AI for Science

We introduce a nonperturbative framework for quantizing chiral solitons in interacting quantum spin chains. This approach provides a direct lattice extension of the well-established $S$-duality between the sine-Gordon and Thirring models, thereby bridging the gap between continuum dualities and their lattice counterparts. By constructing the quantum chiral-soliton operators explicitly, we show how their unconventional dynamics appear in the excitation spectrum and correlation functions across the full Brillouin zone. A key result is that the dominant soliton tunneling amplitude alternates in sign, $\operatorname{sgn}(t_{1+}) = (-1)^{2S+1}$, sharply distinguishing half-odd-integer from integer spin chains. We further identify characteristic signatures of these chiral excitations in the dynamical spin structure factor, demonstrating their visibility in inelastic neutron scattering. Our results open a route to experimentally probing nonperturbative features of dual quantum field theories in condensed-matter settings.

Random-matrix theory helps disentangle signal from noise in large data sets. We analyze rectangular $p \times q$ matrices $W = W_0 + M$ in which the noise $M$ generates a Marchenko-Pastur bulk, whereas the signal $W_0$ injects an extensive set of degenerate singular values. Keeping $\mathrm{rank}$ $W_0/q$ finite as $p,q \to \infty$, we show that the trace of the resolvent of $W^{\top} W$ obeys a quartic equation for one degenerate signal, yielding an exact spectral density, and derive explicit asymptotics in the strong-signal regime. We map out a detailed generalized Baik-Ben Arous-Péché (BBP) phase diagram and clarify how a finite density of spikes reshapes the bulk edges. We further derive a $1/3$-scaling law for the critical signal strength in terms of the rank ratio for rectangular matrices in the finite-to-extensive-rank crossover. Numerical simulations validate the theory and illustrate its relevance for high-dimensional inference tasks with multiple degenerate signals and more general signal distributions.

Renormalization is an essential technique in field-theoretic descriptions of natural phenomena, where the absence of a UV-complete description yields an abundance of divergent quantities. While the renormalization prescription has been thoroughly refined for equilibrium systems, consistently extending it to out-of-equilibrium systems is an active area of research. In this paper, we identify a mutual information-based measure of renormalizability that applies to quantum field theories both in and out of equilibrium. Specifically, we use mutual information to characterize correlations between infinitesimal shells in momentum space and show that the logarithmic derivative of mutual information with mode separation, at large mode separation, is a measure of renormalizability. We first consider Minkowski spacetime, where we introduce dynamics by performing an interaction quench, initializing the field in the free theory vacuum and then turning on the interaction. We show that the late-time mutual information relaxes to that for the interacting vacuum and the logarithmic derivative at large mode separation is negative for super-renormalizable theories, zero for renormalizable (marginal) theories, and positive for non-renormalizable theories. We then consider a conformally-coupled scalar field on the Poincaré patch of de Sitter spacetime, initializing the field in the Bunch-Davies vacuum in the asymptotic past. For different self-interactions and at any finite time, we find that the resulting mutual information has the same qualitative behavior as a function of mode separation, demonstrating that it can be used as a reliable indicator of renormalizability.

The Boltzmann distribution for an equilibrium system constrains the statistics of the system by the energetics. Despite the non-equilibrium generalization of the Boltzmann distribution being studied extensively, a unified framework valid for far-from-equilibrium discrete state systems is lacking. Here, we derive an exact path-integral representation for discrete state processes and represent it using the exponential of the action for stochastic transition dynamics. Solving the variational problem, the effective action is shown to be equal to the inferred entropy production rate (a thermodynamic quantity) and a non-quadratic dissipation function of the thermodynamic length (TL) defined for microscopic stochastic currents (a dynamic quantity). This formulates a far-from-equilibrium analog of the Boltzmann distribution, namely, the minimum action principle. The non-quadratic dissipation function is physically attributed to incorporating non-Gaussian fluctuations or far-from-equilibrium non-conservative driving. Further, an exact large deviation dynamical rate functional is derived. The equivalence of the variational formulation with the information geometric formulation is proved. The non-quadratic TL recovers the non-quadratic thermodynamic-kinetic uncertainty relation (TKUR) and the speed limits, which are tighter than the close-to-equilibrium quadratic formulations. Moreover, if the transition affinities are known, the non-quadratic TL recovers the fluctuation relation (FR). The minimum action principle manifests the non-quadratic TKUR and FR as two faces corresponding to the thermodynamic inference and partial control descriptions, respectively. In addition, the validity of these results is extended to coarse-grained observable currents, strengthening the experimental/numerical applicability of them.

