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The majority of the baryonic matter in the universe is in the form of astrophysical plasmas. The mass of the hot X-ray emitting gas in a cluster of galaxies has more mass than the galaxies in the cluster. With the launch of the XRISM microcalorimeter mission, space-based X-ray observations will achieve a record spectral resolving power of $R\equiv E/\Delta E \sim 1200$. With this resolving power, emission features associated with fine-structure energy levels of some species will be resolved, sometimes for the first time. The plasma code, CLOUDY, was not originally designed for high-resolution X-ray spectroscopy and throughout its history did not resolve fine-structure components of Lyman lines. Here we expand CLOUDY to resolve these fine-structure energy levels and obtain predicted X-ray spectra that match the resolution of new microcalorimeter observations. We show how the Lyman lines can be used as column density indicators and examine their sensitivity to external radiation fields and turbulence., Comment: 14 pages, 11 figures

We present a simple, yet powerful column density diagnostic for plasmas enabled by X-ray microcalorimeter observations. With the recent developments of the spectral simulation code Cloudy, inspired by the high spectral resolution of XRISM and Athena, we make predictions for the intensity ratio of the resolved fine-structure lines Ly$\alpha_1$ and Ly$\alpha_2$ of H-like ions. We show that this ratio can be observationally constrained and used as a plasma column density indicator. We demonstrate this with a XRISM observation of the high-mass X-ray binary Centaurus X-3. This diagnostic is useful for a wide range of X-ray emitting plasmas either collisionally or radiatively ionized., Comment: 3 pages, 4 figures

Detections of fast X-ray transients (FXTs) have been accrued over the last few decades. However, their origin has remained mysterious. There is now rapid progress thanks to timely discoveries and localisations with the Einstein Probe mission. Early results indicate that FXTs may frequently, but not always, be associated with gamma-ray bursts (GRBs). Here, we report on the multi-wavelength counterpart of FXT EP240414a, which has no reported gamma-ray counterpart. The transient is located 25.7~kpc in projection from a massive galaxy at $z=0.40$. We perform comprehensive photometric and spectroscopic follow-up. The optical light curve shows at least three distinct emission episodes with timescales of $\sim 1, 4$ and 15 days and peak absolute magnitudes of $M_R \sim -20$, $-21$, and $-19.5$, respectively. The optical spectrum at early times is extremely blue, inconsistent with afterglow emission. It may arise from the interaction of both jet and supernova shock waves with the stellar envelope and a dense circumstellar medium, as has been suggested for some Fast Blue Optical Transients (LFBOTs). At late times, the spectrum evolves to a broad-lined~Type~Ic supernova, similar to those seen in collapsar long-GRBs. This implies that the progenitor of EP240414a is a massive star creating a jet-forming supernova inside a dense envelope, resulting in an X-ray outburst with a luminosity of $\sim 10^{48}$ erg s$^{-1}$, and the complex observed optical/IR light curves. If correct, this argues for a causal link between the progenitors of long-GRBs, FXTs and LFBOTs., Comment: 36 pages, 13 figures, submitted to ApJ

Optical spectra of the Very Late Thermal Pulse (VLTP) object V4334 Sgr have shown a rapidly changing spectrum resulting from shocks in the outflow, which created a new bipolar nebula inside the old nebula. We see C II and C III emission lines emerging typical of a [WC 11-10]-type star. The strong increase of [O III] and [S III] emission lines indicate the possible onset of photoionisation in the new ejecta., Comment: 2 pages, 3 figures, accepted for publication in the proceedings of IAU Symposium 384: Planetary Nebulae: a Universal Toolbox in the Era of Precision Astrophysics

Exposure bias is a well-known issue in recommender systems where items and suppliers are not equally represented in the recommendation results. This bias becomes particularly problematic over time as a few items are repeatedly over-represented in recommendation lists, leading to a feedback loop that further amplifies this bias. Although extensive research has addressed this issue in model-based or neighborhood-based recommendation algorithms, less attention has been paid to online recommendation models, such as those based on top-K contextual bandits, where recommendation models are dynamically updated with ongoing user feedback. In this paper, we study exposure bias in a class of well-known contextual bandit algorithms known as Linear Cascading Bandits. We analyze these algorithms in their ability to handle exposure bias and provide a fair representation of items in the recommendation results. Our analysis reveals that these algorithms fail to mitigate exposure bias in the long run during the course of ongoing user interactions. We propose an Exposure-Aware reward model that updates the model parameters based on two factors: 1) implicit user feedback and 2) the position of the item in the recommendation list. The proposed model mitigates exposure bias by controlling the utility assigned to the items based on their exposure in the recommendation list. Our experiments with two real-world datasets show that our proposed reward model improves the exposure fairness of the linear cascading bandits over time while maintaining the recommendation accuracy. It also outperforms the current baselines. Finally, we prove a high probability upper regret bound for our proposed model, providing theoretical guarantees for its performance.

