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Fine-tuning Large Language Models (LLMs) on specific datasets is a common practice to improve performance on target tasks. However, this performance gain often leads to overfitting, where the model becomes too specialized in either the task or the characteristics of the training data, resulting in a loss of generalization. This paper introduces Selective Self-Rehearsal (SSR), a fine-tuning approach that achieves performance comparable to the standard supervised fine-tuning (SFT) while improving generalization. SSR leverages the fact that there can be multiple valid responses to a query. By utilizing the model's correct responses, SSR reduces model specialization during the fine-tuning stage. SSR first identifies the correct model responses from the training set by deploying an appropriate LLM as a judge. Then, it fine-tunes the model using the correct model responses and the gold response for the remaining samples. The effectiveness of SSR is demonstrated through experiments on the task of identifying unanswerable queries across various datasets. The results show that standard SFT can lead to an average performance drop of up to $16.7\%$ on multiple benchmarks, such as MMLU and TruthfulQA. In contrast, SSR results in close to $2\%$ drop on average, indicating better generalization capabilities compared to standard SFT., Comment: 14 pages, 8 figures

Finding the optimal learning rate for language model pretraining is a challenging task. This is not only because there is a complicated correlation between learning rate, batch size, number of training tokens, model size, and other hyperparameters but also because it is prohibitively expensive to perform a hyperparameter search for large language models with Billions or Trillions of parameters. Recent studies propose using small proxy models and small corpus to perform hyperparameter searches and transposing the optimal parameters to large models and large corpus. While the zero-shot transferability is theoretically and empirically proven for model size related hyperparameters, like depth and width, the zero-shot transfer from small corpus to large corpus is underexplored. In this paper, we study the correlation between optimal learning rate, batch size, and number of training tokens for the recently proposed WSD scheduler. After thousands of small experiments, we found a power-law relationship between variables and demonstrated its transferability across model sizes. Based on the observation, we propose a new learning rate scheduler, Power scheduler, that is agnostic about the number of training tokens and batch size. The experiment shows that combining the Power scheduler with Maximum Update Parameterization (muP) can consistently achieve impressive performance with one set of hyperparameters regardless of the number of training tokens, batch size, model size, and even model architecture. Our 3B dense and MoE models trained with the Power scheduler achieve comparable performance as state-of-the-art small language models. We open-source these pretrained models at https://ibm.biz/BdKhLa.

This paper introduces long-context Granite code models that support effective context windows of up to 128K tokens. Our solution for scaling context length of Granite 3B/8B code models from 2K/4K to 128K consists of a light-weight continual pretraining by gradually increasing its RoPE base frequency with repository-level file packing and length-upsampled long-context data. Additionally, we also release instruction-tuned models with long-context support which are derived by further finetuning the long context base models on a mix of permissively licensed short and long-context instruction-response pairs. While comparing to the original short-context Granite code models, our long-context models achieve significant improvements on long-context tasks without any noticeable performance degradation on regular code completion benchmarks (e.g., HumanEval). We release all our long-context Granite code models under an Apache 2.0 license for both research and commercial use.

Padding is often used in tuning LLM models by adding special tokens to shorter training examples to match the length of the longest sequence in each batch. While this ensures uniformity for batch processing, it introduces inefficiencies by including irrelevant padding tokens in the computation and wastes GPU resources. Hugging Face SFT trainer has always offered the option to use packing to combine multiple training examples, allowing for maximal utilization of GPU resources. However, up till now, it did not offer proper masking of each packed training example. This capability has been added to Hugging Face Transformers 4.44. We analyse this new feature and show the benefits across different variations of packing.

