Daily Papers

The proliferation of digital microscopy images, driven by advances in automated whole slide scanning, presents significant opportunities for biomedical research and clinical diagnostics. However, accurately annotating densely packed information in these images remains a major challenge. To address this, we introduce DiffKillR, a novel framework that reframes cell annotation as the combination of archetype matching and image registration tasks. DiffKillR employs two complementary neural networks: one that learns a diffeomorphism-invariant feature space for robust cell matching and another that computes the precise warping field between cells for annotation mapping. Using a small set of annotated archetypes, DiffKillR efficiently propagates annotations across large microscopy images, reducing the need for extensive manual labeling. More importantly, it is suitable for any type of pixel-level annotation. We will discuss the theoretical properties of DiffKillR and validate it on three microscopy tasks, demonstrating its advantages over existing supervised, semi-supervised, and unsupervised methods. The code is available at https://github.com/KrishnaswamyLab/DiffKillR.

Invertible neural networks based on coupling flows (CF-INNs) have various machine learning applications such as image synthesis and representation learning. However, their desirable characteristics such as analytic invertibility come at the cost of restricting the functional forms. This poses a question on their representation power: are CF-INNs universal approximators for invertible functions? Without a universality, there could be a well-behaved invertible transformation that the CF-INN can never approximate, hence it would render the model class unreliable. We answer this question by showing a convenient criterion: a CF-INN is universal if its layers contain affine coupling and invertible linear functions as special cases. As its corollary, we can affirmatively resolve a previously unsolved problem: whether normalizing flow models based on affine coupling can be universal distributional approximators. In the course of proving the universality, we prove a general theorem to show the equivalence of the universality for certain diffeomorphism classes, a theoretical insight that is of interest by itself.

We study diffeomorphisms of Banach spaces satisfying generalized hyperbolicity: the stable and unstable subspaces are invariant only up to inclusion, need not depend continuously on the point, and expansivity may fail. On closed manifolds, this condition is equivalent to Axiom~A with strong transversality. We introduce a continuous-selection method that converts uniform orbitwise estimates into bounded continuous solutions of cohomological equations for generalized-hyperbolic cocycles. For diffeomorphisms in the uniform global \(C^1\) category, this yields continuous semiconjugacies in both directions under sufficiently small bounded Lipschitz perturbations, and topological stability in the sense of Walters. For the infinite product of one-dimensional Morse-Smale systems on \(\ell^p(\mathbb Z)\), \(1\leq p\leq\infty\), we construct compatible forward and reverse cohomological solution operators and prove structural stability, including for perturbations that couple coordinates, although the product is not expansive. For \(p=\infty\) this gives a structurally stable diffeomorphism with uncountably many hyperbolic fixed points, in contrast with the finitely many basic sets of Axiom~A diffeomorphisms. The cocycle analysis yields Lipschitz shadowing for the induced operator on bounded continuous vector fields.

Transfer learning is a crucial technique for handling a small amount of data that is potentially related to other abundant data. However, most of the existing methods are focused on classification tasks using images and language datasets. Therefore, in order to expand the transfer learning scheme to regression tasks, we propose a novel transfer technique based on differential geometry, namely the Geometrically Aligned Transfer Encoder (GATE). In this method, we interpret the latent vectors from the model to exist on a Riemannian curved manifold. We find a proper diffeomorphism between pairs of tasks to ensure that every arbitrary point maps to a locally flat coordinate in the overlapping region, allowing the transfer of knowledge from the source to the target data. This also serves as an effective regularizer for the model to behave in extrapolation regions. In this article, we demonstrate that GATE outperforms conventional methods and exhibits stable behavior in both the latent space and extrapolation regions for various molecular graph datasets.

A set of infinitesimal {rm Virasoro_{,L}}rm Virasoro_{,R} diffeomorphisms are presented which act non-trivially on the horizon of a generic Kerr black hole with spin J. The covariant phase space formalism provides a formula for the Virasoro charges as surface integrals on the horizon. Integrability and associativity of the charge algebra are shown to require the inclusion of `Wald-Zoupas' counterterms. A counterterm satisfying the known consistency requirement is constructed and yields central charges c_L=c_R=12J. Assuming the existence of a quantum Hilbert space on which these charges generate the symmetries, as well as the applicability of the Cardy formula, the central charges reproduce the macroscopic area-entropy law for generic Kerr black holes.

Invertible neural networks (INNs) are neural network architectures with invertibility by design. Thanks to their invertibility and the tractability of Jacobian, INNs have various machine learning applications such as probabilistic modeling, generative modeling, and representation learning. However, their attractive properties often come at the cost of restricting the layer designs, which poses a question on their representation power: can we use these models to approximate sufficiently diverse functions? To answer this question, we have developed a general theoretical framework to investigate the representation power of INNs, building on a structure theorem of differential geometry. The framework simplifies the approximation problem of diffeomorphisms, which enables us to show the universal approximation properties of INNs. We apply the framework to two representative classes of INNs, namely Coupling-Flow-based INNs (CF-INNs) and Neural Ordinary Differential Equations (NODEs), and elucidate their high representation power despite the restrictions on their architectures.