The very late thermal pulse (VLTP) affects the evolution of $\sim$20\% of 1--8\,$\mathrm M_\odot$ stars, repeating the last phases of the red giant within a few years and leading to the formation of a new, but hydrogen-poor nebula within the old planetary nebula (PN). The strong dust formation in the latter obscures the optical and near-infrared radiation of the star. We aimed to determine the reheating timescale of the central star in Sakurai's object, which is an important constraint for the poorly understood VLTP evolution. We observed the radio continuum emission of Sakurai's object for almost 20 years from 2004 to 2023. Continuous, multi-frequency observations proved to be essential to distinguish between phases dominated by photoionization and shock ionization. The flux density fluctuates by more than a factor 40 within months to years. The spectral index remained negative between 2006 and 2017 and is close to zero since 2019. The emission region is barely resolved since 2021. Non-thermal radio emission observed from 2004 to 2017 traces shocks induced by wind interactions due to discrete mass-loss events. Thermal emission dominates during the period 2019--2023 and may indicate photoionization of the nebula by the central star., Comment: 6 pages, 3 figures, 2 tables, Astronomy & Astrophysics, accepted after minor revision

Two typical forms of bias in user interaction data with recommender systems (RSs) are popularity bias and positivity bias, which manifest themselves as the over-representation of interactions with popular items or items that users prefer, respectively. Debiasing methods aim to mitigate the effect of selection bias on the evaluation and optimization of RSs. However, existing debiasing methods only consider single-factor forms of bias, e.g., only the item (popularity) or only the rating value (positivity). This is in stark contrast with the real world where user selections are generally affected by multiple factors at once. In this work, we consider multifactorial selection bias in RSs. Our focus is on selection bias affected by both item and rating value factors, which is a generalization and combination of popularity and positivity bias. While the concept of multifactorial bias is intuitive, it brings a severe practical challenge as it requires substantially more data for accurate bias estimation. As a solution, we propose smoothing and alternating gradient descent techniques to reduce variance and improve the robustness of its optimization. Our experimental results reveal that, with our proposed techniques, multifactorial bias corrections are more effective and robust than single-factor counterparts on real-world and synthetic datasets., Comment: SIGIR 2024

The nature of the minute-to-hour long Fast X-ray Transients (FXTs) localised by telescopes such as Chandra, Swift, and XMM-Newton remains mysterious, with numerous models suggested for the events. Here, we report multi-wavelength observations of EP240315a, a 1600 s long transient detected by the Einstein Probe, showing it to have a redshift of z=4.859. We measure a low column density of neutral hydrogen, indicating that the event is embedded in a low-density environment, further supported by direct detection of leaking ionising Lyman-continuum. The observed properties are consistent with EP240315a being a long-duration gamma-ray burst, and these observations support an interpretation in which a significant fraction of the FXT population are lower-luminosity examples of similar events. Such transients are detectable at high redshifts by the Einstein Probe and, in the (near) future, out to even larger distances by SVOM, THESEUS, and Athena, providing samples of events into the epoch of reionisation., Comment: 41 pages, 7 figures, submitted

Conventional reinforcement learning (RL) methods can successfully solve a wide range of sequential decision problems. However, learning policies that can generalize predictably across multiple tasks in a setting with non-Markovian reward specifications is a challenging problem. We propose to use successor features to learn a policy basis so that each (sub)policy in it solves a well-defined subproblem. In a task described by a finite state automaton (FSA) that involves the same set of subproblems, the combination of these (sub)policies can then be used to generate an optimal solution without additional learning. In contrast to other methods that combine (sub)policies via planning, our method asymptotically attains global optimality, even in stochastic environments.

