Search

Here, we present the outcomes from the second Large Language Model (LLM) Hackathon for Applications in Materials Science and Chemistry, which engaged participants across global hybrid locations, resulting in 34 team submissions. The submissions spanned seven key application areas and demonstrated the diverse utility of LLMs for applications in (1) molecular and material property prediction; (2) molecular and material design; (3) automation and novel interfaces; (4) scientific communication and education; (5) research data management and automation; (6) hypothesis generation and evaluation; and (7) knowledge extraction and reasoning from scientific literature. Each team submission is presented in a summary table with links to the code and as brief papers in the appendix. Beyond team results, we discuss the hackathon event and its hybrid format, which included physical hubs in Toronto, Montreal, San Francisco, Berlin, Lausanne, and Tokyo, alongside a global online hub to enable local and virtual collaboration. Overall, the event highlighted significant improvements in LLM capabilities since the previous year's hackathon, suggesting continued expansion of LLMs for applications in materials science and chemistry research. These outcomes demonstrate the dual utility of LLMs as both multipurpose models for diverse machine learning tasks and platforms for rapid prototyping custom applications in scientific research., Comment: 98 pages

In a setting where segmentation models have to be built for multiple datasets, each with its own corresponding label set, a straightforward way is to learn one model for every dataset and its labels. Alternatively, multi-task architectures with shared encoders and multiple segmentation heads or shared weights with compound labels can also be made use of. This work proposes a novel label sharing framework where a shared common label space is constructed and each of the individual label sets are systematically mapped to the common labels. This transforms multiple datasets with disparate label sets into a single large dataset with shared labels, and therefore all the segmentation tasks can be addressed by learning a single model. This eliminates the need for task specific adaptations in network architectures and also results in parameter and data efficient models. Furthermore, label sharing framework is naturally amenable for incremental learning where segmentations for new datasets can be easily learnt. We experimentally validate our method on various medical image segmentation datasets, each involving multi-label segmentation. Furthermore, we demonstrate the efficacy of the proposed method in terms of performance and incremental learning ability vis-a-vis alternative methods.

Wireless networking is encouraged by the constant enhancement of sensors' ability and wireless communication. To provide service quality support for multimedia viz. audio and video streams, the IEEE 802.11e MAC (Media Access Control) improves basic 802.11 MAC. IEEE 802.11 standard series such as IEEE 802.11a, b, g, n, p, and ac have been promoted and specified in the current communications and connection development. Each standard has functionality that matches the kind of applications for which the standard is intended. IEEE 802.11ac has better performance with fewer interferences and achieves gigabits per second capacity transfer rates. This paper discusses the comparative examination of the IEEE 802.11a, IEEE 802.11b, IEEE 802.11g, IEEE 802.11n, IEEE 802.11p, and IEEE 802.11ac standards which increase accuracy and performance pertaining to the IEEE 802.11 standard. In this paper, we investigate the design requirements for numerous simultaneous peer-to-peer connections. Further, this study offers a systematic review and analysis of the MAC layer in WMN (Wireless Mesh Network) and also highlights their open research issues and challenges. Finally, this paper discusses various potential directions for future research in this area with an emphasis on their strengths and limitations., Comment: 20 pages, 5 figures, to be published in Wireless Pers Commun

Sign languages are the language of hearing-impaired people who use visuals like the hand, facial, and body movements for communication. There are different signs and gestures representing alphabets, words, and phrases. Nowadays approximately 300 sign languages are being practiced worldwide such as American Sign Language (ASL), Chinese Sign Language (CSL), Indian Sign Language (ISL), and many more. Sign languages are dependent on the vocal language of a place. Unlike vocal or spoken languages, there are no helping words in sign language like is, am, are, was, were, will, be, etc. As only a limited population is well-versed in sign language, this lack of familiarity of sign language hinders hearing-impaired people from communicating freely and easily with everyone. This issue can be addressed by a sign language recognition (SLR) system which has the capability to translate the sign language into vocal language. In this paper, a continuous SLR system is proposed using a deep learning model employing Long Short-Term Memory (LSTM), trained and tested on an ISL primary dataset. This dataset is created using MediaPipe Holistic pipeline for tracking face, hand, and body movements and collecting landmarks. The system recognizes the signs and gestures in real-time with 88.23% accuracy., Comment: 14 pages, 4 figures, Wireless Pers Commun

