Plain SGD (stochastic gradient descent) delivers mean MSE (mean squared error) 44% below VAdam in the paper's crypto benchmark. VAdam, the volatility-conditioned Adam variant proposed by Nagdiya, Kapoor and Tokekar, improves on Adam by just 0.000019. That gain comes from a single run, without repeated seeds or significance tests to put it in perspective. This evidence gives crypto traders no reason to switch optimizers.
How volatility changes the update
VAdam feeds market volatility into Adam's training updates. Adam scales each parameter's step using running estimates of the gradient's mean and variance. The paper describes its addition as a volatility-aware adaptive gradient optimization framework. In ordinary Adam, the learning rate and first-moment coefficient stay fixed even as crypto volatility changes regimes.
VAdam takes the rolling standard deviation of daily log returns over a window and normalizes it to produce a regime score. A high score reduces the learning rate and also changes beta1, with a sensitivity parameter controlling each adjustment. Everything else follows standard Adam, including bias correction.
The promised benefit is "more conservative updates during highly volatile periods" alongside faster learning in calm markets. This volatility input affects network training alone. It never determines position size. The paper contains no strategy.
The authors use Yahoo Finance daily OHLCV for BTC, ETH, SOL, XRP and ADA. Their samples contain 2,238 to 3,068 observations per coin, split chronologically 70/15/15 for training, validation and testing. The prediction target is the next-step return. Log returns, rolling volatility, normalized volume and spread features form the inputs, with Min-Max scaling throughout. Each optimizer trains the same MLP: 64 hidden units, ReLU, dropout 0.20, learning rate 0.001, batch 32 and 100 epochs.
The reported improvements over Adam are 0.65% in mean MSE, 0.67% in price sMAPE and 1.28% in epochs to convergence. XRP supplies the largest individual gain, a 4.65% reduction in MSE.
We could not resolve one detail of the update. Each batch of 32 observations covers 32 different days. We did not find which day's volatility controls the step for that batch.
What does the 0.65% buy?
Mean MSE falls from 0.002952 to 0.002933. The absolute improvement is 0.000019. Convergence takes 15.4 epochs rather than 15.6, saving a fifth of an epoch, and price sMAPE falls from 3.9613% to 3.9347%. AdamW provides a useful comparison: changing only Adam's treatment of weight decay yields 0.002951.
The authors acknowledge the small size of the gains. They describe them as "modest but consistent" and write in the conclusion that "the observed improvements were moderate." Their case consequently depends on "consistent," where the evidence becomes thin. We did not find repeated seeds, confidence intervals or significance tests in the setup. XRP's 4.65% improvement is the only per-asset VAdam result we found.
VAdam also receives more tuning. It adds three hyperparameters, volatility sensitivity, momentum sensitivity and window length, and the paper states that "these parameters were selected using validation-set tuning." The baselines all retain a learning rate of 0.001. A 0.65% advantage, with three tuned degrees of freedom against none, cannot be distinguished from the benefit of that tuning.
The benchmark belongs to SGD
The results section acknowledges SGD's strongest overall forecasting accuracy under the MLP. It then emphasizes VAdam's consistent improvements over the Adam-family optimizers. That narrower comparison is the authors' defense, confining VAdam's win to a family that loses on this model. Neither the abstract nor the conclusion mentions SGD's result; both limit their claims to the Adam family. The authors never say VAdam beats SGD. Our headline concerns relevance: someone reading only the abstract would miss the simplest baseline's victory.
The margin is large.
SGD records MSE of 0.001656, compared with VAdam's 0.002933. MAE is 0.0277 versus 0.0394, and sMAPE is 2.7693% versus 3.9347%. The paper measures stability through validation-loss variance, where a lower figure means a smoother path. SGD scores 0.000069 against VAdam's 0.000373. Across the paper's five-coin averages, convergence is the sole column VAdam wins: SGD takes 17.8 epochs, VAdam 15.4.
Even against Adam, VAdam has slightly higher validation-loss variance, 0.000373 versus 0.000367. The paper nevertheless describes VAdam's Bitcoin validation curve as a "smoother convergence trajectory". Its stability column gives the opposite reading.
VAdam's directional accuracy is 50.22%. Adam and AdamW reach 50.79%, SGD reaches 51.49% and Nadam reaches 51.75%. Among the four Adam-family methods, the optimizer designed to respond to market regimes finishes last at predicting tomorrow's return sign.
Five coins, little evidence of a regime effect
The per-asset table does not establish the regime claim. It reports epochs of 20.83 for ADA, 11.33 for ETH and 18.17 for XRP. These are multiples of one sixth, as expected when integer epoch counts are averaged over six optimizers. The MSEs confirm that reading: averaging the five coin-level figures gives the same value as averaging the six optimizer-level figures in the main comparison table.
The per-asset table therefore combines all optimizers. It orders coins by forecasting difficulty, from BTC at MSE 0.000919 to ADA at 0.003898. It cannot tell us how VAdam compares with Adam.
The paper links the larger errors for SOL and ADA to "stronger volatility," and says VAdam improved most clearly on XRP and other assets with larger volatility swings. Under that hypothesis, SOL, with pooled MSE 0.003659, and ADA should be where the improvement appears. We found a figure only for XRP. Its pooled MSE of 0.002651 puts it in the middle of the group.
Directional accuracy presents the greater difficulty. Hit rates across all six optimizers range from 49.50% to 51.75%, with each result averaging five test sets. A 15% test share of 2,238 to 3,068 days supplies roughly 336 to 460 forecasts per coin. Treating coins as independent gives about 1,700 to 2,300 forecasts, enough for a standard error near 1.0 to 1.2 points around a 50% hit rate.
Nadam's 1.75 points is the largest departure from 50%, and it remains under two standard errors. Correlation between coins increases the true error. Every optimizer's result therefore remains within coin-flip territory.
We found no trading rule, transaction costs, Sharpe or drawdown in the paper. It falls one step short of the daily-BTC study covered in /articles/the-limits-of-machine-learning-in-daily-return-forecasting-evidence-from-volatil, which at least supplied a trading Sharpe we could audit. There is also an unresolved change of units. The target is a next-step return, whereas the reported sMAPE measures price; we did not find the conversion from forecasts to prices.
We ran no test of our own. We hold no cryptocurrency price history, and applying the volatility conditioning to equities would test a different signal.
The paper establishes a narrow result. With one 64-unit MLP, one split and five coins, tuned volatility scaling improves Adam's mean MSE by 0.000019 without sacrificing convergence speed. I would reconsider VAdam after it beat learning-rate-tuned SGD across many seeds on a model larger than a single hidden layer. For now, the baseline owns the paper's strongest result.