{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,2]],"date-time":"2026-09-02T12:23:04Z","timestamp":1788351784838,"version":"build-2803163510"},"reference-count":26,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2026,9,2]],"date-time":"2026-09-02T00:00:00Z","timestamp":1788307200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100009103","name":"Shaanxi Provincial Department of Education","doi-asserted-by":"publisher","award":["24JP176"],"award-info":[{"award-number":["24JP176"]}],"id":[{"id":"10.13039\/501100009103","id-type":"DOI","asserted-by":"publisher"}]},{"award":["24JP176"],"award-info":[{"award-number":["24JP176"]}],"id":[{"id":"https:\/\/ror.org\/00jb7xy46","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Modern out-of-order processors depend critically on TAGE family branch predictors, which often struggle with context-fragile branches whose outcomes are highly sensitive to slight perturbations in the most recent global history. Existing predictors are confined to single-path factual reasoning and lack any mechanism to explicitly probe the local stability of a prediction. We formalise this limitation from an information entropy perspective: a context-fragile branch corresponds to a high conditional entropy region in the joint space of recent history bits and branch outcomes, where a single bit flip in the youngest history can shift the posterior branch probability across the decision boundary. To address this, we propose Mirror-TAGE, a lightweight microarchitectural framework that integrates counterfactual stability modeling with replay-guided selective overrides. Building on a TAGE-SC-L baseline following Seznec, Mirror-TAGE injects controlled bit-level perturbations into the youngest global history bits to construct two mirrored views, screened by an entropy-based reliability filter. We define a local prediction entropy, derive an information-theoretic characterisation of override correctness via DRT-filtered agreement, and decompose uncertainty into aleatoric and epistemic components. Under a paired causally consistent learning framework on synthetic workloads isolating the context-fragile regime, Mirror-TAGE achieves a 0.82 pp gain (66% override correctness, 7.5% overhead). Of successful overrides, 78% occur at entropy &gt; 0.85 bits, consistent with the entropy-guided criterion, though partly driven by the entry gate design. Six SPEC CPU 2017 traces confirm no accuracy degradation, with gains of up to 0.38 pp. These results support entropy-guided counterfactual stability modelling as a promising branch prediction paradigm.<\/jats:p>","DOI":"10.3390\/e28090977","type":"journal-article","created":{"date-parts":[[2026,9,2]],"date-time":"2026-09-02T12:04:16Z","timestamp":1788350656000},"page":"977","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Information-Entropy-Guided Counterfactual Stability Modeling and Replay-Based Selective Override for Context-Fragile Branch Prediction"],"prefix":"10.3390","volume":"28","author":[{"given":"Yijie","family":"Cheng","sequence":"first","affiliation":[{"name":"School of Electronic Engineering, Xi\u2019an University of Posts and Telecommunications, Xi\u2019an 710121, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"software","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"},{"role":"data-curation","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"},{"role":"visualization","vocabulary":"credit"}]},{"given":"Chengrui","family":"Yin","sequence":"additional","affiliation":[{"name":"School of Electronic Engineering, Xi\u2019an University of Posts and Telecommunications, Xi\u2019an 710121, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"},{"role":"visualization","vocabulary":"credit"}]},{"given":"Yong","family":"Tan","sequence":"additional","affiliation":[{"name":"School of Electronic Engineering, Xi\u2019an University of Posts and Telecommunications, Xi\u2019an 710121, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"},{"role":"resources","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"project-administration","vocabulary":"credit"}]},{"given":"Xiaofeng","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Electronic Engineering, Xi\u2019an University of Posts and Telecommunications, Xi\u2019an 710121, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"resources","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"supervision","vocabulary":"credit"},{"role":"project-administration","vocabulary":"credit"},{"role":"funding-acquisition","vocabulary":"credit"}]}],"member":"1968","published-online":{"date-parts":[[2026,9,2]]},"reference":[{"key":"ref_1","first-page":"23","article-title":"A case for (partially) tagged geometric history length branch prediction","volume":"8","author":"Seznec","year":"2006","journal-title":"J. Instr. Level Parallelism"},{"key":"ref_2","first-page":"1","article-title":"The L-TAGE branch predictor","volume":"9","author":"Seznec","year":"2007","journal-title":"J. Instr. Level Parallelism"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Jim\u00e9nez, D.A., and Lin, C. (2001). Dynamic branch prediction with perceptrons. Proceedings of the 7th International Symposium on High-Performance Computer Architecture (HPCA), Monterrey, Mexico, 19\u201324 January 2001, IEEE.","DOI":"10.1109\/HPCA.2001.903263"},{"key":"ref_4","unstructured":"Seznec, A. (2014, January 15). TAGE-SC-L branch predictors. Proceedings of the 4th Championship Branch Prediction (CBP-4), Minneapolis, MN, USA."},{"key":"ref_5","unstructured":"Seznec, A. (2016, January 19). TAGE-SC-L branch predictors again. Proceedings of the 5th Championship Branch Prediction (CBP-5), Seoul, Republic of Korea."},{"key":"ref_6","unstructured":"Ishii, Y. (2014, January 15). Global-local combined branch history: The alternative way to improve TAGE branch predictor. Proceedings of the 4th Championship Branch Prediction (CBP-4), Minneapolis, MN, USA."