IAES Inter national J our nal of Articial Intelligence (IJ-AI) V ol. 14, No. 6, December 2025, pp. 4902 ∼ 4912 ISSN: 2252-8938, DOI: 10.11591/ijai.v14.i6.pp4902-4912 ❒ 4902 Optimizing sparse ter nary compr ession with thr esholds f or communication-efcient federated lear ning Nith yaniranjana Murth y Chittaiah, Manjula Sunkadakatte Haladappa Department of Computer Science and Engineering, Uni v ersity V isv esv araya Colle ge of Engineering, Bang alore Uni v ersity , Beng aluru, India Article Inf o Article history: Recei v ed Oct 26, 2024 Re vised Oct 24, 2025 Accepted No v 8, 2025 K eyw ords: Communication ef cienc y Distrib uted machine learning Federated learning Sparse ternary compression STC threshold ABSTRA CT Federated learning (FL) enables decentralized model traini ng while preserving client data pri v ac y , yet suf fers from signicant communication o v erhead due to frequent parameter e xchanges. This study in v estig ates ho w v arying sparse ternary com pression (STC) thresholds impact communication ef cienc y and model accurac y across the CIF AR-10 and MedMN IST datasets. Experiments tested thresholds ranging from 1.0 to 1.9 and batch sizes of 10, 15, and 20. Results demonstrated that selecting thresholds between 1.2 and 1.5 reduced total communication costs by approximately 10–15%, while maintaining acceptable accurac y le v els. These ndings suggest that careful threshold tuning can achie v e substantial communication sa vings wit h minimal compromise in model performance, of fering practical guidance for impro ving the ef cienc y and scalability of FL systems. This is an open access article under the CC BY -SA license . Corresponding A uthor: Nith yaniranjana Murth y Chittaiah Department of Computer Science and Engineering, Uni v ersity of V isv esv araya Colle ge of Engineering Bang alore Uni v ersity Beng aluru, Karnataka, India Email: nith ya.semantic@gmail.com 1. INTR ODUCTION Federated learning (FL) represents a decentralized approach to machine learning, where se v eral cl ients w ork together to train a shared model without direct ly sharing local datasets. Unlik e traditional approaches that rely on central ized data aggre g ation for model de v elopment, FL ensures tha t data remains on each client de vice, thus enhancing pri v ac y . This decentralized setup is particularly adv antageous in domains lik e healthcare, nance, and mobile systems, where data sensiti vity is a primary concern [1]. Despite the potential adv antages, FL f aces signicant challenges, particularly in terms of communication ef cienc y . In a typical FL setup, model updates are iterati v ely sent by clients to a central serv er , which aggre g ates these updates and returns a global model to the clients. Modern machine learning models often consist of m illions of parameters, and communicating these updates can lead to substantial netw ork bandwidth consumption, especially in resource-constrained en vironments. As a result, the frequenc y and v olume of these communic ations can become a bottleneck, af fecting both the scalability and ef cienc y of FL systems [2]. FL inte grates data from a v ariety of de vices, such as sensors, mobile phones, and IoT systems, each possessing distinct data characteristics and serving applications across domains lik e healthcare, nance, and online education. Ho we v er , FL encounters challenges including pri v ac y risks, implementation dif culties, hardw are constraints, communication costs, and de vice una v ailability [3]-[5]. Man y applications across v arious domains in v olv e sensiti v e personal data, making it crucial for all stak eholders, including companies, agencies, J ournal homepage: http://ijai.iaescor e .com Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Artif Intell ISSN: 2252-8938 ❒ 4903 and researchers, to tak e collecti v e res pon s ibility in safe guarding this information from misuse and ab use [6]-[8]. V arious model compression strate gies ha v e emer ged to m itig ate communication bottlenecks. One s uch technique is sparse ternary compression (STC), which reduces the size of the model updates by compressing them into three discrete states: -1, 0, and 1. By representing the model updates in this ternary form, the number of bits required for transmission is signicantly reduced, leading