Binary Representation Research Articles

A Latent Space Model for Weighted Keyword Co-occurrence Networks with Applications in Knowledge Discovery in Statistics

Keywords are widely recognized as pivotal in conveying the central idea of academic articles. In this article, we construct a weighted and dynamic keyword co-occurrence network and propose a latent space model for analyzing it. Our model has two special characteristics. First, it is applicable to weighted networks however, most previous models were primarily designed for unweighted networks. Simply replacing the frequency of keyword co-occurrence with binary values would result in a significant loss of information. Second, our model can handle the situation where network nodes evolve over time, and assess the effect of new nodes on network connectivity. We utilize the projected gradient descent algorithm to estimate the latent positions and establish the theoretical properties of the estimators. In the real data application, we study the keyword co-occurrence network within the field of statistics. We identify popular keywords over the whole period as well as within each time period. For keyword pairs, our model provides a new way to assess the association between them. Finally, we observe that the interest of statisticians in emerging research areas has gradually grown in recent years. Supplementary materials for this article are available online

Quantifying and visualising uncertainty in deep learning-based segmentation for radiation therapy treatment planning: What do radiation oncologists and therapists want?

Background and purposeDuring the ESTRO 2023 physics workshop on “AI for the fully automated radiotherapy treatment chain”, the topic of deep learning (DL) segmentation was discussed. Despite its widespread use in radiotherapy, the time needed to evaluate and correct DL segmentations remains burdensome. While segmentation uncertainty could be beneficial for clinicians, there is a lack of understanding on what information should be presented to ease their task. This study aimed to gather insights from clinicians on uncertainty visualisation options. Materials and methodsTwo sessions of structured interviews were conducted across four institutions already using DL segmentation clinically. The first session focused on the main problems hindering the clinical use of DL. In the second session, ten visualisation options displaying uncertainty information at different levels (structure, slice, or voxel) with binary or continuous values were presented. Dosimetric information was also present in some visualisations. For each case, sixteen clinicians (radiation oncologists and radiation therapists) were asked to grade an overall score, the usability, the training required, and the expected time gain. ResultsParticipants preferred the binary voxel-level uncertainty visualisation, followed by binary structure-level uncertainty visualisation. Combining structure-level and voxel-level visualisation methods has been proposed as a promising approach. The benefits of dosimetric information were perceived diversely among participants since it complexifies the display but could be useful for the online adaptive workflow. ConclusionPreferences for uncertainty visualisation methods were assessed within a multi-institutional experienced group of clinicians. Further refinement of preferences may help in selecting the best options for clinical implementation.

Optimising Text Steganography with Alpha-Based Representative Binary: Analysing Contain Letter Used and Capacity Ratio

Text steganography has become essential for secure communication in the digital age, offering a method to hide messages within seemingly ordinary text. This paper introduces the Alpha-based Representative Binary technique, an advanced feature-based method for text steganography. It utilizes both capital and small letters to represent 2-bit binary values, embedding more information without altering the visual integrity of the text. By assigning different binary values to uppercase and lowercase letters, this technique optimizes the balance between information density and detectability. Embedding 2-bit values strikes an ideal balance, as it allows for a higher capacity of hidden information while maintaining a low profile. This study evaluates the performance of the Alpha-based Representative Binary technique against existing methods like QUAD and One-Flow-2-bit, focusing on two metrics performance: the total character count in the stego text (contain letter used) and the amount of data that can be embedded relative to the cover text size (capacity ratio). The findings underscore the technique's strengths in maintaining secure and undetectable hidden messages within text. This paper highlights the evolution and effectiveness of feature-based methods, emphasizing the need for continued innovation to address detection risks and content modification challenges. By providing a detailed analysis and potential improvements, this paper aims to contribute to the development of more robust and undetectable text steganography systems. The perceptions gained from this paper is expected as valuable for researchers and practitioners in the field of secure communication.