AI Infrastructure plays a key role in the speed and cost-competitiveness of developing and deploying advanced AI models. The current demand for powerful AI infrastructure for model training is driven by the emergence of generative AI and foundational models, where on occasion thousands of GPUs must cooperate on a single training job for the model to be trained in a reasonable time. Delivering efficient and high-performing AI training requires an end-to-end solution that combines hardware, software and holistic telemetry to cater for multiple types of AI workloads. In this report, we describe IBM's hybrid cloud infrastructure that powers our generative AI model development. This infrastructure includes (1) Vela: an AI-optimized supercomputing capability directly integrated into the IBM Cloud, delivering scalable, dynamic, multi-tenant and geographically distributed infrastructure for large-scale model training and other AI workflow steps and (2) Blue Vela: a large-scale, purpose-built, on-premises hosting environment that is optimized to support our largest and most ambitious AI model training tasks. Vela provides IBM with the dual benefit of high performance for internal use along with the flexibility to adapt to an evolving commercial landscape. Blue Vela provides us with the benefits of rapid development of our largest and most ambitious models, as well as future-proofing against the evolving model landscape in the industry. Taken together, they provide IBM with the ability to rapidly innovate in the development of both AI models and commercial offerings., Comment: Corresponding Authors: Talia Gershon, Seetharami Seelam,Brian Belgodere, Milton Bonilla

Key-value (KV) caching plays an essential role in accelerating decoding for transformer-based autoregressive large language models (LLMs). However, the amount of memory required to store the KV cache can become prohibitive at long sequence lengths and large batch sizes. Since the invention of the transformer, two of the most effective interventions discovered for reducing the size of the KV cache have been Multi-Query Attention (MQA) and its generalization, Grouped-Query Attention (GQA). MQA and GQA both modify the design of the attention block so that multiple query heads can share a single key/value head, reducing the number of distinct key/value heads by a large factor while only minimally degrading accuracy. In this paper, we show that it is possible to take Multi-Query Attention a step further by also sharing key and value heads between adjacent layers, yielding a new attention design we call Cross-Layer Attention (CLA). With CLA, we find that it is possible to reduce the size of the KV cache by another 2x while maintaining nearly the same accuracy as unmodified MQA. In experiments training 1B- and 3B-parameter models from scratch, we demonstrate that CLA provides a Pareto improvement over the memory/accuracy tradeoffs which are possible with traditional MQA, enabling inference with longer sequence lengths and larger batch sizes than would otherwise be possible

Large Language Models (LLMs) trained on code are revolutionizing the software development process. Increasingly, code LLMs are being integrated into software development environments to improve the productivity of human programmers, and LLM-based agents are beginning to show promise for handling complex tasks autonomously. Realizing the full potential of code LLMs requires a wide range of capabilities, including code generation, fixing bugs, explaining and documenting code, maintaining repositories, and more. In this work, we introduce the Granite series of decoder-only code models for code generative tasks, trained with code written in 116 programming languages. The Granite Code models family consists of models ranging in size from 3 to 34 billion parameters, suitable for applications ranging from complex application modernization tasks to on-device memory-constrained use cases. Evaluation on a comprehensive set of tasks demonstrates that Granite Code models consistently reaches state-of-the-art performance among available open-source code LLMs. The Granite Code model family was optimized for enterprise software development workflows and performs well across a range of coding tasks (e.g. code generation, fixing and explanation), making it a versatile all around code model. We release all our Granite Code models under an Apache 2.0 license for both research and commercial use., Comment: Corresponding Authors: Rameswar Panda, Ruchir Puri; Equal Contributors: Mayank Mishra, Matt Stallone, Gaoyuan Zhang

Mixture-of-Experts (MoE) language models can reduce computational costs by 2-4$\times$ compared to dense models without sacrificing performance, making them more efficient in computation-bounded scenarios. However, MoE models generally require 2-4$\times$ times more parameters to achieve comparable performance to a dense model, which incurs larger GPU memory requirements and makes MoE models less efficient in I/O-bounded scenarios like autoregressive generation. In this work, we propose a hybrid dense training and sparse inference framework for MoE models (DS-MoE) which achieves strong computation and parameter efficiency by employing dense computation across all experts during training and sparse computation during inference. Our experiments on training LLMs demonstrate that our DS-MoE models are more parameter-efficient than standard sparse MoEs and are on par with dense models in terms of total parameter size and performance while being computationally cheaper (activating 30-40% of the model's parameters). Performance tests using vLLM show that our DS-MoE-6B model runs up to $1.86\times$ faster than similar dense models like Mistral-7B, and between $1.50\times$ and $1.71\times$ faster than comparable MoEs, such as DeepSeekMoE-16B and Qwen1.5-MoE-A2.7B.