to lo wer communication costs. Ho we v er , the ef fecti v eness of STC is closely tied to the select ion of the compression threshold, which inuences the e xtent of sparsity in the updates. Selecting an appropriate threshold helps balance communication sa vings with model performance; ho we v er , a poorly chosen v alue may cause signicant information de gradation or f ail to compress suf ciently [9]. FL can be applied in v arious domains, including smart retai l, ener gy management, smart cit ies, nance, v ehicle-to-v ehicle communication, and healthcare [10], [11]. Applications such as patient monitoring, moisture detection in crops, and predicti v e te xt in k e yboards use FL to obtain data-dri v en insights. W ith the in v olv ement of sensiti v e personal data, ensuring pri v ac y is paramount. F or instance, the General Data Protection Re gulation (GDPR) is one of se v eral re gulatory frame w orks adopted in re gions including the EU and UK to safe guard personal data [12], [13]. The paper in v estig ates the impact of v arying STC thresholds, specically focusing on v alues of 1.0, 1.2, 1.5, 1.7, and 1.5, on communication ef cienc y and model accurac y in FL. Systematic e xperimentation is conducted with dif ferent threshold v alues, follo wed by an analysis of the ef fects on a well-established machine learning task. Insights are of fered on ho w STC thresholds af fect the trade-of f between communication cost and model performance. Our study aims to of fer guidance on choosing optimal STC thresholds to enhance ef cienc y , scalability , and the practical use of FL in real-w orld scenarios. 2. RELA TED W ORK McMahan et al. [14] introduced the concept of FL through the de v elopment of the Federated A v eraging (FedA vg) algorithm, which enables aggre g ation of locally computed gradients from multiple decentralized de vices. F ollo wing this w ork, FL be g an recei ving increased attention due to its ability t o perform machine learni n g directly on local cli ent data wit hout requiring c entral data transfer . This foundational study demonstrated the feasibility of training models across distrib uted systems while preserving user pri v ac y , pa ving the w ay for wider adoption in both research and industry . Sattler et al. [15] introduced STC to reduce communication costs in FL by compressing model updates. STC b uilds on top-k gradient sparsication and adds ternarization with optimal Golomb encoding, enabling more ef cient do wnstream communication. Quantized SGD (QSGD), proposed by Alistarh et al. [16], is a technique that minimizes communication o v erhead in distrib uted machine learning by quantizing gradients. QSGD enhances training ef cienc y and scalability by reducing the data e xchanged between w ork ers during gradient descent while maintaining con v er gence. Bernstein e t al. [17] presented signSGD, a compression technique that pro vides theoretical con v er gence guarantees on independent and identically distrib uted (IID) data. The technique reduces the bit size for each gradient update by a f actor of 32 by con v erting each update into a binary sign. Additionally , signSGD performs do wnload compression by aggre g ating binary updates from all clients through a majority v oting mechanism. Rothchild et al. [18] introduced FetchSGD to address communicat ion bottlenecks and con v er gence issues in FL. In resear ch by W ang et al. [19], communication cost optimization w as identied as a crucial f actor , with three primary techniques suggested for reduction: i) allo wing local updates to reduce the frequenc y of communication, ii) compressing messages to lo wer the v olume of data transmitted, and iii) reducing communication traf c at the serv er by lim iting the number of parti cipating clients per round. Research conducted by Y ang et al. [20] focused on wireless communication using the principle of Ov er -the-Air computation. A model for FL w as designed by e xploiting signal superposition of wireless de vices, combined with beamforming design and joint de vice selection, to enhance statistical learning performance. Chen et al. [21] identied challenges in wireless communication and proposed a model that jointly selects users and allocates resources, ef fecti v ely reducing pack et loss and impro ving FL model performance. Emphasis w as also placed on reducing ener gy consumption during local training and transmission, which is a k e y consideration for impro ving FL ef cienc y . Cheng et al. [22] e xamined tw o primary f actors for reducing communication costs: i) i ncreasing computational po wer on local de vices to allo w for more local updates before global aggre g ation, Optimizing spar se ternary compr ession with thr esholds for ... (Nithyanir anjana Murthy Chittaiah) Evaluation Warning : The document was created with Spire.PDF for Python.
