PDNS: Diverse Applications in Research

• PDNS is a polysemous acronym representing distinct concepts such as positive-dominated negative synthesizing in recommender systems, PIR-based DNS for privacy, and heterogeneous graph benchmarks.
• In recommender systems, PDNS introduces synthetic negative embedding to mitigate false negatives, yielding measurable improvements in Recall and MF metrics on large datasets.
• Each PDNS application—from diffusion neural samplers to power distribution network simulation—illustrates domain-specific methodologies that require precise disambiguation in scholarly work.

Searching arXiv for recent and canonical uses of “PDNS” across domains to ground the encyclopedia entry. PDNS is a polysemous acronym used in multiple research domains, including recommender systems, privacy-preserving Domain Name System design, graph learning benchmarks derived from passive DNS, diffusion-based generative modeling, topological semimetals, and power-distribution-network simulation. In the arXiv literature, the term denotes at least six technically distinct constructs: positive-dominated negative synthesizing for implicit collaborative filtering (Shi et al., 2022), a DNS extension leveraging single-server PIR for collusion-resistant name resolution (Xiao et al., 28 Jul 2025), PDNS-Net, a heterogeneous graph benchmark for malicious domain classification (Kumarasinghe et al., 2022), the Proximal Diffusion Neural Sampler for stochastic optimal control on path measures (Guo et al., 4 Oct 2025), the pseudo Dirac nodal sphere state in condensed-matter physics (Wang et al., 2018), and power distribution network simulation in circuit and systems research, as exemplified by MATEX (Zhuang et al., 2015). Because these usages are unrelated except for the shared acronym, interpretation depends entirely on disciplinary context.

1. Acronymal scope and disciplinary usage

In recommender systems, PDNS denotes positive-dominated negative synthesizing, a negative-sampling strategy proposed for implicit collaborative filtering to mitigate the effect of false negatives in hard negative sampling (Shi et al., 2022). In networking and privacy research, PDNS denotes a DNS architecture that leverages single-server PIR to strengthen privacy guarantees and removes the non-collusion assumption required by proxy-based designs such as Oblivious DoH (Xiao et al., 28 Jul 2025). In cybersecurity and graph learning, PDNS appears in PDNS-Net, a dataset constructed from passive DNS relations for malicious domain classification on heterogeneous graphs (Kumarasinghe et al., 2022). In generative modeling, PDNS refers to the Proximal Diffusion Neural Sampler, which applies a proximal-point method on the space of path measures to diffusion-based sampling from unnormalized targets (Guo et al., 4 Oct 2025). In topological condensed matter, PDNS abbreviates pseudo Dirac nodal sphere, a semimetallic state in which band crossings form an approximately spherical two-dimensional manifold in momentum space (Wang et al., 2018). In EDA and circuit simulation, PDNS is used as shorthand for power distribution network simulation, as in the MATEX framework for distributed transient simulation of power distribution networks (Zhuang et al., 2015).

This dispersion of meaning suggests that “PDNS” functions less as a stable term of art than as an acronym repeatedly reintroduced in local subfields. A plausible implication is that bibliographic disambiguation is essential whenever the acronym appears in titles, abstracts, or keyword indexes.

2. PDNS in recommender systems: positive-dominated negative synthesizing

The recommender-systems usage arises in the paper “Enhancing Recommender Systems: A Strategy to Mitigate False Negative Impact” (Shi et al., 2022). The setting is implicit collaborative filtering with pairwise Bayesian Personalized Ranking, in which hard negative sampling methods such as DNS may increasingly select false negatives as the model improves. The paper reports that, in experiments on Taobao and Tmall, the harder the negatives (larger pool $H$), the more severe the late-training overfitting: performance first climbs, then collapses, and that excluding known false negatives in synthetic tests on ML-100k and Douban gradually mitigates overfitting (Shi et al., 2022).

PDNS is defined as a two-step procedure per positive pair $(u,i)$. First, a pool $\mathcal{C}$ of $H$ negatives is sampled uniformly from $\mathcal{I}\setminus \mathcal{I}_u$, and the hardest candidate is selected by

$$j = \arg\max_{k\in\mathcal{C}} \mathbf{e}_u\cdot\mathbf{e}_k.$$

Second, a synthetic negative embedding is formed by positive-dominated mixing: $$\widetilde{\mathbf{e}_{j'}}=\alpha\,\mathbf{e}_i+(1-\alpha)\,\mathbf{e}_j,\qquad \alpha\in(0.7,1].$$ The mixed embedding $\widetilde{\mathbf{e}_{j'}}$ replaces $\mathbf{e}_j$ in the BPR loss (Shi et al., 2022).

