Prompts for pre-trained language models (PLMs) have shown remarkable performance by bridging the gap between pre-training tasks and various downstream tasks. Among these methods, prompt tuning, which freezes PLMs and only tunes soft prompts, provides
an efficient and effective solution for adapting large-scale PLMs to downstream tasks. However, prompt tuning is yet to be fully explored. In our pilot experiments, we find that prompt tuning performs comparably with conventional full-model fine-tuning when downstream data are sufficient, whereas it performs much worse under few-shot learning settings, which may hinder the application of prompt tuning in practice. We attribute this low performance to the manner of initializing soft prompts. Therefore, in this work, we propose to pre-train prompts by adding soft prompts into the pre-training stage to obtain a better initialization. We name this Pre-trained Prompt Tuning framework PPT. To ensure the generalization of PPT, we formulate similar classification tasks into a unified task form and pre-train soft prompts for this unified task. Extensive experiments show that tuning pre-trained prompts for downstream tasks can reach or even outperform full-model fine-tuning under both full-data and few-shot settings. Our approach is effective and efficient for using large-scale PLMs in practice.
This paper considers joint analysis of multiple functionally related structures in classification tasks. In particular, our method developed is driven by how functionally correlated brain structures vary together between autism and control groups. To
do so, we devised a method based on a novel combination of (1) non-Euclidean statistics that can faithfully represent non-Euclidean data in Euclidean spaces and (2) a non-parametric integrative analysis method that can decompose multi-block Euclidean data into joint, individual, and residual structures. We find that the resulting joint structure is effective, robust, and interpretable in recognizing the underlying patterns of the joint variation of multi-block non-Euclidean data. We verified the method in classifying the structural shape data collected from cases that developed and did not develop into Autistic Spectrum Disorder (ASD).
In this paper, we study the asymptotic estimate of solution for a mixed-order time-fractional diffusion equation in a bounded domain subject to the homogeneous Dirichlet boundary condition. Firstly, the unique existence and regularity estimates of so
lution to the initial-boundary value problem are considered. Then combined with some important properties, including a maximum principle for a time-fractional ordinary equation and a coercivity inequality for fractional derivatives, the energy method shows that the decay in time of the solution is dominated by the term $t^{-alpha}$ as $ttoinfty$.
Few-shot object detection, which aims at detecting novel objects rapidly from extremely few annotated examples of previously unseen classes, has attracted significant research interest in the community. Most existing approaches employ the Faster R-CN
N as basic detection framework, yet, due to the lack of tailored considerations for data-scarce scenario, their performance is often not satisfactory. In this paper, we look closely into the conventional Faster R-CNN and analyze its contradictions from two orthogonal perspectives, namely multi-stage (RPN vs. RCNN) and multi-task (classification vs. localization). To resolve these issues, we propose a simple yet effective architecture, named Decoupled Faster R-CNN (DeFRCN). To be concrete, we extend Faster R-CNN by introducing Gradient Decoupled Layer for multi-stage decoupling and Prototypical Calibration Block for multi-task decoupling. The former is a novel deep layer with redefining the feature-forward operation and gradient-backward operation for decoupling its subsequent layer and preceding layer, and the latter is an offline prototype-based classification model with taking the proposals from detector as input and boosting the original classification scores with additional pairwise scores for calibration. Extensive experiments on multiple benchmarks show our framework is remarkably superior to other existing approaches and establishes a new state-of-the-art in few-shot literature.
In this paper, we study the twisted Fourier-Mukai partners of abelian surfaces. Following the work of Huybrechts [doi:10.4171/CMH/465], we introduce the twisted derived equivalence between abelian surfaces. We show that there is a twisted derived Tor
elli theorem for abelian surfaces over fields with characteristic $ eq 2$. Over complex numbers, twisted derived equivalence corresponds to rational Hodge isometries between the second cohomology groups, which is in analogy to the work of Huybrechts and Fu-Vial on K3 surfaces. Their proof relies on the global Torelli theorem over $mathbb{C}$, which is missing in positive characteristics. To overcome this issue, we extend Shiodas trick on singular cohomology groups to etale and crystalline cohomology groups and make use of Tates isogeny theorem to give a characterization of twisted derived equivalence on abelian surfaces via using so called principal quasi-isogeny.
The recent advances in the study of thermodynamics of microscopic processes have driven the search for new developments in energy converters utilizing quantum effects. We here propose a universal framework to describe the thermodynamics of a quantum
engine fueled by quantum projective measurements. Standard quantum thermal machines operating in a finite-time regime with a driven Hamiltonian that does not commute in different times have the performance decreased by the presence of coherence, which is associated with a larger entropy production and irreversibility degree. However, we show that replacing the standard hot thermal reservoir by a projective measurement operation with general basis in the Bloch sphere and controlling the basis angles suitably could improve the performance of the quantum engine as well as decrease the entropy change during the measurement process. Our results go in direction of a generalization of quantum thermal machine models where the fuel comes from general sources beyond the standard thermal reservoir.
