State-space models (SSMs) offer efficient sequence modeling but lag behind Transformers on benchmarks that require in-context retrieval. Prior work links this gap to a small set of attention heads, termed Gather-and-Aggregate (G&A), which SSMs struggle to reproduce. We propose *retrieval-aware distillation*, which converts a pretrained Transformer into a hybrid student by preserving only these retrieval-critical heads and distilling the rest into recurrent heads. We identify the essential heads via ablation on a synthetic retrieval task, producing a hybrid with sparse, non-uniform attention placement. We show that preserving **just 2% of attention heads recovers over 95% of teacher performance on retrieval-heavy tasks** (10 heads in a 1B model), requiring far fewer heads than hybrids that retain at least 25%. We further find that large recurrent states often compensate for missing retrieval: once retrieval is handled by these heads, the SSM backbone can be simplified with limited loss, even with an $8\times$ reduction in state dimension. By reducing both the attention cache and the SSM state, the resulting hybrid is $5$--$6\times$ more memory-efficient than comparable hybrids,
While Transformers underpin modern large language models (LMs), there is a growing list of alternative architectures with new capabilities, promises, and tradeoffs. This makes choosing the right LM architecture challenging. Recently proposed hybrid architectures seek a best-of-all-worlds approach that reaps the benefits of all architectures. Hybrid design is difficult for two reasons: it requires manual expert-driven search, and new hybrids must be trained from scratch. We propose Manticore, a framework that addresses these challenges by automating the design of hybrid architectures while reusing pretrained models to create pretrained hybrids. Our approach augments ideas from differentiable Neural Architecture Search (NAS) by incorporating simple projectors that translate features between pretrained blocks from different architectures. We then fine-tune hybrids that combine pretrained models from different architecture families -- such as the GPT series and Mamba -- end-to-end. With Manticore, we enable LM selection without training multiple models, the construction of pretrained hybrids from existing pretrained models, and the ability to program pretrained hybrids to have certain
The Transiting Exoplanet Survey Satellite (TESS) mission has observed hundreds of millions of stars, substantially contributing to the available pool of high-precision photometric space data. Among them are the relatively rare $γ$ Doradus / $δ$ Scuti ($γ$ Dor / $δ$ Sct) hybrid pulsators, which have been previously studied using Kepler data. These stars are perfect laboratories to probe both inner and outer interior stellar layers thanks to them exhibiting both pressure and gravity modes. We seek to classify an all-sky sample of AF stars observed by TESS to find previously undiscovered hybrid pulsators and supply them in a catalogue of candidates. We also aim to compare the light curves produced with the TESS-Gaia Light Curve (TGLC) pipeline, currently underused in variability studies, with other publicly available light curves. We compared dominant and secondary frequencies of confirmed hybrid pulsators in Kepler, extended mission Quick Look Pipeline (QLP) data, and nominal and extended mission TGLC data. We then used a feature-based positive unlabelled (PU) learning classifier to search for new hybrid pulsators amongst TESS AF stars and investigated the properties of the detected
In the framework of the Born-Oppenheimer Effective Field Theory, the hyperfine structure of heavy quarkonium hybrids at leading order in the 1/m Q expansion is determined by two potentials. We estimate those potentials by interpolating between the known short distance behavior and the long distance behavior calculated in the QCD Effective String Theory. The long distance behavior depends, at leading order, on two parameters which can be obtained from the long distance behavior of the heavy quarkonium potentials (up to sign ambiguities). The short distance behavior depends, at leading order, on two extra paramentes, which are obtained from a lattice calculation of the lower lying charmonium hybrid multiplets. This allows us to predict the hyperfine splitting both of bottomonium hybrids and of higher multiplets of charmonium hybrids. We carry out a careful error analysis and compare with other approaches.