The modeling of diffusion processes on graphs is the basis for many network science and machine learning approaches. Entropic measures of network-based diffusion have recently been employed to investigate the reversibility of these processes and the diversity of the modeled systems. While results about their steady state are well-known, very few exact results about their finite-time evolution exist. Here, we introduce the conditional entropy of heat diffusion in graphs, and outline a mathematical framework that contextualizes diffusion and conditional entropy within the theories of continuous-time Markov chains and information theory. In particular, we highlight that this entropic measure satisfies an information-theoretical version of the second law of thermodynamics, thereby providing a parallelism between diffusion dynamics on networks and their physical counterparts. Furthermore, we obtain explicit results for its evolution on complete, path, and circulant graphs, as well as a mean-field approximation for Erdös-Rényi graphs. We also obtain asymptotic results for general networks and provide bounds for the evolution of conditional entropy. Finally, we experimentally demonstrate several properties of conditional entropy for diffusion over random graphs, such as the Watts-Strogatz model.

Simulation Based Inference (SBI) is shown to yield more accurate resonance parameter estimates than traditional chi-squared minimization in certain cases of model misspecification, demonstrated through a case study of pi-pi scattering and the rho(770) resonance. Models fit to some data sets using chi-squared minimization can predict inaccurate pole positions for the rho(770), while SBI provides more robust predictions across the same models and data. This result is significant both as a proof of concept that SBI can handle model misspecification, and because accurate modeling of pi-pi scattering is essential in the study of many contemporary physical systems (e.g., a1(1260), omega(782)). The method of Simulation Based Inference is shown to lead to a more accurate resonance parameter estimation than traditional chi-squared minimization in certain cases of model misspecification in a case-study of pi-pi scattering and the rho(770)-resonance. Models fit to certain data sets using chi-squared minimization can make inaccurate predictions for the pole position of the rho(770). SBI is shown to make a more robust predictions for the pole positions. This is significant, both as a proof of concept that the SBI method can be used in cases of model misspecification, and because models of pi-pi scattering are a crucial part to many physical systems of contemporary interest (e.g., a1(1260), omega(782)).

A chaotic attractor is formed in a finite region in phase space by the long-term trajectory of a three or higher-dimensional dissipative system. The attractor is a fractional-dimensional geometry, whose dimension is a fraction but less than the dimension of the phase space. The geometry of an attractor can be as complex as a multi-wing geometry. The emergence and confinement of such a complex geometrical attractor can be understood by the Nambu mechanics without numerically solving the governing equations of the dynamics. In this article, we show that the four-wing geometry of an attractor appears in the phase space by the intersection of two energy-like Hamiltonian functions. We further show that the dynamical equations require the localization range of these surfaces so that their intersection is confined to a certain region of the phase space. We analytically find the required conditions based on the system parameters for the localization of the attractor.

