{"id":"eb219ac0-a0b9-4e78-806a-f8459e747f2d","arxiv_id":"1908.04116","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"The paper demonstrates that a batch-gradient-descent version of the Adam optimizer can train a feed-forward equalizer for 120-Gbit/s PAM8 optical interconnects, matching RLS performance and beating LMS with fewer training samples.","lead":"The authors apply the machine-learning optimizer Adam to train a time-domain equalizer in a 120-Gbit/s PAM8 optical link, and report that it converges with fewer training samples than the standard LMS algorithm. The result is a modest, incremental improvement to receiver DSP for short-reach optical interconnects.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Global-optimality from convex MSE is asserted, and the experimental comparison hides tuning parameters θ and α; the paper's central claims are not independently supported as reported.","rationale":"The reader identifies unreported θ and α as the weakest assumption; I agree this is a concrete, testable gap. My pass adds a second issue: the global-optimality guarantee is asserted rather than derived, and for Adam with fixed step size on a convex quadratic the statement is not a standard theorem. This reinforces the reader's conditional verdict rather than changing it. Because the central application is plausible and the experimental setup is coherent, I do not see grounds for rejection; the deficiency is missing evidence and missing parameter reporting, which a conditional acceptance requiring a reproducibility check would address. Hence UNCHANGED, with agreement partial: my additional concern is different in kind, though complementary, to the reader's.","tokens_in":6130,"tokens_out":3560,"duration_ms":36126,"concrete_test":"Reproduce the offline equalization of the recorded PAM8 frames (same training sequence length M=300, taps N=181, iterations I=120, β1=0.9, β2=0.999, and post-filter/MLSD chain) while sweeping θ over {0.001, 0.01, 0.1} and α over {0, 0.5, 0.9}. If the BER versus ROP curves at the 7% FEC limit shift by more than about 0.5 dB across that grid, or if LMS with 300 training samples outperforms BGD-based Adam for any grid point, the claimed superiority is tuning-dependent. If the curves are essentially unchanged, the experimental claim is robust.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The abstract makes two load-bearing claims: BGD-based Adam 'can obtain globally optimal tap coefficients without being trapped in locally optimal tap coefficients', and the experimental results show it 'works well' in 120-Gbit/s PAM8. The weakest point is that neither claim is secured by what is reported. First, the global-convergence statement (Section II, after Eq. 10) is asserted with a citation to a survey, not proven; MSE is convex, but Adam with fixed step size θ is not guaranteed to converge to the minimum, and the guarantee is not a property of convexity alone. Second, the experiments in Section IV are irreproducible without θ (Algorithm 1 input) and α (Eq. 11 post-filter coefficient), whose values are never disclosed. The comparison with LMS/RLS (300 vs 1200 training samples, BER versus ROP in Fig. 3) therefore cannot be separated from the particular tuning choices, especially because LMS and RLS also depend on their own step sizes and fitting parameters that are not specified. The 'more efficient than LMS/RLS' and 'fast and stable convergence' conclusions may hold for the chosen operating point, but the paper gives no evidence that they hold robustly across reasonable parameter choices.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes applying the Adam optimization algorithm in batch (BGD) mode to train the tap coefficients of a feed-forward equalizer for short-reach PAM8 optical interconnects. The authors formulate the MSE cost function, derive the gradient expression in Eq. (4), present Algorithm 1 for the BGD-Adam update, and report experimental results at 120 Gbit/s over 2-km SSMF. The experiments compare MSE convergence and BER versus received optical power for BGD-Adam, LMS, and RLS, and a complexity comparison is given in Eqs. (12)-(14). The paper claims that BGD-Adam achieves globally optimal taps without local-minimum trapping, converges fast and stably, uses fewer training samples