We consider the problem of accurate quantization for language models, where both the weights and activations are uniformly quantized to 4 bits per parameter, the lowest bitwidth format natively supported by GPU hardware. In this context, the key challenge is activation quantization: it is known that language models contain outlier channels whose values on average are orders of magnitude higher than than other channels, which prevents accurate low-bitwidth quantization with known techniques. We systematically study this phenomena and find that these outlier channels emerge early in training, and that they occur more frequently in layers with residual streams. We then propose a simple strategy which regularizes a layer's inputs via quantization-aware training (QAT) and its outputs via activation kurtosis regularization. We show that regularizing both the inputs and outputs is crucial for preventing a model's "migrating" the difficulty in input quantization to the weights, which makes post-training quantization (PTQ) of weights more difficult. When combined with weight PTQ, we show that our approach can obtain a W4A4 model that performs competitively to the standard-precision W16A16 baseline.

Exploring new strategies for controlling the magnetic domain propagation is the key to realize ultrafast, high-density domain wall-based memory and logic devices for next generation computing. These strategies include strain modulation in multiferroic devices, geometric confinement and area-selective pinning of domain wall. 2D Van der Waals materials introduce localized modifications to the interfacial magnetic order, enabling control over the propagation of magnetic domains. Here, using Lorentz-Transmission Electron Microscopy (L-TEM) along with the Modified Transport of Intensity equations (MTIE), we demonstrate controlled domain expansion with in-situ magnetic field in a ferromagnet (Permalloy, NiFe) interfacing with a 2D Van der Waals material Graphene (Gr). The Gr/NiFe interface exhibits distinctive domain expansion rate with magnetic field selectively near the interface which is further analyzed using micromagnetic simulations. Our findings are crucial for comprehending direct visualization of interface controlled magnetic domain expansion, offering insights for developing future domain wall-based technology., Comment: Merged Manuscript and supplementary file. Submitted to Communications Physics (under review)

Vision Transformer (ViT) has emerged as a prominent architecture for various computer vision tasks. In ViT, we divide the input image into patch tokens and process them through a stack of self attention blocks. However, unlike Convolutional Neural Networks (CNN), ViTs simple architecture has no informative inductive bias (e.g., locality,etc. ). Due to this, ViT requires a large amount of data for pre-training. Various data efficient approaches (DeiT) have been proposed to train ViT on balanced datasets effectively. However, limited literature discusses the use of ViT for datasets with long-tailed imbalances. In this work, we introduce DeiT-LT to tackle the problem of training ViTs from scratch on long-tailed datasets. In DeiT-LT, we introduce an efficient and effective way of distillation from CNN via distillation DIST token by using out-of-distribution images and re-weighting the distillation loss to enhance focus on tail classes. This leads to the learning of local CNN-like features in early ViT blocks, improving generalization for tail classes. Further, to mitigate overfitting, we propose distilling from a flat CNN teacher, which leads to learning low-rank generalizable features for DIST tokens across all ViT blocks. With the proposed DeiT-LT scheme, the distillation DIST token becomes an expert on the tail classes, and the classifier CLS token becomes an expert on the head classes. The experts help to effectively learn features corresponding to both the majority and minority classes using a distinct set of tokens within the same ViT architecture. We show the effectiveness of DeiT-LT for training ViT from scratch on datasets ranging from small-scale CIFAR-10 LT to large-scale iNaturalist-2018., Comment: CVPR 2024. Project Page: https://rangwani-harsh.github.io/DeiT-LT

Pretrained language models underpin several AI applications, but their high computational cost for training limits accessibility. Initiatives such as BLOOM and StarCoder aim to democratize access to pretrained models for collaborative community development. However, such existing models face challenges: limited multilingual capabilities, continual pretraining causing catastrophic forgetting, whereas pretraining from scratch is computationally expensive, and compliance with AI safety and development laws. This paper presents Aurora-M, a 15B parameter multilingual open-source model trained on English, Finnish, Hindi, Japanese, Vietnamese, and code. Continually pretrained from StarCoderPlus on 435 billion additional tokens, Aurora-M surpasses 2 trillion tokens in total training token count. It is the first open-source multilingual model fine-tuned on human-reviewed safety instructions, thus aligning its development not only with conventional red-teaming considerations, but also with the specific concerns articulated in the Biden-Harris Executive Order on the Safe, Secure, and Trustworthy Development and Use of Artificial Intelligence. Aurora-M is rigorously evaluated across various tasks and languages, demonstrating robustness against catastrophic forgetting and outperforming alternatives in multilingual settings, particularly in safety evaluations. To promote responsible open-source LLM development, Aurora-M and its variants are released at https://huggingface.co/collections/aurora-m/aurora-m-models-65fdfdff62471e09812f5407 ., Comment: Preprint