4904 ❒ ISSN: 2252-8938 and ii) selecting more participants for each round by enhancing parallelism. Simulation results indicated that increasing parallelism signicantly reduced communication costs. Ho we v er , its ef fecti v eness became apparent only after reaching a specic threshold, compared to simply increasing the computational po wer on participant de vices. Liu et al. [7] e xtended the concept to v ertical federated learning (VFL), which in v olv es the same set of users or participants with dif ferent feature sets. F or e xample, in the same city , a local bank and a local retail compan y may share the same customer base b ut maintain distinct feature sets, f acilitating collaborati v e model b uilding. A no v el algorithm called Federated Stochastic Block Coordinate Descent (FedBCD) w as introduced, enabling se v eral local updates before communicating with the global serv er for aggre g ation. The algorithm also ensured local con v er gence with fe wer communication rounds. FedZip, a compression frame w ork for FL, w as introduced by Malekijoo et al. [23] to address communication o v erhead, ener gy consumption, and performance de gradation. Sparsication w as achie v ed using T op-z pruning, while K-means clustering, quantization of model weights, and Huf fman encoding were emplo yed for model compression. When applied to client-to-serv er communication, FedZip impro v ed communication ef cienc y in FL systems with minimal ef fects on accurac y and con v er gence. Haddadpour et al. [24] focused on reducing uplink communication costs by compressing messages sent from client de vices to the central serv er . T o pre v ent information loss during compression, the central serv er generates a con v e x combination of the pre vious global model and the aggre g ated updates from local models. 3. METHODOLOGY 3.1. Resear ch design The study aimed to e v aluate the impact of v arying STC thresholds on communication ef cienc y and model accurac y in a FL conte xt. Experiments tested STC threshold v alues of 1.0, 1.2, 1.5 , 1.7, and 1.9 across batch sizes of 10, 15, and 20. T w o di v erse image classication datasets—CIF AR-10 and MedMNIST—were selected to represent both natural images and medical imaging tasks, supporting broader applicability . Data w as partitioned in a non-IID (Non-Independent and Identically Distrib uted) manner to mimic realistic client heterogeneity typical in federated settings. This design enabled a systematic analysis of ho w dif ferent threshold settings and batch sizes inuence communication cost and model performance across v arying data characteristics. 3.2. Experimental pr ocedur e The e xperimental procedure in v olv ed se v eral k e y steps designed to systematically e v aluate the impact of STC thresholds on FL performance. Data partitioning: The CIF AR-10 and MedMNIST datasets were used to pro vide di v erse e v aluation scenarios. Data w as partitioned among multiple simulated clients (de vices) to replicate a FL system with non-IID (non-independent and identically distrib uted) distrib utions (see T able 1 for en vironment conguration). This setup aimed to closely mimic real-w orld heterogeneity , where data is une v enly distrib uted across participants. T able 1. Federated learning conguration details Conguration attrib ute Client count Selection fraction Labels per client Mini-batch size Dataset balance f actor Assigned v alue 10 0.1 2 10, 15, 20 1.0 Model training: a con v olutional neural netw ork (CNN) architecture based on V GG11 * w as emplo yed as the client-side model. Hyperparameters and model congurations used for CIF AR-10 and MedMNIST e xperiments are summarized in T able 2. Each client trained the model locally on its partitioned data for a x ed number of