than LMS, and is more efficient due to parallel matrix operations.","tokens_in":6390,"tokens_out":4592,"duration_ms":49733,"significance":"If the claims are supported, the paper would be a useful application of a well-known optimizer to an important equalization problem in short-reach optical links. The gradient derivation in Eq. (4) is correct, the complexity formula in Eqs. (12)-(14) is explicit, and the experimental setup is realistic and clearly described. The main value is the experimental demonstration that batch Adam can train FFE taps successfully in a 120-Gbit/s PAM8 system. However, the global-convergence guarantee is asserted without proof, and the experimental comparison omits key tuning parameters, so the strength of the central claims currently exceeds what the manuscript demonstrates.","major_comments":[{"comment":"The statement that BGD-based Adam is 'guaranteed to converge to globally optimal solution for convex error function' is not established by the manuscript or by the cited survey. Convexity alone does not imply convergence of the fixed-step Adam update in Algorithm 1; standard Adam convergence results require additional conditions such as decaying step sizes, bounded gradients, or similar assumptions. Please either provide a precise convergence theorem for Algorithm 1 with the exact assumptions used, or weaken the claim to an empirical observation. This is load-bearing because the abstract's 'globally optimal tap coefficients' claim rests on this sentence.","section":"Section II, after Eq. (10)"},{"comment":"The experimental comparison varies two parameters at once: BGD-Adam and RLS use 300 training samples while LMS uses 1200. The conclusion that BGD-Adam is 'more efficient' than LMS is therefore not separable from the choice of training length, and no study of sensitivity to training length is given. In addition, the critical hyperparameters are not reported: the step size θ in Algorithm 1, the post-filter coefficient α in Eq. (11), the LMS step size, and the RLS forgetting factor. Without these values, the reported BER and MSE curves cannot be reproduced, and the reader cannot tell whether the good performance reflects the method or the particular tuning.","section":"Section IV, Fig. 3 and Section III, Eq. (11)"},{"comment":"The convergence comparison in Fig. 2 is misleading because one BGD-Adam iteration processes M training samples, whereas one LMS or RLS iteration processes one sample. The claim that LMS/RLS 'cannot converge even after 200 iterations' while BGD-Adam converges after 100 iterations therefore compares different numbers of training samples per iteration. Please plot convergence against the total number of training samples consumed, or against wall-clock time, so that the 'fast and stable convergence' claim can be assessed fairly.","section":"Section IV, Fig. 2"},{"comment":"The efficiency claim is not fully supported by the reported complexity data. The formulas show CBGD-Adam > CLMS, so the statement that BGD-Adam is 'more efficient than conventional serial algorithms, such as LMS' relies entirely on unquantified parallel processing. The paper does not report runtime, parallel speedup, or any hardware-specific benchmark. Please either provide such measurements or explicitly restrict the efficiency claim to the parallel implementation and state that serial computational complexity remains higher than LMS.","section":"Abstract and Section IV, Eqs. (12)-(14) and Table I"}],"minor_comments":[{"comment":"The word 'Principle' in the section title should be 'Principle'.","section":"Title of Section II"},{"comment":"Algorithm 1 has an 'end while' on line 8 but no corresponding 'while' statement; please specify the iteration loop explicitly.","section":"Algorithm 1"},{"comment":"The sentence 'where x are the received training samples' should be 'where x_i are the received training samples' for clarity.","section":"Eq. (1)"},{"comment":"The phrases 'Its acknowledged' and 'Its very possible' contain grammatical errors and should be corrected.","section":"Section II, paragraph after Eq. (10)"},{"comment":"The phrase 'field programmable gata array' contains a typo; it should be 'field programmable gate array'.","section":"Section II, paragraph after Eq. (10)"},{"comment":"The MSE plots in Fig. 2 