For the 3D localization problem using point spread function (PSF) engineering, we propose a novel enhancement of our previously introduced localization neural network, LocNet. The improved network is a physics-informed neural network (PINN) that we call PiLocNet. Previous works on the localization problem may be categorized separately into model-based optimization and neural network approaches. Our PiLocNet combines the unique strengths of both approaches by incorporating forward-model-based information into the network via a data-fitting loss term that constrains the neural network to yield results that are physically sensible. We additionally incorporate certain regularization terms from the variational method, which further improves the robustness of the network in the presence of image noise, as we show for the Poisson and Gaussian noise models. This framework accords interpretability to the neural network, and the results we obtain show its superiority. Although the paper focuses on the use of single-lobe rotating PSF to encode the full 3D source location, we expect the method to be widely applicable to other PSFs and imaging problems that are constrained by known forward processes., Comment: 25 pages, 4 figures

Two dimensional conformal field theories with the extended $\mathcal{W}_3$ symmetry algebra have an infinite number of mutually commuting conserved charges, which are referred to as the quantum Boussinesq charges. In this work we construct local operators whose zero modes are precisely these conserved charges. For this purpose we study the higher spin conformal field theory on the torus and compute thermal correlators involving the stress tensor and the spin-3 current in a higher spin module of the W3 algebra. In addition we independently obtain the excited state eigenvalues of the quantum Boussinesq charges within the higher spin module via the ODE/IM correspondence. A judicious combination of these data allows us to derive the local operators, whose integrals are the conserved charges of the integrable hierarchy., Comment: 24 pages

High runtime memory and high latency puts significant constraint on Vision Transformer training and inference, especially on edge devices. Token pruning reduces the number of input tokens to the ViT based on importance criteria of each token. We present a Background Aware Vision Transformer (BAViT) model, a pre-processing block to object detection models like DETR/YOLOS aimed to reduce runtime memory and increase throughput by using a novel approach to identify background tokens in the image. The background tokens can be pruned completely or partially before feeding to a ViT based object detector. We use the semantic information provided by segmentation map and/or bounding box annotation to train a few layers of ViT to classify tokens to either foreground or background. Using 2 layers and 10 layers of BAViT, background and foreground tokens can be separated with 75% and 88% accuracy on VOC dataset and 71% and 80% accuracy on COCO dataset respectively. We show a 2 layer BAViT-small model as pre-processor to YOLOS can increase the throughput by 30% - 40% with a mAP drop of 3% without any sparse fine-tuning and 2% with sparse fine-tuning. Our approach is specifically targeted for Edge AI use cases., Comment: 7 pages, 2 tables, 4 figures, FITML workshop@NeuRIPS 2024

Activation functions introduce non-linearity into Neural Networks, enabling them to learn complex patterns. Different activation functions vary in speed and accuracy, ranging from faster but less accurate options like ReLU to slower but more accurate functions like SiLU or SELU. Typically, same activation function is used throughout an entire model architecture. In this paper, we conduct a comprehensive study on the effects of using mixed activation functions in YOLO-based models, evaluating their impact on latency, memory usage, and accuracy across CPU, NPU, and GPU edge devices. We also propose a novel approach that leverages Neural Architecture Search (NAS) to design YOLO models with optimized mixed activation functions.The best model generated through this method demonstrates a slight improvement in mean Average Precision (mAP) compared to baseline model (SiLU), while it is 22.28% faster and consumes 64.15% less memory on the reference NPU device., Comment: 7 pages, 4 figures, FITML workshop, NeuRIPS 2024

Deep neural networks (DNNs) can deteriorate in accuracy when deployment data differs from training data. While performing online training at all timesteps can improve accuracy, it is computationally expensive. We propose DecTrain, a new algorithm that decides when to train a monocular depth DNN online using self-supervision with low overhead. To make the decision at each timestep, DecTrain compares the cost of training with the predicted accuracy gain. We evaluate DecTrain on out-of-distribution data, and find DecTrain maintains accuracy compared to online training at all timesteps, while training only 44% of the time on average. We also compare the recovery of a low inference cost DNN using DecTrain and a more generalizable high inference cost DNN on various sequences. DecTrain recovers the majority (97%) of the accuracy gain of online training at all timesteps while reducing computation compared to the high inference cost DNN which recovers only 66%. With an even smaller DNN, we achieve 89% recovery while reducing computation by 56%. DecTrain enables low-cost online training for a smaller DNN to have competitive accuracy with a larger, more generalizable DNN at a lower overall computational cost., Comment: 8 pages

