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This paper presents Dolphin, a novel decoder-decoder architecture for energy-efficient processing of long contexts in language models. Our approach addresses the significant energy consumption and latency challenges inherent in on-device models. Dolphin employs a compact 0.5B parameter decoder to distill extensive contextual information into a memory embedding, substantially reducing the input length for the primary 7B parameter decoder model. Inspired by vision-language models, we repurpose the image embedding projector to encode long textual contexts, effectively treating extended context as a distinct modality. This innovative method enables processing of substantially longer contexts without the typical computational overhead associated with extended input sequences. Empirical evaluations demonstrate a 10-fold improvement in energy efficiency and a 5-fold reduction in latency compared to conventional full-length context processing methods without losing quality of the response. Our work contributes to the development of more sustainable and scalable language models for on-device applications, addressing the critical need for energy-efficient and responsive AI technologies in resource-constrained environments while maintaining the accuracy to understand long contexts. This research has implications for the broader field of natural language processing, particularly in the domain of efficient model design for resource-limited settings. By enabling more sophisticated AI capabilities on edge devices, Dolphin paves the way for advanced language processing in a wide range of applications where computational resources are at a premium. The Dolphin model is publicly available at https://huggingface.co/NexaAIDev/Dolphin.

Curating, processing, and combining large-scale medical imaging datasets from national studies is a non-trivial task due to the intense computation and data throughput required, variability of acquired data, and associated financial overhead. Existing platforms or tools for large-scale data curation, processing, and storage have difficulty achieving a viable cost-to-scale ratio of computation speed for research purposes, either being too slow or too expensive. Additionally, management and consistency of processing large data in a team-driven manner is a non-trivial task. We design a BIDS-compliant method for an efficient and robust data processing pipeline of large-scale diffusion-weighted and T1-weighted MRI data compatible with low-cost, high-efficiency computing systems. Our method accomplishes automated querying of data available for processing and process running in a consistent and reproducible manner that has long-term stability, while using heterogenous low-cost computational resources and storage systems for efficient processing and data transfer. We demonstrate how our organizational structure permits efficiency in a semi-automated data processing pipeline and show how our method is comparable in processing time to cloud-based computation while being almost 20 times more cost-effective. Our design allows for fast data throughput speeds and low latency to reduce the time for data transfer between storage servers and computation servers, achieving an average of 0.60 Gb/s compared to 0.33 Gb/s for using cloud-based processing methods. The design of our workflow engine permits quick process running while maintaining flexibility to adapt to newly acquired data.

Large Language Models (LLMs) have showcased exceptional ability in causal reasoning from textual information. However, will these causalities remain straightforward for Vision Large Language Models (VLLMs) when only visual hints are provided? Motivated by this, we propose a novel Multimodal Causal Reasoning benchmark, namely MuCR, to challenge VLLMs to infer semantic cause-and-effect relationship when solely relying on visual cues such as action, appearance, clothing, and environment. Specifically, we introduce a prompt-driven image synthesis approach to create siamese images with embedded semantic causality and visual cues, which can effectively evaluate VLLMs' causal reasoning capabilities. Additionally, we develop tailored metrics from multiple perspectives, including image-level match, phrase-level understanding, and sentence-level explanation, to comprehensively assess VLLMs' comprehension abilities. Our extensive experiments reveal that the current state-of-the-art VLLMs are not as skilled at multimodal causal reasoning as we might have hoped. Furthermore, we perform a comprehensive analysis to understand these models' shortcomings from different views and suggest directions for future research. We hope MuCR can serve as a valuable resource and foundational benchmark in multimodal causal reasoning research. The project is available at: https://github.com/Zhiyuan-Li-John/MuCR, Comment: 20 pages

New particles beyond the Standard Model of particle physics, such as axions, can be effectively searched through their interactions with electrons. We use the large liquid xenon detector PandaX-4T to search for novel electronic recoil signals induced by solar axions, neutrinos with anomalous magnetic moment, axion-like particles, dark photons, and light fermionic dark matter. A detailed background model is established with the latest datasets with 1.54 $\rm tonne \cdot year$ exposure. No significant excess above the background has been observed, and we have obtained competitive constraints for axion couplings, neutrino magnetic moment, and fermionic dark matter interactions.