would be easier to interpret if the axes were labeled and the definition of 'iteration' for LMS and RLS were stated in the caption or text.","section":"Section IV, Fig. 2"}],"recommendation":"major_revision","confidential_remarks":"The paper is likely within scope for a short applied-optics journal, and the experimental demonstration appears usable after revision. The main risk is overclaiming: the global convergence statement should be removed or proved, and the quantitative claims need to be restated with the missing hyperparameters disclosed. I would not reject, because the core empirical finding is plausible and the derivation is sound."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a modest, legitimate engineering paper — Adam applied to batch-gradient-descent training of a feed-forward equalizer — backed by a real 120-Gbit/s PAM8 experiment. It is not a breakthrough, and the headline \"globally optimal\" claim is not supported. But the core demonstration is plausible and worth a referee's time.\n\nWhat's new: the specific combination of BGD-based Adam for FFE tap training in PAM8 optical interconnects. The algorithm itself is Kingma and Ba's; the MSE cost is a standard convex quadratic. The paper's contribution is an application and an experimental check. That is a routine but honest increment.\n\nWhat's done well: the gradient derivation in Eq. (4) is correct. The experimental setup is described in enough detail to follow: 43-GBaud PAM8, 2-km SSMF, FFE with 181 taps, post filter and MLSD. The comparison shows BGD-Adam with 300 training samples performs about like RLS with 300 and better than LMS with 1200. That is a concrete, useful data point for short-reach links where training overhead matters.\n\nSoft spots, in order of importance. First, the global-convergence assertion after Eq. (10) — \"guaranteed to converge to globally optimal solution for convex error function\" — is not proven and is not a property of Adam with fixed step size. Convexity alone does not give that guarantee for this algorithm; the cited survey does not provide a theorem for Adam. The MSE cost is convex, so any local minimum is global, but the algorithm still needs a convergence proof or a careful statement about step-size decay. Second, two key parameters are never disclosed: the step size θ in Algorithm 1 and the post-filter coefficient α in Eq. (11). Without those, the experiment is not fully reproducible, and the comparison with LMS/RLS cannot be separated from tuning choices. The LMS and RLS step sizes and forgetting factors are also absent. This is a minor-to-moderate problem: the authors show the method works, but not how robust it is across parameter settings. Third, the complexity discussion is only suggestive. The parallel-processing advantage is plausible, but the runtime comparison is not measured, and the complexity formula comes from the authors' prior work.\n\nThe citation pattern is fine. Adam is cited properly, the application references are appropriate. No sign of self-citation abuse.\n\nWho this is for: people working on DSP for short-reach optical interconnects, especially those considering ML-style training for equalizers. It is a useful data point, not a reference implementation.\n\nRecommendation: send it to peer review. A competent referee can ask for the missing parameters, a softened global-convergence claim, and ideally a small robustness sweep. Those are fixable. The work is honest and the experiment appears real.","headline":"A modest but honest application of Adam to FFE training in PAM8, with a real experiment; the global-optimality claim is overreach and key tuning parameters are missing.","tokens_in":6912,"tokens_out":2093,"would_cite":false,"duration_ms":21160,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Batch-gradient Adam equalizer trains PAM8 taps on 300 samples","keywords":["Adam optimizer","batch gradient descent","time-domain equalizer","feed-forward equalizer","PAM8","optical interconnects","mean square error","adaptive equalization"],"falsifier":"Repeat the 120-Gbit/s PAM8 training experiment holding all parameters fixed except Adam's step size $\\theta$, sweeping it from roughly 0.001 to 0.5, and record the number of iterations to a fixed MSE target. If the iteration count varies substantially