The strangeonium-like $s\bar{s}g$ hybrids are investigated from lattice QCD in the quenched approximation. In the Coulomb gauge, spatially extended operators are constructed for $1^{--}$ and $(0,1,2)^{-+}$ states with the color octet $s\bar{s}$ component being separated from the chromomagnetic field strength by spatial distances $r$, whose matrix elements between the vacuum and the corresponding states are interpreted as Bethe-Salpeter (BS) wave functions. In each of the $(1,2)^{-+}$ channels, the masses and the BS wave functions are reliably derived. The $1^{-+}$ ground state mass is around 2.1-2.2 GeV, and that of $2^{-+}$ is around 2.3-2.4 GeV, while the masses of the first excited states are roughly 1.4 GeV higher. This mass splitting is much larger than the expectation of the phenomenological flux-tube model or constituent gluon model for hybrids, which is usually a few hundred MeV. The BS wave functions with respect to $r$ show clear radial nodal structures of non-relativistic two-body system, which imply that $r$ is a meaningful dynamical variable for these hybrids and motivate a color halo picture of hybrids that the color octet $s\bar{s}$ is surrounded by gluonic degrees o
Svestka (Solar Phys. 1989, 121, 399) on the basis of the Solar Maximum Mission observations introduced a new class of flares, the so-called flare hybrids. When they start, they look as typical compact flares (phase 1), but later on they look like flares with arcades of magnetic loops (phase 2). We summarize the features of flare hybrids in soft and hard X-rays as well as in extreme-ultraviolet; these allow us to distinguish them from other flares. Additional energy release or long plasma cooling timescales have been suggested as possible cause of phase 2. Estimations of frequency of flare hybrids have been given. Magnetic configurations supporting their origin have been presented. In our opinion, flare hybrids are quite frequent and a difference between lengths of two interacting systems of magnetic loops is a crucial parameter for recognizing their features.
One of the most important tasks in high energy physics is search for the exotic states, such as glueball, hybrid and multi-quark states. The transitions $ψ(ns)\to ψ(ms)+ππ$ and $Υ(ns)\to Υ(ms)+ππ$ attract great attentions because they may reveal characteristics of hybrids. In this work, we analyze those transition modes in terms of the theoretical framework established by Yan and Kuang. It is interesting to notice that the intermediate states between the two gluon-emissions are hybrids, therefore by fitting the data, we are able to determine the mass spectra of hybrids. The ground hybrid states are predicted as 4.23 GeV (for charmonium) and 10.79 GeV (for bottonium) which do not correspond to any states measured in recent experiments, thus it may imply that very possibly, hybrids mix with regular quarkonia to constitute physical states. Comprehensive comparisons of the potentials for hybrids whose parameters are obtained in this scenario with the lattice results are presented.
We exhibit closed hyperbolic manifolds with arbitrarily small systole in each dimension that are not quasi-arithmetic in the sense of Vinberg, and are thus not commensurable to those constructed by Agol, Belolipetsky--Thomson, and Bergeron--Haglund--Wise. This is done by taking hybrids of the manifolds constructed by the latter authors.
In this work we present magnetization data on hybrids consisting of multilayers (MLs) of man- ganites [La0.33Ca0.67MnO3/La0.60Ca0.40MnO3]15 in contact with a low-Tc Nb superconductor (SC). Although a pure SC should behave diamagnetically in respect to the external magnetic field in our ML-SC hybrids we observed that the magnetization of the SC follows that of the ML. Our intriguing experimental results show that the SC below its TSC c becomes ferromagnetically coupled to the ML. As a result in the regime where diamagnetic behaviour of the SC was expected its bulk magne- tization switches only whenever the coercive field of the ML is exceeded. By employing specific experiments where the ML was selectively biased or not we demonstrate that the ML inflicts its magnetic properties on the whole hybrid. Possible explanations are discussed in connection to recent theoretical proposals and experimental findings that were obtained in relative hybrids.
