Any global mirror of open-source version control is incomplete, but the reasons a commit is missing are not interchangeable: a project may have force-pushed it away (so it no longer exists upstream), or the mirror may never have ingested it (a true collection gap). We release a commit-provenance dataset that separates these cases at scale by comparing two views of the same commit graph: the GHArchive event stream, a historical witness of what GitHub advertised at push time, and the World of Code (WoC) V2604 object database, an accumulated union of periodic fetches that never deletes a collected commit. Walking each reference's PushEvent chain reconstructs force-pushes structurally (a before that is not the prior head breaks the fast-forward chain; no recorded flag exists across eras), and joining every advertised commit against WoC membership yields a three-way label. Over 1,118,116,350 advertised commits, 53.35% are present in WoC, 6.47% are rewritten (orphaned by a later force-push, an upstream edit and a correct absence), and 40.18% are never-ingested (the candidate collection gap). About one missing-commit case in fifteen is a rewrite the project erased, not a mirror gap. We re
The study of Differential Privacy (DP) in Natural Language Processing often views the task of text privatization as a $\textit{rewriting}$ task, in which sensitive input texts are rewritten to hide explicit or implicit private information. In order to evaluate the privacy-preserving capabilities of a DP text rewriting mechanism, $\textit{empirical privacy}$ tests are frequently employed. In these tests, an adversary is modeled, who aims to infer sensitive information (e.g., gender) about the author behind a (privatized) text. Looking to improve the empirical protections provided by DP rewriting methods, we propose a simple post-processing method based on the goal of aligning rewritten texts with their original counterparts, where DP rewritten texts are rewritten $\textit{again}$. Our results show that such an approach not only produces outputs that are more semantically reminiscent of the original inputs, but also texts which score on average better in empirical privacy evaluations. Therefore, our approach raises the bar for DP rewriting methods in their empirical privacy evaluations, providing an extra layer of protection against malicious adversaries.
Large language models (LLMs) exhibit remarkable generative capabilities but raise ethical and security concerns by memorizing sensitive data, reinforcing biases, and producing harmful content. These risks have spurred interest in LLM unlearning, the task of removing knowledge associated with undesirable data from pre-trained models. However, most existing methods assume access to clean, well-defined forget data samples, whereas real-world forget data could often be low-quality, synthetically rewritten, or watermarked, casting doubt on the reliability of unlearning. This work presents the first study of unlearning under perturbed or low-fidelity forget data, referred to as noisy forget sets. By systematically benchmarking state-of-the-art LLM unlearning methods, RMU and NPO, on such noisy forget sets, we find that unlearning remains surprisingly robust to perturbations, provided that core semantic signals are preserved. To explain this robustness, we propose a saliency-based interpretation: key semantic components that drive forgetting remain consistently influential despite substantial variation in surface form. This suggests that unlearning algorithms are primarily guided by deep
Conversational search supports multi-turn user-system interactions to solve complex information needs. Different from the traditional single-turn ad-hoc search, conversational search encounters a more challenging problem of context-dependent query understanding with the lengthy and long-tail conversational history context. While conversational query rewriting methods leverage explicit rewritten queries to train a rewriting model to transform the context-dependent query into a stand-stone search query, this is usually done without considering the quality of search results. Conversational dense retrieval methods use fine-tuning to improve a pre-trained ad-hoc query encoder, but they are limited by the conversational search data available for training. In this paper, we leverage both rewritten queries and relevance judgments in the conversational search data to train a better query representation model. The key idea is to align the query representation with those of rewritten queries and relevant documents. The proposed model -- Query Representation Alignment Conversational Dense Retriever, QRACDR, is tested on eight datasets, including various settings in conversational search and ad
In this study, considering the Fisher information metric (Fisher metric) given by a specific form, which is the form of weights in statistical physics, we rewrite the Einstein-Hilbert (EH) action. Then, determining the transformation rules of the Fisher metric, etc under the coarse-graining, we perform the coarse-graining toward that rewritten EH action. We finally show an existence of a trivial fixed-point. Here, the existence of a trivial fixed-point is not trivial for us because we consider the metric given by the Fisher metric, which is not the normal metric and has to satisfy some constraint in the formalism of the the Fisher metric. We use the path-integral in our analysis. At this time we have to accept that a fundamental constraint in the formalism of the Fisher metric is broken at the quantum level. However we consider we can accept this with the thought that some constraints and causal relations held at the classical level usually get broken at the quantum level. We finds some problems of the Fisher metric. The space-time we consider is two-dimensional.
