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Let $K=\mathbb{Q}[\iota]$ and $N=K[\sqrt[4]{\alpha}]$, $\alpha\in\mathbb{Z}[\iota]$, $alpha=fg^2h^3$, $f$, $g$, $h\in \mathbb{Z}[\iota]$ are pairwise coprime and square free. Let $\mathcal{O}_N$ be the ring of integers of $N$. In this article we construct normalised integral basis for $\mathcal{O}_N$ over $\mathbb{Z}[\iota]$, that is an integral basis of the form \[ \left\{1,\frac{f_1(\alpha)}{d_1},\frac{f_2(\alpha)}{d_2},\frac{f_{3}(\alpha)}{d_3}\right\} \] where $d_i \in \mathbb{Z}[i]$ and $f_i(X)$, $\leq i\leq 3$ are monic polynomials of degree $i$ over $\mathbb{Z}[\iota]$. We explicitly determine what $d_i$, $1\leq i\leq n-1$ are in terms of $f$, $g$ and $h$., Comment: 29 pages

Deep learning methods are at the forefront of automated epileptic seizure detection and onset zone localization using scalp-EEG. However, the performance of deep learning methods rely heavily on the quality of annotated training datasets. Scalp EEG is susceptible to high noise levels, which in turn leads to imprecise annotations of the seizure timing and characteristics. This label noise presents a significant challenge in model training and generalization. In this paper, we introduce a novel statistical framework that informs a deep learning model of label ambiguity, thereby enhancing the overall seizure detection performance. Our Bayesian UncertaiNty-aware Deep Learning, BUNDL, strategy offers a straightforward and model-agnostic method for training deep neural networks with noisy training labels that does not add any parameters to existing architectures. By integrating domain knowledge into the statistical framework, we derive a novel KL-divergence-based loss function that capitalizes on uncertainty to better learn seizure characteristics from scalp EEG. Additionally, we explore the impact of improved seizure detection on the task of automated onset zone localization. We validate BUNDL using a comprehensive simulated EEG dataset and two publicly available datasets, TUH and CHB-MIT. BUNDL consistently improves the performance of three base models on simulated data under seven types of label noise and three EEG signal-to-noise ratios. Similar improvements were observed in the real-world TUH and CHB-MIT datasets. Finally, we demonstrate that BUNDL improves the accuracy of seizure onset zone localization. BUNDL is specifically designed to address label ambiguities, enabling the training of reliable and trustworthy models for epilepsy evaluation.

In this paper, we investigate certain graphs defined on groups, with a focus on infinite groups. The graphs discussed are the power graph, the enhanced power graph, and the commuting graph whose vertex set is a group $G$. The power graph is a graph in which two vertices are adjacent if one is some power of the other. In the enhanced power graph, an edge joins two vertices if they generate a cyclic subgroup of $G$. In the commuting graph, two vertices are adjacent if they commute in $G$. We prove a necessary and sufficient condition for any two of these graphs to be equal. This extends existing results for finite groups. In addition, we show that the power graph of the locally quaternion group is isomorphic to the commuting graph of the locally dihedral group. Lastly, we also answer a question posed by P. J. Cameron about the existence of groups $G_1$ and $G_2$ both of whom have power graph not equal to commuting graph but the power graph of $G_1$ and the commuting graph of $G_2$ are isomorphic., Comment: 2 figures

Video generation has been used to generate visual plans for controlling robotic systems. Given an image observation and a language instruction, previous work has generated video plans which are then converted to robot controls to be executed. However, a major bottleneck in leveraging video generation for control lies in the quality of the generated videos, which often suffer from hallucinatory content and unrealistic physics, resulting in low task success when control actions are extracted from the generated videos. While scaling up dataset and model size provides a partial solution, integrating external feedback is both natural and essential for grounding video generation in the real world. With this observation, we propose VideoAgent for self-improving generated video plans based on external feedback. Instead of directly executing the generated video plan, VideoAgent first refines the generated video plans using a novel procedure which we call self-conditioning consistency, utilizing feedback from a pretrained vision-language model (VLM). As the refined video plan is being executed, VideoAgent collects additional data from the environment to further improve video plan generation. Experiments in simulated robotic manipulation from MetaWorld and iTHOR show that VideoAgent drastically reduces hallucination, thereby boosting success rate of downstream manipulation tasks. We further illustrate that VideoAgent can effectively refine real-robot videos, providing an early indicator that robotics can be an effective tool in grounding video generation in the physical world.