across the sweep, or if a step-size-optimized LMS with 300 training samples matches the BGD-based Adam BER, then the claimed speed and sample-efficiency advantages would be shown to be tuning-dependent rather than intrinsic to batch-gradient Adam.","tokens_in":5958,"feed_emoji":"📶","tokens_out":7301,"duration_ms":69896,"temperature":0.7,"pith_summary":"The paper proposes using the Adam optimizer, a machine-learning workhorse, with batch gradient descent to train the tap coefficients of a feed-forward time-domain equalizer in PAM-based optical interconnect links. Its thesis is that this combination converges to the globally optimal tap settings of the mean-square-error cost function, does so in roughly 100 iterations, and needs only 300 training samples, where LMS needs 1200 and often fails to converge. The motivation is that future short-reach optical links will need fast, stable, parallel-friendly equalizer training as symbol rates and modulation levels rise. The paper demonstrates the approach in a 120-Gbit/s PAM8 experiment over 2 km of fiber, reporting BER close to RLS and better than LMS at the 7% FEC limit.","feed_headline":"Batch-gradient Adam equalizer trains PAM8 taps on 300 samples","feed_subtitle":"Adam-based feed-forward equalizer matches RLS quality in PAM8 links with far fewer samples than LMS.","key_machinery":"The central object is Algorithm 1, the BGD-based Adam update loop for FFE taps. It forms an $(M-N+1)$-by-$N$ received-sample matrix $\\mathbf{R}$, a transmitted training vector $\\mathbf{Y}$, and the MSE cost $J(\\boldsymbol{\\omega})=\\frac{1}{M-N+1}(\\mathbf{R}\\boldsymbol{\\omega}-\\mathbf{Y})^T(\\mathbf{R}\\boldsymbol{\\omega}-\\mathbf{Y})$, whose gradient is $\\mathbf{G}_t=\\frac{2}{M-N+1}\\mathbf{R}^T(\\mathbf{R}\\boldsymbol{\\omega}_{t-1}-\\mathbf{Y})$. The Adam machinery maintains exponentially decaying first- and second-moment estimates $\\mathbf{m}_t$ and $\\mathbf{v}_t$, bias-corrects them with $1-\\beta_1^t$ and $1-\\beta_2^t$, and updates taps as $\\boldsymbol{\\omega}_t=\\boldsymbol{\\omega}_{t-1}-\\theta\\,\\hat{\\mathbf{m}}_t/(\\sqrt{\\hat{\\mathbf{v}}_t}+\\epsilon)$. This update is what carries the central claim: the per-tap adaptive step sizes are credited with fast, stable, precise convergence, while the batch update over the full training block is credited with reaching the global optimum of the convex MSE surface.","core_discovery":"On the paper's own terms, the discovery is that Adam's adaptive step-size mechanism transfers cleanly from stochastic machine-learning optimization to batch training of an FFE. Because the FFE's MSE cost is a convex quadratic in the tap vector, the paper argues that updating from all stored training samples, rather than sample-by-sample as LMS and RLS do, sidesteps local minima and gives stable descent. The Adam moment estimates and bias correction then shrink the effective step size in later iterations, allowing a precise final tap setting with low MSE. Experimentally, the paper reports that BGD-based Adam reaches an MSE near 0.1 after 100 iterations, requires 300 training samples to match RLS's BER and beat LMS's with 1200 samples, and yields a roughly 1-dB sensitivity gain over LMS at the 7% FEC limit. The paper concludes that this makes BGD-based Adam a promising TDE training method for future PAM-based optical interconnects.","pith_inferences":["Editorial extension: because the FFE MSE cost is a convex quadratic, the global-optimality part of the claim is a property of batch descent on that surface, not of Adam itself; Adam's real contribution here is faster, smoother approach to that global optimum.","Editorial extension: the paper compares iteration counts but not wall-clock time per iteration; on serial hardware the $O(N^2)$-per-iteration matrix product could erase the convergence advantage, so the practical benefit is tied to parallel execution.","Editorial extension: the same BGD-based Adam update could be applied with a mini-batch of received samples instead of the full block, trading memory for iteration count, and to nonlinear equalizers where the cost surface is not convex and the local-trap claim would be non-trivial.","Editorial extension: since the results depend on two unreported tuning constants $\\theta$ and $\\alpha$, publishing their