In our previous article [arXiv:2307.12552], we introduced local topological order (LTO) axioms for quantum spin systems which allowed us to define a physical boundary (associated to a cut of the lattice) manifested by a net of boundary algebras in one dimension lower. This gives a formal setting for topological holography, where the braided tensor category of DHR bimodules of the physical boundary algebra captures the bulk topological order. In this article, we extend the LTO axioms to quantum spin systems equipped with a topological boundary (domain wall with the trivial phase), again producing a physical boundary algebra for the bulk-boundary system, whose category of (topological) boundary DHR bimodules recovers the topological boundary order. We perform this analysis in explicit detail for Levin-Wen and Walker-Wang bulk-boundary systems. Along the way, we introduce a 2D braided categorical net of algebras built from a unitary braided fusion category (UBFC). Such nets arise as boundary algebras of Walker-Wang models. We consider the canonical state on this braided categorical net corresponding to the standard topological boundary for the Walker-Wang model. Interestingly, in this state, the cone von Neumann algebras are type I with finite dimensional centers, in contrast with the type II and III cone von Neumann algebras from the Levin-Wen models studied in [arXiv:2307.12552]. Their superselection sectors recover the underlying unitary category of our UBFC, and we conjecture the superselection category also captures the fusion and braiding.

We analyse a generalisation of Zöttl and Stark's model of active spherical particles [Phys. Rev. Lett. 108, 218104 (2012)] and prolate spheroidal particles [Eur. Phys. J. E 36(1), 4 (2013)] suspended in cylindrical Poiseuille flow, to particle dynamics in an arbitrary unidirectional steady laminar flow through a straight duct geometry. Our primary contribution is to describe a Hamiltonian formulation of these systems and provide explicit forms of the constants of motions in terms of the arbitrary fluid velocity field. The Hamiltonian formulation provides a convenient and robust approach to the computation of particle orbits whilst also providing new insights into the dynamics, specifically the way in which orbits are trapped within basins defined by a potential well. In addition to considering spherical and prolate spheroidal particles, we also illustrate that the model can be adapted to oblate spheroidal particles.

Topological data analysis (TDA) aims to extract noise-robust features from a data set by examining the number and persistence of holes in its topology. We provide an efficient quantum algorithm for a computational problem closely related to a core task in TDA -- determining whether a given hole persists across different length scales. Further, we prove the problem itself is $\mathsf{BQP}_1$-hard, implying that a classical solution is extremely unlikely; this stands in contrast to all previous quantum approaches to TDA, where the problems were also intractable for quantum computers, or where a rigorous proof of classical hardness still remains open. This result implies an {exponential} quantum speedup for this problem under standard complexity-theoretic assumptions. Our approach relies on encoding the persistence of a hole in a variant of the guided sparse Hamiltonian problem, where the guiding state is constructed from a harmonic representative of the hole.

High-fidelity simulation of spatiotemporal dynamics is computationally prohibitive, necessitating efficient super-resolution techniques to reconstruct high-resolution data from coarse-grained inputs. Traditional data-driven methods often lack physical constraints, and simple physics-informed learning struggles with irregular spatial geometries and intricately evolving temporal dynamics. To tackle these challenges, we propose a Physics-augmented Koopman-enhanced Graph Convolutional Network (P-K-GCN) for spatiotemporal super-resolution on irregular geometries. Specifically, a continuous spline-based GCN is first designed to extract spatial dependencies directly from coarse graph, and Koopman operator theory is incorporated to project the nonlinear dynamics into a compact latent space where temporal progression is linearized. Second, we augment the optimization objective with a physics-based loss to force the data-driven reconstructions to adhere to physical laws for improving predictive fidelity and robustness. Finally, we provide a rigorous theoretical analysis, establishing that the physics augmentation and Koopman regularization mathematically guarantees a reduction in super-resolution error by diminishing Rademacher complexity and tightening generalization bounds. We evaluate our framework on reconstructing spatially high-resolution cardiac electrodynamics across a 3D heart geometry from sparse low-resolution measurements. Numerical experiments demonstrate that our method achieves superior accuracy compared to baseline models.

The quality of recorded data depends on the stability of the sensor system that acquires it. Sensor motion and aging can degrade the performance and stability of downstream data-driven methods. We present a Wasserstein-GAN-inspired approach for unsupervised inference of physically interpretable transformation parameters that map a changed detector response distribution back to a nominal reference distribution. In contrast to standard generative modeling, the generator is used as a learnable calibration transformation whose trainable weights represent the sought parameters, while the critic provides a distributional distance signal via the Wasserstein objective. We validate the approach on a tracking-detector toy model with controlled layer shifts and demonstrate its application on high-granularity Geant4-simulated calorimeter data with cell-wise aging effects. The method recovers aging coefficients for individual cells with correlation to ground truth and improves agreement between calibrated and reference energy-sum distributions, while exhibiting the expected degradation at increasing channel-to-channel noise levels. These results indicate that adversarial distribution matching can serve as a data-driven component of calibration strategies in settings where direct labels for degradation parameters are unavailable.