We introduce MCUBench, a benchmark featuring over 100 YOLO-based object detection models evaluated on the VOC dataset across seven different MCUs. This benchmark provides detailed data on average precision, latency, RAM, and Flash usage for various input resolutions and YOLO-based one-stage detectors. By conducting a controlled comparison with a fixed training pipeline, we collect comprehensive performance metrics. Our Pareto-optimal analysis shows that integrating modern detection heads and training techniques allows various YOLO architectures, including legacy models like YOLOv3, to achieve a highly efficient tradeoff between mean Average Precision (mAP) and latency. MCUBench serves as a valuable tool for benchmarking the MCU performance of contemporary object detectors and aids in model selection based on specific constraints., Comment: Code and data are available at https://github.com/Deeplite/deeplite-torch-zoo

Superrotations are local extensions of the Lorentz group at null infinity that have been argued to be symmetries of gravitational scattering. In their smooth version, they can be identified with the group of diffeomorphisms on the celestial sphere. Their canonical realization requires treating the celestial metric as a variable in the gravitational phase space, along with the news and shear tensors. In this paper, we derive the resulting Poisson brackets (PB). The standard PB algebra of the news and shear tensors is augmented by distributional terms at the boundaries of null infinity, including novel PB relations between the celestial metric and the radiative variables., Comment: 72 pages

Humans naturally build mental models of object interactions and dynamics, allowing them to imagine how their surroundings will change if they take a certain action. While generative models today have shown impressive results on generating/editing images unconditionally or conditioned on text, current methods do not provide the ability to perform object manipulation conditioned on actions, an important tool for world modeling and action planning. Therefore, we propose to learn an action-conditional generative models by learning from unlabeled videos of human hands interacting with objects. The vast quantity of such data on the internet allows for efficient scaling which can enable high-performing action-conditional models. Given an image, and the shape/location of a desired hand interaction, CosHand, synthesizes an image of a future after the interaction has occurred. Experiments show that the resulting model can predict the effects of hand-object interactions well, with strong generalization particularly to translation, stretching, and squeezing interactions of unseen objects in unseen environments. Further, CosHand can be sampled many times to predict multiple possible effects, modeling the uncertainty of forces in the interaction/environment. Finally, method generalizes to different embodiments, including non-human hands, i.e. robot hands, suggesting that generative video models can be powerful models for robotics.

Wide Area Measurement Systems (WAMS) can guide system operators' to increase their situational awareness by expanding observability of their supervise area and adjoining systems. Power system oscillations in the electrical grid are a matter of contention. It may transform the stable operation of the power system into an unstable system when oscillations grow and if no corrective actions are taken to mitigate them. This paper manifests the utilization of the synchrophasor technology for situational awareness by oscillation detection. An algorithm is proposed for the low-frequency oscillation-related analysis based on Prony and Fast Fourier Transform (FFT) methods. It gives better insight during the grid disturbance and other events related to power system operation. The effectiveness of this algorithm is validated by two case studies in the Western Regional Indian power grid., Comment: 15 Pages, 14 Figures, 2 Tables

In the present work, we focus on the space-time isogeometric discretization of a parabolic problem with a nonlocal diffusion coefficient. The use of a space-time discretization with smooth basis functions yields advantages in the approximation of the solution. The existence of the unique solution for continuous and discrete space-time variational formulations is proven. We also establish the a priori error estimate for the space-time isogeometric scheme. The non-linear system is linearized through Picard's method and a suitable preconditioner for the linearized system is provided. Finally, to confirm the theoretical findings, results of some numerical experiments are presented.

In order to unravel the present situation of the PBH overproduction problem, our study emphasizes the critical role played by the equation of state (EoS) parameter $w$ within the framework of effective field theory (EFT) of non-singular bounce. Our analysis focuses on a wide range of EoS parameter values that are still optimal for explaining the latest data from the pulsar timing array (PTA). As a result of our study, the most advantageous window, $0.31 \leq w \leq 1/3$, is identified as the location of a substantial PBH abundance, $f_{\rm PBH} \in (10^{-3},1)$ with large mass PBHs, $M_{\rm PBH}\sim {\cal O}(10^{-7}-10^{-3})M_{\odot}$, in the SIGW interpretation of the PTA signal. When confronted with PTA, we find that the overproduction avoiding circumstances are between $1\sigma-2\sigma$, while the EoS parameter lies inside the narrow window, $0.31