iterations. After local training, model parameters were compressed using the STC technique before transmission to the central serv er , aiming to reduce communication costs. T able 2. Models and h yperparameters used in e xperiments P arameter CIF AR-10 v alue MedMNIST v alue Model architecture V GG11 * V GG11 * Learning rate 0.016 0.010 Optimizer SGD SGD Loss function Cross-entrop y Cross-entrop y Iterations 20,000 20,000 Int J Artif Intell, V ol. 14, No. 6, December 2025: 4902–4912 Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Artif Intell ISSN: 2252-8938 ❒ 4905 Note: V GG11 * denotes a streamlined adaptation of the V GG11 model [25], where dropout and batch normalization layers ha v e been e xcluded, and both the con v olutional lter count and the dimensions of the fully connected layers ha v e been scaled do wn to half. STC: the STC te chnique reduces model updates to three states: -1, 0, and 1, ef fecti v ely lo wering the number of bits needed for communication. Compression is controlled by a threshold parameter τ , which go v erns the sparsity of the updates. The STC algorithm operates as in (1). STC ( g i ) = 1 if g i ≥ τ − 1 if g i ≤ − τ 0 if − τ < g i < τ (1) Where g i represents an indi vidual model gradient component. Elements with absolute v alues e xceeding τ are retained with their sign, while others are zeroed out. Experiments systematically v aried τ across v alues 1.0, 1.2, 1.5, 1.7, and 1.9 to study its inuence on both communication cost and accurac y . This range enabled a detailed analysis of ho w increas ed sparsication impacts the trade-of f between compression ef cienc y and model performance. The ternarization approach also enables encoding gradients with fe wer bits, reducing communication o v erhead signicantly . Model aggre g ation and update: the central serv er aggre g ated compressed updates from all participating clients using weighted a v eraging, as in (2). w ( t +1) = K X k =1 n k n w ( t ) k (2) Here, w ( t +1) denotes the global model at round t + 1 , w ( t ) k are the parameters from client k , n k is the number of samples on client k , and n is the total number of samples across all clients. The aggre g ated global model w as then redistrib uted to all clients for the ne xt round of local training. Performance e v aluation: performance w as assessed using tw o primary metrics: model accurac y and communication cost, measured in bits transmitted. Accurac y w as e v aluated on held-out v alidation data, while communication cost accounted for the total number of bits sent during each communication round. Experiments were repeated o v er multiple rounds to analyze con v er gence beha vior and to compare the ef fects of dif ferent thresholds and batch sizes across both datasets. 3.3. T esting and data acquisition The testing phase i n v olv ed running the FL training process with each STC threshold v alue. Res ults, including model accurac y and communication cost, were recorded at each iteration. The data acquisition process w as automated using scripts that logged the necessary metrics, ensuring consistent and reliable data collection. The recorded data w as then analyzed to identify trends and dra w conclusions about the ef fecti v eness of dif ferent STC thresholds in FL systems. The res earch follo wed a rigorous e xperime ntal protocol, ensuring that the results are scientically v alid and reproducible. The methods used for testing and data acquisition were based on established practices in FL research pro viding a solid foundation for the conclusions dra wn in the study . 4. RESUL TS The e xperimental ndings e v aluating t he impact of STC thresholds on communication ef cienc y and model performance in FL are presented in this section. Results were systematically analyzed for dif ferent thresholds (1.0, 1.2, 1.5, 1.7, and 1.9) and batch sizes (10, 15, and 20), us ing tw o datasets: CIF AR-10 and MedMNIST . K e y aspects e xam ined include total communication cost, model accurac y across training iterations, and maximum accurac y achie v ed across batch sizes. These analyses re v eal the balance between reducing communication o v erhead and maintaining model ef fecti v eness, of fering practical guidance for selecting appropriate STC thresholds in di v erse FL scenarios. Threshold 1.9 is e xcluded from all plots due to cons istently lo w accurac y . Its inclusion w ould distort axis scaling and obscure meaningful comparisons across other thresholds. Optimizing spar se ternary compr ession with thr esholds for ... (Nithyanir anjana Murthy Chittaiah) Evaluation Warning : The document was created with Spire.PDF for Python.
