which is a common type of topology optimization. In this paper, we first formulate the conventional topology optimization by the solid isotropic material with penalization method. Next, we formulate the topology optimization using CNN. Finally, we show the effectiveness of the proposed topology optimization method by solving a verification example, namely a topology optimization problem aimed at maximizing stiffness. In this research, as a result of solving the verification example for a small design area of 16x32 element, we obtain the solution different from the previous topology optimization method. This result suggests that stiffness information of structure can be extracted and analyzed for structural design by analyzing the density distribution using CNN like an image. This suggests that CNN technology can be utilized in the structural design and topology optimization.

cs.LG↗