A unique feature of quantum chromodynamics (QCD), the theory of strong interactions, is the possibility for gluonic degrees of freedom to participate in the construction of physical hadrons, which are color singlets, in an analogous manner to valence quarks. Hadrons with no valence quarks are called glueballs, while hadrons where both gluons and valence quarks combine to form a color singlet are called hybrids. The unambiguous identification of such states among the experimental hadron spectrum has been thus far not possible. Glueballs are particularly difficult to establish experimentally since the lowest lying ones are expected to strongly mix with conventional mesons. On the other hand, hybrids should be easier to single out because the set of quantum numbers available to their lowest excitations may be exotic, i.e., not realized in conventional quark-antiquark systems. Particularly promising for discovery appear to be heavy hybrids, which are made of gluons and a heavy-quark-antiquark pair (charm or bottom). In the heavy-quark sector systematic tools can be used that are not available in the light-quark sector. In this paper we use a nonrelativistic effective field theory to un
The internal structures of $J^{PC}=1^{--}, (0,1,2)^{-+}$ charmonium-like hybrids are investigated under lattice QCD in the quenched approximation. We define the Bethe-Salpeter wave function $Φ_n(r)$ in the Coulomb gauge as the matrix element of a spatially extended hybrid-like operator $\bar{c}{c}g$ between the vacuum and $n$-th state for each $J^{PC}$ with $r$ being the spatial separation between a localized $\bar{c}c$ component and the chromomagnetic strength tensor. These wave functions exhibit some similarities for states with the aforementioned different quantum numbers, and their $r$-behaviors (no node for the ground states and one node for the first excited states) imply that $r$ can be a meaningful dynamical variable for these states. Additionally, the mass splittings of the ground states and first excited states of charmonium-like hybrids in these channels are obtained for the first time to be approximately 1.2-1.4 GeV. These results do not support the flux-tube description of heavy-quarkonium-like hybrids in the Born-Oppenheimer approximation. In contrast, a charmonium-like hybrid can be viewed as a "color halo" charmonium for which a relatively localized color octet $\ba
QCD Laplace sum rules are used to calculate heavy quarkonium (charmonium and bottomonium) hybrid masses in several distinct $J^{PC}$ channels. Previous studies of heavy quarkonium hybrids did not include the effects of dimension-six condensates, leading to unstable sum rules and unreliable mass predictions in some channels. We have updated these sum rules to include dimension-six condensates, providing new mass predictions for the spectra of heavy quarkonium hybrids. We confirm the finding of other approaches that the negative-parity $J^{PC}=(0,1,2)^{-+},\,1^{--}$ states form the lightest hybrid supermultiplet and the positive-parity $J^{PC}=(0,1)^{+-},\,(0,1,2)^{++}$ states are members of a heavier supermultiplet. Our results disfavor a pure charmonium hybrid interpretation of the $X(3872)$, in agreement with previous work.
We show that the dynamics of the Quark-Gluon Plasma is such that during hadronization the creation of hybrids will predominate over the creation of mesons, giving a novel signature of the existence of QGP. At T = 0 the $(q\bar{q}g)$ hybrids are known to decay strongly into a pair of mesons. We find that at temperatures relevant to the QGP, this channel is forbidden. This would lead to significant modifications of the photonic signals of the QGP.
The extraction of classical degrees of freedom in quantum mechanics is studied in the stochastic variational method. By using this classicalization, a hybrid model constructed from quantum and classical variables (quantum-classical hybrids) is derived. In this procedure, conservation laws such as energy are maintained, and Ehrenfest's theorem is still satisfied with modification. The criterion for the applicability of quantum-classical hybrids is also discussed.
Hybrid rice breeding crossbreeds different rice lines and cultivates the resulting hybrids in fields to select those with desirable agronomic traits, such as higher yields. Recently, genomic selection has emerged as an efficient way for hybrid rice breeding. It predicts the traits of hybrids based on their genes, which helps exclude many undesired hybrids, largely reducing the workload of field cultivation. However, due to the limited accuracy of genomic prediction models, breeders still need to combine their experience with the models to identify regulatory genes that control traits and select hybrids, which remains a time-consuming process. To ease this process, in this paper, we proposed a visual analysis method to facilitate interactive hybrid rice breeding. Regulatory gene identification and hybrid selection naturally ensemble a dual-analysis task. Therefore, we developed a parametric dual projection method with theoretical guarantees to facilitate interactive dual analysis. Based on this dual projection method, we further developed a gene visualization and a hybrid visualization to verify the identified regulatory genes and hybrids. The effectiveness of our method is demonstr
Hybrid language models that interleave attention with recurrent components are increasingly competitive with pure Transformers, yet standard LoRA practice applies adapters uniformly without considering the distinct functional roles of each component type. We systematically study component-type LoRA placement across two hybrid architectures -- Qwen3.5-0.8B (sequential, GatedDeltaNet + softmax attention) and Falcon-H1-0.5B (parallel, Mamba-2 SSM + attention) -- fine-tuned on three domains and evaluated on five benchmarks. We find that the attention pathway -- despite being the minority component -- consistently outperforms full-model adaptation with 5-10x fewer trainable parameters. Crucially, adapting the recurrent backbone is destructive in sequential hybrids (-14.8 pp on GSM8K) but constructive in parallel ones (+8.6 pp). We further document a transfer asymmetry: parallel hybrids exhibit positive cross-task transfer while sequential hybrids suffer catastrophic forgetting. These results establish that hybrid topology fundamentally determines adaptation response, and that component-aware LoRA placement is a necessary design dimension for hybrid architectures.