We propose a novel optical flow based approach to enhance the axial resolution of anisotropic 3D EM volumes to achieve isotropic 3D reconstruction. Assuming spatial continuity of 3D biological structures in well aligned EM volumes, we reasoned that optical flow estimation techniques, often applied for temporal resolution enhancement in videos, can be utilized. Pixel level motion is estimated between neighboring 2D slices along z, using spatial gradient flow estimates to interpolate and generate new 2D slices resulting in isotropic voxels. We leverage recent state-of-the-art learning methods for video frame interpolation and transfer learning techniques, and demonstrate the success of our approach on publicly available ultrastructure EM volumes.

We present the Pilot Survey Phase 2 data release for the Wide-field ASKAP L-band Legacy All-sky Blind surveY (WALLABY), carried-out using the Australian SKA Pathfinder (ASKAP). We present 1760 HI detections (with a default spatial resolution of 30") from three pilot fields including the NGC 5044 and NGC 4808 groups as well as the Vela field, covering a total of ~180 deg$^2$ of the sky and spanning a redshift up to $z \simeq 0.09$. This release also includes kinematic models for over 126 spatially resolved galaxies. The observed median rms noise in the image cubes is 1.7 mJy per 30" beam and 18.5 kHz channel. This corresponds to a 5$\sigma$ HI column density sensitivity of $\sim 9.1\times10^{19}(1 + z)^4$ cm$^{-2}$ per 30" beam and $\sim 20$ km/s channel, and a 5$\sigma$ HI mass sensitivity of $\sim 5.5\times10^8 (D/100$ Mpc)$^{2}$ M$_{\odot}$ for point sources. Furthermore, we also present for the first time 12" high-resolution images ("cut-outs") and catalogues for a sub-sample of 80 sources from the Pilot Survey Phase 2 fields. While we are able to recover sources with lower signal-to-noise ratio compared to sources in the Public Data Release 1, we do note that some data quality issues still persist, notably, flux discrepancies that are linked to the impact of side lobes associated with the dirty beams due to inadequate deconvolution. However, in spite of these limitations, the WALLABY Pilot Survey Phase 2 has already produced roughly a third of the number of HIPASS sources, making this the largest spatially resolved HI sample from a single survey to date., Comment: 25 pages, 16 figures, 6 tables, accepted for publication in Publications of the Astronomical Society of Australia (PASA)

We find an upper bound for the number of groups of order $n$ up to isomorphism in the variety $G = A_pA_qA_r$, where $p$, $q$ and $r$ are distinct primes. We also find a bound on the orders and on the number of conjugacy classes of subgroups that are maximal amongst the subgroups of the general linear group that are also in the variety $A_qA_r$.

Let m be a cube-free positive integer and let p be a prime such that p does not divide m. In this paper we find the number of conjugacy classes of completely reducible solvable cube-free subgroups in GL(2, q) of order m, where q is a power of p.

Let $m$ be a positive integer such that $p$ does not divide $m$ where $p$ is prime. In this paper we find the number of conjugacy classes of completely reducible cyclic subgroups in GL$(2, q)$ of order $m$, where $q$ is a power of $p$.