Stochastic diffusion processes are pervasive in nature, from the seemingly erratic Brownian motion to the complex interactions of synaptically-coupled spiking neurons. Recently, drawing inspiration from Langevin dynamics, neuromorphic diffusion models were proposed and have become one of the major breakthroughs in the field of generative artificial intelligence. Unlike discriminative models that have been well developed to tackle classification or regression tasks, diffusion models as well as other generative models such as ChatGPT aim at creating content based upon contexts learned. However, the more complex algorithms of these models result in high computational costs using today's technologies, creating a bottleneck in their efficiency, and impeding further development. Here, we develop a spintronic voltage-controlled magnetoelectric memory hardware for the neuromorphic diffusion process. The in-memory computing capability of our spintronic devices goes beyond current Von Neumann architecture, where memory and computing units are separated. Together with the non-volatility of magnetic memory, we can achieve high-speed and low-cost computing, which is desirable for the increasing scale of generative models in the current era. We experimentally demonstrate that the hardware-based true random diffusion process can be implemented for image generation and achieve comparable image quality to software-based training as measured by the Frechet inception distance (FID) score, achieving ~10^3 better energy-per-bit-per-area over traditional hardware.

Opinion Dynamics is an interdisciplinary area of research. Psychology and Sociology have proposed models of how individuals form opinions and how social interactions influence this process. Socio-Physicists have interpreted patterns in opinion formation as arising from non-linearity in the underlying process, shaping the models. Agent-based modeling has offered a platform to study the Opinion Dynamics of large groups. This paper recasts recent models in opinion formation into a proper dynamical system, injecting the idea of clock time into evolving opinions. The time interval between successive receipts of new information (frequency of information receipts) becomes a factor to study. Social media has shrunk time intervals between information receipts, increasing their frequency. The recast models show that shorter intervals and larger networks increase an individual's propensity for polarization, defined as an inability to hold a neutral opinion. A Polarization number based on sociological parameters is proposed, with critical values beyond which individuals are prone to polarization, depending on psychological parameters. Reduced time intervals and larger interacting groups can push the Polarization number to critical values, contributing to polarization. The Extent of Polarization is defined as the width of the region around neutral within which an individual cannot hold an opinion. Results are reported for model parameters found in the literature. The findings offer an opportunity to adjust model parameters to align with empirical evidence, aiding the study of Opinion Dynamics in large social networks using Agent-Based Modeling., Comment: This article has been published in Complexity journal. For citation purposes, please refer to the final published version:https://doi.org/10.1155/2024/4742401

A key challenge in manipulation is learning a policy that can robustly generalize to diverse visual environments. A promising mechanism for learning robust policies is to leverage video generative models, which are pretrained on large-scale datasets of internet videos. In this paper, we propose a visuomotor policy learning framework that fine-tunes a video diffusion model on human demonstrations of a given task. At test time, we generate an example of an execution of the task conditioned on images of a novel scene, and use this synthesized execution directly to control the robot. Our key insight is that using common tools allows us to effortlessly bridge the embodiment gap between the human hand and the robot manipulator. We evaluate our approach on four tasks of increasing complexity and demonstrate that harnessing internet-scale generative models allows the learned policy to achieve a significantly higher degree of generalization than existing behavior cloning approaches., Comment: Project page: https://dreamitate.cs.columbia.edu/

Selective state-space models (SSMs) like Mamba overcome some of the shortcomings of Transformers, such as quadratic computational complexity with sequence length and large inference-time memory requirements from the key-value cache. Moreover, recent studies have shown that SSMs can match or exceed the language modeling capabilities of Transformers, making them an attractive alternative. In a controlled setting (e.g., same data), however, studies so far have only presented small scale experiments comparing SSMs to Transformers. To understand the strengths and weaknesses of these architectures at larger scales, we present a direct comparison between 8B-parameter Mamba, Mamba-2, and Transformer models trained on the same datasets of up to 3.5T tokens. We also compare these models to a hybrid architecture consisting of 43% Mamba-2, 7% attention, and 50% MLP layers (Mamba-2-Hybrid). Using a diverse set of tasks, we answer the question of whether Mamba models can match Transformers at larger training budgets. Our results show that while pure SSMs match or exceed Transformers on many tasks, they lag behind Transformers on tasks which require strong copying or in-context learning abilities (e.g., 5-shot MMLU, Phonebook) or long-context reasoning. In contrast, we find that the 8B Mamba-2-Hybrid exceeds the 8B Transformer on all 12 standard tasks we evaluated (+2.65 points on average) and is predicted to be up to 8x faster when generating tokens at inference time. To validate long-context capabilities, we provide additional experiments evaluating variants of the Mamba-2-Hybrid and Transformer extended to support 16K, 32K, and 128K sequences. On an additional 23 long-context tasks, the hybrid model continues to closely match or exceed the Transformer on average. To enable further study, we release the checkpoints as well as the code used to train our models as part of NVIDIA's Megatron-LM project.

