arXiv subjects

Denis Bykov

Publications and source records attributed to Denis Bykov.

6 recordsLinked to original sources

arXiv2026

Q2D-Web: A Large-Scale Benchmark for Retrieval in Agentic RAG Systems

Evaluating first-stage retrievers in large-scale production RAG requires a benchmark that pairs a large-scale corpus with a large set of agent-reformulated search queries based on real user queries and their conversation threads, and that labels many relevant documents per query. No existing public benchmark evaluates this setting: large-scale collections typically provide only a small number of evaluation queries, whereas benchmarks with many queries generally contain only millions of documents. Moreover, most benchmarks assess human-written queries, while the first-stage retrievers in agentic RAG pipelines serve machine-written reformulations whose distribution differs from human search behavior. To overcome these evaluation gaps, we introduce Q2D-Web (Query2Doc-Web), a large-scale agentic retrieval benchmark consisting of a 190M-document web corpus and 70k agentic search queries in ten languages, reformulated from real-world user queries in production systems. Q2D-Web provides three sets of fixed relevance judgments: agent citations, production rankings, and a combined set that unions both signals and adds LLM-based judgments of unlabeled pooled documents to reduce false negatives. We benchmark 13 retrievers including lexical, dense, and late-interaction models and find that their relative ordering is largely insensitive to the choice of judgment set, while diverging substantially across topical domains, query languages, and query types. To enable fast evaluation, we also study subcorpus sampling as an approximation to full-corpus evaluations. Retaining a third of the corpus, selected by reciprocal rank fusion over pooled retriever runs, preserves the full-corpus model ranking under the combined judgments while raising absolute Recall@1000 only by 3 to 7 points. The public leaderboard is accessible under: https://huggingface.co/spaces/perplexity-ai/q2d-web-leaderboard

cs.IR↗

arXiv2026

WANDR: A Benchmark for Wide and Deep Research

WANDR (Wide ANd Deep Research) is a benchmark of 500 realistic, challenging data-collection tasks for research agents. Each task requires a system to discover a large set of entities that satisfy specified criteria (breadth), investigate each entity through multiple coordinated web searches (depth), and return independently verifiable records with supporting sources and excerpts. Tasks are represented as qualification key hierarchies that specify the entities, relationships, evidence, and required count at each level; a hierarchy with n companies, m employees per company, and k sources per employee requires n x m x k records. This structure supports diverse workflows such as market mapping, due diligence, literature review, product comparison, and talent sourcing, with targets ranging from dozens to thousands of records. WANDR replaces static gold answer sets with task-specific judges that refetch cited pages and verify each record against its evidence, allowing evaluation of current and changing facts. Record verdicts are aggregated into soft and hard precision, recall, and F1 scores that distinguish factual quality, coverage, and hierarchical completeness. The tasks are derived from de-identified product-usage logs and produced through a semi-automated pipeline with automated checks, empirical audits, and human review where needed. We evaluate six production research systems and find that the benchmark is far from saturated: at high effort, the strongest system reaches only 0.363 soft F1 and 0.133 hard F1. Performance degrades as target volume and hierarchy depth increase, with incomplete discovery, missing enrichment, and incomplete evidence construction remaining major bottlenecks. The benchmark and evaluation harness are available at https://github.com/perplexityai/wandr.

cs.LG↗

arXiv2026

Diffusion-Pretrained Dense and Contextual Embeddings

In this report, we introduce pplx-embed, a family of multilingual embedding models that employ multi-stage contrastive learning on a diffusion-pretrained language model backbone for web-scale retrieval. By leveraging bidirectional attention through diffusion-based pretraining, our models capture comprehensive bidirectional context within passages, enabling the use of mean pooling and a late chunking strategy to better preserve global context across long documents. We release two model types: pplx-embed-v1 for standard retrieval, and pplx-embed-context-v1 for contextualized embeddings that incorporate global document context into passage representations. pplx-embed-v1 achieves competitive performance on the MTEB(Multilingual, v2), MTEB(Code), MIRACL, BERGEN, and ToolRet retrieval benchmarks, while pplx-embed-context-v1 sets new records on the ConTEB benchmark. Beyond public benchmarks, pplx-embed-v1 demonstrates strong performance on our internal evaluation suite, focusing on real-world, large-scale search scenarios constructed from 1B production web pages. These results validate the models' effectiveness in production environments where retrieval quality and efficiency are critical at scale.