We propose an image-conditioned diffusion model to estimate high angular resolution diffusion weighted imaging (DWI) from a low angular resolution acquisition. Our model, which we call QID$^2$, takes as input a set of low angular resolution DWI data and uses this information to estimate the DWI data associated with a target gradient direction. We leverage a U-Net architecture with cross-attention to preserve the positional information of the reference images, further guiding the target image generation. We train and evaluate QID$^2$ on single-shell DWI samples curated from the Human Connectome Project (HCP) dataset. Specifically, we sub-sample the HCP gradient directions to produce low angular resolution DWI data and train QID$^2$ to reconstruct the missing high angular resolution samples. We compare QID$^2$ with two state-of-the-art GAN models. Our results demonstrate that QID$^2$ not only achieves higher-quality generated images, but it consistently outperforms the GAN models in downstream tensor estimation across multiple metrics. Taken together, this study highlights the potential of diffusion models, and QID$^2$ in particular, for q-space up-sampling, thus offering a promising toolkit for clinical and research applications., Comment: Accepted at MICCAI 2024 International Workshop on Computational Diffusion MRI. Zijian Chen and Jueqi Wang contributed equally to this work

We propose a lesion-aware graph neural network (LEGNet) to predict language ability from resting-state fMRI (rs-fMRI) connectivity in patients with post-stroke aphasia. Our model integrates three components: an edge-based learning module that encodes functional connectivity between brain regions, a lesion encoding module, and a subgraph learning module that leverages functional similarities for prediction. We use synthetic data derived from the Human Connectome Project (HCP) for hyperparameter tuning and model pretraining. We then evaluate the performance using repeated 10-fold cross-validation on an in-house neuroimaging dataset of post-stroke aphasia. Our results demonstrate that LEGNet outperforms baseline deep learning methods in predicting language ability. LEGNet also exhibits superior generalization ability when tested on a second in-house dataset that was acquired under a slightly different neuroimaging protocol. Taken together, the results of this study highlight the potential of LEGNet in effectively learning the relationships between rs-fMRI connectivity and language ability in a patient cohort with brain lesions for improved post-stroke aphasia evaluation., Comment: Accepted at MICCAI 2024 International Workshop on Machine Learning in Clinical Neuroimaging (MLCN)

A vertex coloring of a graph is said to be pseudocomplete if, for any two distinct colors, there exists at least one edge with those two colors as its end vertices. The pseudoachromatic number of a graph is the greatest number of colors possible used in a pseudocomplete coloring. This paper studies properties relating to additivity of the pseudoachromatic number under the join. Errors from the literature are corrected and the notion of weakly critical is introduced in order to study the problem.

Large-scale computing systems are increasingly using accelerators such as GPUs to enable peta- and exa-scale levels of compute to meet the needs of Machine Learning (ML) and scientific computing applications. Given the widespread and growing use of ML, including in some scientific applications, optimizing these clusters for ML workloads is particularly important. However, recent work has demonstrated that accelerators in these clusters can suffer from performance variability and this variability can lead to resource under-utilization and load imbalance. In this work we focus on how clusters schedulers, which are used to share accelerator-rich clusters across many concurrent ML jobs, can embrace performance variability to mitigate its effects. Our key insight to address this challenge is to characterize which applications are more likely to suffer from performance variability and take that into account while placing jobs on the cluster. We design a novel cluster scheduler, PAL, which uses performance variability measurements and application-specific profiles to improve job performance and resource utilization. PAL also balances performance variability with locality to ensure jobs are spread across as few nodes as possible. Overall, PAL significantly improves GPU-rich cluster scheduling: across traces for six ML workload applications spanning image, language, and vision models with a variety of variability profiles, PAL improves geomean job completion time by 42%, cluster utilization by 28%, and makespan by 47% over existing state-of-the-art schedulers.