In this letter, we report the dark matter search results from the commissioning run and the first science run of the PandaX-4T experiment. A blind analysis is carried out on the entire data set. The data processing is improved compared to previous work, unifying the low-level signal reconstruction in a wide energy range up to 120 keV. With a total exposure of 1.54 tonne$\cdot$year, no significant excess of nuclear recoil events is found. The lowest 90% confidence level exclusion on the spin-independent cross section is $1.6 \times 10^{-47} \mathrm{cm}^2$ at a dark matter mass of 40 GeV$/c^2$. Our results represent the most stringent constraint for a dark matter mass above 100 GeV$/c^2$.

We present a theoretical explanation of the ``grokking'' phenomenon, where a model generalizes long after overfitting,for the originally-studied problem of modular addition. First, we show that early in gradient descent, when the ``kernel regime'' approximately holds, no permutation-equivariant model can achieve small population error on modular addition unless it sees at least a constant fraction of all possible data points. Eventually, however, models escape the kernel regime. We show that two-layer quadratic networks that achieve zero training loss with bounded $\ell_{\infty}$ norm generalize well with substantially fewer training points, and further show such networks exist and can be found by gradient descent with small $\ell_{\infty}$ regularization. We further provide empirical evidence that these networks as well as simple Transformers, leave the kernel regime only after initially overfitting. Taken together, our results strongly support the case for grokking as a consequence of the transition from kernel-like behavior to limiting behavior of gradient descent on deep networks., Comment: Accepted by ICML 2024

The PandaX-4T liquid xenon detector at the China Jinping Underground Laboratory is used to measure the solar $^8$B neutrino flux by detecting neutrinos through coherent scattering with xenon nuclei. Data samples requiring the coincidence of scintillation and ionization signals (paired), as well as unpaired ionization-only signals (US2), are selected with energy threshold of approximately 1.1 keV (0.33 keV) nuclear recoil energy. Combining the commissioning run and the first science run of PandaX-4T, a total exposure of 1.25 and 1.04 tonne$\cdot$year are collected for the paired and US2, respectively. After unblinding, 3 and 332 events are observed with an expectation of 2.8$\pm$0.5 and 251$\pm$32 background events, for the paired and US2 data, respectively. A combined analysis yields a best-fit $^8$B neutrino signal of 3.5 (75) events from the paired (US2) data sample, with $\sim$37\% uncertainty, and the background-only hypothesis is disfavored at 2.64$\sigma$ significance. This gives a solar $^8$B neutrino flux of ($8.4\pm3.1$)$\times$10$^6$ cm$^{-2}$s$^{-1}$, consistent with the standard solar model prediction. This is the first indication of solar $^8$B neutrino ``fog'' in a dark matter direct detection experiment.

AI agents have become increasingly significant in various domains, enabling autonomous decision-making and problem-solving. To function effectively, these agents require a planning process that determines the best course of action and then executes the planned actions. In this paper, we present an efficient on-device Planner-Action framework that separates planning and action execution into two distinct components: a planner agent based on Phi-3 Mini, a 3.8 billion parameter LLM optimized for edge devices, and an action agent using the Octopus model for function execution. The planner agent first responds to user queries by decomposing tasks into a sequence of sub-steps, which are then executed by the action agent. To optimize performance on resource-constrained devices, we employ model fine-tuning instead of in-context learning, reducing computational costs and energy consumption while improving response times. Our approach involves using GPT-4 to generate diverse planning queries and responses based on available functions, with subsequent validations to ensure data quality. We fine-tune the Phi-3 Mini model on this curated dataset, achieving a 97\% success rate in our in-domain test environment. To address multi-domain planning challenges, we developed a multi-LoRA training method that merges weights from LoRAs trained on distinct function subsets. This approach enables flexible handling of complex, multi-domain queries while maintaining computational efficiency on resource-constrained devices. To support further research, we have open-sourced our model weights at \url{https://huggingface.co/NexaAIDev/octopus-planning}. For the demo, please refer to \url{https://www.nexa4ai.com/octo-planner}.