Mitigating Disparate Elevation Differences between Adjacent Topobathymetric Data Models Using Binary Code

Integrating coastal topographic and bathymetric data for creating regional seamless topobathymetric digital elevation models of the land/water interface presents a complex challenge due to the spatial and temporal gaps in data acquisitions. The Coastal National Elevation Database (CoNED) Applications Project develops topographic (land elevation) and bathymetric (water depth) regional scale digital elevation models by integrating multiple sourced disparate topographic and bathymetric data models. These integrated regional models are broadly used in coastal and climate science applications, such as sediment transport, storm impact, and sea-level rise modeling. However, CoNED’s current integration method does not address the occurrence of measurable vertical discrepancies between adjacent near-shore topographic and bathymetric data sources, which often create artificial barriers and sinks along their intersections. To tackle this issue, the CoNED project has developed an additional step in its integration process that collectively assesses the input data to define how to transition between these disparate datasets. This new step defines two zones: a micro blending zone for near-shore transitions and a macro blending zone for the transition between high-resolution (3 m or less) to moderate-resolution (between 3 m and 10 m) bathymetric datasets. These zones and input data sources are reduced to a multidimensional array of zeros and ones. This array is compiled into a 16-bit integer representing a vertical assessment for each pixel. This assessed value provides the means for dynamic pixel-level blending between disparate datasets by leveraging the 16-bit binary notation. Sample site RMSE assessments demonstrate improved accuracy, with values decreasing from 0.203–0.241 using the previous method to 0.126–0.147 using the new method. This paper introduces CoNED’s unique approach of using binary code to improve the integration of coastal topobathymetric data.

Combining Zhegalkin Polynomials and SAT Solving for Context-specific Boolean Modeling of Biological Systems.

Large amounts of knowledge regarding biological processes are readily available in the literature and aggregated in diverse databases. Boolean networks are powerful tools to render that knowledge into models that can mimic and simulate biological phenomena at multiple scales. Yet, when a model is required to understand or predict the behavior of a biological system in given conditions, existing information often does not completely match this context. Networks built from only prior knowledge can overlook mechanisms, lack specificity, and just partially recapitulate experimental observations. To address this limitation, context-specific data needs to be integrated. However, the brute-force identification of qualitative rules matching these data becomes infeasible as the number of candidates explodes for increasingly complex systems. Here, we used Zhegalkin polynomials to transform this identification into a binary value assignment for exponentially fewer variables, which we addressed with a state-of-the-art SAT solver. We evaluated our implemented method alongside two widely recognized tools, CellNetOptimizer and Caspo-ts, on both artificial toy models and large-scale models based on experimental data from the HPN-DREAM challenge. Our approach demonstrated benchmark-leading capabilities on networks of significant size and intricate complexity. It thus appears promising for the in silico modeling of ever more comprehensive biological systems.

Uncountable group of continuous transformations of unit segment preserving tails of Q_2-representation of numbers

We consider two-base Q2-representation of numbers of segment [0;1] which is defined by two bases q0 ∈ (0;1), q1 = 1-q0 and alphabet A={0,1}, (αn) ∈ A × A × .... It is a generalization of classic binary representation q0=1/2. In the article we prove that the set of all continuous bijections of segment [0;1] preserving "tails" of Q2-representation of numbers forms an uncountable non-abelian group with respect to composition such that it is a subgroup of the group of continuous transformations preserving frequencies of digits of Q2-representation of numbers. Construction of such transformations (bijections) is based on the left and right shift operators for digits of Q2-representation of numbers.

Improved implementation of serial pseudorandom/natural code converters used in absolute position encoders

Abstract Pseudorandom encoders represent a significant type of absolute position encoders that can be implemented using only a single code track on a code disk and a single reading head, making them especially suitable for high-resolution position measurements. Since pseudorandom code words used for encoding positions are not compatible with other electronics, pseudorandom encoders include a converter that translates the pseudorandom code into the natural binary code. This paper proposes an improved implementation of the serial Fibonacci pseudorandom/natural code converter used in pseudorandom position encoders. The improvement is based on modifying the way bits are written into the converter’s shift register, which reduces the propagation delay inside the code converter, thus enabling an increase in the clock frequency. Simulations of the proposed solution, performed in Multisim software, provide a realistic picture of its behaviour and performance. Based on the simulation results, the proposed solution enables a significant increase in the clock frequency of the code converter by 180.54% or 57.56%, depending on the encoder resolution. This significantly boosts the speed of code conversion and enhances the overall performance of the position encoder. The proposed solution is highly valuable for numerous position measurement applications, especially in the increasingly relevant high-resolution applications.