In this paper, we propose the first method to modify the prosodic features of a given speech signal using actor-critic reinforcement learning strategy. Our approach uses a Bayesian framework to identify contiguous segments of importance that links segments of the given utterances to perception of emotions in humans. We train a neural network to produce the variational posterior of a collection of Bernoulli random variables; our model applies a Markov prior on it to ensure continuity. A sample from this distribution is used for downstream emotion prediction. Further, we train the neural network to predict a soft assignment over emotion categories as the target variable. In the next step, we modify the prosodic features (pitch, intensity, and rhythm) of the masked segment to increase the score of target emotion. We employ an actor-critic reinforcement learning to train the prosody modifier by discretizing the space of modifications. Further, it provides a simple solution to the problem of gradient computation through WSOLA operation for rhythm manipulation. Our experiments demonstrate that this framework changes the perceived emotion of a given speech utterance to the target. Further, we show that our unified technique is on par with state-of-the-art emotion conversion models from supervised and unsupervised domains that require pairwise training., Comment: 7 pages, 10 figures

We derive various novel free boundary problems as limits of a coupled bulk-surface reaction-diffusion system modelling ligand-receptor dynamics on evolving domains. These limiting free boundary problems may be formulated as Stefan-type problems on an evolving hypersurface. Our results are new even in the setting where there is no domain evolution. The models are of particular relevance to a number of applications in cell biology. The analysis utilises $L^\infty$-estimates in the manner of De Giorgi iterations and other technical tools, all in an evolving setting. We also report on numerical simulations.

In our recent research, we have developed a framework called GraphSnapShot, which has been proven an useful tool for graph learning acceleration. GraphSnapShot is a framework for fast cache, storage, retrieval and computation for graph learning. It can quickly store and update the local topology of graph structure and allows us to track patterns in the structure of graph networks, just like take snapshots of the graphs. In experiments, GraphSnapShot shows efficiency, it can achieve up to 30% training acceleration and 73% memory reduction for lossless graph ML training compared to current baselines such as dgl.This technique is particular useful for large dynamic graph learning tasks such as social media analysis and recommendation systems to process complex relationships between entities.

The power graph of a group $G$ is a graph with vertex set $G$, in which two vertices are adjacent if one is some power of the other. In the commuting graph, with $G$ as the vertex set, two vertices are joined by an edge if they commute in $G$. The enhanced power graph of a group $G$ is a graph with vertex set $G$ and an edge joining two vertices $x$ and $y$ if $\langle x,y\rangle$ is cyclic. In this paper, we answer a question posed by P. J. Cameron, namely, if there exist groups $G$ and $H$ such that the power graph of $G$ is isomorphic to the commuting graph of $H$. We show that the answer is yes if $G$ is the generalised quaternion group and $H$ is the dihedral group. We also show that the enhanced power graph of the dicyclic group is isomorphic to the commuting graph of the dihedral group., Comment: Accepted for presentation at ICGTA 2024 (https://presidencyuniversity.in/pu-icgta24-international-conference/)

Modern wide field radio surveys typically detect millions of objects. Techniques based on machine learning are proving to be useful for classifying large numbers of objects. The self-organizing map (SOM) is an unsupervised machine learning algorithm that projects a many-dimensional dataset onto a two- or three-dimensional lattice of neurons. This dimensionality reduction allows the user to visualize common features of the data better and develop algorithms for classifying objects that are not otherwise possible with large datasets. To this aim, we use the PINK implementation of a SOM. PINK incorporates rotation and flipping invariance so that the SOM algorithm may be applied to astronomical images. In this cookbook we provide instructions for working with PINK, including preprocessing the input images, training the model, and offering lessons learned through experimentation. The problem of imbalanced classes can be improved by careful selection of the training sample and increasing the number of neurons in the SOM (chosen by the user). Because PINK is not scale-invariant, structure can be smeared in the neurons. This can also be improved by increasing the number of neurons in the SOM. We also introduce pyink, a Python package used to read and write PINK binary files, assist in common preprocessing operations, perform standard analyses, visualize the SOM and preprocessed images, and create image-based annotations using a graphical interface. A tutorial is also provided to guide the user through the entire process. We present an application of PINK to VLA Sky Survey (VLASS) images. We demonstrate that the PINK is generally able to group VLASS sources with similar morphology together. We use the results of PINK to estimate the probability that a given source in the VLASS QuickLook Catalogue is actually due to sidelobe contamination., Comment: Accepted for publication in Astronomy and Computing

