arXiv research

Secure neural network inference on untrusted platforms using holographic reduced representations.

HGConv uses HRR to efficiently detect malware, outperforming existing methods.

Hrrformer uses HRR to speed up self-attention for long sequences.

Representation learning is at the heart of what makes deep learning effective. In this work, we introduce a new framework for representation learning that we call "Holographic Neural Architectures" (HNAs). In the same way that an observer can experience the 3D structure of a holographed object by looking at its hologra…

Learning embeddings of entities and relations is an efficient and versatile method to perform machine learning on relational data such as knowledge graphs. In this work, we propose holographic embeddings (HolE) to learn compositional vector space representations of entire knowledge graphs. The proposed method is relate…

Study uses holography to analyze entanglement entropy in deformed CFTs.

AI enhances pollen recognition in veterinary imaging using holographic microscopy.

Holographic energy equals Hamiltonian energy.

Holographic principle matches deformed Liouville theory action.

Minkowski space is a physically important space-time for which the finding an adequate holographic description is an urgent problem. In this paper we develop further the proposal made in hep-th/0303006 for the description as a duality between Minkowski space-time and a Conformal Field Theory defined on the boundary of …

Study improves pollen detection in optical and holographic images using deep learning.

We extend the holographic formula for the critical $Q$-curvature to all $Q$-curvatures.

This paper derives an explicit formula for Branson's Q-curvature in even-dimensional conformal geometry. The ingredients in the formula come from the Poincare metric in one higher dimension; hence the formula is called holographic. When specialized to the conformally flat case, the holographic formula expresses Q-curva…

In the presence of boundaries the integrated conformal anomaly is modified by the boundary terms so that the anomaly is non-vanishing in any (even or odd) dimension. The boundary terms are due to extrinsic curvature whose exact structure in $d=3$ and $d=4$ has recently been identified. In this note we present a hologra…

New framework constructs holographic tensor networks using hyperbolic buildings.

Any traversally generic vector flow on a compact manifold $X$ with boundary leaves some residual structure on its boundary $\d X$. A part of this structure is the flow-generated causality map $C_v$, which takes a region of $\d X$ to the complementary region. By the Holography Theorem from \cite{K4}, the map $C_v$ allow…

Bit threads provide an alternative description of holographic entanglement, replacing the Ryu-Takayanagi minimal surface with bulk curves connecting pairs of boundary points. We use bit threads to prove the monogamy of mutual information (MMI) property of holographic entanglement entropies. This is accomplished using t…

Researchers create holographic super-embeddings for M5 and M2 branes.

We introduce new aspects in conformal geometry of some very natural second-order differential operators. These operators are termed shift operators. In the flat space, they are intertwining operators which are closely related to symmetry breaking differential operators. In the curved case, they are closely connected wi…

We reinterpret special relativity, or more precisely its de Sitter deformation, in terms of 3d conformal geometry, as opposed to (3+1)d spacetime geometry. An inertial observer, usually described by a geodesic in spacetime, becomes instead a choice of ways to reverse the conformal compactification of a Euclidean vector…

Holographic Invariant Storage uses vector architectures to ensure LLM safety at design time.

We formulate the holographic principle for knots and links. For the "space" of all knots and links, torus knots T(2m+1,2) and torus links L(2m,2) play the role of the "boundary" of this space. Using the holographic principle, we find the skein relation of knots and links with the help of the recurrence relation for pol…

Generalizes holographic method to higher codimension submanifolds.

We prove that the boundary of the future of a surface $K$ consists precisely of the points $p$ that lie on a null geodesic orthogonal to $K$ such that between $K$ and $p$ there are no points conjugate to $K$ nor intersections with another such geodesic. Our theorem has applications to holographic screens and their asso…

Deep learning tackles low-photon nanoscale holographic phase retrieval.

The holographic duality can be extended to include quantum theories with broken coordinate invariance leading to the appearance of the gravitational anomalies. On the gravity side one adds the gravitational Chern-Simons term to the bulk action which gauge invariance is only up to the boundary terms. We analyze in detai…

We develop a systematic method for renormalizing the AdS/CFT prescription for computing correlation functions. This involves regularizing the bulk on-shell supergravity action in a covariant way, computing all divergences, adding counterterms to cancel them and then removing the regulator. We explicitly work out the ca…

We argue that Horava-Lifshitz (HL) gravity provides the minimal holographic dual for Lifshitz-type field theories with anisotropic scaling and dynamical exponent z. First we show that Lifshitz spacetimes are vacuum solutions of HL gravity, without need for additional matter. Then we perform holographic renormalization …

A learning algorithm optimizes beamforming for holographic transceivers in far-field communication.