The BigCode project, an open-scientific collaboration focused on the responsible development of Large Language Models for Code (Code LLMs), introduces StarCoder2. In partnership with Software Heritage (SWH), we build The Stack v2 on top of the digital commons of their source code archive. Alongside the SWH repositories spanning 619 programming languages, we carefully select other high-quality data sources, such as GitHub pull requests, Kaggle notebooks, and code documentation. This results in a training set that is 4x larger than the first StarCoder dataset. We train StarCoder2 models with 3B, 7B, and 15B parameters on 3.3 to 4.3 trillion tokens and thoroughly evaluate them on a comprehensive set of Code LLM benchmarks. We find that our small model, StarCoder2-3B, outperforms other Code LLMs of similar size on most benchmarks, and also outperforms StarCoderBase-15B. Our large model, StarCoder2- 15B, significantly outperforms other models of comparable size. In addition, it matches or outperforms CodeLlama-34B, a model more than twice its size. Although DeepSeekCoder- 33B is the best-performing model at code completion for high-resource languages, we find that StarCoder2-15B outperforms it on math and code reasoning benchmarks, as well as several low-resource languages. We make the model weights available under an OpenRAIL license and ensure full transparency regarding the training data by releasing the SoftWare Heritage persistent IDentifiers (SWHIDs) of the source code data.

Distribution matching methods for language model alignment such as Generation with Distributional Control (GDC) and Distributional Policy Gradient (DPG) have not received the same level of attention in reinforcement learning from human feedback (RLHF) as contrastive methods such as Sequence Likelihood Calibration (SLiC), Direct Preference Optimization (DPO) and its variants. We identify high variance of the gradient estimate as the primary reason for the lack of success of these methods and propose a self-normalized baseline to reduce the variance. We further generalize the target distribution in DPG, GDC and DPO by using Bayes' rule to define the reward-conditioned posterior. The resulting approach, referred to as BRAIn - Bayesian Reward-conditioned Amortized Inference acts as a bridge between distribution matching methods and DPO and significantly outperforms prior art in summarization and Antropic HH tasks., Comment: Accepted at ICML 2024 (main conference)

The impurity incorporation in host high-spin orbit coupling materials like platinum has shown improved charge-to-spin conversion by modifying the up-spin and down-spin electron trajectories by bending or skewing them in opposite directions. This enables efficient generation, manipulation, and transport of spin currents. In this study, we irradiate the platinum with non-focus dense plasma to incorporate the oxygen ion species. We systematically analyze the spin Hall angle of the oxygen plasma irradiated Pt films using spin torque ferromagnetic resonance. Our results demonstrate a 2.4 times enhancement in the spin Hall effect after plasma treatment of Pt as compared to pristine Pt. This improvement is attributed to the introduction of disorder and defects in the Pt lattice, which enhances the spin-orbit coupling and leads to more efficient charge-to-spin conversion without breaking the spin-orbit torque symmetries. Our findings offer a new method of dense plasma-based modification of material for the development of advanced spintronic devices based on Pt and other heavy metals.