Comparison of a machine learning model with a conventional rule-based selective dry cow therapy algorithm for detection of intramammary infections

We trained machine learning models to identify intramammary infections (IMI) in late lactation cows at dry-off to guide antibiotic treatment, and compared their performance to a rule-based algorithm that is currently used on dairy farms in the US. We conducted an observational test-characteristics study using a data set of 3,645 cows approaching dry-off from 68 US dairy herds. The outcome variables of interest were cow-level IMI caused by all pathogens, major pathogens, and Streptococcus and Strep-like organisms (SSLO), which were determined using aerobic culture of aseptic quarter-milk samples and identification of isolates using MALDI-TOF. Individual cow records were extracted from the farm software to create 53 feature variables at the cow and 39 at the herd-level which were derived from cow-level descriptive data, records of clinical mastitis events, results from routine testing of milk for volume and concentrations of somatic cell count (SCC), fat, and protein. ML algorithms evaluated were logistic regression, decision tree, random forest, light gradient-boosting machine, naïve bayes, and neural networks. For comparison, cows were also classified according to a conventional rule-based algorithm that considered a cow as high risk for IMI if she had at one or more high SCC (>200,000 cells/ml) tests or ≥2 cases of clinical mastitis during the lactation of enrollment. Area under the curve (AUC) and Youden's index were used to compare models, in addition to binary classification metrics, including sensitivity, specificity, and predictive values. ML models had slightly higher AUC and Youden's index values than the rule-based algorithm for all IMI outcomes of interest. However, these improvements in prediction accuracy were substantially less than what we had considered necessary for the technology to be a worthwhile alternative to the rule-based algorithm. Therefore, evidence is lacking to support the wholesale use of ML-guided selective dry cow therapy at the moment. We recommend that producers wanting to implement algorithm-guided SDCT use a rule-based method.

Evaluating Scholastic Achievement in Pediatric Brain Tumor Survivors Compared With Healthy Controls

BackgroundRadiotherapy (RT) causes cognitive deficits in pediatric brain tumor survivors (PBTS). Traditionally, this is measured using neuropsychological testing, which lack pre-diagnosis baseline and do not necessarily trigger action. This pilot project investigated a novel patient-centered outcome of scholastic performance using state-collected educational data. MethodsWe retrospectively analyzed scholastic achievements in children residing in Florida. Eligibility in the treatment group received brain-directed RT between 2007 – 2020 at our institution. Controls were matched at a 3:1 ratio by age, grade, district, and free or reduced lunch (FRL) eligibility. The Florida Department of Education provided educational records for both groups. Generalized linear mixed-effects models were used to predict scholastic outcomes with covariates age, time (binary value of pre- or post-RT), treatment group, and the primary independent variable as the interaction term between time and treatment. Scholastic data was matched with institutional clinical data. ResultsFifty PBTS and 150 matched controls were included for analysis. Median age of PBTS was 12, 12% identified as Black, and 18% as Hispanic. Fifty-two percent were FRL eligible. Forty percent received craniospinal irradiation, and 56% received chemotherapy. Post-RT PBTS had 21 times the odds of receiving accommodations (p=0.006), twice the odds of being retained (p=0.010), and 42% lower odds than controls receiving a passing mathematics score (p=0.068). ConclusionsTo our knowledge, this is the first American experience to successfully link individual scholastic and clinical data. Scholastic performance serves as a meaningful patient-centered outcome complementing the existing suite of neuropsychological testing.

On monochromatic arithmetic progressions in binary words associated with pattern sequences

Let ev(n) denote the number of occurrences of a fixed pattern v in the binary expansion of n∈N. In this paper we study monochromatic arithmetic progressions in the class of binary words (ev(n)mod2)n≥0, which includes the famous Thue–Morse word t and Rudin–Shapiro word r. We prove that the length of a monochromatic arithmetic progression of difference d≥3 starting at 0 in r is at most (d+3)/2, with equality for infinitely many d. We also compute the maximal length of a monochromatic arithmetic progression in r of difference 2k−1 and 2k+1. For a general pattern v we show that the maximal length of a monochromatic arithmetic progression of difference d is at most linear in d. Moreover, we prove that a linear lower bound holds for suitable subsequences (dk)k≥0 of differences. We also offer a number of related problems and conjectures.