In NGC 2992, a galaxy-scale ionized gas outflow driven by AGN has long been recognized, yet its impact on the host galaxy has remained elusive. In this paper, we utilize data from the archival Very Large Telescope (VLT)/MUSE to present a spatially resolved analysis of stellar populations in this galaxy. Two different stellar population templates are employed to fit the stellar continuum, allowing us to determine the light-weighted stellar age, metallicity, the fraction of the young stellar population (age $<100$ Myr, $P_{\rm Y}$), and the average age and metallicity of $P_{\rm Y}$. Our results reveal the presence of a very young stellar population ($\leq40$ Myr) within the dust lane and nearly along the galaxy's major axis. The light-weighted stellar age and the fraction of $P_{\rm Y}$ show negative trends along the major and minor axes. The average age and metallicity of $P_{\rm Y}$ present positive trends with increasing distance, except along the northern direction of the major axis. Within the circumnuclear region ($<1$ kpc), the distribution of the young stellar population is spatially anti-correlated with the AGN outflow cone. The highest fraction of $P_{\rm Y}$ is observed at the outskirts of the nuclear radio bubble in the northern region near the nucleus. Considering the coupling efficiency and timescales, we propose that the AGN outflow in this galaxy may exert both negative and positive feedback on its host. Additionally, the star formation and the AGN activities could be attributed to the interaction between NGC 2992 and NGC 2993., Comment: 15 pages, 9 figures, accepted for publication in ApJ

The increase in academic dishonesty cases among college students has raised concern, particularly due to the shift towards online learning caused by the pandemic. We aim to develop and implement a method capable of generating tailored questions for each student. The use of Automatic Question Generation (AQG) is a possible solution. Previous studies have investigated AQG frameworks in education, which include validity, user-defined difficulty, and personalized problem generation. Our new AQG approach produces logical equivalence problems for Discrete Mathematics, which is a core course for year-one computer science students. This approach utilizes a syntactic grammar and a semantic attribute system through top-down parsing and syntax tree transformations. Our experiments show that the difficulty level of questions generated by our AQG approach is similar to the questions presented to students in the textbook [1]. These results confirm the practicality of our AQG approach for automated question generation in education, with the potential to significantly enhance learning experiences.

Purpose: In diffusion MRI (dMRI), the volumetric and bundle analyses of whole-brain tissue microstructure and connectivity can be severely impeded by an incomplete field-of-view (FOV). This work aims to develop a method for imputing the missing slices directly from existing dMRI scans with an incomplete FOV. We hypothesize that the imputed image with complete FOV can improve the whole-brain tractography for corrupted data with incomplete FOV. Therefore, our approach provides a desirable alternative to discarding the valuable dMRI data, enabling subsequent tractography analyses that would otherwise be challenging or unattainable with corrupted data. Approach: We propose a framework based on a deep generative model that estimates the absent brain regions in dMRI scans with incomplete FOV. The model is capable of learning both the diffusion characteristics in diffusion-weighted images (DWI) and the anatomical features evident in the corresponding structural images for efficiently imputing missing slices of DWI outside of incomplete FOV. Results: For evaluating the imputed slices, on the WRAP dataset the proposed framework achieved PSNRb0=22.397, SSIMb0=0.905, PSNRb1300=22.479, SSIMb1300=0.893; on the NACC dataset it achieved PSNRb0=21.304, SSIMb0=0.892, PSNRb1300=21.599, SSIMb1300= 0.877. The proposed framework improved the tractography accuracy, as demonstrated by an increased average Dice score for 72 tracts (p < 0.001) on both the WRAP and NACC datasets. Conclusions: Results suggest that the proposed framework achieved sufficient imputation performance in dMRI data with incomplete FOV for improving whole-brain tractography, thereby repairing the corrupted data. Our approach achieved more accurate whole-brain tractography results with extended and complete FOV and reduced the uncertainty when analyzing bundles associated with Alzheimer's Disease., Comment: 20 pages, 11 figures