We demonstrate how horizon symmetries of AdS black holes are realised in the hydrodynamic actions for the dynamics of the dual stress tensor. A recent approach for obtaining such actions involves a choice of horizon boundary conditions, and we show that diffeomorphisms that preserve these give rise to symmetries of the corresponding hydrodynamic action. We obtain explicit hydrodynamic actions for small amplitude perturbations of black holes in JT and AdS_3 gravity using this approach and demonstrate explicitly the existence of these symmetries. For a natural choice of boundary conditions, the resulting actions manifestly realise gauge symmetries previously proposed for effective theories of maximal chaos.

We study primordial gravitational waves produced during inflation in quantum gravity at a Lifshitz point proposed by Ho{rmr}ava. Assuming power-counting renormalizability, foliation preserving diffeomorphism invariance, and the condition of detailed balance, we show that primordial gravitational waves are circularly polarized due to parity violation. The chirality of primordial gravitational waves is a quite robust prediction of quantum gravity at a Lifshitz point which can be tested through observations of cosmic microwave background radiation and stochastic gravitational waves.

In this paper, we propose an alternating numerical scheme for constructing quasi-periodic solutions to a class of nonlinear partial differential equations (PDEs) with bounded perturbations, including the one-dimensional nonlinear Schrödinger (NLS) equations and nonlinear wave (NLW) equations under periodic and Dirichlet boundary conditions. A key observation concerning the resonant Q-equations allows us to establish directly a local diffeomorphism between the amplitudes and the drifted frequencies. This renders the proof considerably cleaner, since it avoids the Birkhoff normal form and the associated coordinate transformations required in classical KAM theory for PDEs.Unlike in the finite-dimensional setting, the lattice boxes must also include the spatial index, so that the multiscale induction has to be carried out in one additional dimension. This introduces two difficulties. First, the measure estimate for the excluded set of ``bad'' frequencies must account for the spatial index. For both the NLS and NLW equations, the linear frequencies and their differences are integers or close to integers; this allows the spatial dependence to be controlled through the modulus of the temporal index, so that the excluded measure remains under control. Second, a singular set may contain sites with the same temporal index but widely separated spatial indices, which obstructs the ``inversion implies localization'' process. For the one-dimensional NLS and NLW equations, however, such sites occur only in pairs with opposite spatial indices. They can therefore be separated by small boxes, after which the global inverse is obtained from the local inverses via the resolvent identity. Numerical experiments illustrate the scheme for nonlinear traveling and standing waves, exhibiting both the computed quasi-periodic solutions and the convergence of the iteration.

We investigate the anomaly-induced activation of a gauge-invariant scalar degree of freedom in General Relativity, the conformalon mode, directly at the level of \(2\to2\) scattering amplitudes. The analysis couples anomalous three-point functions of conformal sectors, involving gravitons \((TTT)\) and Abelian gauge currents \((TJJ)\), through single-graviton exchange derived from the quadratic expansion of the Einstein--Hilbert action. Unlike related treatments based on the nonlocal anomaly action, these interactions are suppressed by the Planck scale. We show that the conformalon, invariant under linearized diffeomorphisms, admits an interpretation as an effective scalar correction to scattering amplitudes, both in virtual exchange channels and in effective real-emission processes. Around flat space, this behaviour arises from anomaly-induced nonlocal massless insertions on the external graviton and photon legs of the three-point functions, sewn through the scalar component of the graviton propagator in de Donder gauge. The resulting anomaly-mediated \(4\)-point interaction reduces to contact terms, with the Planck mass setting the suppression scale. The construction consistently matches the spin decomposition of flat-space conformal Ward identities in momentum space, which determine the vertices, with the corresponding spin decomposition of the graviton propagator. In the eikonal limit, these interactions generate contact corrections to the leading logarithmic phase in impact-parameter space. We further show that anomaly-mediated \(2\to2\) graviton amplitudes associated with the virtual exchange of such modes exhibit a characteristic double-copy structure.

We introduce Lagrangian Flow Networks (LFlows) for modeling fluid densities and velocities continuously in space and time. By construction, the proposed LFlows satisfy the continuity equation, a PDE describing mass conservation in its differentiable form. Our model is based on the insight that solutions to the continuity equation can be expressed as time-dependent density transformations via differentiable and invertible maps. This follows from classical theory of the existence and uniqueness of Lagrangian flows for smooth vector fields. Hence, we model fluid densities by transforming a base density with parameterized diffeomorphisms conditioned on time. The key benefit compared to methods relying on numerical ODE solvers or PINNs is that the analytic expression of the velocity is always consistent with changes in density. Furthermore, we require neither expensive numerical solvers, nor additional penalties to enforce the PDE. LFlows show higher predictive accuracy in density modeling tasks compared to competing models in 2D and 3D, while being computationally efficient. As a real-world application, we model bird migration based on sparse weather radar measurements.