Prompting with natural language instructions has recently emerged as a popular method of harnessing the capabilities of large language models. Given the inherent ambiguity present in natural language, it is intuitive to consider the possible advantages of prompting with less ambiguous prompt styles, such as the use of pseudo-code. In this paper we explore if prompting via pseudo-code instructions helps improve the performance of pre-trained language models. We manually create a dataset of pseudo-code prompts for 132 different tasks spanning classification, QA and generative language tasks, sourced from the Super-NaturalInstructions dataset. Using these prompts along with their counterparts in natural language, we study their performance on two LLM families - BLOOM and CodeGen. Our experiments show that using pseudo-code instructions leads to better results, with an average increase (absolute) of 7-16 points in F1 scores for classification tasks and an improvement (relative) of 12-38% in aggregate ROUGE-L scores across all tasks. We include detailed ablation studies which indicate that code comments, docstrings, and the structural clues encoded in pseudo-code all contribute towards the improvement in performance. To the best of our knowledge our work is the first to demonstrate how pseudo-code prompts can be helpful in improving the performance of pre-trained LMs., Comment: Published in EMNLP 2023 main track

The BigCode community, an open-scientific collaboration working on the responsible development of Large Language Models for Code (Code LLMs), introduces StarCoder and StarCoderBase: 15.5B parameter models with 8K context length, infilling capabilities and fast large-batch inference enabled by multi-query attention. StarCoderBase is trained on 1 trillion tokens sourced from The Stack, a large collection of permissively licensed GitHub repositories with inspection tools and an opt-out process. We fine-tuned StarCoderBase on 35B Python tokens, resulting in the creation of StarCoder. We perform the most comprehensive evaluation of Code LLMs to date and show that StarCoderBase outperforms every open Code LLM that supports multiple programming languages and matches or outperforms the OpenAI code-cushman-001 model. Furthermore, StarCoder outperforms every model that is fine-tuned on Python, can be prompted to achieve 40\% pass@1 on HumanEval, and still retains its performance on other programming languages. We take several important steps towards a safe open-access model release, including an improved PII redaction pipeline and a novel attribution tracing tool, and make the StarCoder models publicly available under a more commercially viable version of the Open Responsible AI Model license.

The BigCode project is an open-scientific collaboration working on the responsible development of large language models for code. This tech report describes the progress of the collaboration until December 2022, outlining the current state of the Personally Identifiable Information (PII) redaction pipeline, the experiments conducted to de-risk the model architecture, and the experiments investigating better preprocessing methods for the training data. We train 1.1B parameter models on the Java, JavaScript, and Python subsets of The Stack and evaluate them on the MultiPL-E text-to-code benchmark. We find that more aggressive filtering of near-duplicates can further boost performance and, surprisingly, that selecting files from repositories with 5+ GitHub stars deteriorates performance significantly. Our best model outperforms previous open-source multilingual code generation models (InCoder-6.7B and CodeGen-Multi-2.7B) in both left-to-right generation and infilling on the Java, JavaScript, and Python portions of MultiPL-E, despite being a substantially smaller model. All models are released under an OpenRAIL license at https://hf.co/bigcode.

Real-world datasets exhibit imbalances of varying types and degrees. Several techniques based on re-weighting and margin adjustment of loss are often used to enhance the performance of neural networks, particularly on minority classes. In this work, we analyze the class-imbalanced learning problem by examining the loss landscape of neural networks trained with re-weighting and margin-based techniques. Specifically, we examine the spectral density of Hessian of class-wise loss, through which we observe that the network weights converge to a saddle point in the loss landscapes of minority classes. Following this observation, we also find that optimization methods designed to escape from saddle points can be effectively used to improve generalization on minority classes. We further theoretically and empirically demonstrate that Sharpness-Aware Minimization (SAM), a recent technique that encourages convergence to a flat minima, can be effectively used to escape saddle points for minority classes. Using SAM results in a 6.2\% increase in accuracy on the minority classes over the state-of-the-art Vector Scaling Loss, leading to an overall average increase of 4\% across imbalanced datasets. The code is available at: https://github.com/val-iisc/Saddle-LongTail., Comment: NeurIPS 2022. Code: https://github.com/val-iisc/Saddle-LongTail

Large language models (LLMs) have been shown to be able to perform new tasks based on a few demonstrations or natural language instructions. While these capabilities have led to widespread adoption, most LLMs are developed by resource-rich organizations and are frequently kept from the public. As a step towards democratizing this powerful technology, we present BLOOM, a 176B-parameter open-access language model designed and built thanks to a collaboration of hundreds of researchers. BLOOM is a decoder-only Transformer language model that was trained on the ROOTS corpus, a dataset comprising hundreds of sources in 46 natural and 13 programming languages (59 in total). We find that BLOOM achieves competitive performance on a wide variety of benchmarks, with stronger results after undergoing multitask prompted finetuning. To facilitate future research and applications using LLMs, we publicly release our models and code under the Responsible AI License.