Potentially Hazardous Asteroids (PHAs) are a special subset of Near-Earth Objects (NEOs) that can come close to the Earth and are large enough to cause significant damage in the event of an impact. Observations and researches of Earth-PHAs have been underway for decades. Here, we extend the concept of PHAs to Mars and study the feasibility of detecting Mars-PHAs in the near future. We focus on PHAs that truly undergo close approaches with a planet (dubbed CAPHAs) and aim to compare the actual quantities of Earth-CAPHAs and Mars-CAPHAs by conducting numerical simulations incorporating the Yarkovsky effect, based on observed data of the main asteroid belt. The estimated number of Earth-CAPHAs and Mars-CAPHAs are 4675 and 16910, respectively. The occurrence frequency of Mars-CAPHAs is about 52 per year, which is 2.6 times that of Earth-CAPHAs, indicating significant potential for future Mars-based observations. Furthermore, a few Mars-CAPHAs are predicted to be observable even from Earth around the time of next Mars opposition in 2025., Comment: 7 pages, 2 figures, accepted for publication in Monthly Notices of the Royal Astronomical Society Letters

Language models have been effective in a wide range of applications, yet the most sophisticated models are often proprietary. For example, GPT-4 by OpenAI and various models by Anthropic are expensive and consume substantial energy. In contrast, the open-source community has produced competitive models, like Llama3. Furthermore, niche-specific smaller language models, such as those tailored for legal, medical or financial tasks, have outperformed their proprietary counterparts. This paper introduces a novel approach that employs \textit{functional tokens} to integrate \textbf{multiple open-source models}, each optimized for particular tasks. Our newly developed Octopus v4 model leverages \textit{functional tokens} to intelligently direct user queries to the most appropriate vertical model and reformat the query to achieve the best performance. Octopus v4, an evolution of the Octopus v1, v2, and v3 models, excels in selection and parameter understanding and reformatting. Additionally, we explore the use of graph as a versatile data structure that effectively coordinates multiple open-source models by harnessing the capabilities of the Octopus model and \textit{functional tokens}. Use our open-sourced GitHub (\url{https://www.nexa4ai.com/}) to try Octopus v4 models (\url{https://huggingface.co/NexaAIDev/Octopus-v4}), and contrite to a larger graph of language models. By activating models less than 10B parameters, we achieved SOTA MMLU score of 74.8 among the same level models.

Image compression at extremely low bitrates (below 0.1 bits per pixel (bpp)) is a significant challenge due to substantial information loss. In this work, we propose a novel two-stage extreme image compression framework that exploits the powerful generative capability of pre-trained diffusion models to achieve realistic image reconstruction at extremely low bitrates. In the first stage, we treat the latent representation of images in the diffusion space as guidance, employing a VAE-based compression approach to compress images and initially decode the compressed information into content variables. The second stage leverages pre-trained stable diffusion to reconstruct images under the guidance of content variables. Specifically, we introduce a small control module to inject content information while keeping the stable diffusion model fixed to maintain its generative capability. Furthermore, we design a space alignment loss to force the content variables to align with the diffusion space and provide the necessary constraints for optimization. Extensive experiments demonstrate that our method significantly outperforms state-of-the-art approaches in terms of visual performance at extremely low bitrates., Comment: Submitted to IEEE TCSVT

This paper introduces a novel benchmark as part of the AIS 2024 Real-Time Image Super-Resolution (RTSR) Challenge, which aims to upscale compressed images from 540p to 4K resolution (4x factor) in real-time on commercial GPUs. For this, we use a diverse test set containing a variety of 4K images ranging from digital art to gaming and photography. The images are compressed using the modern AVIF codec, instead of JPEG. All the proposed methods improve PSNR fidelity over Lanczos interpolation, and process images under 10ms. Out of the 160 participants, 25 teams submitted their code and models. The solutions present novel designs tailored for memory-efficiency and runtime on edge devices. This survey describes the best solutions for real-time SR of compressed high-resolution images., Comment: CVPR 2024, AI for Streaming (AIS) Workshop