Dual-mask: Progressively sparse multi-task architecture learning

Multi-task architecture learning has achieved significant success by learning optimal sharing architectures for different tasks. However, previous works to learn branched architectures for different tasks can sometimes lead to unsatisfying multi-task performance, as not all detailed branches are relevant to a specific task. Task-relevant architectures can be sparse, including only partial channels or layers in the entire architecture (i.e., a sub-network). In addition, most previous works rely on a heuristic architecture selection procedure that could not support continuous architecture optimization. To this end, in this paper, we propose dual-mask, a progressively sparse multi-task architecture learning method. Starting with a task-free architecture, it identifies the informative features along two-level, channels and layers, for each task, while suppressing conflicting or noisy parts in a differentiable manner, so that better task-specific sub-networks are captured. Specifically, the channel and layer selection modules produce respective hybrid binary and real value masks, designed to pick salient channels and layers for each task, respectively. To jointly optimize masks with model parameters, we propose an importance-guided relaxation method for solving the stochastic binary optimization problem, after which the interference or noise parts can be pruned by masks. Additionally, a progressive training strategy with continuation is provided that gradually sparsity the task-specific sub-networks. Experiments show that dual-mask achieves superior performance than SOTA multi-task methods.

Disclosure policies in all-pay auctions with affiliated values

We consider all-pay auctions with private and affiliated binary values. The organizer commits ex ante to fully disclosing or concealing bidders’ valuations. We examine the effects of full disclosure on bidders’ welfare and the organizer’s revenue (i.e., expected aggregate bid). We find that full disclosure, as opposed to full concealment, always yields a higher welfare for bidders. On the other hand, full concealment yields a higher revenue if the affiliation in bidders’ valuations is low or if there are only two bidders. Conversely, if the affiliation is high and there are sufficiently many bidders, full disclosure tends to increase revenue.

Interval-specific likelihood ratios and probability-based models for interpreting combined CSF biomarkers for Alzheimer’s disease

BackgroundIn Alzheimer’s disease (AD) diagnosis, a cerebrospinal fluid (CSF) biomarker panel is commonly interpreted with binary cutoff values. However, these values are not generic and do not reflect the disease continuum. We explored the use of interval-specific likelihood ratios (LRs) and probability-based models for AD using a CSF biomarker panel. MethodsCSF biomarker (Aβ1-42, tTau and pTau181) data for both a clinical discovery cohort of 241 patients (measured with INNOTEST) and a clinical validation cohort of 129 patients (measured with EUROIMMUN), both including AD and non-AD dementia/cognitive complaints were retrospectively retrieved in a single-center study. Interval-specific LRs for AD were calculated and validated for univariate and combined (Aβ1-42/tTau and pTau181) biomarkers, and a continuous bivariate probability-based model for AD, plotting Aβ1-42/tTau versus pTau181 was constructed and validated. ResultsLR for AD increased as individual CSF biomarker values deviated from normal. Interval-specific LRs of a combined biomarker model showed that once one biomarker became abnormal, LRs increased even further when another biomarker largely deviated from normal, as replicated in the validation cohort. A bivariate probability-based model predicted AD with a validated accuracy of 88% on a continuous scale. ConclusionsInterval-specific LRs in a combined biomarker model and prediction of AD using a continuous bivariate biomarker probability-based model, offer a more meaningful interpretation of CSF AD biomarkers on a (semi-)continuous scale with respect to the post-test probability of AD across different assays and cohorts.

Enhancing recognition and interpretation of functional phenotypic sequences through fine-tuning pre-trained genomic models

BackgroundDecoding human genomic sequences requires comprehensive analysis of DNA sequence functionality. Through computational and experimental approaches, researchers have studied the genotype-phenotype relationship and generate important datasets that help unravel complicated genetic blueprints. Thus, the recently developed artificial intelligence methods can be used to interpret the functions of those DNA sequences.MethodsThis study explores the use of deep learning, particularly pre-trained genomic models like DNA_bert_6 and human_gpt2-v1, in interpreting and representing human genome sequences. Initially, we meticulously constructed multiple datasets linking genotypes and phenotypes to fine-tune those models for precise DNA sequence classification. Additionally, we evaluate the influence of sequence length on classification results and analyze the impact of feature extraction in the hidden layers of our model using the HERV dataset. To enhance our understanding of phenotype-specific patterns recognized by the model, we perform enrichment, pathogenicity and conservation analyzes of specific motifs in the human endogenous retrovirus (HERV) sequence with high average local representation weight (ALRW) scores.ResultsWe have constructed multiple genotype-phenotype datasets displaying commendable classification performance in comparison with random genomic sequences, particularly in the HERV dataset, which achieved binary and multi-classification accuracies and F1 values exceeding 0.935 and 0.888, respectively. Notably, the fine-tuning of the HERV dataset not only improved our ability to identify and distinguish diverse information types within DNA sequences but also successfully identified specific motifs associated with neurological disorders and cancers in regions with high ALRW scores. Subsequent analysis of these motifs shed light on the adaptive responses of species to environmental pressures and their co-evolution with pathogens.ConclusionsThese findings highlight the potential of pre-trained genomic models in learning DNA sequence representations, particularly when utilizing the HERV dataset, and provide valuable insights for future research endeavors. This study represents an innovative strategy that combines pre-trained genomic model representations with classical methods for analyzing the functionality of genome sequences, thereby promoting cross-fertilization between genomics and artificial intelligence.