We announce the C23.01 update of Cloudy. This corrects a simple coding error, present since $\sim$ 1990, in one routine that required a conversion from the line-center to the mean normalization of the Ly$\alpha$ optical depth. This affects the destruction of H I Ly$\alpha$ by background opacities. Its largest effect is upon the Ly$\alpha$ intensity in high-ionization dusty clouds, where the predicted intensity is now up to three times stronger. Other properties that depend on Ly$\alpha$ destruction, such as grain infrared emission, change in response., Comment: 4 pages, 1 figure

Over the past decades, libraries of stellar spectra have been used in a large variety of science cases, including as sources of reference spectra for a given object or a given spectral type. Despite the existence of large libraries and the increasing number of projects of large-scale spectral surveys, there is to date only one very high-resolution spectral library offering spectra from a few hundred objects from the southern hemisphere (UVES-POP) . We aim to extend the sample, offering a finer coverage of effective temperatures and surface gravity with a uniform collection of spectra obtained in the northern hemisphere. Between 2010 and 2020, we acquired several thousand echelle spectra of bright stars with the Mercator-HERMES spectrograph located in the Roque de Los Muchachos Observatory in La Palma, whose pipeline offers high-quality data reduction products. We have also developed methods to correct for the instrumental response in order to approach the true shape of the spectral continuum. Additionally, we have devised a normalisation process to provide a homogeneous normalisation of the full spectral range for most of the objects. We present a new spectral library consisting of 3256 spectra covering 2043 stars. It combines high signal-to-noise and high spectral resolution over the entire range of effective temperatures and luminosity classes. The spectra are presented in four versions: raw, corrected from the instrumental response, with and without correction from the atmospheric molecular absorption, and normalised (including the telluric correction)., Comment: 17 pages, 18 figures Preview and access to the library: https://www.royer.se/melchiors.html

Learning in high-dimensional action spaces is a key challenge in applying reinforcement learning (RL) to real-world systems. In this paper, we study the possibility of controlling power networks using RL methods. Power networks are critical infrastructures that are complex to control. In particular, the combinatorial nature of the action space poses a challenge to both conventional optimizers and learned controllers. Hierarchical reinforcement learning (HRL) represents one approach to address this challenge. More precisely, a HRL framework for power network topology control is proposed. The HRL framework consists of three levels of action abstraction. At the highest level, there is the overall long-term task of power network operation, namely, keeping the power grid state within security constraints at all times, which is decomposed into two temporally extended actions: 'do nothing' versus 'propose a topology change'. At the intermediate level, the action space consists of all controllable substations. Finally, at the lowest level, the action space consists of all configurations of the chosen substation. By employing this HRL framework, several hierarchical power network agents are trained for the IEEE 14-bus network. Whereas at the highest level a purely rule-based policy is still chosen for all agents in this study, at the intermediate level the policy is trained using different state-of-the-art RL algorithms. At the lowest level, either an RL algorithm or a greedy algorithm is used. The performance of the different 3-level agents is compared with standard baseline (RL or greedy) approaches. A key finding is that the 3-level agent that employs RL both at the intermediate and the lowest level outperforms all other agents on the most difficult task. Our code is publicly available.

Pool-based active learning (AL) is a promising technology for increasing data-efficiency of machine learning models. However, surveys show that performance of recent AL methods is very sensitive to the choice of dataset and training setting, making them unsuitable for general application. In order to tackle this problem, the field Learning Active Learning (LAL) suggests to learn the active learning strategy itself, allowing it to adapt to the given setting. In this work, we propose a novel LAL method for classification that exploits symmetry and independence properties of the active learning problem with an Attentive Conditional Neural Process model. Our approach is based on learning from a myopic oracle, which gives our model the ability to adapt to non-standard objectives, such as those that do not equally weight the error on all data points. We experimentally verify that our Neural Process model outperforms a variety of baselines in these settings. Finally, our experiments show that our model exhibits a tendency towards improved stability to changing datasets. However, performance is sensitive to choice of classifier and more work is necessary to reduce the performance the gap with the myopic oracle and to improve scalability. We present our work as a proof-of-concept for LAL on nonstandard objectives and hope our analysis and modelling considerations inspire future LAL work., Comment: Accepted at ECML 2023