We present a systematic search for extraplanar X-ray point sources around 19 late-type, highly inclined disk galaxies residing in the Virgo cluster, based on archival Chandra observations reaching a source detection sensitivity of $L\rm(0.5- 8~keV)\sim10^{38}\rm~erg~s^{-1}$. Based on the cumulative source surface density distribution as a function of projected vertical distance from the disk mid-plane, we identify a statistically significant ($\sim3.3\sigma$) excess of $\sim20$ X-ray sources within a projected vertical off-disk distance of $0.92'-2.5'$ ($\sim4.4-12\ \mathrm{kpc}$), the presence of which cannot be explained by the bulk stellar content of the individual galaxies, nor by the cosmic X-ray background. On the other hand, there is no significant evidence for an excess of extraplanar X-ray sources in a comparison sample of field late-type edge-on galaxies, for which Chandra observations reaching a similar source detection sensitivity are available. We discuss possible origins for the observed excess, which include low-mass X-ray binaries (LMXBs) associated with globular clusters, supernova-kicked LMXBs, high-mass X-ray binaries born in recent star formation induced by ram pressure stripping of the disk gas, as well as a class of intra-cluster X-ray sources previously identified around early-type member galaxies of Virgo. We find that none of these X-ray populations can naturally dominate the observed extraplanar excess, although supernova-kicked LMXBs and the effect of ram pressure are most likely relevant, Comment: 15 pages, 4 figures. Accepted for publication in ApJ

A multimodal AI agent is characterized by its ability to process and learn from various types of data, including natural language, visual, and audio inputs, to inform its actions. Despite advancements in large language models that incorporate visual data, such as GPT-4V, effectively translating image-based data into actionable outcomes for AI agents continues to be challenging. In this paper, we introduce a multimodal model that incorporates the concept of functional token specifically designed for AI agent applications. To ensure compatibility with edge devices, our model is optimized to a compact size of less than 1B parameters. Like GPT-4, our model can process both English and Chinese. We demonstrate that this model is capable of operating efficiently on a wide range of edge devices, including as constrained as a Raspberry Pi.

We present a systematic search for periodic X-ray sources in the bulge of M31, using ~ 2 Ms of archival Chandra observations spanning a temporal baseline of 16 years. Utilizing the Gregory-Loredo algorithm that is designed for photon-counting, phase-folded light curves, we detect seven periodic X-ray sources, among which four are newly discovered. Three of these sources are novae, the identified periods of which range between 1.3-2.0 hour and is most likely the orbital period. The other four sources are low-mass X-ray binaries, the identified periods of which range between 0.13-19.3 hour and are also likely orbital due to a clear eclipsing/dipping behavior in the light curve. We address implications on the X-ray binary population of the M31 bulge. Our study demonstrates the potential of using archival X-ray observations to systematically identify periodic X-ray sources in external galaxies, which would provide valuable information about the underlying exotic stellar populations., Comment: 19 pages, 7 figures, accepted for publication in Monthly Notices of the Royal Astronomical Society

Adam with decoupled weight decay, also known as AdamW, is widely acclaimed for its superior performance in language modeling tasks, surpassing Adam with $\ell_2$ regularization in terms of generalization and optimization. However, this advantage is not theoretically well-understood. One challenge here is that though intuitively Adam with $\ell_2$ regularization optimizes the $\ell_2$ regularized loss, it is not clear if AdamW optimizes a specific objective. In this work, we make progress toward understanding the benefit of AdamW by showing that it implicitly performs constrained optimization. More concretely, we show in the full-batch setting, if AdamW converges with any non-increasing learning rate schedule whose partial sum diverges, it must converge to a KKT point of the original loss under the constraint that the $\ell_\infty$ norm of the parameter is bounded by the inverse of the weight decay factor. This result is built on the observation that Adam can be viewed as a smoothed version of SignGD, which is the normalized steepest descent with respect to $\ell_\infty$ norm, and a surprising connection between normalized steepest descent with weight decay and Frank-Wolfe.

Language models have shown effectiveness in a variety of software applications, particularly in tasks related to automatic workflow. These models possess the crucial ability to call functions, which is essential in creating AI agents. Despite the high performance of large-scale language models in cloud environments, they are often associated with concerns over privacy and cost. Current on-device models for function calling face issues with latency and accuracy. Our research presents a new method that empowers an on-device model with 2 billion parameters to surpass the performance of GPT-4 in both accuracy and latency, and decrease the context length by 95\%. When compared to Llama-7B with a RAG-based function calling mechanism, our method enhances latency by 35-fold. This method reduces the latency to levels deemed suitable for deployment across a variety of edge devices in production environments, aligning with the performance requisites for real-world applications.