The digital pheromone: Building digital identity of smartphone users based on time-varying multivariates

The increasing reliance on smartphones necessitates secure, accurate user identification methods. This study introduces “digital pheromones”, a novel digital identity creation method based on smartphone user behaviors. Represented by a 56-bit binary number, this identity is derived from quantization and concatenation of 14 time-varying smartphone variables. Motivated by the need for enhanced security and privacy, the study employs statistical analysis to measure user behavior dispersion, showing that wider dispersion variables facilitate faster user uniqueness at lower quantization levels. The results demonstrate 100% uniqueness, ensuring no two users share the same 56-bit identity. This research offers a robust framework for future advancements in smartphone user authentication and identification systems.

Quantum number conservation: a tool in the design and analysis of high energy experiments

The Clifford Unification algebra Cl 7,7 is shown to provide a unified description of all the elementary fermions and hadrons in terms of seven binary quantum numbers. Four of these are defined in existing theories, namely spin-direction, fermion/anti-fermion pairing and the two commuting generators in the SU(3) description of quark colour. A Cl 3,3 sub-algebra integrates the Cl 1,3 space-time and Dirac algebras providing a new definition of time direction and identifying parity as a new quantum number. A further two quantum numbers are related to the commuting generators of an SU(3) description of fermion generations. All seven are conserved in the decays and interactions of charged particles, suggesting that quantum number conservation provides a useful tool in the design and interpretation of high energy experiments. This is especially relevant when neutral particles and parity are involved.

A real-time and energy-efficient SRAM with mixed-signal in-memory computing near CMOS sensors

In-memory computing (IMC) represents a promising approach to reducing latency and enhancing the energy efficiency of operations required for calculating convolution products of images. This study proposes a fully differential current-mode architecture for computing image convolutions across all four quadrants, intended for deep learning applications within CMOS imagers utilizing IMC near the CMOS sensor. This architecture processes analog signals provided by a CMOS sensor without the need for analog-to-digital conversion. Furthermore, it eliminates the necessity for data transfer between memory and analog operators as convolutions are computed within modified SRAM memory. The paper suggests modifying the structure of a CMOS SRAM cell by incorporating transistors capable of performing multiplications between binary (−1 or +1) weights and analog signals. Modified SRAM cells can be interconnected to sum the multiplication results obtained from individual cells. This approach facilitates connecting current inputs to different SRAM cells, offering highly scalable and parallelized calculations. For this study, a configurable module comprising nine modified SRAM cells with peripheral circuitry has been designed to calculate the convolution product on each pixel of an image using a 3×3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$3 \ imes 3$$\\end{document} mask with binary values (−1 or 1). Subsequently, an IMC module has been designed to perform 16 convolution operations in parallel, with input currents shared among the 16 modules. This configuration enables the computation of 16 convolutions simultaneously, processing a column per cycle. A digital control circuit manages both the readout or memorization of digital weights, as well as the multiply and add operations in real-time. The architecture underwent testing by performing convolutions between binary masks of 3 × 3 values and images of 32 × 32 pixels to assess accuracy and scalability when two IMC modules are vertically integrated. Convolution weights are stored locally as 1-bit digital values. The circuit was synthesized in 180 nm CMOS technology, and simulation results indicate its capability to perform a complete convolution in 3.2 ms, achieving an efficiency of 11,522 1-b TOPS/W (1-b tera-operations per second per watt) with a similarity to ideal processing of 96%.