Atom interferometers are among the most sensitive instruments for precision measurements and tests of fundamental physics. Their performance, however, is ultimately limited by quantum projection noise when uncorrelated atomic ensembles are employed. Cavity-assisted generation of entangled states has proven to be a promising route toward quantum-enhanced interferometry beyond the standard quantum limit. In this work, we present the realization and characterization of a monolithic bow-tie cavity developed to achieve a strong collective atom-light coupling with strontium atoms. Unlike conventional standing-wave Fabry-Pérot resonators, the traveling-wave geometry of the bow-tie cavity provides homogeneous atom-light coupling over the entire atomic ensemble, making it particularly suitable for entanglement-enhanced atom interferometry with freely falling atoms. The monolithic cavity architecture presents several scientifically relevant features such as high mechanical stability, high finesse, robustness against mirror misalignment, optical and atomic access and the option of generating squeezed states through different strategies. The cavity was realized for operation on the strontium $(5s^2) ^1S_0-(5s5p) ^3P_1$ transition at 689 nm and achieves a finesse of $\mathcal{F}=5.7\times 10^4$ while keeping the transmission of a single mirror sufficiently large to allow for efficient atomic information extraction. In this geometry, the cavity supports two foci with waists of 164 $μ$m and 31 $μ$m which gives access to different regimes of atom-cavity coupling. For ensembles containing up to $10^5$ atoms, the cavity is expected to enable metrological gains approaching 24 dB of spin squeezing through cavity-feedback squeezing, and 28 dB through quantum non-demolition measurements, demonstrating its potential as a platform for next-generation quantum-enhanced atom interferometers.

The biomechanics of pulsed-jet propulsion in aquatic animals, including squids and jellyfish, provide valuable insights into energy-efficient locomotion. In these organisms, flexible funnel deformation enables rapid acceleration and maneuverability while minimizing energy use. Drawing inspiration from these biological systems, this study investigates performance trade-offs between rigid and flexible nozzle geometries in pulsed-jet propulsion systems. A multi-objective Bayesian optimization framework integrated with three-dimensional fluid-structure interaction (FSI) simulations identifies nozzle designs that maximize hydrodynamic impulse and minimize jet energy input. The optimization reveals fundamentally distinct performance characteristics for rigid and flexible nozzles. Rigid nozzles achieve the highest impulse amplification, up to 5 times that of a baseline cylindrical nozzle, but at substantially increased energy expenditure. In contrast, flexible nozzles yield lower peak impulse enhancement of about 2.5 times while achieving significantly greater propulsion efficiency. The maximum normalized impulse-to-energy ratio for flexible nozzles is about 1.8 times higher than that of rigid configurations, indicating more effective conversion of input energy into useful propulsive output. Analysis of the flow physics shows that optimized rigid nozzles enhance performance through geometry-induced internal entrainment, secondary vortex formation, and contraction-driven jet acceleration. This results in stronger vortex circulation and downstream convection. Flexible nozzles use traveling expansion-contraction deformation waves that promote additional entrainment during expansion and accelerate the internally entrained fluid during contraction to improve pressure recovery, reduce pressure-energy expenditure, and mitigate negative pressure impulse contributions.