The key theoretical result is that PDNS exactly rescales the score-difference argument of the sigmoid by $\beta=1-\alpha$. If $(u,i)$0, then the PDNS loss becomes

$(u,i)$1

This induces what the paper terms gradient flattening: very hard triplets no longer dominate with gradient approximately $(u,i)$2, while milder triplets receive stronger gradients than under DNS (Shi et al., 2022). The paper further gives an equivalent soft-loss form,

$(u,i)$3

so explicit embedding mixing may be replaced by a single soft factor in the loss.

Empirically, the reported results show that PDNS + LightGCN achieves Recall@50 improvements of 3.4–4.7% over the best alternative; with MF improvements of 3.1–6.9%, and that on Taobao, Tmall, and Gowalla the PDNS learning curves remain flat or gently rising late in training whereas DNS and MixGCF collapse (Shi et al., 2022). This positions PDNS not as a new recommender architecture, but as a sampling and loss-modulation strategy that can be integrated into existing pairwise-learning pipelines.

3. PDNS in DNS privacy: single-server PIR for collusion resistance

In networking research, PDNS denotes a privacy-preserving DNS design introduced in “Collusion Resistant DNS With Private Information Retrieval” (Xiao et al., 28 Jul 2025). The motivating claim is that plaintext DNS exposes every query to on-path eavesdroppers, DoT and DoH encrypt the channel but still reveal both client identity and query to the recursive resolver, and ODoH removes direct resolver visibility of client IP but depends on a non-collusion assumption between proxy and resolver (Xiao et al., 28 Jul 2025). PDNS is proposed specifically to eliminate that assumption.

The system consists of three components: a PDNS Client, a PIR-enabled Resolver (ReR), and Authoritative Name Servers (ANSes). The protocol begins with a setup phase, in which the client runs $(u,i)$4 and the resolver builds an encrypted cache $(u,i)$5. For each lookup $(u,i)$6, the client computes an index $(u,i)$7, produces a PIR query $(u,i)$8, and sends it to the resolver. The resolver returns $(u,i)$9, and the client extracts the requested slot $\mathcal{C}$0 (Xiao et al., 28 Jul 2025). If the slot contains a valid, unexpired A, AAAA, or NS record, the client returns the answer; otherwise it performs iterative DNS lookup against ANSes over DoH or DoT and uses an EDNS-PR extension so that the resolver cache can be populated without revealing the client IP to the ANS.

The PIR backend uses Spiral, described as a single-server, stateless PIR scheme built on LWE-based homomorphic encryption. The core homomorphic retrieval is expressed as

$\mathcal{C}$1

and the client recovers $\mathcal{C}$2 (Xiao et al., 28 Jul 2025).

The privacy claim is formalized by a theorem sketch stating that PDNS achieves client-query privacy against a malicious resolver: $\mathcal{C}$3 The paper states that PDNS reveals only $\mathcal{C}$4 (cache size) and record lengths; no information about $\mathcal{C}$5, and that even if the resolver colludes with any other party, the homomorphic encryption hides the requested index (Xiao et al., 28 Jul 2025).

The performance evaluation uses an 8-core AMD EPYC 3.0 GHz, 8 GB RAM platform, traces of 20 M real DNS queries (122 K unique domains), and cache configurations of 64 MB and 512 MB. Reported median latencies are approximately 25 ms for DoUDP, 69 ms for DoH, 272 ms for ODoH, 600 ms for DoH over Tor, 208 ms for PDNS with 64 MB cache, and 450 ms for PDNS with 512 MB cache. An FPGA-accelerated PDNS configuration is reported at 70 ms (Xiao et al., 28 Jul 2025). Throughput is correspondingly lower than conventional DNS—approximately 8 QPS for PDNS at 64 MB and 4 QPS at 512 MB, versus 500 QPS for DoH and 1 000 QPS for DoUDP—so scalability is the stated bottleneck. The paper therefore characterizes PDNS as offering full query-privacy and collusion resistance with acceptable performance today and a hardware-acceleration path to higher throughput (Xiao et al., 28 Jul 2025).

