SearcharxivSearch

arXiv subjects

Andrei Ovsiannikov

Publications and source records attributed to Andrei Ovsiannikov.

3 recordsLinked to original sources

Scaling Graph Neural Networks for Friend Recommendation: Multi-Hash User Embeddings and Temporal Neighbor Sampling

Friend recommendation is inherently graph-structured: the relevance of a potential connection depends on multi-hop social context rather than user attributes alone. However, deploying message-passing GNNs on a production-scale social graph with hundreds of millions of users and tens of billions of edges requires addressing numerous modeling and systems challenges. We present a scalable end-to-end GNN ranking system for production social graphs, focusing on two design choices that are critical in this setting: multi-hash ID embeddings and temporal neighbor sampling. Multi-hash embeddings are common for high-cardinality features, but industrial GNN systems typically either ignore trainable IDs or accept full embedding tables, exceeding 200 GB for our graph. We integrate multi-hash as the primary node representation, reducing the ID-embedding table size by more than 98 percent while preserving ranking quality. Temporal neighbor sampling is well understood in principle, but existing implementations scan full adjacency lists, which is a non-starter for users with tens of thousands of friends. We implement timestamp-sorted CSR storage with binary search, reducing the per-node temporal sampling cost from $O(deg(v) + k)$ to $O(\log(deg(v)) + k)$. Beyond these components, we show that this combination scales and yields measurable production impact. On a graph with 194M users and 28B edges, offline ablations isolate each design choice's contribution. In an online A/B test, our system increases friend additions from recommendations by 16 percent and unique friend adders by 11.5 percent over a strong production baseline. We release our framework for distributed training and inference on large temporal graphs.

cs.IR

Magnetohydrodynamics in turbulent dynamo regime: the stability problem

This paper investigates stochastic solenoidal magnetohydrodynamics within the field-theoretic Martin-Siggia-Rose-De Dominicis-Janssen formalism, with a specific focus on the stability of the system when spatial mirror (parity) symmetry is explicitly broken. Under helical forcing, the one-particle-irreducible magnetic response function already at one loop contains a curl-type contribution that dominates the bare resistive term in the infrared limit, leading to exponential instability of the trivial state $\langle \mathbf{b} \rangle = \mathbf{0}$. We re-examine a stabilization mechanism proposed in [L. T. Adzhemyan, et al., Theor. Math. Phys. 72, 940-950 (1987)], in which the system evolves into a phase with a dynamically spontaneously broken rotational symmetry and a generated mean magnetic field $\langle \mathbf{b} \rangle = \mathbf{B}_0$. By deriving a self-consistency condition for $ \mathbf{B}_0$, we show that for any physically admissible (infrared) form of the pumping function, the model admits only a singular solution. We illustrate this with the standard power-law and "massive" pumping functions. We further show that previous claims of a finite $ \mathbf{B}_0$ arose from an inconsistent truncation of asymptotic expansions. We argue that a consistent physical resolution requires including a bare curl term in the stochastic induction equation, which naturally arises from a parity-violating modification of Ohm's law. With this modification, stabilization of the system by spontaneous symmetry breaking becomes a viable field-theoretic description of large-scale mean-field generation (turbulent dynamo) in helical turbulent magnetohydrodynamics.

physics.plasm-ph

Two-Loop Turbulent Helical Magnetohydrodynamics: Large-Scale Dynamo and Energy Spectrum

We present a two-loop field-theoretic analysis of incompressible helical magnetohydrodynamics (MHD) in fully developed stationary turbulence. A key feature of helical MHD is the appearance of an infrared-unstable ``mass-like'' term in the loop diagrams of the magnetic response function. Physically, this term corresponds to the relevant perturbation of the Joule damping, proportional to $\boldsymbol{\nabla} \times \boldsymbol{b}$ ($\boldsymbol{b} =$ magnetic field). Its presence destabilizes the trivial ground state $\langle \boldsymbol{b} \rangle = 0$ and forces us to look for a mechanism for stabilizing the system. We show that such stabilization can be achieved in two ways: (i) by introducing into induction equation an external mass-like parameter that precisely cancels these dangerous loop corrections (kinematic regime), or (ii) via spontaneous breaking of the rotational symmetry, leading to a new ground state with nonzero large-scale magnetic field (turbulent dynamo regime). For the latter case, we study the two-loop correction to the spontaneously generated magnetic field and demonstrate that Goldstone-like corrections to Alfv\'en modes along with some other anisotropic structures arise. Our results also confirm that the emergent mean magnetic field leads to a steeper slope of the magnetic energy spectrum, $-11/3 + 2\gamma_{b\star}$ (with $\gamma_{b\star} = -0.1039 - 0.4202\rho^2$, for $|\rho| \leqslant 1$ as the degree of helicity), compared to the Kolmogorov velocity spectrum of $-11/3$, thereby breaking equipartition.

physics.plasm-ph