4906 ❒ ISSN: 2252-8938 4.1. T otal bits sent up vs. batch size f or differ ent sparse ter nary compr ession thr esholds (in MB) The rst aspect of the analysis focused on e v aluating communication ef cienc y in the FL s ystem by measuring the total bits sent during the training process. Figures 1 and 2 illustrate ho w total bits sent v aried with dif ferent batch s izes and STC thresholds across tw o datasets: CIF AR-10 and MedMNIST . F or the CIF AR-10 dataset (Figure 1), the results indicated a general trend where increasing the STC threshold resulted in lo wer total bi ts sent across batch sizes. Higher thresholds (such as 1.5) ef fecti v ely reduced the v olume of communication, particularly at lar ger batch sizes. This beha vior sugges ts that aggressi v e compression successfully reduces the data that must be transmitted between clients and the serv er , thereby lo wering communication o v erhead. The MedMNIST dataset results (Figure 2) generally reinforced these ndings. Ho we v er , while higher thresholds still reduced communication costs, the e xtent of this reduction w as less uniform across batch sizes, lik ely attrib utable to the dataset’ s inherent comple xity and distrib ution characteristics. Ov erall, the ndings across both datasets emphasize the v alue of tuning STC thresholds to optimize communication ef cienc y in FL setups. Careful sel ection of the threshold parameter enables signicant reductions in transmission v olume, b ut it remains essential to balance this g ain with potential impacts on model accurac y , as discussed in subsequent sections. Results for threshold 1.9 are e xcluded from the table and gures due to consistently poor accurac y , illustrating that e xcessi v e compression de grades model performance be yond acceptable limits. The numerical v alues corresponding to Figures 1 and 2 are summarized in T able 3, detailing total bits sent for each STC threshold and batch size combination. Figure 1. T otal bits sent up vs. batch size for dif ferent STC thresholds on CIF AR-10 Figure 2. T otal bits sent up vs. batch size for dif ferent STC thresholds on MedMNIST Int J Artif Intell, V ol. 14, No. 6, December 2025: 4902–4912 Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Artif Intell ISSN: 2252-8938 ❒ 4907 T able 3. T otal bits sent up (MB) vs. batch size for dif ferent STC thresholds on CIF AR-10 and MedMNIST Batch size CIF AR-10 MedMNIST 1.0 1.2 1.5 1.7 1.0 1.2 1.5 1.7 10 1574.49 1573.26 1574.03 1570.65 1572.18 1572.49 1575.15 1573.39 15 1574.06 1573.24 1571.68 1572.66 1572.70 1572.30 1572.20 1572.23 20 1572.60 1573.50 1571.53 1571.08 1573.52 1571.55 1571.65 1570.90 Note: Threshold 1.9 is e xcluded due to consistently poor accurac y 4.2. Accuracy vs. iterations f or differ ent sparse ter nary compr ession thr esholds The second aspect of the analysis focused on e v aluating model accurac y as training progressed o v er iterations, highlighting con v er gence beha vior under dif ferent STC thresholds. Figures 3 and 4 sho w the accurac y curv es for the CIF AR-10 and MedMNIST datasets, respecti v ely , across thresholds 1.0, 1.2, 1.5, 1.7, and 1.9. F or the CIF AR-10 results (Figure 3), accurac y impro v ed steadily o v er 20,000 iterations for thresholds 1.0, 1.2, and 1.5. Threshold 1.0 consistently deli v ered the highest accurac y at con v er gence, demonstrating more stable learning with less a ccurac y drop. Threshold 1.5 sho wed competiti v e early con v er gence b ut e xhibited slightly more v ariability in late training stages. Thresholds 1.7 and 1.9 led to noticeably de graded accurac y , with threshold 1.9 f ailing to impro v e signicantly during training. This pattern indicates that o v erly aggressi v e compression (high thresholds) can harm learning by discarding too much gradient information. Figure 3. CIF AR-10: accurac y vs. iterations for dif ferent STC thresholds Figure 4. MedMNIST : accurac y vs. iterations for dif ferent STC thresholds Optimizing spar se ternary compr ession with thr esholds for ... (Nithyanir anjana Murthy Chittaiah) Evaluation Warning : The document was created with Spire.PDF for Python.