The electrification revolution in automobile industry and others demands annual production capacity of batteries at least on the order of 102 gigawatts hours, which presents a twofold challenge to supply of key materials such as cobalt and nickel and
to recycling when the batteries retire. Pyrometallurgical and hydrometallurgical recycling are currently used in industry but suffer from complexity, high costs, and secondary pollution. Here we report a direct-recycling method in molten salts (MSDR) that is environmentally benign and value-creating based on a techno-economic analysis using real-world data and price information. We also experimentally demonstrate the feasibility of MSDR by upcycling a low-nickel polycrystalline LiNi0.5Mn0.3Co0.2O2 (NMC) cathode material that is widely used in early-year electric vehicles into Ni-rich (Ni > 65%) single-crystal NMCs with increased energy-density (>10% increase) and outstanding electrochemical performance (>94% capacity retention after 500 cycles in pouch-type full cells). This work opens up new opportunities for closed-loop recycling of electric vehicle batteries and manufacturing of next-generation NMC cathode materials.
Over complex numbers, the Fourier-Mukai partners of abelian varieties are well-understood. A celebrated result is Orlovs derived Torelli theorem. In this note, we study the FM-partners of abelian varieties in positive characteristic. We notice that,
in odd characteristics, two abelian varieties of odd dimension are derived equivalent if their associated Kummer stacks are derived equivalent, which is Krug and Sosnas result over complex numbers. For abelian surfaces in odd characteristic, we show that two abelian surfaces are derived equivalent if and only if their associated Kummer surfaces are isomorphic. This extends the result [doi:10.1215/s0012-7094-03-12036-0] to odd characteristic fields, which solved a classical problem originally from Shioda. Furthermore, we establish the derived Torelli theorem for supersingular abelian varieties and apply it to characterize the quasi-liftable birational models of supersingular generalized Kummer varieties.
We present a systematic study of the diffuse hot gas around early-type galaxies (ETGs) residing in the Virgo cluster, based on archival {it Chandra} observations. Our representative sample consists of 79 galaxies with low-to-intermediate stellar mass
es ($M_* approx 10^{9-11}rm~M_odot$), a mass range that has not been extensively explored with X-ray observations thus far. We detect diffuse X-ray emission in only eight galaxies and find that in five cases a substantial fraction of the detected emission can be unambiguously attributed to truly diffuse hot gas, based on their spatial distribution and spectral properties. For the individually non-detected galaxies, we constrain their average X-ray emission by performing a stacking analysis, finding a specific X-ray luminosity of $L_{rm X}/M_* sim 10^{28}{rm~erg~s^{-1}~M_{odot}^{-1}}$, which is consistent with unresolved stellar populations. The apparent paucity of truly diffuse hot gas in these low- and intermediate-mass ETGs may be the result of efficient ram pressure stripping by the hot intra-cluster medium. However, we also find no significant diffuse hot gas in a comparison sample of 57 field ETGs of similar stellar masses, for which archival {it Chandra} observations with similar sensitivity are available. This points to the alternative possibility that galactic winds evacuate the hot gas from the inner region of low- and intermediate-mass ETGs, regardless of the galactic environment. Nevertheless, we do find strong morphological evidence for on-going ram pressure stripping in two galaxies (NGC 4417 and NGC 4459). A better understanding of the roles of ram pressure stripping and galactic winds in regulating the hot gas content of ETGs, invites sensitive X-ray observations for a large galaxy sample.
In settings ranging from weather forecasts to political prognostications to financial projections, probability estimates of future binary outcomes often evolve over time. For example, the estimated likelihood of rain on a specific day changes by the
hour as new information becomes available. Given a collection of such probability paths, we introduce a Bayesian framework -- which we call the Gaussian latent information martingale, or GLIM -- for modeling the structure of dynamic predictions over time. Suppose, for example, that the likelihood of rain in a week is 50%, and consider two hypothetical scenarios. In the first, one expects the forecast is equally likely to become either 25% or 75% tomorrow; in the second, one expects the forecast to stay constant for the next several days. A time-sensitive decision-maker might select a course of action immediately in the latter scenario, but may postpone their decision in the former, knowing that new information is imminent. We model these trajectories by assuming predictions update according to a latent process of information flow, which is inferred from historical data. In contrast to general methods for time series analysis, this approach preserves the martingale structure of probability paths and better quantifies future uncertainties around probability paths. We show that GLIM outperforms three popular baseline methods, producing better estimated posterior probability path distributions measured by three different metrics. By elucidating the dynamic structure of predictions over time, we hope to help individuals make more informed choices.