In the rapidly evolving domain of artificial intelligence, Large Language Models (LLMs) play a crucial role due to their advanced text processing and generation abilities. This study introduces a new strategy aimed at harnessing on-device LLMs in invoking software APIs. We meticulously compile a dataset derived from software API documentation and apply fine-tuning to LLMs with capacities of 2B, 3B and 7B parameters, specifically to enhance their proficiency in software API interactions. Our approach concentrates on refining the models' grasp of API structures and syntax, significantly enhancing the accuracy of API function calls. Additionally, we propose \textit{conditional masking} techniques to ensure outputs in the desired formats and reduce error rates while maintaining inference speeds. We also propose a novel benchmark designed to evaluate the effectiveness of LLMs in API interactions, establishing a foundation for subsequent research. Octopus, the fine-tuned model, is proved to have better performance than GPT-4 for the software APIs calling. This research aims to advance automated software development and API integration, representing substantial progress in aligning LLM capabilities with the demands of practical software engineering applications.

We report the discovery of the 10 kilo-parsec (kpc) scale radio lobes in the Sombrero galaxy (NGC 4594), using data from the Continuum Halos in Nearby Galaxies - an Expanded Very Large Array (VLA) Survey (CHANG-ES) project. We further examine the balance between the magnetic pressure inside the lobes and the thermal pressure of the ambient hot gas. At the radii $r$ of ~(1-10) kpc, the magnetic pressure inside the lobes and the thermal pressure of the ambient hot gas are generally in balance. This implies that the jets could expand into the surroundings at least to r ~ 10 kpc. The feedback from the active galactic nucleus (AGN) jet responsible for the large-scale lobes may help to explain the unusually high X-ray luminosity of this massive quiescent isolated disk galaxy, although more theoretical work is needed to further examine this possibility., Comment: 8 pages, 3 figures, 2 tables, accepted for publication in ApJ

Supermassive black holes in galaxies spend majority of their lifetime in the low-luminosity regime, powered by hot accretion flow. Strong winds launched from the hot accretion flow have the potential to play an important role in active galactic nuclei (AGN) feedback. Direct observational evidence for these hot winds with temperature around 10 keV, has been obtained through the detection of highly ionized iron emission lines with Doppler shifts in two prototypical low-luminosity AGNs, namely M81* and NGC 7213. In this work, we further identify blueshifted H-like O/Ne emission lines in the soft X-ray spectra of these two sources. These lines are interpreted to be associated with additional outflowing components possessing velocity around several $10^3$ km/s and lower temperature (~0.2-0.4 keV). Blue-shifted velocity and the X-ray intensity of these additional outflowing components are hard to be explained by previously detected hot wind freely propagating to larger radii. Through detailed numerical simulations, we find the newly detected blue-shifted emission lines would come from circumnuclear gas shock-heated by the hot wind instead. Hot wind can provide larger ram pressure force on the clumpy circumnuclear gas than the gravitational force from central black hole, effectively impeding the black hole accretion of gas. Our results provide strong evidences for the energy and momentum feedback by the hot AGN wind., Comment: 19 pages, 9 figures, submitted to ApJ

Recently, many deep image compression methods have been proposed and achieved remarkable performance. However, these methods are dedicated to optimizing the compression performance and speed at medium and high bitrates, while research on ultra low bitrates is limited. In this work, we propose a ultra low bitrates enhanced invertible encoding network guided by traditional transformation theory, experiments show that our codec outperforms existing methods in both compression and reconstruction performance. Specifically, we introduce the Block Discrete Cosine Transformation to model the sparsity of features and employ traditional Haar transformation to improve the reconstruction performance of the model without increasing the bitstream cost., Comment: 6 pages, 8 figures, accepted by ICCE 2024

In this paper, we study the Shen-Yin-Zhao type filtration on the derived category of twisted K3 surfaces. We introduce the so called twisted Beauville-Voisin class on a twisted K3 surface and use it to extend the work in \cite{OG13, SYZ20} to the case of twisted K3 surfaces. It shares many nice properties as the untwisted case. For instance, the filtration is preserved under any Fourier-Mukai transformation. As an application, we obtain a new filtration on the Chow group of zero cycles on the Bridgeland moduli space of twisted K3 surfaces. It is birational invariant and can be viewed as a candidate for the conjectural Beauville-Voisin filtration. We compare this filtration with Voisin's filtration and show they coincide on the locally free loci. Some other applications (such as Bloch's conjecture for birational automorphisms) are discussed at the end., Comment: 2o pages, comments are welcome!