4908 ❒ ISSN: 2252-8938 F or MedMNIST (Figure 4), similar trends were observ ed. Thresholds 1.0 and 1.5 achie v ed higher and smoother accurac y g ains across training rounds, with threshold 1.0 generally con v er ging at slightly higher accurac y . Threshold 1.2 also deli v ered competiti v e performance, reinforci ng that moderately lo w thresholds preserv e critical learning signals. Con v ersely , thresholds 1.7 and 1.9 consistently lagged in accurac y across iterations, indicating diminished learning capacity due to e xcessi v e sparsication. These results conrm that selecting lo wer STC thresholds (e.g., 1.0, 1.2) supports better con v er gence and model accurac y while still of fering meaningful compression benets. The trade-of f between communication reduction and model performance is e vident: while higher thresholds reduce data transfer costs, the y risk compromising accurac y . Careful selection of STC thresholds is thus essential for balancing ef cienc y and learning quality in FL settings. 4.3. Max accuracy vs. batch size f or differ ent sparse ter nary compr ession thr esholds The nal aspect of the a nalysis e xamined the maximum accurac y achie v ed at dif ferent batch sizes for each STC threshold. Figures 5 and 6 display these results for t he CIF AR-10 and MedMNIST datasets, respecti v ely , sho wing ho w threshold selecti on and batch size interact to inuence model performance. F or the CIF AR-10 dataset (Figure 5), thresholds 1.0 and 1.2 consistently achie v ed higher maximum accurac y across all batch sizes compared to higher thresholds such as 1.5, 1.7, and 1.9. The results sho wed that as b a tch size increased from 10 to 20, accurac y impro v ed most noticeably for lo wer thresholds. F or instance, threshold 1.0 peak ed near 71% at batch size 20, highlighting its stability and rob ustness e v en as communication cost increased. By contrast, thresholds 1.7 and 1.9 sho wed lo wer and atter trends, indicating de graded performance lik ely due to e xcessi v e sparsication of gradient updates. This beha vior suggests that aggressi v e compression harms learning signal retention, particularly in lar ger batch congurations. F or the MedMNIST dataset (Figure 6), a dif ferent pattern emer ged. Threshold 1.5 generally achie v ed competiti v e or e v en superior accurac y at ba tch size 15, peaking abo v e 70%. Threshold 1.0 maintained strong performance b ut did not al w ays outperform 1.5, especially at mid-sized batches. Meanwhile, thresholds 1.7 and 1.9 ag ain sho wed weak er accurac y across batch sizes, reinforcing that o v erly aggressi v e sparsication reduces learning capacity . The v ariability across batch sizes and thresholds in MedMNIST emphasizes that optimal threshold selection may be dataset-specic and should consider data comple xity and distrib ution. Ov erall, these results highlight the importance of selecting STC thresholds carefully to balance communication ef cienc y with m od e l accurac y . Lo wer thresholds (e.g., 1.0, 1.2) generally f a v or accurac y at the cost of higher communication v olume, while higher thresholds reduce communication b ut risk learning de gradation, especially at lar ger batch sizes. T ailoring thresholds to dataset properties and batch size can thus enhance FL performance. The detailed numerical v alues corresponding to Figures 5 and 6 are pro vided in T able 4, summarizing the maximum accurac y achie v ed for each threshold and batch size combination. Figure 5. CIF AR-10: max accurac y vs. batch size for dif ferent STC thresholds Int J Artif Intell, V ol. 14, No. 6, December 2025: 4902–4912 Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Artif Intell ISSN: 2252-8938 ❒ 4909 Figure 6. MedMNIST : max accurac y vs. batch size for dif ferent STC thresholds T able 4. Max accurac y (%) vs. batch size for dif ferent STC thresholds on CIF AR-10 and MedMNIST Batch size CIF AR-10 MedMNIST 1.0 1.2 1.5 1.7 1.0 1.2 1.5 1.7 10 65.83 66.38 62.78 62.12 65.71 65.54 63.29 55.42 15 68.82 68.36 67.24 62.19 69.03 65.38 70.38 56.46 20 71.12 69.37 68.85 63.39 68.15 66.07 64.62 66.84 4.4. Summary heatmaps of accuracy and communication cost T o complement the detailed analyses