Introduction: Music generation is a complex task that has received significant attention in recent years, and deep learning techniques have shown promising results in this field. Objectives: While extensive work has been carried out on generating Piano and other Western music, there is limited research on generating classical Indian music due to the scarcity of Indian music in machine-encoded formats. In this technical paper, methods for generating classical Indian music, specifically tabla music, is proposed. Initially, this paper explores piano music generation using deep learning architectures. Then the fundamentals are extended to generating tabla music. Methods: Tabla music in waveform (.wav) files are pre-processed using the librosa library in Python. A novel Bi-LSTM with an Attention approach and a transformer model are trained on the extracted features and labels. Results: The models are then used to predict the next sequences of tabla music. A loss of 4.042 and MAE of 1.0814 are achieved with the Bi-LSTM model. With the transformer model, a loss of 55.9278 and MAE of 3.5173 are obtained for tabla music generation. Conclusion: The resulting music embodies a harmonious fusion of novelty and familiarity, pushing the limits of music composition to new horizons.

Large Language Models (LLMs) with hundreds of billions of parameters have transformed the field of machine learning. However, serving these models at inference time is both compute and memory intensive, where a single request can require multiple GPUs and tens of Gigabytes of memory. Multi-Head Attention is one of the key components of LLMs, which can account for over 50% of LLMs memory and compute requirement. We observe that there is a high amount of redundancy across heads on which tokens they pay attention to. Based on this insight, we propose Clustered Head Attention (CHAI). CHAI combines heads with a high amount of correlation for self-attention at runtime, thus reducing both memory and compute. In our experiments, we show that CHAI is able to reduce the memory requirements for storing K,V cache by up to 21.4% and inference time latency by up to 1.73x without any fine-tuning required. CHAI achieves this with a maximum 3.2% deviation in accuracy across 3 different models (i.e. OPT-66B, LLAMA-7B, LLAMA-33B) and 5 different evaluation datasets.

Sonomyography (SMG) is a non-invasive technique that uses ultrasound imaging to detect the dynamic activity of muscles. Wearable SMG systems have recently gained popularity due to their potential as human-computer interfaces for their superior performance compared to conventional methods. This paper demonstrates real-time positional proportional control of multiple gestures using a multiplexed 8-channel wearable SMG system. The amplitude-mode ultrasound signals from the SMG system were utilized to detect muscle activity from the forearm of 8 healthy individuals. The derived signals were used to control the on-screen movement of the cursor. A target achievement task was performed to analyze the performance of our SMG-based human-machine interface. Our wearable SMG system provided accurate, stable, and intuitive control in real-time by achieving an average success rate greater than 80% with all gestures. Furthermore, the wearable SMG system's abilities to detect volitional movement and decode movement kinematic information from SMG trajectories using standard performance metrics were evaluated. Our results provide insights to validate SMG as an intuitive human-machine interface.

Speculative Decoding is a widely used technique to speed up inference for Large Language Models (LLMs) without sacrificing quality. When performing inference, speculative decoding uses a smaller draft model to generate speculative tokens and then uses the target LLM to verify those draft tokens. The speedup provided by speculative decoding heavily depends on the choice of the draft model. In this work, we perform a detailed study comprising over 350 experiments with LLaMA-65B and OPT-66B using speculative decoding and delineate the factors that affect the performance gain provided by speculative decoding. Our experiments indicate that the performance of speculative decoding depends heavily on the latency of the draft model, and the draft model's capability in language modeling does not correlate strongly with its performance in speculative decoding. Based on these insights we explore a new design space for draft models and design hardware-efficient draft models for speculative decoding. Our newly designed draft model for LLaMA-65B can provide 111% higher throughput than existing draft models and can generalize further to the LLaMA-2 model family and supervised fine-tuned models.