Additive manufacturing, especially laser powder bed fusion (L-PBF), is widely used for fabricating metal parts with intricate geometries. However, parts produced via L-PBF suffer from varied surface roughness which affects the dynamic or fatigue properties. Accurate prediction of fatigue properties as a function of surface roughness is a critical requirement for qualifying L-PBF parts. In this work, an analytical methodology is put forth to predict the fatigue life of L-PBF components having heterogeneous surface roughness. Thirty-six Hastelloy X specimens are printed using L-PBF followed by industry-standard heat treatment procedures. Half of these specimens are built with as-printed gauge sections and the other half is printed as cylinders from which fatigue specimens are extracted via machining. Specimens are printed in a vertical orientation and an orientation 30 degree from the vertical axis. The surface roughness of the specimens is measured using computed tomography and parameters such as the maximum valley depth are used to build an extreme value distribution. Fatigue testing is conducted at an isothermal condition of 500-degree F. It is observed that the rough specimens fail much earlier compared to the machined specimens due to the deep valleys present on the surfaces of the former ones. The valleys act as notches leading to high strain localization. Following this observation, a functional relationship is formulated analytically that considers surface valleys as notches and correlates the strain localization around those notches with fatigue life, using the Coffin-Manson-Basquin and Ramberg-Osgood equation. In conclusion, the proposed analytical model successfully predicts the fatigue life of L-PBF specimens at an elevated temperature undergoing different strain loadings.

We study two dimensional systems with extended conformal symmetry generated by the ${\mathcal W}_3$ algebra. These are expected to have an infinite number of commuting conserved charges, which we refer to as the quantum Boussinesq charges. We compute the eigenvalues of the quantum Boussinesq charges in both the vacuum and first excited states of the higher spin module through the ODE/IM correspondence. By studying the higher spin conformal field theory on the torus, we also calculate thermal correlators involving the energy-momentum tensor and the spin-3 current by making use of the Zhu recursion relations. By combining these results, we show that it is possible to derive the current densities, whose integrals are the quantum Boussinesq charges. We also evaluate the thermal expectation values of the conserved charges, and show that these are quasi-modular differential operators acting on the character of the higher spin module., Comment: 49 pages. References added, typos corrected

X-ray is one of the prevalent image modalities for the detection and diagnosis of the human body. X-ray provides an actual anatomical structure of an organ present with disease or absence of disease. Segmentation of disease in chest X-ray images is essential for the diagnosis and treatment. In this paper, a framework for the segmentation of X-ray images using artificial intelligence techniques has been discussed. Here data has been pre-processed and cleaned followed by segmentation using SegNet and Residual Net approaches to X-ray images. Finally, segmentation has been evaluated using well known metrics like Loss, Dice Coefficient, Jaccard Coefficient, Precision, Recall, Binary Accuracy, and Validation Accuracy. The experimental results reveal that the proposed approach performs better in all respect of well-known parameters with 16 batch size and 50 epochs. The value of validation accuracy, precision, and recall of SegNet and Residual Unet models are 0.9815, 0.9699, 0.9574, and 0.9901, 0.9864, 0.9750 respectively., Comment: 10 pages, 3 figures