In this letter, we propose that a proper constituent gluon mass $m_g$=450 MeV can be applied to identify the hybrids composed of quarks and gluons. By investigating the spectra and decay widths of the light hybrids $(q\bar{q}g)$ with $J^P=1^{-+}$, we find the $π_1(1600)$ and $η_1(1855)$ may not be explained as $1^{-+}$ hybrids, simultaneously, and the $η_1(1855)$ observed by BESIII may not be a hybrid. In addition, we predict an existence of a hybrid $η_1(1640)$, which can be verified by searching the $a_1(1260)π$ channel. Moreover, we suggest the $K_1(1270)\bar{K}$ and $K_1(1270)π$ as the golden channels to search for an isospin-0 and an isospin-$\frac{1}{2}$ hybrids, respectively.
We investigate the potential performance improvements of double-hybrid density functionals by replacing the standard opposite-spin-scaled MP2 (SOS-MP2) with the modified opposite-spin-scaled MP2 (MOS-MP2) in the nonlocal correlation component. Using the large and diverse GMTKN55 dataset, we find that MOS-double hybrids provide significantly better accuracy compared to SOS-MP2-based double hybrids when empirical dispersion correction is not employed. The non-covalent interaction subsets account for the majority of this improvement. Adding the DFT-D4 dispersion correction to MOS-type double hybrids does not provide any superior performance over conventional dispersion-corrected SOS-MP2-based double hybrids. Nevertheless, for nine tested transition metal sets, dispersion-corrected spin-component-scaled (SCS) double hybrids are still significantly better than any MOS-double hybrid functional.
Masses and current couplings of the charmonium and bottomonium hybrids $ \overline{c}gc$ and $\overline{b}gb$ with spin-parities $J^{\mathrm{PC} }=0^{++},\ 0^{+-},\ 0^{-+},\ 0^{--}$ and $1^{++},\ 1^{+-},\ 1^{-+},\ 1^{--}$ are calculated using QCD two-point sum rule method. Computations are performed by taking into account gluon condensates up to dimension 12 including terms $\sim \langle g_{s}^{3}G^{3}\rangle ^{2}$. The parameters of the bottom-charm hybrids $\overline{b}gc$ with quantum numbers $J^{\mathrm{PC }}=0^{+},\ 0^{-},\ 1^{+}$, and $1^{-}$ are calculated as well. In computations the dominance of the pole contribution to sum rule results is ensured. It is demonstrated that all charmonia hybrids decay strongly to two-meson final states. The bottomonium hybrids $0^{-+}$ and $1^{-+}$ as well as the bottom-charm hybrid mesons $0^{-(+)}$ and $1^{-(+)}$ may be stable against strong two-meson decay modes. Results of the present work are compared with ones obtained using the sum rule and alternative approaches. Our predictions for parameters of the heavy hybrid mesons may be useful to study their various decay channels which are important for interpretation of ongoing and future ex
Hybrid quarkonia -exotic hadrons with explicit gluonic degrees of freedom- have gained increasing attention in hadron spectroscopy, particularly with the ongoing discovery of new XYZ mesons. In this work, we update the spectrum of heavy hybrid mesons in the charmonium and bottomonium sectors using the Born-Oppenheimer Effective Field Theory framework, by incorporating the latest lattice QCD results for hybrid static potentials. We refine earlier calculations and analyze allowed transitions from hybrids to conventional quarkonia, including both spin-conserved and spin-flip decays. We carry out a comprehensive error analysis and discuss the reliability of our results. We compare them to experimental data of the Particle Data Group, which allows us to identify hybrid candidates among the observed XYZ states. We provide hybrid or quarkonium interpretations for nearly all heavy isospin-zero mesons observed and incorporate new hybrid candidates.