Robot learning tasks are extremely compute-intensive and hardware-specific. Thus the avenues of tackling these challenges, using a diverse dataset of offline demonstrations that can be used to train robot manipulation agents, is very appealing. The Train-Offline-Test-Online (TOTO) Benchmark provides a well-curated open-source dataset for offline training comprised mostly of expert data and also benchmark scores of the common offline-RL and behaviour cloning agents. In this paper, we introduce DiffClone, an offline algorithm of enhanced behaviour cloning agent with diffusion-based policy learning, and measured the efficacy of our method on real online physical robots at test time. This is also our official submission to the Train-Offline-Test-Online (TOTO) Benchmark Challenge organized at NeurIPS 2023. We experimented with both pre-trained visual representation and agent policies. In our experiments, we find that MOCO finetuned ResNet50 performs the best in comparison to other finetuned representations. Goal state conditioning and mapping to transitions resulted in a minute increase in the success rate and mean-reward. As for the agent policy, we developed DiffClone, a behaviour cloning agent improved using conditional diffusion., Comment: NeurIPS 2023 Train Offline Test Online Workshop and Competition (Best Paper Oral Presentation / Winning Competition Submission)

We define and investigate the property of being `exponent-critical' for a finite group. A finite group is said to be exponent-critical if its exponent is not the least common multiple of the exponents of its proper non-abelian subgroups. We explore properties of exponent-critical groups and give a characterization of such groups. This characterization generalises a classical result of Miller and Moreno on minimal non-abelian groups; interesting families of $p$-groups appear., Comment: 18 pages. Minor revisions to introduction and abstract

Federated Learning (FL) is a machine-learning approach enabling collaborative model training across multiple decentralized edge devices that hold local data samples, all without exchanging these samples. This collaborative process occurs under the supervision of a central server orchestrating the training or via a peer-to-peer network. The significance of FL is particularly pronounced in industries such as healthcare and finance, where data privacy holds paramount importance. However, training a model under the Federated learning setting brings forth several challenges, with one of the most prominent being the heterogeneity of data distribution among the edge devices. The data is typically non-independently and non-identically distributed (non-IID), thereby presenting challenges to model convergence. This report delves into the issues arising from non-IID and heterogeneous data and explores current algorithms designed to address these challenges.

Deep Learning (DL) workloads have rapidly increased in popularity in enterprise clusters and several new cluster schedulers have been proposed in recent years to support these workloads. With rapidly evolving DL workloads, it is challenging to quickly prototype and compare scheduling policies across workloads. Further, as prior systems target different aspects of scheduling (resource allocation, placement, elasticity etc.), it is also challenging to combine these techniques and understand the overall benefits. To address these challenges we propose Blox, a modular toolkit which allows developers to compose individual components and realize diverse scheduling frameworks. We identify a set of core abstractions for DL scheduling, implement several existing schedulers using these abstractions, and verify the fidelity of these implementations by reproducing results from prior research. We also highlight how we can evaluate and compare existing schedulers in new settings: different workload traces, higher cluster load, change in DNN workloads and deployment characteristics. Finally, we showcase Blox's extensibility by composing policies from different schedulers, and implementing novel policies with minimal code changes. Blox is available at \url{https://github.com/msr-fiddle/blox}., Comment: To be presented at Eurosys'24

Control theory deals with the study of controlling dynamical systems. Robots today are growing increasingly complex and moving out of factory floors to real world environment. These robots have to interact with real world environment factors such as disturbances and this requires the robot to have a control system that is robust. Testing control algorithms on robots in real world environment can pose critical safety issues and can be financially expensive. This has resulted in a heavy emphasis on using simulation to test control algorithms before deploying them in real world environments. Designing control algorithms is an iterative process that starts with modelling the target system in simulation, designing a controller, testing the controller in simulation and then changing the controller parameters to design a better controller. This report explores how an approximated system model of a target hardware system can be developed, which can then be used to design a LQR controller for the target system. The controller is then tested under a disturbance, on hardware and in simulation, and the system response is recorded. The system response from hardware and simulation are then compared to validate the use of approximated system models in simulation for designing and testing control algorithms.