Traditional systems designed for task oriented dialog utilize knowledge present only in structured knowledge sources to generate responses. However, relevant information required to generate responses may also reside in unstructured sources, such as documents. Recent state of the art models such as HyKnow and SeKnow aimed at overcoming these challenges make limiting assumptions about the knowledge sources. For instance, these systems assume that certain types of information, such as a phone number, is always present in a structured knowledge base (KB) while information about aspects such as entrance ticket prices, would always be available in documents. In this paper, we create a modified version of the MutliWOZ-based dataset prepared by SeKnow to demonstrate how current methods have significant degradation in performance when strict assumptions about the source of information are removed. Then, in line with recent work exploiting pre-trained language models, we fine-tune a BART based model using prompts for the tasks of querying knowledge sources, as well as, for response generation, without making assumptions about the information present in each knowledge source. Through a series of experiments, we demonstrate that our model is robust to perturbations to knowledge modality (source of information), and that it can fuse information from structured as well as unstructured knowledge to generate responses.

Domain adversarial training has been ubiquitous for achieving invariant representations and is used widely for various domain adaptation tasks. In recent times, methods converging to smooth optima have shown improved generalization for supervised learning tasks like classification. In this work, we analyze the effect of smoothness enhancing formulations on domain adversarial training, the objective of which is a combination of task loss (eg. classification, regression, etc.) and adversarial terms. We find that converging to a smooth minima with respect to (w.r.t.) task loss stabilizes the adversarial training leading to better performance on target domain. In contrast to task loss, our analysis shows that converging to smooth minima w.r.t. adversarial loss leads to sub-optimal generalization on the target domain. Based on the analysis, we introduce the Smooth Domain Adversarial Training (SDAT) procedure, which effectively enhances the performance of existing domain adversarial methods for both classification and object detection tasks. Our analysis also provides insight into the extensive usage of SGD over Adam in the community for domain adversarial training., Comment: ICML 2022. Code: https://github.com/val-iisc/SDAT

The laws of quantum physics endow superior performance and security for information processing: quantum sensing harnesses nonclassical resources to enable measurement precision unmatched by classical sensing, whereas quantum cryptography aims to unconditionally protect the secrecy of the processed information. Here, we present the theory and experiment for entanglement-enhanced covert sensing, a paradigm that simultaneously offers high measurement precision and data integrity by concealing the probe signal in an ambient noise background so that the execution of the protocol is undetectable with a high probability. We show that entanglement offers a performance boost in estimating the imparted phase by a probed object, as compared to a classical protocol at the same covertness level. The implemented entanglement-enhanced covert sensing protocol operates close to the fundamental quantum limit by virtue of its near-optimum entanglement source and quantum receiver. Our work is expected to create ample opportunities for quantum information processing at unprecedented security and performance levels., Comment: 19 pages, 12 figures

Recent methods for knowledge grounded dialogs generate responses by incorporating information from an external textual document. These methods do not require the exact document to be known during training and rely on the use of a retrieval system to fetch relevant documents from a large index. The documents used to generate the responses are modeled as latent variables whose prior probabilities need to be estimated. Models such as RAG and REALM, marginalize the document probabilities over the documents retrieved from the index to define the log likelihood loss function which is optimized end-to-end. In this paper, we develop a variational approach to the above technique wherein, we instead maximize the Evidence Lower bound (ELBO). Using a collection of three publicly available open-conversation datasets, we demonstrate how the posterior distribution, that has information from the ground-truth response, allows for a better approximation of the objective function during training. To overcome the challenges associated with sampling over a large knowledge collection, we develop an efficient approach to approximate the ELBO. To the best of our knowledge we are the first to apply variational training for open-scale unsupervised knowledge grounded dialog systems.