We present JWST images of the well-known planetary nebula NGC 6720 (the Ring Nebula), covering wavelengths from 1.6$\mu$m to 25 $\mu$m. The bright shell is strongly fragmented with some 20 000 dense globules, bright in H$_2$, with a characteristic diameter of 0.2 arcsec and density $n_{\rm H} \sim 10^5$-$10^6$ cm$^{-3}$. The shell contains a thin ring of polycyclic aromatic hydrocarbon (PAH) emission. H$_2$ is found throughout the shell and in the halo. H$_2$ in the halo may be located on the swept-up walls of a biconal polar flow. The central cavity is shown to be filled with high ionization gas and shows two linear structures. The central star is located 2 arcsec from the emission centroid of the cavity and shell. Linear features (`spikes') extend outward from the ring, pointing away from the central star. Hydrodynamical simulations are shown which reproduce the clumping and possibly the spikes. Around ten low-contrast, regularly spaced concentric arc-like features are present; they suggest orbital modulation by a low-mass companion with a period of about 280 yr. A previously known much wider companion is located at a projected separation of about 15 000 au; we show that it is an M2-M4 dwarf. The system is therefore a triple star. These features, including the multiplicity, are similar to those seen in the Southern Ring Nebula (NGC 3132) and may be a common aspect of such nebulae., Comment: 25 pages, 23 figures. Submitted to Monthly Notices of the Royal Astronomical Society. Corrected typos in metadata

We present high angular-resolution observations of Sakurai's object using the Atacama Large Millimeter Array, shedding new light on its morpho-kinematical structure. The millimetre continuum emission, observed at an angular resolution of 20 milliarcsec (corresponding to 70 AU), reveals a bright compact central component whose spectral index indicates that it composed of amorphous carbon dust. Based on these findings, we conclude that this emission traces the previously suggested dust disc observed in mid-infrared observations. Therefore, our observations provide the first direct imaging of such a disc. The H$^{12}$CN($J$=4$\rightarrow$3) line emission, observed at an angular resolution of 300 milliarcsec (corresponding to 1000 AU), displays bipolar structure with a north-south velocity gradient. From the position-velocity diagram of this emission we identify the presence of an expanding disc and a bipolar molecular outflow. The inclination of the disc is determined to be $i$=72$^\circ$. The derived values for the de-projected expansion velocity and the radius of the disc are $v_{\rm exp}$=53 km s$^{-1}$ and $R$=277 AU, respectively. On the other hand, the de-projected expansion velocity of the bipolar outflow detected in the H$^{12}$CN($J$=4$\rightarrow$3) emission of approximately 1000 km s$^{-1}$. We propose that the molecular outflow has an hourglass morphology with an opening angle of around 60$^{\circ}$. Our observations unambiguously show that an equatorial disc and bipolar outflows formed in Sakurai's object in less than 30 years after the born-again event occurred, providing important constraints for future modelling efforts of this phenomenon., Comment: 9 pages, 5 figures. Accepted for publication as a Letter in Astronomy and Astrophysics

Active Inference is a recent framework for modeling planning under uncertainty. Empirical and theoretical work have now begun to evaluate the strengths and weaknesses of this approach and how it might be improved. A recent extension - the sophisticated inference (SI) algorithm - improves performance on multi-step planning problems through recursive decision tree search. However, little work to date has been done to compare SI to other established planning algorithms. SI was also developed with a focus on inference as opposed to learning. The present paper has two aims. First, we compare performance of SI to Bayesian reinforcement learning (RL) schemes designed to solve similar problems. Second, we present an extension of SI - sophisticated learning (SL) - that more fully incorporates active learning during planning. SL maintains beliefs about how model parameters would change under the future observations expected under each policy. This allows a form of counterfactual retrospective inference in which the agent considers what could be learned from current or past observations given different future observations. To accomplish these aims, we make use of a novel, biologically inspired environment designed to highlight the problem structure for which SL offers a unique solution. Here, an agent must continually search for available (but changing) resources in the presence of competing affordances for information gain. Our simulations show that SL outperforms all other algorithms in this context - most notably, Bayes-adaptive RL and upper confidence bound algorithms, which aim to solve multi-step planning problems using similar principles (i.e., directed exploration and counterfactual reasoning). These results provide added support for the utility of Active Inference in solving this class of biologically-relevant problems and offer added tools for testing hypotheses about human cognition., Comment: 31 pages, 5 figures