Both cellular automata (CA) and lattice-gas automata (LG) provide finite algorithmic presentations for certain classes of infinite dynamical systems studied by symbolic dynamics; it is customary to use the term `cellular automaton' or `lattice gas' for the dynamic system itself as well as for its presentation. The two kinds of presentation share many traits but also display profound differences on issues ranging from decidability to modeling convenience and physical implementability. Following a conjecture by Toffoli and Margolus, it had been proved by Kari (and by Durand--Lose for more than two dimensions) that any invertible CA can be rewritten as an LG (with a possibly much more complex ``unit cell''). But until now it was not known whether this is possible in general for noninvertible CA--which comprise ``almost all'' CA and represent the bulk of examples in theory and applications. Even circumstantial evidence--whether in favor or against--was lacking. Here, for noninvertible CA, (a) we prove that an LG presentation is out of the question for the vanishingly small class of surjective ones. We then turn our attention to all the rest--noninvertible and nonsurjective--which compr
In this note we try to bring out the ideas of Hamming's classic paper on coding theory in a form understandable by undergraduate students of mathematics.
About twenty years ago we wrote a paper, "Boolean Functions whose Fourier Transform is Concentrated on the First Two Levels", \cite{FKN}. In it we offered several proofs of the statement that Boolean functions $f(x_1,x_2,\dots,x_n)$, whose Fourier coefficients are concentrated on the lowest two levels are close to a constant function or to a function of the form $f=x_k$ or $f=1-x_k$. Returning to the paper lately, we noticed that the presentation of the first proof is rather cumbersome, and includes several typos. In this note we rewrite that proof, as a service to the public.
Classical soft graviton theorem gives the gravitational wave-form at future null infinity at late retarded time $u$ for a general classical scattering. The large $u$ expansion has three known universal terms: the constant term, the term proportional to $1/u$ and the term proportional to $\ln u/u^2$, whose coefficients are determined solely in terms of the momenta of incoming and the outgoing hard particles, including the momenta carried by outgoing gravitational and electromagnetic radiation produced during scattering. For the constant term, also known as the memory effect, the dependence on the momenta carried away by the final state radiation / massless particles is known as non-linear memory or null memory. It was shown earlier that for the coefficient of the $1/u$ term the dependence on the momenta of the final state massless particles / radiation cancels and the result can be written solely in terms of the momenta of the incoming particles / radiation and the final state massive particles. In this note we show that the same result holds for the coefficient of the $\ln u/u^2$ term. Our result implies that for scattering of massless particles the coefficients of the $1/u$ and $\
We propose RCEM, a Robust Conversational search EMbedder that is additionally equipped with LLM's query reformulation capability without losing base model's generalization. Unlike prior conversational dense retrieval approaches that learn direct conversation-to-passage matching, RCEM aligns conversations, prepended by special token, to LLM-rewritten queries, while preserving the original embedding space. The unchanged embedding space automatically maps the rewritten-query to the relevant passages. As a result, RCEM (1) reduces overfitting by simplifying the alignment task from long passages to shorter rewritten queries, (2) eliminates the need for conversation-to-passage relevance labels for training, and (3) maintains its original embedding space that allows conversational queries against indexes built by original embedder without rebuilding them. Extensive experiments show that RCEM consistently outperforms prior approaches, achieving up to 30% improvement under distributional shift.
Statistical watermarking is a common approach for verifying whether text was written by a language model. Most existing schemes assume autoregressive generation, where tokens are produced left to right and contextual hashing is well defined. Diffusion language models generate text by denoising tokens in arbitrary order, so these schemes cannot be applied directly. A recent watermark by Gloaguen et al. addresses this gap for LLaDA 8B Instruct and reports true positive detection above 99%. This paper studies what happens when watermarked text is rewritten not once but several times. Using the same watermark configuration, 1,605 watermarked completions of about 300 tokens each are produced across five WaterBench domains. Each completion is rewritten by four open weight language models, from 1.5B to 8B parameters, none of which know the watermark key. Five rewrite styles are tested: paraphrase, humanize, simplify, academic, and summarize expand. Each style is chained for up to five hops, producing 160,500 rewritten texts in total. The watermark is detected on 87.9% of the original outputs at the standard significance threshold. After a single rewrite, detection falls to between 14% and
Machine learning models and libraries can train datasets of different sizes and perform prediction and classification operations, but machine learning models and libraries cause slow and long training times on large datasets. This article introduces EmbeddedML, a training-time-optimized and mathematically enhanced machine learning library. The speed was increased by approximately times compared to scikit-learn without any loss in terms of accuracy in regression models such as Multiple Linear Regression. Logistic Regression and Support Vector Machines (SVM) algorithms have been mathematically rewritten to reduce training time and increase accuracy in classification models. With the applied mathematical improvements, training time has been reduced by approximately 2 times for SVM on small datasets and by around 800 times on large datasets, and by approximately 4 times for Logistic Regression, compared to the scikit-learn implementation. In summary, the EmbeddedML library offers regression, classification, clustering, and dimensionality reduction algorithms that are mathematically rewritten and optimized to reduce training time.