Meta Learning has been in focus in recent years due to the meta-learner model's ability to adapt well and generalize to new tasks, thus, reducing both the time and data requirements for learning. However, a major drawback of meta learner is that, to reach to a state from where learning new tasks becomes feasible with less data, it requires a large number of iterations and a lot of time. We address this issue by proposing various acceleration techniques to speed up meta learning algorithms such as MAML (Model Agnostic Meta Learning). We present 3.73X acceleration on a well known RNN optimizer based meta learner proposed in literature [11]. We introduce a novel method of training tasks in clusters, which not only accelerates the meta learning process but also improves model accuracy performance. Keywords: Meta learning, RNN optimizer, AGI, Performance optimization

An $L(2,1)$-labelling of a finite graph $\Gamma$ is a function that assigns integer values to the vertices $V(\Gamma)$ of $\Gamma$ (colouring of $V(\Gamma)$ by ${\mathbb{Z}}$) so that the absolute difference of two such values is at least $2$ for adjacent vertices and is at least $1$ for vertices which are precisely distance $2$ apart. The lambda number $\lambda(\Gamma)$ of $\Gamma$ measures the least number of integers needed for such a labelling (colouring). A power graph $\Gamma_G$ of a finite group $G$ is a graph with vertex set as the elements of $G$ and two vertices are joined by an edge if and only if one of them is a positive integer power of the other. It is known that $\lambda(\Gamma_G) \geq |G|$ for any finite group. In this paper we show that if $G$ is a finite group of a prime power order, then $\lambda(\Gamma_G) = |G|$ if and only if $G$ is neither cyclic nor a generalized quaternion $2$-group. This settles a partial classification of finite groups achieving the lower bound of lambda number., Comment: 8 pages, 3 figures

We show the enhancement of distillable key rate for quantum key distribution(QKD), by local filtering, for several bound entangled states. Through our work it becomes evident that the local filtration operations, while transforming one bound entangled state to another, have the potential to increase the utility of the new state for QKD. We demonstrate three examples of `one way distillable key rate' enhancement by local filtering and in this process, discover new bound entangled states which are key distillable., Comment: Final version minor changes

Speech produced by human vocal apparatus conveys substantial non-semantic information including the gender of the speaker, voice quality, affective state, abnormalities in the vocal apparatus etc. Such information is attributed to the properties of the voice source signal, which is usually estimated from the speech signal. However, most of the source estimation techniques depend heavily on the goodness of the model assumptions and are prone to noise. A popular alternative is to indirectly obtain the source information through the Electroglottographic (EGG) signal that measures the electrical admittance around the vocal folds using dedicated hardware. In this paper, we address the problem of estimating the EGG signal directly from the speech signal, devoid of any hardware. Sampling from the intractable conditional distribution of the EGG signal given the speech signal is accomplished through optimization of an evidence lower bound. This is constructed via minimization of the KL-divergence between the true and the approximated posteriors of a latent variable learned using a deep neural auto-encoder that serves an informative prior. We demonstrate the efficacy of the method at generating the EGG signal by conducting several experiments on datasets comprising multiple speakers, voice qualities, noise settings and speech pathologies. The proposed method is evaluated on many benchmark metrics and is found to agree with the gold standard while proving better than the state-of-the-art algorithms on a few tasks such as epoch extraction., Comment: Submitted to IEEE/ACM Transactions on Audio, Speech and Language Processing

Despite their tremendous success in modelling high-dimensional data manifolds, deep neural networks suffer from the threat of adversarial attacks - Existence of perceptually valid input-like samples obtained through careful perturbation that lead to degradation in the performance of the underlying model. Major concerns with existing defense mechanisms include non-generalizability across different attacks, models and large inference time. In this paper, we propose a generalized defense mechanism capitalizing on the expressive power of regularized latent space based generative models. We design an adversarial filter, devoid of access to classifier and adversaries, which makes it usable in tandem with any classifier. The basic idea is to learn a Lipschitz constrained mapping from the data manifold, incorporating adversarial perturbations, to a quantized latent space and re-map it to the true data manifold. Specifically, we simultaneously auto-encode the data manifold and its perturbations implicitly through the perturbations of the regularized and quantized generative latent space, realized using variational inference. We demonstrate the efficacy of the proposed formulation in providing resilience against multiple attack types (black and white box) and methods, while being almost real-time. Our experiments show that the proposed method surpasses the state-of-the-art techniques in several cases.