We present a complete and consistent exposition of the regularization, renormalization, and resummation procedures in the setup of having a contraction and then non-singular bounce followed by inflation with a sharp transition from slow-roll (SR) to ultra-slow roll (USR) phase for generating primordial black holes (PBHs). We consider following an effective field theory (EFT) approach and study the quantum loop corrections to the power spectrum from each phase. We demonstrate the complete removal of quadratic UV divergences after renormalization and softened logarithmic IR divergences after resummation and illustrate the scheme-independent nature of our renormalization approach. We further show that the addition of a contracting and bouncing phase allows us to successfully generate PBHs of solar-mass order, $M_{\rm PBH}\sim {\cal O}(M_{\odot})$, by achieving the minimum e-folds during inflation to be $\Delta N_{\rm Total}\sim {\cal O}(60)$ and in this process successfully evading the strict no-go theorem. We notice that varying the effective sound speed between $0.88\leq c_{s}\leq 1$, allows the peak spectrum amplitude to lie within $10^{-3}\leq A \leq 10^{-2}$, indicating that causality and unitarity remain protected in the theory. We analyse PBHs in the extremely small, $M_{\rm PBH}\sim {\cal O}(10^{-33}-10^{-27})M_{\odot}$, and the large, $M_{\rm PBH}\sim {\cal O}(10^{-6}-10^{-1})M_{\odot}$, mass limits and confront the PBH abundance results with the latest microlensing constraints. We also study the cosmological beta functions across all phases and find their interpretation consistent in the context of bouncing and inflationary scenarios while satisfying the pivot scale normalization requirement. Further, we estimate the spectral distortion effects and shed light on controlling PBH overproduction., Comment: 108 pages, 17 figures, 2 tables, 3 appendices, Comments are welcome, Revised version accepted for publication in European Physical Journal C

In mobile communication scenarios, the acquired channel state information (CSI) rapidly becomes outdated due to fast-changing channels. Opportunistic transmitter selection based on current CSI for secrecy improvement may be outdated during actual transmission, negating the diversity benefit of transmitter selection. Motivated by this problem, we propose a joint CSI prediction and predictive selection of the optimal transmitter strategy based on historical CSI by exploiting the temporal correlation among CSIs. The proposed solution utilizes the multi-task learning (MTL) framework by employing a single Long Short-Term Memory (LSTM) network architecture that simultaneously learns two tasks of predicting the CSI and selecting the optimal transmitter in parallel instead of learning these tasks sequentially. The proposed LSTM architecture outperforms convolutional neural network (CNN) based architecture due to its superior ability to capture temporal features in the data. Compared to the sequential task learning models, the MTL architecture provides superior predicted secrecy performance for a large variation in the number of transmitters and the speed of mobile nodes. It also offers significant computational and memory efficiency, leading to a substantial saving in computational time by around 40 percent.

Quantization lowers memory usage, computational requirements, and latency by utilizing fewer bits to represent model weights and activations. In this work, we investigate the generalization properties of quantized neural networks, a characteristic that has received little attention despite its implications on model performance. In particular, first, we develop a theoretical model for quantization in neural networks and demonstrate how quantization functions as a form of regularization. Second, motivated by recent work connecting the sharpness of the loss landscape and generalization, we derive an approximate bound for the generalization of quantized models conditioned on the amount of quantization noise. We then validate our hypothesis by experimenting with over 2000 models trained on CIFAR-10, CIFAR-100, and ImageNet datasets on convolutional and transformer-based models.

The soft excess in active galactic nuclei (AGNs) may arise through a combination of relativistic reflection and the effects of a warm corona at the surface of the accretion disc. Detailed examination of the soft excess can therefore constrain models of the transport and dissipation of accretion energy. Here, we analyze 34 XMM-Newton observations from 14 Type I AGNs with the reXcor spectral model which self-consistently combines emission from a warm corona with relativistic reflection assuming a lamppost corona. The model divides accretion energy between the disc, the warm corona, and the lamppost. The XMM-Newton observations span a factor of 188 in Eddington ratio ($\lambda_{\mathrm{obs}}$) and 350 in black hole mass, and we find that a warm corona is a significant contributor to the soft excess for 13 of the 14 AGNs with a mean warm corona heating fraction of $0.51$. The reXcor fits reveal that the fraction of accretion energy dissipated in the lamppost is anti-correlated with $\lambda_{\mathrm{obs}}$. In contrast, the relationship between $\lambda_{\mathrm{obs}}$ and both the optical depth and heating fraction of the warm corona appears to transition from an anti-correlation to a correlation at $\lambda_{\mathrm{obs,t}} \approx 0.15$. Therefore, at least one other physical process in addition to the accretion rate is needed to explain the evolution of the warm corona. Overall, we find that a warm corona appears to be a crucial depository of accretion energy in AGNs across a broad range of $\lambda_{\mathrm{obs}}$ and black hole mass., Comment: 22 pages, 44 figures, accepted by MNRAS