values would let other groups test whether the advantage persists across step-size sweeps."],"forward_implications":["BGD-based Adam FFE reaches an MSE near 0.1 after about 100 iterations, whereas LMS and RLS in the same setup have not converged after 200 iterations.","With 300 training samples, BGD-based Adam matches the BER of RLS with 300 samples and beats LMS with 1200 samples, both back-to-back and after 2 km of SSMF.","At the 7% FEC limit, BGD-based Adam achieves roughly 1 dB better receiver sensitivity than LMS, indicating more tolerance to limited bandwidth and noise.","The training complexity is $N[2(M-N+1)+9]I$, lying between LMS and RLS, and the matrix-based updates permit parallel implementation that can accelerate training.","The post-filter plus MLSD removes the extra ISI that the post filter introduces, so the equalized PAM8 signal can be detected at 120 Gbit/s."],"supporting_citations":[{"why":"Supplies the Adam update rule: moment estimates, bias correction, and elementwise adaptive step sizes.","marker":"[8]"},{"why":"Source for the claim that batch gradient descent converges to the global optimum of convex error functions such as MSE.","marker":"[12]"},{"why":"Supports the statement that fixed step size in conventional BGD risks divergence if large and slow convergence if small.","marker":"[11]"},{"why":"Supports the post-filter plus MLSD processing that removes the known ISI introduced by the post filter.","marker":"[15]"},{"why":"Provides the computational-complexity model used to compare BGD-based Adam, LMS, and RLS training costs.","marker":"[16]"}],"fun_headline_variants":["Adam batch training for PAM8 equalizer cuts samples to 300","BGD-Adam FFE matches RLS in PAM8 with 300 samples","Adam-based equalizer: 300 samples beat LMS in PAM8 links","Batch Adam tunes PAM8 taps, rivals RLS, beats LMS","Adam FFE for PAM8: 4x fewer samples than LMS training"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The reported speed and sample-efficiency advantages depend on unstated choices for Adam's step size $\\theta$ and the post-filter coefficient $\\alpha$, so the reader cannot tell whether the results reflect the method itself or the tuning chosen for this particular experiment.","fun_headline_variants_meta":{"raw":{"variants":["Adam batch training for PAM8 equalizer cuts samples to 300","BGD-Adam FFE matches RLS in PAM8 with 300 samples","Adam-based equalizer: 300 samples beat LMS in PAM8 links","Batch Adam tunes PAM8 taps, rivals RLS, beats LMS","Adam FFE for PAM8: 4x fewer samples than LMS training"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000215,"raw_usage":{"total_tokens":1412,"prompt_tokens":915,"completion_tokens":497,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":531,"completion_tokens_details":{"reasoning_tokens":395}},"tokens_in":531,"tokens_out":497,"duration_ms":5513,"temperature":1.0,"reasoning_tokens":395,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T13:50:35.295997+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Repeat the 120-Gbit/s PAM8 training experiment holding all parameters fixed except Adam's step size $\\theta$, sweeping it from roughly 0.001 to 0.5, and record the number of iterations to a fixed MSE target. If the iteration count varies substantially across the sweep, or if a step-size-optimized LMS with 300 training samples matches the BGD-based Adam BER, then the claimed speed and sample-efficiency advantages would be shown to be tuning-dependent rather than intrinsic to batch-gradient Adam.","supporting_citations":[{"cited_title":"Goodfellow, Y","cited_arxiv_id":null,"evidence_quote":"Supports the statement that fixed step size in conventional BGD risks divergence if large and slow convergence if small."},{"cited_title":"Digital signal processing for short-reach optical communications: a review of current technologies and future trends,","cited_arxiv_id":null,"evidence_quote":"Supports the post-filter plus MLSD processing that removes the known ISI introduced by the post filter."},{"cited_title":"Joint fde and mlsd algorithm for 56-gbit/s optical ftn-pam4 system using 10g-class optics,","cited_arxiv_id":null,"evidence_quote":"Provides the computational-complexity model used to compare BGD-based Adam, LMS, and RLS training costs."}],"review_version":1}