Conversational information seeking (CIS) systems aim to model the user's information need within the conversational context and retrieve the relevant information. One major approach to modeling the conversational context aims to rewrite the user utterance in the conversation to represent the information need independently. Recent work has shown the benefit of expanding the rewritten utterance with relevant terms. In this work, we hypothesize that breaking down the information of an utterance into multi-aspect rewritten queries can lead to more effective retrieval performance. This is more evident in more complex utterances that require gathering evidence from various information sources, where a single query rewrite or query representation cannot capture the complexity of the utterance. To test this hypothesis, we conduct extensive experiments on five widely used CIS datasets where we leverage LLMs to generate multi-aspect queries to represent the information need for each utterance in multiple query rewrites. We show that, for most of the utterances, the same retrieval model would perform better with more than one rewritten query by 85% in terms of nDCG@3. We further propose a mul
This paper introduces Qrlew, an open source library that can parse SQL queries into Relations -- an intermediate representation -- that keeps track of rich data types, value ranges, and row ownership; so that they can easily be rewritten into differentially-private equivalent and turned back into SQL queries for execution in a variety of standard data stores. With Qrlew, a data practitioner can express their data queries in standard SQL; the data owner can run the rewritten query without any technical integration and with strong privacy guarantees on the output; and the query rewriting can be operated by a privacy-expert who must be trusted by the owner, but may belong to a separate organization.
Since the celebrated theorem of Lax and Wendroff, we know a necessary condition that any numerical scheme for hyperbolic problem should satisfy: it should be written in flux form. A variant can also be formulated for the entropy. Even though some schemes, as for example those using continuous finite element, do not formally cast into this framework, it is a very convenient one. In this paper, we revisit this, introduce a different notion of local conservation which contains the previous one in one space dimension, and explore its consequences. This gives a more flexible framework that allows to get, systematically, entropy stable schemes, entropy dissipative ones, or accomodate more constraints. In particular, we can show that continuous finite element method can be rewritten in the finite volume framework, and all the quantities involved are explicitly computable. We end by presenting the only counter example we are aware of, i.e a scheme that seems not to be rewritten as a finite volume scheme.
Incomplete utterance rewriting has recently raised wide attention. However, previous works do not consider the semantic structural information between incomplete utterance and rewritten utterance or model the semantic structure implicitly and insufficiently. To address this problem, we propose a QUEry-Enhanced Network (QUEEN). Firstly, our proposed query template explicitly brings guided semantic structural knowledge between the incomplete utterance and the rewritten utterance making model perceive where to refer back to or recover omitted tokens. Then, we adopt a fast and effective edit operation scoring network to model the relation between two tokens. Benefiting from proposed query template and the well-designed edit operation scoring network, QUEEN achieves state-of-the-art performance on several public datasets.
The theory of Poisson-Lie groups and Lie bialgebras plays a major role in the study of one dimensional integrable systems; many families of integrable systems can be recovered from a Lax pair which is constructed from a Lie bialgebra associated to a Poisson-Lie group. A higher homotopy notion of Poisson-Lie groups and Lie bialgebras has been studied using Lie algebra crossed-modules and $L_2$-algebras, which gave rise to the notion of (strict) Lie 2-bialgebras and Poisson-Lie 2-groups . In this paper, we use these structures to generalize the construction of a Lax pairs and introduce an appropriate notion of {higher homotopy integrability}. Within this framework, we introduce a higher homotopy version of the Kac-Moody algebra, with which the 2-Lax equation can be rewritten as a zero 2-curvature condition in 2+1d. An explicit characterization of our higher Kac-Moody algebra will be given, and we also demonstrate how it governs the 2-Lax pairs and the symmetries of a 3d topological-holomorphic field theory studied recently. This 3d theory thus serves as an example of a physical system that exhibits the sort of 2-graded integrability that we have defined here.
The Miyawaki lifting is a lifting of Siegel modular forms introduced by Ikeda in his 2006 paper. In the same paper, he also conjectured a formula for the norms of Miyawaki lifts. In this paper, we show that his conjectural formula can be rewritten into a refined GGP type formula.
Magic sets are a Datalog to Datalog rewriting technique to optimize query answering. The rewritten program focuses on a portion of the stable model(s) of the input program which is sufficient to answer the given query. However, the rewriting may introduce new recursive definitions, which can involve even negation and aggregations, and may slow down program evaluation. This paper enhances the magic set technique by preventing the creation of (new) recursive definitions in the rewritten program. It turns out that the new version of magic sets is closed for Datalog programs with stratified negation and aggregations, which is very convenient to obtain efficient computation of the stable model of the rewritten program. Moreover, the rewritten program is further optimized by the elimination of subsumed rules and by the efficient handling of the cases where binding propagation is lost. The research was stimulated by a challenge on the exploitation of Datalog/\textsc{dlv} for efficient reasoning on large ontologies. All proposed techniques have been hence implemented in the \textsc{dlv} system, and tested for ontological reasoning, confirming their effectiveness. Under consideration for pu