Solving the pressure-Poisson equation remains the primary computational bottleneck in incompressible unstructured flow solvers primarily due to the inherent sensitivity of traditional linear solvers to mesh irregularities. This work introduces a data-driven algebraic multigrid (AMG) smoother that uses a modified graph convolutional isomorphism network (GCIN). The graph neural network predicts optimal polynomial coefficients to construct a sparse pseudo-inverse operator across diverse grid topologies. The coefficients are optimized to reduce the residual after each V-cycle iteration. By directly capturing the algebraic structure of the system from the sparse coefficient matrix, the proposed method maintains the solver's linearity while adapting to local anisotropies in unstructured grids. Our framework demonstrates significant performance gains by reducing the number of V-cycles required for a given tolerance and delivering wall-clock speedups from 4% to 37% across diverse benchmarks. Notably, the model exhibits robust generalization by maintaining efficiency on meshes up to 128 times larger than those seen in training, and by accelerating the solver's convergence on unseen industry-relevant problems such as the AirfRANS dataset.

We report on a study of the interacting phase diagram of $3.65^\circ$-twisted WSe$_2$ at moiré hole filling $ν=1$, in which we find previously-overlooked types of magnetism. Specifically, in part of the phase diagram we obtain a magnetic order parameter which modulates in space with four different non-zero wave vectors, corresponding to the three $M$-points and one $K$-point of the moiré Brillouin zone. These multi-Q orders, which can be coplanar or non-coplanar, are continuous deformations of the $120^\circ$ spin-valley anti-ferromagnet (AFM), where the unit cell has expanded by a factor of four. Interestingly, we find that the multi-Q states are stabilized for experimentally relevant values of interaction strength and displacement field, and are accompanied by a softening of the spin fluctuations near the $M$-points of the moiré

Altermagnets exhibit momentum-dependent spin splitting without net magnetization, combining characteristics of both ferromagnets and antiferromagnets, making them highly interesting for spintronics applications. CrSb is a prime candidate with a high Néel temperature ($\sim700$~K) and a large exchange-driven splitting of $\sim0.6$--1~eV. Using ab-initio calculations, we consider slabs of various orientations in the ultrathin limit. We find that (100) oriented slabs have spin-degenerate bands. In (0001) oriented slabs, the exchange-driven altermagnetic spin splitting collapses, but including spin-orbit coupling restores a residual anisotropic splitting of $\sim70$~meV. In contrast, the (110) oriented slabs show an altermagnetic spin splitting of $\sim400$~meV, and emerges as a robust candidate for realizing large, exchange-driven altermagnetism

Shelf seas are important for the economy and the carbon cycle, but shelf sea observations for carbon pools are often sparse, or highly uncertain. An alternative can be provided by carbon reanalyses (whether assimilating proxy variables, such as chlorophyll-$a$, or directly carbon), but these are often expensive to run. We propose to use a computationally cheap ensemble of neural networks (i.e. deep ensemble) to learn the relationship between the directly observable (atmospheric, riverine and ocean) variables and marine carbon pools from a coupled physics-biogeochemistry model. The deep ensemble was trained on a North-West European Shelf (NWES) physical-biogeochemistry model free run simulation. After training, the deep ensemble was run using inputs from the NWES reanalysis instead of the free run, demonstrating that it can efficiently predict several NWES carbon pools (e.g., detritus, zooplankton, heterotrophic bacteria) in much better agreement with the reanalysis than the free run, while also providing uncertainty information. We further show that the deep ensemble performs similarly well when it is driven directly by the observations assimilated into the reanalysis, with the limitation that carbon pools can then be predicted only at the observed locations and times. We focus on explainability of the results and demonstrate potential use of the deep ensembles for future climate what-if scenarios. We suggest that model-informed machine learning presents a viable alternative to expensive reanalyses and could complement observations, wherever they are missing and/or highly uncertain.

Machine-learning emulators are increasingly used for weather prediction and have the potential to extend skill on subseasonal-to-seasonal timescales by learning dynamically important sources of predictability. A key challenge is whether the models can exploit predictability anchors, such as stratospheric variability, that influence tropospheric circulation beyond short lead times. We test how architectural inductive bias affects emulation of sudden stratospheric warming (SSW) dynamics using paired idealised Isca simulations that differ only in an imposed wave-2 heating perturbation. Across convolutional, transformer, and graph-based architectures trained for one-step prediction, model differences are modest when the stratosphere is dynamically quiet but widen substantially when SSW-like variability is active. Our results identify explicit three-dimensional vertical coupling as a key inductive bias for machine-learning emulation of stratospheric dynamics. However, Eliassen-Palm flux diagnostics show that low forecast error does not guarantee physically faithful wave-mean-flow interaction, with coherent errors remaining in stratospheric wave-driving structure.