We show that holographic renormalization of relativistic gravity in asymptotically Lifshitz spacetimes naturally reproduces the structure of gravity with anisotropic scaling: The holographic counterterms induced near anisotropic infinity take the form of the action for gravity at a Lifshitz point, with the appropriate …

We prove the conjecture that a monopole in three-dimensional anti-de Sitter space can be completely determined by its ``holographic'' image on the conformal boundary two-sphere.

We prove universal recursive formulas for Branson's $Q$-curvatures in terms of respective lower-order $Q$-curvatures, lower-order GJMS-operators and holographic coefficients.

Study on bit threads and their locking properties in holographic spacetimes.

Suppose that $Σ=\partialΩ$ is the $n$-dimensional boundary, with positive (inward) mean curvature $H$, of a connected compact $(n+1)$-dimensional Riemannian spin manifold $(Ω^{n+1},g)$ whose scalar curvature $R\ge -n(n+1)k^2$, for some $k\textgreater{}0$. If $Σ$ admits an isometric and isospin immersion $F$ into the hy…

The Ryu-Takayanagi (RT) formula relates the entanglement entropy of a region in a holographic theory to the area of a corresponding bulk minimal surface. Using the max flow-min cut principle, a theorem from network theory, we rewrite the RT formula in a way that does not make reference to the minimal surface. Instead, …

We define a holographic dual to the Donaldson-Witten topological twist of $\mathcal{N}=2$ gauge theories on a Riemannian four-manifold. This is described by a class of asymptotically locally hyperbolic solutions to $\mathcal{N}=4$ gauged supergravity in five dimensions, with the four-manifold as conformal boundary. Und…

In this paper, we initiate the study of holographic renormalization group flows acting on the metric of four-manifolds. In particular, we derive a set of equations which govern the evolution of a generic Kähler four-manifold along the renormalization group flow in seven-dimensional gauged supergravity. The physical ele…

Using holographic renormalization coupled with the Caffarelli/Silvestre\cite{caffarelli} extension theorem, we calculate the precise form of the boundary operator dual to a bulk scalar field rather than just its average value. We show that even in the presence of interactions in the bulk, the boundary operator dual to …

In the first part of this paper we provide a short introduction to the AdS/CFT correspondence and to holographic renormalization. We discuss how QFT correlation functions, Ward identities and anomalies are encoded in the bulk geometry. In the second part we develop a Hamiltonian approach to the method of holographic re…

Efficiently estimates neural connectivity using ensemble stimulation.

A 'holographic formula' expressing the functional determinant of the scattering operator in an asymptotically locally anti-de Sitter(ALAdS) space has been proposed in terms of a relative functional determinant of the scalar Laplacian in the bulk. It stems from considerations in AdS/CFT correspondence of a quantum corre…

Active learning method for neural population dynamics using optogenetics.

We prove a universal recursive formulas for Branson's $Q$-curvature of order eight in terms of lower-order $Q$-curvatures, lower-order GJMS-operators and holographic coefficients. The results prove a special case of a conjecture in {arXiv:0905.3992}.

The holographic description in the presence of gravitational Chern-Simons term is studied. The modified gravitational equations are integrated by using the Fefferman-Graham expansion and the holographic stress-energy tensor is identified. The stress-energy tensor has both conformal anomaly and gravitational or, if re-f…

New formula connects holographic entanglement entropy to Willmore energy in 5D.

HR in 8D encodes unique conformal gravity with negative curvature.

The change in Holographic entanglement entropy (HEE) for small fluctuations about pure anti De Sitter (AdS) is obtained by a perturbative expansion of the area functional in terms of the change in the bulk metric and the embedded extremal surface. However, it is known that change in the embedding appears in second orde…

For an embedded conformal hypersurface with boundary, we construct critical order local invariants and their canonically associated differential operators. These are obtained holographically in a construction that uses a singular Yamabe problem and a corresponding minimal hypersurface with boundary. They include an ext…