cs.LG↗

arXiv2025

On the Maiorana-McFarland Class Extensions

The closure $\mathcal{M}_{m}^{\#}$ and the extension $\widehat{\mathcal{M}}_{m}$ of the Maiorana--McFarland class $\mathcal{M}_{m}$ in $m = 2n$ variables relative to the extended-affine equivalence and the bent function construction $f \oplus \mathrm{Ind}_{U}$ are considered, where $U$ is an affine subspace of $\mathbb{F}_{2}^{m}$ of dimension $m/2$. We obtain an explicit formula for $|\widehat{\mathcal{M}}_{m}|$ and an upper bound for $|\widehat{\mathcal{M}}_{m}^{\#}|$. Asymptotically tight bounds for $|\mathcal{M}_{m}^{\#}|$ are proved as well, for instance, $|\mathcal{M}_{8}^{\#}| \approx 2^{77.865}$. Metric properties of $\mathcal{M}_{m}$ and $\mathcal{M}_{m}^{\#}$ are also investigated. We find the number of all closest bent functions to the set $\mathcal{M}_{m}$ and provide an upper bound of the same number for $\mathcal{M}_{m}^{\#}$. The average number $E(\mathcal{M}_{m})$ of $m/2$-dimensional affine subspaces of $\mathbb{F}_{2}^{m}$ such that a function from $\mathcal{M}_{m}$ is affine on each of them is calculated. We obtain that similarly defined $E(\mathcal{M}_{m}^{\#})$ satisfies $E(\mathcal{M}_{m}^{\#}) < E(\mathcal{M}_{m})$ and $E(\mathcal{M}_{m}^{\#}) = E(\mathcal{M}_{m}) - o(1)$.

cs.CR↗

arXiv2023

On additive differential probabilities of the composition of bitwise exclusive-or and a bit rotation

Properties of the additive differential probability $\mathrm{adp}^{\mathrm{XR}}$ of the composition of bitwise XOR and a bit rotation are investigated, where the differences are expressed using addition modulo $2^n$. This composition is widely used in ARX constructions consisting of additions modulo $2^n$, bit rotations and bitwise XORs. Differential cryptanalysis of such primitives may involve maximums of $\mathrm{adp}^{\mathrm{XR}}$, where some of its input or output differences are fixed. Although there is an efficient way to calculate this probability (Velichkov et al, 2011), many of its properties are still unknown. In this work, we find maximums of $\mathrm{adp}^{\mathrm{XR}}$, where the rotation is one bit left/right and one of its input differences is fixed. Some symmetries of $\mathrm{adp}^{\mathrm{XR}}$ are obtained as well. We provide all its impossible differentials in terms of regular expression patterns and estimate the number of them. This number turns out to be maximal for the one bit left rotation and noticeably less than the number of impossible differentials of bitwise XOR.

cs.CR↗

arXiv2022

On the image of an affine subspace under the inverse function within a finite field

We consider the function $x^{-1}$ that inverses a finite field element $x \in \mathbb{F}_{p^n}$ ($p$ is prime, $0^{-1} = 0$) and affine $\mathbb{F}_{p}$-subspaces of $\mathbb{F}_{p^n}$ such that their images are affine subspaces as well. It is proven that the image of an affine subspace $L$, $|L| > 2$, is an affine subspace if and only if $L = q \mathbb{F}_{p^k}$, where $q \in \mathbb{F}_{p^n}^{*}$ and $k \mid n$. In other words, it is either a subfield of $\mathbb{F}_{p^n}$ or a subspace consisting of all elements of a subfield multiplied by $q$. This generalizes the results that were obtained for linear invariant subspaces in 2006. As a consequence, we propose a sufficient condition providing that a function $A(x^{-1}) + b$ has no invariant affine subspaces $U$ of cardinality $2 < |U| < p^n$ for an invertible linear transformation $A: \mathbb{F}_{p^n} \to \mathbb{F}_{p^n}$ and $b \in \mathbb{F}_{p^n}^{*}$. As an example, it is shown that the condition works for S-box of AES. Also, we demonstrate that some functions of the form $\alpha x^{-1} + b$ have no invariant affine subspaces except for $\mathbb{F}_{p^n}$, where $\alpha, b \in \mathbb{F}_{p^n}^{*}$ and $n$ is arbitrary.

cs.CR↗