We describe the 2023 release of the spectral synthesis code Cloudy. Since the previous major release, migrations of our online services motivated us to adopt git as our version control system. This change alone led us to adopt an annual release scheme, accompanied by a short release paper, the present being the inaugural. Significant changes to our atomic and molecular data have improved the accuracy of Cloudy predictions: we have upgraded our instance of the Chianti database from version 7 to 10; our H- and He-like collisional rates to improved theoretical values; our molecular data to the most recent LAMDA database, and several chemical reaction rates to their most recent UDfA and KiDA values. Finally, we describe our progress on upgrading Cloudy's capabilities to meet the requirements of the X-ray microcalorimeters aboard the upcoming XRISM and Athena missions, and outline future development that will make Cloudy of use to the X-ray community., Comment: 18 pages, 10 figures, accepted for publication in RMxAA

In multi-agent problems requiring a high degree of cooperation, success often depends on the ability of the agents to adapt to each other's behavior. A natural solution concept in such settings is the Stackelberg equilibrium, in which the ``leader'' agent selects the strategy that maximizes its own payoff given that the ``follower'' agent will choose their best response to this strategy. Recent work has extended this solution concept to two-player differentiable games, such as those arising from multi-agent deep reinforcement learning, in the form of the \textit{differential} Stackelberg equilibrium. While this previous work has presented learning dynamics which converge to such equilibria, these dynamics are ``coupled'' in the sense that the learning updates for the leader's strategy require some information about the follower's payoff function. As such, these methods cannot be applied to truly decentralised multi-agent settings, particularly ad hoc cooperation, where each agent only has access to its own payoff function. In this work we present ``uncoupled'' learning dynamics based on zeroth-order gradient estimators, in which each agent's strategy update depends only on their observations of the other's behavior. We analyze the convergence of these dynamics in general-sum games, and prove that they converge to differential Stackelberg equilibria under the same conditions as previous coupled methods. Furthermore, we present an online mechanism by which symmetric learners can negotiate leader-follower roles. We conclude with a discussion of the implications of our work for multi-agent reinforcement learning and ad hoc collaboration more generally., Comment: International Conference on Autonomous Agents and Multi-Agent Systems (AAMAS) 2024

Hierarchical methods in reinforcement learning have the potential to reduce the amount of decisions that the agent needs to perform when learning new tasks. However, finding reusable useful temporal abstractions that facilitate fast learning remains a challenging problem. Recently, several deep learning approaches were proposed to learn such temporal abstractions in the form of options in an end-to-end manner. In this work, we point out several shortcomings of these methods and discuss their potential negative consequences. Subsequently, we formulate the desiderata for reusable options and use these to frame the problem of learning options as a gradient-based meta-learning problem. This allows us to formulate an objective that explicitly incentivizes options which allow a higher-level decision maker to adjust in few steps to different tasks. Experimentally, we show that our method is able to learn transferable components which accelerate learning and performs better than existing prior methods developed for this setting. Additionally, we perform ablations to quantify the impact of using gradient-based meta-learning as well as other proposed changes., Comment: Published in Transactions on Machine Learning Research (TMLR)

After becoming ionized, low-density astrophysical plasmas will begin a process of slow recombination. Models for this still have significant uncertainties. The recombination cannot normally be observed in isolation, because the ionization follows the evolutionary time scale of the ionizing source. Laboratory experiments are unable to reach the appropriate conditions because of the required very long time scales. The extended nebula around the very late helium flash (VLTP) star V4334 Sgr provides a unique laboratory for this kind of study. The sudden loss of the ionizing UV radiation after the VLTP event has allowed the nebula to recombine free from other influences. More than 290 long slit spectra taken with FORS1/2 at the ESO VLT between 2007 and 2022 are used to follow the time evolution of lines of H, He, N, S, O, Ar. Hydrogen and helium lines, representing most of the ionized mass, do not show significant changes. A small increase is seen in [N II] (+2.8 %/yr; significance 2.7 sigma), while we see a decrease in [O III] (-1.96 %/yr; 2.0 sigma). The [S II] lines show a change of +3.0 %/yr; 1.6 sigma). The lines of [S III] and of Ar III] show no significant change. For [S III], the measurement differs from the predicted decrease by 4.5 sigma. A possible explanation is that the fraction of [S IV] and higher is larger than expected. Such an effect could provide a potential solution for the sulfur anomaly in planetary nebulae., Comment: 13 pages, 8 figures, 3 tables; Accepted for Publication in ApJ