presented in the pre vious subsections, Figures 7 and 8 pro vide heatmap visualizations summarizing the combined ef fects of STC threshold and batch size on both maximum accurac y and total communication cost. F or the CI F AR-10 dataset (Figure 7), Figure 7(a) sho ws that lo wer STC thresholds (1.0, 1.2) combined with lar ger batch sizes (20) achie v e the highest maximum accurac y (e xceeding 71%), while Figure 7(b) re v eals a clear reduction in communication cost as t h e threshold increases, conrming the trade-of f between model performance and transmission ef cienc y . (a) (b) Figure 7. CIF AR-10 Heatmaps: (a) max accurac y (%) by STC threshold and batch size and (b) total communication (MB) by STC threshold and batch size F or MedMNIST (Figure 8), a similar pattern is observ ed, though with notable v ariations across Optimizing spar se ternary compr ession with thr esholds for ... (Nithyanir anjana Murthy Chittaiah) Evaluation Warning : The document was created with Spire.PDF for Python.
4910 ❒ ISSN: 2252-8938 thresholds and batch sizes as presented in Figures 8(a) and 8(b). The accurac y heatmap highlights that threshold 1.5 at batch size 15 yields strong accurac y , while communic ation cost remains consistently sensiti v e to threshold adjustments. These visual s u m maries underscore the importance of careful threshold tuning tailored to both the data distrib ution and t he desired balance between accurac y and communication sa vings in FL deplo yments. (a) (b) Figure 8. MedMNIST Heatmaps: (a) max accurac y (%) by STC threshold and batch size and (b) total communication (MB) by STC threshold and batch size These ndings pro vide a comprehensi v e understanding of the role of STC threshold selection in FL across dif ferent datasets and batch sizes. The results demonstrate a clear trade-of f between communication ef cienc y and model accurac y that v aries with both dataset characteristics and training conguration. Higher STC thresholds generally reduced total communication costs in both CIF AR-10 and MedMNIST e xperiments, conrming their ef fecti v eness for minimizing data transmission o v erhead. Ho we v er , this benet came at the cost of accurac y , particularly e vident at lar ger batch sizes and for thresholds abo v e 1.5, where e xcessi v e sparsication de graded learning performance. In the accurac y vs. iterations analysis, lo wer thresholds (1.0, 1.2) consistently supported smoother and higher con v er gence, while higher thresholds f ailed to maintain learning stability across training rounds. Similarly , in maximum accurac y vs. batch size e v aluations, CIF AR-10 results f a v ored lo wer thresholds for achie ving the highest accurac y , especially at lar ger batch sizes. MedMNIST sho wed more v aried beha vior , with threshold 1.5 performing competiti v ely at mid-sized batches b ut still re v ealing accurac y losses at higher thresholds lik e 1.7 and 1.9. Ov erall, these results highlight the importance of carefully selecting and tuning STC thresholds based on dataset comple xity and batch size to balance communication ef cienc y with model delity in FL systems. 4.5. Comparati v e analysis The study e xtends the foundational w ork of Sattler et al. [15] by thoroughly in v estig ating STC thresholds be yond the baseline v alue ( τ = 1 . 0 ). Our e xperimental results, as detailed in Figures 1-6 and T ables 3-4, re v eal distinct adv antages of our proposed thresholds ( τ = 1 . 2 , τ = 1 . 5 , and τ = 1 . 7 ) o v er the base paper’ s τ = 1 . 0 . W e consistently observ e reduced communication o v erhead, with signicant sa vings (e.g., up to ∼ 2.5 MB ), while simultaneously achie ving competiti v e or superior accurac y . F or instance, τ = 1 . 5 frequently outperform s τ = 1 . 0 in MedMNIST at mid-sized batches, demonstrating that careful STC tuning can yield better communication-accurac y trade-of fs without signicant performance compromise. Be yond STC-specic comparisons, our ndings contrib ute to the broader eld of communication- ef cient FL. While methods lik e QSGD [16], signSGD [17], and FedZip [23] of fer v arious compression mechanisms, our lightweight threshold tuning strate gy for STC stands out. It pro vides dataset-adapti v e compression that a v oids the more comple x serv er -side decoding or architectural changes often associated with other techniques. Int J Artif Intell, V ol. 14, No. 6, December 2025: 4902–4912 Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Artif Intell ISSN: 2252-8938 ❒ 4911 5. CONCLUSION This study in v estig ated the ef fect of v arying STC thresholds specically τ = 1 . 