In this paper we prove a lower bound result for extremely large values of $L(\frac{1}{2},χ_p)$ with prime numbers $p\equiv 1\pmod 8$.

We simplify and improve the main fundamental theorems of positive characteristic generic vanishing theory. As a quick corollary of the theory, we prove that a normal variety $X$ of maximal Albanese dimension satisfies $H^0(X, ω_X) \neq 0$ and that if $\mathrm{Alb}(X)$ is ordinary, then $S^0(X, ω_X) \neq 0$.

We study almost complete intersection ideals in a polynomial ring, generated by powers of all the variables together with a power of their sum. Our main result is an explicit description of the reduced Gröbner bases for these ideals under any term order. Our approach is primarily combinatorial, focusing on the structure of the initial ideal. We associate a lattice path to each monomial in the vector space basis of an Artinian monomial complete intersection and introduce a reflection operation on these paths, which enables a key counting argument. As a consequence, we provide a new proof that Artinian monomial complete intersections possess the strong Lefschetz property over fields of characteristic zero. Our results also offer new insights into the longstanding problem of classifying the weak Lefschetz property for such intersections in characteristic $p$. Furthermore, we show that the number of Gröbner basis elements in each degree is connected to several well-known sequences, including the (generalized) Catalan, Motzkin, and Riordan numbers, and connect these numbers to the study of entanglement detection in spin systems within quantum physics.

We consider an inverse boundary value problem for the biharmonic operator with the first order perturbation in a bounded domain of dimension three or higher. Assuming that the first and the zeroth order perturbations are known in a neighborhood of the boundary, we establish log-type stability estimates for these perturbations from a partial Dirichlet-to-Neumann map. Specifically, measurements are taken only on an arbitrarily small open subsets of the boundary.

We prove that for $n \leq 4$ and $p > 5$, quasi--Gorenstein $F$--pure and $\mathbb{Q}_p$--rational $n$--fold singularities are canonical. This is analogous to the usual fact that rational Gorenstein singularities are canonical. The proof is based on a careful analysis of the dual complex of a dlt modification of a log canonical singularity. The result for $n = 4$ is contingent upon the existence of log resolutions.

Let $W_d(n)$ be the number of $2n$-step walks in $\mathbb{Z}^d$ which begin and end at the origin. We study the exponent of $2$ in the prime factorisation of this number; i.e., $w_d(n) = ν_2(W_d(n))$. We show that, for each $d$, there is a relationship between $w_d(n)$ and the number $s_2(n)$ of $1$s in the binary expansion of $n$. For example, $w_d(n) = s_2(n)$ if $d$ is odd and $w_d(n) = 2s_2(n)$ if $ν_2(d) = 1$; while $w_d(n) \ge 3s_2(n)$ if $ν_2(d) = 2$. The pattern changes further when $ν_2(d) \ge 3$. However, for each $d$, we give the best analogous estimate of $w_d(n)$ together with a description of all $n$ where equality is attained. The methods we develop apply to a wider range of problems as well, and so might be of independent interest.

Transversally Kähler foliations are a generalisation of Kähler manifolds, appearing naturally in the complex non-Kähler setting. We give a self-contained proof of how the classical methods used in the proof of the Aubin-Yau theorem adapt to the transversally Kähler case under the homological orientability condition. We apply this result to obtain a new, simpler proof of the already known Vaisman Aubin-Yau theorem.