4. PDNS in cybersecurity graph learning: PDNS-Net

A distinct usage appears in “PDNS-Net: A Large Heterogeneous Graph Benchmark Dataset of Network Resolutions for Graph Learning” (Kumarasinghe et al., 2022). Here the acronym refers not to a method but to a dataset derived from passive DNS resolutions for malicious domain classification. The graph is defined as a heterogeneous graph

$\mathcal{C}$6

with node types $\mathcal{C}$7 and relation types resolve, similar, and subdomain_of (Kumarasinghe et al., 2022). The similar relation is based on trigram-TFIDF & cosine $\mathcal{C}$8.

The data-collection pipeline begins with malicious seed domains from VirusTotal feeds over one week (11–18 Oct 2020) and benign seeds from the top 1 million Alexa domains that persistently appear for 90 days. These are expanded using Farsight DNSDB by querying IPs hosting malicious seed domains, then querying all domains resolving to those IPs, and then querying additional IPs serving newly found domains. Final pruning removes IP nodes of degree greater than 1 500, public hosting domains such as wix.com, and isolated single-domain connected components (Kumarasinghe et al., 2022).

The resulting full dataset contains 447 068 total nodes and 897 588 total edges, with 373 475 domains and 73 593 IPs. Domain labels are binary, with 20 354 malicious and 353 121 benign. A sampled subgraph, mPDNS-Net, contains 7 495 domains, 4 505 IPs, and 37 285 edges (Kumarasinghe et al., 2022). The paper emphasizes scale by noting that PDNS-Net is approximately 38× IMDB and 17× DBLP in node count.

The benchmark task is binary node classification on domains. The loss is cross-entropy,

$\mathcal{C}$9

and the reported evaluation metrics are Accuracy, Precision, Recall, F1, AUC, and False Positive Rate (Kumarasinghe et al., 2022). Baselines include homogeneous GNNs—GCN, GraphSAGE, GAT—and heterogeneous GNNs—RGCN, HGT, HeteroSAGE, and HeteroGAT—trained with Adam, lr $H$0, weight_decay $H$1, 200 epochs, 2 GNN layers (hidden dim=64), and random 80/10/10 train/val/test splits on domain nodes (Kumarasinghe et al., 2022).

The key quantitative result on the full PDNS-Net is that heterogeneous models clearly outperform homogeneous ones. The best reported accuracies are 0.93 for HeteroSAGE and 0.94 for HeteroGAT, while homogeneous baselines range from 0.76 to 0.78 except HGT at 0.90 (Kumarasinghe et al., 2022). The paper states that this reveals a need for further research on large heterogeneous graphs. Although PDNS-Net is derived from passive DNS data, it is a benchmark name rather than a general DNS privacy or systems term.

5. PDNS in generative modeling: Proximal Diffusion Neural Sampler

In diffusion-based generative modeling, PDNS denotes the Proximal Diffusion Neural Sampler introduced in “Proximal Diffusion Neural Sampler” (Guo et al., 4 Oct 2025). The paper frames sampling from an unnormalized target density

$H$2

as a stochastic optimal control problem on path measures. With a reference process $H$3 and terminal reward

$H$4

the optimal path measure is

$H$5

whose terminal law is exactly $H$6 (Guo et al., 4 Oct 2025).

The central idea is to avoid solving this global problem in one shot. Instead, PDNS applies a proximal-point iteration in path space: $H$7 The closed-form update is

$H$8

With $H$9, the $\mathcal{I}\setminus \mathcal{I}_u$0-th iterate satisfies

$\mathcal{I}\setminus \mathcal{I}_u$1

so the terminal marginal geometrically interpolates between reference $\mathcal{I}\setminus \mathcal{I}_u$2 and target $\mathcal{I}\setminus \mathcal{I}_u$3 (Guo et al., 4 Oct 2025).

Each proximal step is instantiated using a weighted denoising cross-entropy (WDCE) objective. In the continuous-diffusion case, the loss is

$\mathcal{I}\setminus \mathcal{I}_u$4

with importance weighting based on

$\mathcal{I}\setminus \mathcal{I}_u$5

or equivalently

$\mathcal{I}\setminus \mathcal{I}_u$6

The stated rationale is that early iterations temper importance weights and thereby prevent mode collapse when the target is multimodal and separated by large energy barriers (Guo et al., 4 Oct 2025).