Spiking neural networks for nonlinear regression of complex transient signals on sustainable neuromorphic processors

In recent years, spiking neural networks were introduced in science as the third generation of artificial neural networks leading to a tremendous energy saving on neuromorphic processors. This sustainable effect is due to the sparse nature of signal processing in-between spiking neurons leading to much less scalar multiplications as in second-generation networks. The spiking neuron’s efficiency is even more pronounced by their inherently recurrent nature being useful for recursive function approximations. We believe that there is a need for a general regression framework for SNNs to explore the high potential of neuromorphic computations. However, besides many classification studies with SNNs in the literature, nonlinear neuromorphic regression analysis represents a gap in research. Hence, we propose a general SNN approach for function approximation applicable for complex transient signal processing taking surrogate gradients due to the discontinuous spike representation into account. However, to pay attention to the need for high memory access during deep SNN network communications, additional spiking Legrendre Memory Units are introduced in the neuromorphic architecture. Path-dependencies and evolutions of signals can be tackled in this way. Furthermore, interfaces between real physical and binary spiking values are necessary. Following this intention, a hybrid approach is introduced, exhibiting an autoencoding strategy between dense and spiking layers. However, to verify the presented framework of nonlinear regression for a wide spectrum of scientific purposes, we see the need for obtaining realistic complex transient short-time signals by an extensive experimental set-up. Hence, a measurement technique for benchmark experiments is proposed with high-frequency oscillations measured by capacitive and piezoelectric sensors resulting in wave propagations and inelastic solid deformations to be predicted by the developed SNN regression analysis. Hence, the proposed nonlinear regression framework can be deployed to a wide range of scientific and technical applications.

Block Cipher Nonlinear Component Generation via Hybrid Pseudo-Random Binary Sequence for Image Encryption

To analyze the security of encryption, an effectual encryption scheme based on colored images utilizing the hybrid pseudo-random binary sequence (HPRBS) and substitution boxes, known as S-boxes, is proposed. The presented work aims to design S-boxes using pseudo-random binary numbers acquired by Linear Feedback Shift Registers (LFSRs) in combination with a modified quadratic chaotic map. Firstly, cryptographically robust S-boxes are constructed by using binary pseudo-random number sequences, and then the cryptographic properties of the presented S-boxes are tested. The suggested S-boxes showed good results. Secondly, an RGB image encryption algorithm utilizing sequences generated by modified quadratic chaotic maps and S-boxes is offered. The new color image encryption techniques comprise two steps, including a permutation and a substitution step. The key association with the content of the image is also addressed. This strategy can result in a “one-time pad” effect and make the algorithm resistant to chosen-plaintext attack (CPA). The proposed scheme has been confirmed to be more valuable than most of the existing schemes. S-boxes are analyzed by the nonlinearity test, bit independence criterion (BIC), linear and differential approximation probabilities (LPs; DPs), and Strict-Avalanche Criterion (SAC) tests. A comparison with different S-boxes presented in the literature is also carried out. The comparison shows encouraging results about the quality of the proposed box. From security and experimental outcomes, the effectiveness of the presented color image encryption technique is verified. The proposed scheme has evident efficiency benefits, which implies that the proposed colored encryption of the image scheme has better potential for application in encryption schemes in real-time.

A novel binary quantizer for variational autoencoder-based image compressor

Neural network-based encoder and decoder are one of the emerging techniques for image compression. To improve the compression rate, these models use a special module called the quantizer that improves the entropy of the generated representation. Here, we propose a novel binary quantizer and an auxiliary support module known as the remapper that co-ordinate for better compression and decompression of an image. The proposed quantizer generates the compressed binary representation whereas the remapper aids in minimizing the reconstruction error during decompression. The combined optimization of the model consisting of the encoder, quantizer, remapper, and the decoder as a single entity is not feasible due to the non-differentiable nature of the quantizer. To mitigate this, we propose a step-by-step training process wherein the encoder and decoder are trained first, then keeping the encoder parameters fixed, the remapper is trained along with the decoder to obtain a fully optimized model. The training is performed with different types of images and the results are compared to understand the best training procedures. Experimental results reveal that the proposed model can compress a 256 × 256 × 3 image to a mere 256 bits, thereby achieving a compression ratio of 6144:1; with excellent perceptual reconstruction during decompression.