This paper classifies complex local representations of the twisted virtual braid group, $TVB_2$, into $\mathrm{GL}_3(\mathbb{C})$. It shows that such representations fall into eight types, all of which are unfaithful and reducible to a two-dimensional representation. Further reducibility to a one-dimensional representation is analyzed for specific types. The paper also examines complex homogeneous local representations of $TVB_n$ into $\mathrm{GL}_{n+1}(\mathbb{C})$ for $n \geq 3$, identifying seven unfaithful types. Additionally, complex local representations of the singular twisted virtual braid group, $STVB_2$, into $\mathrm{M}_3(\mathbb{C})$ are classified into thirteen unfaithful types. Finally, the paper demonstrates that not all complex local extensions of $TVB_2$ representations to $STVB_2$ conform to a $Φ$-type extension.

The instrumental variable (IV) approach is commonly used to infer causal effects in the presence of unmeasured confounding. Existing methods typically aim to estimate the mean causal effects, whereas a few other methods focus on quantile treatment effects. The aim of this work is to estimate the entire interventional distribution. We propose a method called Distributional Instrumental Variable (DIV), which uses generative modelling in a nonlinear IV setting. We establish identifiability of the interventional distribution under general assumptions and demonstrate an 'under-identified' case, where DIV can identify the causal effects while two-step least squares fails to. Our empirical results show that the DIV method performs well for a broad range of simulated data, exhibiting advantages over existing IV approaches in terms of the identifiability and estimation error of the mean or quantile treatment effects. Furthermore, we apply DIV to an economic data set to examine the causal relation between institutional quality and economic development and our results align well with the original study. We also apply DIV to a single-cell data set, where we study the generalizability and stability in predicting gene expression under unseen interventions. The software implementations of DIV are available in R and Python.

On biomedical tabular data, flexible models such as deep networks, gradient-boosted trees, and kernel methods are repeatedly matched or beaten by linear and logistic regression given the same features. The usual reaction is to treat this as a model-side shortfall, to be fixed with more data, a better architecture, or tuning, on the assumption that the nonlinear structure is there and the model has failed to capture it. We argue that these fixes cannot help when the binding limit is the measurement rather than the model, as it frequently is in biomedicine. Additive noise blurs the population-optimal predictor, and because blurring removes a function's fine, rapidly varying detail before its broad shape, it erases nonlinear structure faster than linear structure. A degree-$k$ interaction is attenuated by the $k$-th power of feature reliability, while the linear part is attenuated only once. At the reliabilities typical of biomedical measurement, the nonlinear advantage can vanish even when the underlying biology is strongly nonlinear, and what the noise removes cannot be recovered by a larger cohort or a more flexible model, only by better measurement. The nonlinearity is hidden, not absent, and a tie between linear and flexible models is not by itself a verdict on the biology. These pieces are classical, drawn from measurement-error statistics, psychometrics, and Gaussian analysis, and we assemble them into an exact excess-risk identity. Measurement reliability is one of three conditions, alongside sample size and feature representation, that must align for a flexible model to help, and together they leave only a narrow window that most biomedical tasks fall outside. Across 140 UK Biobank tasks, the gap between flexible and linear models, where it exists, carries the predicted noise signature, and the three conditions can be separated by intervention but not by a benchmark alone.

Motivation: Noisy labels are a common challenge in molecular property prediction because molecular annotations are often obtained from assays, curated databases, or weak annotation pipelines rather than directly observed clean biological states. Treating recorded labels as reliable supervision can cause models to memorize corrupted observations and learn misleading molecular evidence. In multimodal molecular representation learning, this issue can be amplified by graph-text fusion or alignment, which may propagate label-induced errors across modalities. Results: We propose MOLAR, a noise-aware framework for learning multimodal molecular representations from noisy labels. MOLAR separates latent clean-property inference from recorded-label observation: graph and text views contribute residual evidence to a clean-property distribution, and a categorical label-observation channel maps this distribution to recorded labels for training. This formulation derives posterior label reliability and modality-specific molecular evidence from the model. Experiments on naturally noisy molecular benchmarks and controlled label-flipping benchmarks show that MOLAR consistently outperforms representative baselines. Visualization analyses further show that MOLAR provides interpretable reliability and modality-evidence diagnostics.