The empirical evaluation covers 32-well many-well (MW-54), Funnel, 40-component Gaussian Mixture (GMM40), heavy-tailed Student’s-$\mathcal{I}\setminus \mathcal{I}_u$7 mixture (MoS), molecular systems DW-4, LJ-13, and LJ-55, as well as discrete 2D lattice Ising and Potts models and maximum-cut on random graphs up to 128 nodes (Guo et al., 4 Oct 2025). The paper reports that PDNS matches or outperforms the state of the art on five of seven continuous tasks, that non-proximal WDCE collapses modes in ablations whereas proximal steps preserve coverage, and that on discrete tasks PDNS achieves the lowest magnetization and correlation errors with the highest effective sample size (Guo et al., 4 Oct 2025). In this literature, PDNS is therefore a training framework for diffusion samplers rather than a domain-specific application acronym.

6. PDNS in condensed matter and circuit simulation

Two additional usages appear in fields remote from machine learning and networking.

In topological condensed matter, PDNS abbreviates pseudo Dirac nodal sphere, introduced in “Pseudo Dirac Nodal Sphere: Unusual Electronic Structure and Material Realization” (Wang et al., 2018). A PDNS is defined as a state in which two bands cross on a closed two-dimensional spherical surface at the Fermi level. In crystals with discrete point-group symmetries, the sphere is only approximately protected: it consists of a “spherical backbone” of symmetry-protected DNLs plus very weak higher-order interactions that open only negligibly small gaps elsewhere on the sphere (Wang et al., 2018). One minimal Type-I Hamiltonian is

$\mathcal{I}\setminus \mathcal{I}_u$8

The paper distinguishes the density of states of DNP, DNL, and DNS/PDNS systems and reports the unusual property that the long-wavelength plasmon frequency for DNS is, to leading order, independent of carrier density (Wang et al., 2018). Candidate materials include strained MH$\mathcal{I}\setminus \mathcal{I}_u$9 with $$j = \arg\max_{k\in\mathcal{C}} \mathbf{e}_u\cdot\mathbf{e}_k.$$0 Y, Ho, Tb, Nd and strained Si$$j = \arg\max_{k\in\mathcal{C}} \mathbf{e}_u\cdot\mathbf{e}_k.$$1N$$j = \arg\max_{k\in\mathcal{C}} \mathbf{e}_u\cdot\mathbf{e}_k.$$2.

In EDA and circuit analysis, PDNS appears as shorthand for power distribution network simulation in the MATEX paper (Zhuang et al., 2015). MATEX models linear PDNs using modified nodal analysis,

$$j = \arg\max_{k\in\mathcal{C}} \mathbf{e}_u\cdot\mathbf{e}_k.$$3

and computes transients using a matrix exponential kernel with Krylov subspace approximations (Zhuang et al., 2015). The framework decomposes sources by superposition, distributes subtasks across nodes, and uses rational Krylov subspace methods to mitigate stiffness. On IBM power grid benchmarks, MATEX is reported to achieve around 13X over the trapezoidal framework with fixed time step, with errors against fine-step backward Euler below $$j = \arg\max_{k\in\mathcal{C}} \mathbf{e}_u\cdot\mathbf{e}_k.$$4 (Zhuang et al., 2015). Here “PDNS” is not a named algorithm but a domain shorthand used in circuit-simulation discourse.

7. Disambiguation, misconceptions, and scholarly interpretation

A common misconception is to treat PDNS as if it had a single canonical expansion. The arXiv record does not support that interpretation. Instead, the acronym is reused independently across fields whose technical vocabularies do not overlap: recommender systems (Shi et al., 2022), DNS privacy (Xiao et al., 28 Jul 2025), cybersecurity graph learning (Kumarasinghe et al., 2022), diffusion-based Monte Carlo and generative modeling (Guo et al., 4 Oct 2025), topological band theory (Wang et al., 2018), and power-distribution-network simulation (Zhuang et al., 2015).

Another source of confusion is the coexistence of uppercase PDNS and lowercase pDNS. In DNS measurement research, passive DNS is conventionally written pDNS, referring to retrospective collection of DNS query-response tuples observed in flight at recursive or open resolvers (Burton, 2019). PDNS-Net is built from passive DNS relations, but the benchmark name PDNS-Net should not be conflated with the PIR-based DNS protocol PDNS (Kumarasinghe et al., 2022, Xiao et al., 28 Jul 2025). Similarly, PDNS in recommender systems and PDNS in generative modeling share neither objectives nor mathematical structure, despite both being optimization methods.

For scholarly usage, the most reliable practice is to expand the acronym at first mention and include the paper title or domain qualifier when ambiguity is possible. This suggests a broader bibliographic point: in acronym-dense technical writing, cross-domain collisions are sufficiently frequent that abbreviation alone is not a stable identifier.