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arxiv: 2605.29273 · v1 · pith:UYUEWTU3new · submitted 2026-05-28 · 💻 cs.LG · math.OC

A Theoretical and Experimental Study of a Novel Adaptive Learning Algorithm

Sakshi Kumari , Shyam Kumar M , Sushmitha P This is my paper

Pith reviewed 2026-06-29 09:16 UTC · model grok-4.3

classification 💻 cs.LG math.OC
keywords adaptive optimizersAdamAMSGradconvergence proofline of sight approachC-Adammachine learning
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The pith

C-Adam optimizer is proposed with a convergence proof based on the line of sight approach.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines why Adam can fail to converge and why AMSGrad was introduced to fix that behavior. It then defines C-Adam as a variant that applies a line of sight approach to the adaptive learning rate. A theoretical argument is supplied showing that this change produces convergence, and the method is tested on several real-world numerical tasks. A reader would care because many practical models rely on adaptive optimizers yet still risk non-convergence during training.

Core claim

The central claim is that the line of sight approach produces an optimizer called C-Adam whose update rule admits a convergence proof, thereby addressing the non-convergence limitation identified in Adam while retaining the benefits of adaptive learning rates.

What carries the argument

The line of sight approach, which adjusts the second-moment estimate in the adaptive update to enforce convergence.

If this is right

  • C-Adam can replace Adam or AMSGrad in settings where a convergence guarantee is required.
  • Neural network training runs would exhibit reduced risk of oscillation-induced failure.
  • The same line of sight modification could be examined for other adaptive methods that currently lack proofs.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the approach generalizes, similar modifications might restore convergence guarantees to other first-order methods without second-moment tracking.
  • Empirical comparisons on very large models would test whether the added guarantee scales without extra hyper-parameter tuning.

Load-bearing premise

The line of sight approach produces an optimizer variant whose convergence can be proven and that performs at least as well as Adam or AMSGrad on practical tasks.

What would settle it

A training run or benchmark experiment in which C-Adam diverges or reaches a worse final loss than AMSGrad on the same problem and initialization.

Figures

Figures reproduced from arXiv: 2605.29273 by Sakshi Kumari, Shyam Kumar M, Sushmitha P.

Figure 1
Figure 1. Figure 1: Data points along with the true boundary and the corresponding linear classifier-based model [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Comparison of Adam, AMSGrad and C-Adam for the synthetic problem 4.1 [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Training and validation losses of the three optimizers for multiclass classification using logistic [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Training and validation losses of the three optimizers for multiclass classification using a single [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Training and validation losses of the three optimizers for multiclass classification over CIFAR-10 [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: (a) Prediction results across randomly chosen CIFAR-10 dataset. For each image, the true [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Comparison of Adam, AMSGrad, C-Adam and C-Adam [PITH_FULL_IMAGE:figures/full_fig_p016_7.png] view at source ↗
read the original abstract

A crucial component of machine learning algorithms is minimizing loss functions with less computational cost and less oscillations. While adaptive learning rate-based optimizers have been widely used for real-world tasks, they do not guarantee convergence, which is why AMSGrad was later introduced to investigate the non-convergence behaviour of Adam. In this paper, popular adaptive optimization methods like Adam and AMSGrad are critically reviewed with an emphasis on their fundamental design concepts. To address limitations of the above mentioned optimizers, a new optimizer variant, C-Adam, is proposed based on the line of sight approach. A theoretical proof for convergence is also provided and the optimizer is validated through a number of real-life based numerical experiments.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The paper reviews limitations of Adam and AMSGrad, proposes a new optimizer C-Adam derived from a 'line of sight approach,' supplies a convergence proof, and reports numerical experiments on real-world tasks showing improved performance.

Significance. A rigorously proven convergent adaptive optimizer that demonstrably improves on Adam/AMSGrad in experiments would be a useful contribution to the optimization literature; the explicit provision of a proof and reproducible experiments strengthens the work if the derivation holds.

minor comments (3)
  1. [Abstract] The abstract states that a convergence proof is provided but does not indicate the assumptions (e.g., bounded gradients, convexity) under which the result holds; a brief statement of the main assumptions in the abstract would improve accessibility.
  2. [§3] Notation for the line-of-sight update rule and the moment estimates should be cross-referenced to the corresponding equations in §3 to avoid ambiguity for readers familiar with Adam.
  3. [§5] Figure captions for the experimental loss curves should explicitly state the number of independent runs and whether shaded regions represent standard deviation or standard error.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary, recognition of the significance of a rigorously proven convergent adaptive optimizer, and the recommendation of minor revision. No specific major comments were raised in the report.

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained against external benchmarks

full rationale

The paper defines C-Adam via the line-of-sight approach, states a convergence proof, and reports experiments. No load-bearing step reduces by construction to a fitted input, self-citation chain, or renamed known result; the proof and optimizer definition are presented as independent of the target performance claims. The central result therefore does not collapse to its own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no free parameters, axioms, or invented entities can be identified from the provided text.

pith-pipeline@v0.9.1-grok · 5643 in / 985 out tokens · 24597 ms · 2026-06-29T09:16:11.873500+00:00 · methodology

discussion (0)

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Reference graph

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