},{"key":"ref_7","unstructured":"Seznec, A. (2016, January 19). Exploring branch predictability limits with the MTAGE+SC predictor. Proceedings of the 5th Championship Branch Prediction (CBP-5), Seoul, Republic of Korea."},{"key":"ref_8","unstructured":"Jim\u00e9nez, D.A. (2016, January 19). Multiperspective perceptron predictor. Proceedings of the 5th Championship Branch Prediction (CBP-5), Seoul, Republic of Korea."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Jim\u00e9nez, D.A. (2005). Piecewise linear branch prediction. Proceedings of the 32nd Annual International Symposium on Computer Architecture (ISCA), Madison, WI, USA, 4\u20138 June 2005, IEEE.","DOI":"10.1109\/ISCA.2005.40"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Lin, C.K., and Tarsa, S.J. (2019). Branch prediction is not a solved problem: Measurements, opportunities, and future directions. Proceedings of the 2019 IEEE International Symposium on Workload Characterization (IISWC), Orlando, FL, USA, 3\u20135 November 2019, IEEE.","DOI":"10.1109\/IISWC47752.2019.9042108"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Schall, D., Sandberg, A., and Grot, B. (2024). The last-level branch predictor. Proceedings of the 57th IEEE\/ACM International Symposium on Microarchitecture (MICRO), Austin, TX, USA, 2\u20136 November 2024, IEEE.","DOI":"10.1109\/MICRO61859.2024.00042"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Cover, T.M., and Thomas, J.A. (2006). Elements of Information Theory, Wiley. [2nd ed.].","DOI":"10.1002\/047174882X"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/j.sysarc.2005.04.003","article-title":"Improved composite confidence mechanisms for a perceptron branch predictor","volume":"52","author":"Desmet","year":"2006","journal-title":"J. Syst. Archit."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Chen, I.K., Coffey, J.T., and Mudge, T.N. (1996). Analysis of branch prediction via data compression. Proceedings of the 7th International Conference on Architectural Support for Programming Languages and Operating Systems (ASPLOS), Cambridge, MA, USA, 1\u20135 October 1996, ACM.","DOI":"10.1145\/237090.237171"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Zangeneh, S., Pruett, S., Lym, S., and Patt, Y.N. (2020). BranchNet: A convolutional neural network to predict hard-to-predict branches. Proceedings of the 53rd Annual IEEE\/ACM International Symposium on Microarchitecture (MICRO), Athens, Greece, 17\u201321 October 2020, IEEE.","DOI":"10.1109\/MICRO50266.2020.00022"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A mathematical theory of communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. Tech. J."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1109\/JSAIT.2020.2991561","article-title":"The information bottleneck problem and its applications in machine learning","volume":"1","author":"Goldfeld","year":"2020","journal-title":"IEEE J. Sel. Areas Inf. Theory"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"124020","DOI":"10.1088\/1742-5468\/ab3985","article-title":"On the information bottleneck theory of deep learning","volume":"2019","author":"Saxe","year":"2019","journal-title":"J. Stat. Mech. Theory Exp."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1103\/PhysRevLett.85.461","article-title":"Measuring information transfer","volume":"85","author":"Schreiber","year":"2000","journal-title":"Phys. Rev. Lett."},{"key":"ref_20","first-page":"5574","article-title":"What uncertainties do we need in Bayesian deep learning for computer vision?","volume":"30","author":"Kendall","year":"2017","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1007\/s10994-021-05946-3","article-title":"Aleatoric and epistemic uncertainty in machine learning: An introduction to concepts and methods","volume":"110","author":"Waegeman","year":"2021","journal-title":"Mach. Learn."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Bucek, J., Lange, K.D., and Kistowski, J.v. (2018). SPEC CPU2017: Next-generation compute benchmark. Companion of the 2018 ACM\/SPEC International Conference on Performance Engineering, ACM.","DOI":"10.1145\/3185768.3185771"},{"key":"ref_23","unstructured":"Hennessy, J.L., and Patterson, D.A. (2017). Computer Architecture: A Quantitative Approach, Morgan Kaufmann. [6th ed.]."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"78120","DOI":"10.1109\/ACCESS.2019.2917698","article-title":"A survey of computer architecture simulation techniques and tools","volume":"7","author":"Akram","year":"2019","journal-title":"IEEE Access"},{"key":"ref_25","unstructured":"Gober, N., Chacon, G., Wang, L., Gratz, P.V., Jim\u00e9nez, D.A., Teran, E., Pugsley, S., and Kim, J. (2022). The championship simulator: Architectural simulation for education and competition. arXiv."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Bera, R., Kanellopoulos, K., Nori, A.V., Shahroodi, T., Subramoney, S., and Mutlu, O. (2021). Pythia: A customizable hardware prefetching framework using online reinforcement learning. Proceedings of the 54th IEEE\/ACM International Symposium on Microarchitecture (MICRO), Virtual, 18\u201322 October 2021, ACM.","DOI":"10.1145\/3466752.3480114"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/9\/977\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,2]],"date-time":"2026-09-02T12:06:03Z","timestamp":1788350763000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/9\/977"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,2]]},"references-count":26,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2026,9]]}},"alternative-id":["e28090977"],"URL":"https:\/\/doi.org\/10.3390\/e28090977","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,2]]}}}