Instructing the model to generate a sequence of intermediate steps, a.k.a., a chain of thought (CoT), is a highly effective method to improve the accuracy of large language models (LLMs) on arithmetics and symbolic reasoning tasks. However, the mechanism behind CoT remains unclear. This work provides a theoretical understanding of the power of CoT for decoder-only transformers through the lens of expressiveness. Conceptually, CoT empowers the model with the ability to perform inherently serial computation, which is otherwise lacking in transformers, especially when depth is low. Given input length $n$, previous works have shown that constant-depth transformers with finite precision $\mathsf{poly}(n)$ embedding size can only solve problems in $\mathsf{TC}^0$ without CoT. We first show an even tighter expressiveness upper bound for constant-depth transformers with constant-bit precision, which can only solve problems in $\mathsf{AC}^0$, a proper subset of $ \mathsf{TC}^0$. However, with $T$ steps of CoT, constant-depth transformers using constant-bit precision and $O(\log n)$ embedding size can solve any problem solvable by boolean circuits of size $T$. Empirically, enabling CoT dramatically improves the accuracy for tasks that are hard for parallel computation, including the composition of permutation groups, iterated squaring, and circuit value problems, especially for low-depth transformers., Comment: 38 pages, 10 figures. Accepted by ICLR 2024

We present a uniform and sensitive X-ray census of active galactic nuclei (AGNs) in the two nearest galaxy clusters, Virgo and Fornax, utilizing the newly released X-ray source catalogs from the first all-sky scan of SRG/eROSITA. A total of 50 and 10 X-ray sources are found positionally coincident with the nuclei of member galaxies in Virgo and Fornax, respectively, down to a 0.2-2.3 keV luminosity of $\sim10^{39}\rm~erg~s^{-1}$ and reaching out to a projected distance well beyond the virial radius of both clusters. The majority of the nuclear X-ray sources are newly identified. There is weak evidence that the nuclear X-ray sources are preferentially found in late-type hosts. Several hosts are dwarf galaxies with a stellar mass below $\sim10^{9}\rm~M_\odot$. We find that contamination by non-nuclear X-ray emission can be neglected in most cases, indicating the dominance of a genuine AGN. In the meantime, no nuclear X-ray source exhibits a luminosity higher than a few times $10^{41}\rm~erg~s^{-1}$. The X-ray AGN occupation rate is only $\sim$ 3% in both clusters, apparently much lower than that in field galaxies inferred from previous X-ray studies. Both aspects suggest that the cluster environment effectively suppresses AGN activity. The findings of this census have important implications on the interplay between galaxies and their central massive black holes in cluster environments., Comment: 8 pages, 2 figures, 1 table, accepted for publication in ApJL, comments welcome

A fundamental challenge in multi-agent reinforcement learning (MARL) is to learn the joint policy in an extremely large search space, which grows exponentially with the number of agents. Moreover, fully decentralized policy factorization significantly restricts the search space, which may lead to sub-optimal policies. In contrast, the auto-regressive joint policy can represent a much richer class of joint policies by factorizing the joint policy into the product of a series of conditional individual policies. While such factorization introduces the action dependency among agents explicitly in sequential execution, it does not take full advantage of the dependency during learning. In particular, the subsequent agents do not give the preceding agents feedback about their decisions. In this paper, we propose a new framework Back-Propagation Through Agents (BPTA) that directly accounts for both agents' own policy updates and the learning of their dependent counterparts. This is achieved by propagating the feedback through action chains. With the proposed framework, our Bidirectional Proximal Policy Optimisation (BPPO) outperforms the state-of-the-art methods. Extensive experiments on matrix games, StarCraftII v2, Multi-agent MuJoCo, and Google Research Football demonstrate the effectiveness of the proposed method.