Exposure bias is a well-known issue in recommender systems where items and suppliers are not equally represented in the recommendation results. This is especially problematic when bias is amplified over time as a few items (e.g., popular ones) are repeatedly over-represented in recommendation lists and users' interactions with those items will amplify bias towards those items over time resulting in a feedback loop. This issue has been extensively studied in the literature on model-based or neighborhood-based recommendation algorithms, but less work has been done on online recommendation models, such as those based on top-K contextual bandits, where recommendation models are dynamically updated with ongoing user feedback. In this paper, we study exposure bias in a class of well-known contextual bandit algorithms known as Linear Cascading Bandits. We analyze these algorithms on their ability to handle exposure bias and provide a fair representation for items in the recommendation results. Our analysis reveals that these algorithms tend to amplify exposure disparity among items over time. In particular, we observe that these algorithms do not properly adapt to the feedback provided by the users and frequently recommend certain items even when those items are not selected by users. To mitigate this bias, we propose an Exposure-Aware (EA) reward model that updates the model parameters based on two factors: 1) user feedback (i.e., clicked or not), and 2) position of the item in the recommendation list. This way, the proposed model controls the utility assigned to items based on their exposure in the recommendation list. Extensive experiments on two real-world datasets using three contextual bandit algorithms show that the proposed reward model reduces exposure bias amplification in long run while maintaining the recommendation accuracy.

In reinforcement learning, different reward functions can be equivalent in terms of the optimal policies they induce. A particularly well-known and important example is potential shaping, a class of functions that can be added to any reward function without changing the optimal policy set under arbitrary transition dynamics. Potential shaping is conceptually similar to potentials, conservative vector fields and gauge transformations in math and physics, but this connection has not previously been formally explored. We develop a formalism for discrete calculus on graphs that abstract a Markov Decision Process, and show how potential shaping can be formally interpreted as a gradient within this framework. This allows us to strengthen results from Ng et al. (1999) describing conditions under which potential shaping is the only additive reward transformation to always preserve optimal policies. As an additional application of our formalism, we define a rule for picking a single unique reward function from each potential shaping equivalence class., Comment: Fixed mistake in proof that affected several results

Recent works on machine learning for combinatorial optimization have shown that learning based approaches can outperform heuristic methods in terms of speed and performance. In this paper, we consider the problem of finding an optimal topological order on a directed acyclic graph with focus on the memory minimization problem which arises in compilers. We propose an end-to-end machine learning based approach for topological ordering using an encoder-decoder framework. Our encoder is a novel attention based graph neural network architecture called \emph{Topoformer} which uses different topological transforms of a DAG for message passing. The node embeddings produced by the encoder are converted into node priorities which are used by the decoder to generate a probability distribution over topological orders. We train our model on a dataset of synthetically generated graphs called layered graphs. We show that our model outperforms, or is on-par, with several topological ordering baselines while being significantly faster on synthetic graphs with up to 2k nodes. We also train and test our model on a set of real-world computation graphs, showing performance improvements., Comment: To appear in NeurIPS 2022

Hex is a turn-based two-player connection game with a high branching factor, making the game arbitrarily complex with increasing board sizes. As such, top-performing algorithms for playing Hex rely on accurate evaluation of board positions using neural networks. However, the limited interpretability of neural networks is problematic when the user wants to understand the reasoning behind the predictions made. In this paper, we propose to use propositional logic expressions to describe winning and losing board game positions, facilitating precise visual interpretation. We employ a Tsetlin Machine (TM) to learn these expressions from previously played games, describing where pieces must be located or not located for a board position to be strong. Extensive experiments on $6\times6$ boards compare our TM-based solution with popular machine learning algorithms like XGBoost, InterpretML, decision trees, and neural networks, considering various board configurations with $2$ to $22$ moves played. On average, the TM testing accuracy is $92.1\%$, outperforming all the other evaluated algorithms. We further demonstrate the global interpretation of the logical expressions and map them down to particular board game configurations to investigate local interpretability. We believe the resulting interpretability establishes building blocks for accurate assistive AI and human-AI collaboration, also for more complex prediction tasks.