We propose a 1+1 dimensional CFT dual structure for quantum gravity and matter on the extended 2+1 dimensional BTZ black hole, realized as a quotient of the Poincare patch of AdS_3. The quotient spacetime includes regions beyond the singularity, "whiskers", containing timelike and lightlike closed curves, which at first sight seem unphysical. The spacetime includes the usual AdS-asymptotic boundaries outside the horizons as well as boundary components inside the whiskers. We show that local boundary correlators with some endpoints in the whisker regions: (i) are a protected class of amplitudes, dominated by effective field theory even when the associated Witten diagrams appear to traverse the singularity, (ii) describe well-defined diffeomorphism-invariant quantum gravity amplitudes in BTZ, (iii) sharply probe some of the physics inside the horizon but outside the singularity, and (iv) are equivalent to correlators of specific non-local CFT operators in the standard thermofield entangled state of two CFTs. In this sense, the whisker regions can be considered as purely auxiliary spacetimes in which these useful non-local CFT correlators can be rendered as local boundary correlators, and their diagnostic value more readily understood. Our results follow by first performing a novel reanalysis of the Rindler view of standard AdS/CFT duality on the Poincare patch of AdS, followed by exploiting the simple quotient structure of BTZ which turns the Rindler horizon into the BTZ black hole horizon. While most of our checks are within gravitational effective field theory, we arrive at a fully non-perturbative CFT proposal to probe the UV-sensitive approach to the singularity.

Objective perturbation adds a random linear term to a regularized empirical risk and releases the exact perturbed minimizer. We study the finite computation obtained by releasing the N-th iterate of deterministic gradient descent on wmapsto F(w;S)+langle z,wrangle, where zsimmathcal N(0,σ^2I_d) is drawn once before optimization. For strongly convex and smooth objectives with Lipschitz Hessian, we prove an explicit condition under which the map zmapsto w_N is a C^1-diffeomorphism on the bounded domains used in the privacy argument, with a quantitative lower bound on the smallest singular value of its Jacobian. This permits a direct change-of-variables analysis of the finite iterate. For generalized linear models, the resulting privacy-profile bound has no explicit ambient-dimension factor once the iteration condition holds, and its finite-iteration correction decreases geometrically. By letting the free truncation parameter grow slowly with N, we recover the corresponding exact-minimizer certificate in the limit. We also bound the expected excess empirical risk by dσ^2/(2μ) plus a geometrically decreasing optimization term, and transfer the result to population risk without an additional multiplicative condition-number factor in the leading statistical terms.

Fast and scalable alignment of time series is a fundamental challenge in many domains. The standard solution, Dynamic Time Warping (DTW), struggles with poor scalability and sensitivity to noise. We introduce TimePoint, a self-supervised method that dramatically accelerates DTW-based alignment while typically improving alignment accuracy by learning keypoints and descriptors from synthetic data. Inspired by 2D keypoint detection but carefully adapted to the unique challenges of 1D signals, TimePoint leverages efficient 1D diffeomorphisms, which effectively model nonlinear time warping, to generate realistic training data. This approach, along with fully convolutional and wavelet convolutional architectures, enables the extraction of informative keypoints and descriptors. Applying DTW to these sparse representations yield major speedups and typically higher alignment accuracy than standard DTW applied to the full signals. TimePoint demonstrates strong generalization to real-world time series when trained solely on synthetic data, and further improves with fine-tuning on real data. Extensive experiments demonstrate that TimePoint consistently achieves faster and more accurate alignments than standard DTW, making it a scalable solution for time-series analysis. Our code is available at https://github.com/BGU-CS-VIL/TimePoint

The ideal magnetohydrodynamic (MHD) system that governs a conducting plasma---the Maxwell equations together with the conservation laws of mass, momentum and energy---is the same local balance structure that describes hot accretion flows around black holes. We introduce a uniform four-dimensional spacetime dilation \[ Φ_L:\;(t',x',y',z')\mapsto (t,x,y,z)=(Lt',Lx',Ly',Lz'),\qquad L>1, \] and show that it is a smooth, orientation-preserving C^infty diffeomorphism of flat spacetime. Pulling the MHD conservation laws back through Φ_L, we prove that the closed ideal-MHD system is form-invariant (covariant), with the current density rescaling as bm j=bm j'/L, the magnetic diffusivity as η'=η/L, and external sources rescaled by L. The transformation realises three physically distinct effects on the perturbed flow: a linearization to the tangent-space (linearised MHD) system, a movie slow-motion dilation of dissipative and dynamical timescales, and an electron-microscope magnification of small-scale structure. Taking the formal limit Ltoinfty localises the dynamics on a neighbourhood of a horizon: resistivity vanishes, the asymptotic time derivative freezes, and all transient multipolar structure of the infalling plasma redshifts away. The remaining stationary, axisymmetric, asymptotically flat electrovacuum is uniquely the Kerr--Newman geometry, so that the exterior of the compact object is characterised only by its mass M, angular momentum J and charge Q. The result provides a local, conservation-law-based perspective on the black hole no-hair theorem that is complementary to the classical Israel--Carter-- Robinson theorems and to contemporary gravitational-wave and Event Horizon Telescope tests.