2 , 1 . 5 , 1 . 7 , and 1 . 9 —on communi cation ef cienc y and model accurac y in FL using CIF AR-10 and MedMNIST datasets. The e xperimental results demonstrate that careful threshold tuning plays a vital role in balancing communication cost with model performance. Threshold τ = 1 . 2 consistently achie v ed the best trade-of f by of fering high accurac y with reduced communication, while τ = 1 . 5 performed particularly well on MedMNIST with mid-sized batches. Though thresholds τ = 1 . 7 and 1 . 9 resulted in hi gh e r compression, the y sho wed reduced con v er gence quality at lar ger batch sizes, indicating potential o v er -sparsication. Ov erall, our ndings emphasize the need to e xplore thresholds be yond the con v entional baseline ( τ = 1 . 0 ), as moderate v alues (1.2–1.5) can pro vide meaningful impro v ements without compromising accurac y . Future research may e xtend this w ork by quantifying ener gy consumption, e v aluating computational o v erhead, and designing adapti v e thresholding mechanis ms that dynam ically adjust to v arying data distrib utions and training condi tions in heterogeneous FL en vironments. FUNDING INFORMA TION The authors declare that no funding w as recei v ed for conducting this study . A UTHOR CONTRIB UTIONS ST A TEMENT This journal uses the Contrib utor Roles T axonomy (CRediT) to recognize indi vidual author contrib utions, reduce authorship disputes, and f acilitate collaboration. Name of A uthor C M So V a F o I R D O E V i Su P Fu Nith yaniranjana Murth y Chittaiah ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ Manjula Sunkadakatte Haladappa ✓ ✓ ✓ ✓ ✓ C : C onceptualization I : I n v estig ation V i : V i sualizat ion M : M ethodology R : R esources Su : Su pervision So : So ftw are D : D ata Curation P : P roject Administ ration V a : V a lidation O : Writing - O riginal Draft Fu : Fu nding Acquisiti on F o : F o rmal Analysis E : Writing - Re vie w & E diting CONFLICT OF INTEREST ST A TEMENT The authors state no conict of interest. D A T A A V AILABILITY The supporting data of this study are openly a v ailable in the follo wing sources: CIF AR-10: https://www .cs.toronto.edu/ kriz/cif ar .html, and MedMNIST : https://medmnist.com/. REFERENCES [1] J. Chen, H. Y an, Z. Liu, M. Zhang, H. Xiong, and S. Y u, “When federated learning meets pri v ac y-preserving computation, ” A CM Computing Surve ys , v ol. 56, no. 12, 2024, doi: 10.1145/3679013. [2] M. Liu, H. Jiang, J. Chen, A. Badokhon, X. W ei, and M. C. Huang, “ A collaborati v e pri v ac y-preserving deep learning system in distrib uted mobile en vironment, ” Pr oceedings - 2016 International Confer ence on Computational Science and Computational Intellig ence (CSCI) , pp. 192–197, 2017, doi: 10.1109/CSCI.2016.0043. [3] Y . Liu, J. J. Q. Y u, J. Kang, D. Niyato, and S. Zhang, “Pri v ac y-preserving traf c o w prediction: a federated learning approach, ” IEEE Internet of Things J ournal , v ol. 7, no. 8, pp. 7751–7763, 2020, doi: 10.1109/JIO T .2020.2991401. [4] J. Xu, B. S. Glicksber g, C. Su, P . W alk er , J. Bian, and F . W ang, “Federated learning for healthcare informatics, ” J ournal of Healthcar e Informatics Resear c h , v ol. 5, no. 1, 2021, doi: 10.1007/s41666-020-00082-4. [5] K. Y ang, T . Jiang, Y . Shi, and Z. Ding, “Federated learning via o v er -the-air computation, ” IEEE T r ansactions on W ir eless Communications , v ol. 19, no. 3, pp. 2022–2035, 2020, doi: 10.1109/TWC.2019.2961673. [6] Y . Zhao, M. Li, L. Lai , N. Suda, D. Ci vin, and V . Chandra, “Federated learning with non-IID data, ” arXiv:1806.00582v2 , 2018. [7] Y . Liu et al. , “ A communication ef cient v ertical federated learning frame w ork, ” The 2nd International W orkshop on F eder ated Learning for Data Privacy and Condentiality (in Conjunction with NeurIPS 2019) , V ancouv er , Canada, 2019. Optimizing spar se ternary compr ession with thr esholds for ... (Nithyanir anjana Murthy Chittaiah) Evaluation Warning : The document was created with Spire.PDF for Python.