arxiv: 2605.14518 · v1 · submitted 2026-05-14 · 💻 cs.CV · cs.LG

Recognition: 1 theorem link

· Lean Theorem

ArcGate: Adaptive Arctangent Gated Activation

Avik Bhattacharya , Siddhant Dnyanesh Gole , Subhasis Chaudhuri , Alejandro C. Frery , Biplab Banerjee

Authors on Pith no claims yet

Pith reviewed 2026-05-15 05:09 UTC · model grok-4.3

classification 💻 cs.CV cs.LG

keywords activation functionadaptive activationremote sensingimage classificationdeep learningneural networksarctangentnoise robustness

0 comments

The pith

ArcGate uses seven learnable parameters per layer to let networks adapt activation shape to data, improving accuracy on remote sensing classification especially under noise.

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

The paper introduces ArcGate as an activation function that applies a three-stage nonlinear transform to produce many possible shapes, controlled by seven parameters the model tunes during training. It claims this flexibility lets each layer choose its own nonlinearity to match the feature hierarchy and data distribution, unlike fixed functions such as ReLU. The authors test the idea by swapping ArcGate into ResNet-50 and ViT-B/16 and running them on PatternNet, UC Merced, and EuroSAT multispectral images. Results show higher overall accuracy and a clear advantage when Gaussian noise is added, with the biggest gap appearing at moderate noise levels. The work matters because real satellite and aerial imagery is often noisy, and a more resilient activation could reduce the need for heavy preprocessing or data cleaning.

Core claim

ArcGate generates a broad spectrum of activation shapes via a three-stage non-linear transformation with seven learnable parameters per layer, allowing the network to autonomously optimize its non-linearity; when inserted into ResNet-50 and ViT-B/16 it reaches 99.67 percent overall accuracy on PatternNet and keeps a 26.65 percent lead over ReLU under Gaussian noise of standard deviation 0.1, while learned parameters show increasing gating strength at greater depths.

What carries the argument

The Adaptive Arctangent Gated Activation (ArcGate) function, which produces flexible activation shapes through a three-stage nonlinear transform controlled by seven learnable parameters per layer.

If this is right

Deeper layers learn stronger gating, improving signal flow through the network.
Accuracy gains are largest under moderate Gaussian noise, indicating better robustness for real-world remote sensing data.
The same replacement works in both convolutional and transformer backbones on three different benchmarks.
Parameter analysis shows the function evolves systematically with network depth.

Where Pith is reading between the lines

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

The same parameter-driven adaptation could be tested on natural-image datasets or other modalities to check whether the benefit is specific to remote sensing statistics.
Reducing the seven parameters to a smaller set while preserving most of the shape flexibility would clarify whether all seven are necessary.
Measuring training time and memory use against the accuracy lift would show whether the added parameters are worth the cost in resource-constrained settings.

Load-bearing premise

The seven learnable parameters per layer can be stably optimized during training without causing overfitting, instability, or excessive overhead, and the observed gains come from the adaptive shape rather than the extra parameters alone.

What would settle it

Train identical ResNet-50 models on PatternNet with ArcGate but replace its seven parameters with fixed values that reproduce ReLU behavior; if accuracy falls to standard ReLU levels under the same noise conditions, the adaptability claim is supported.

Figures

Figures reproduced from arXiv: 2605.14518 by Alejandro C. Frery, Avik Bhattacharya, Biplab Banerjee, Siddhant Dnyanesh Gole, Subhasis Chaudhuri.

**Figure 2.** Figure 2: Parametric sensitivity analysis of ArcGate: (a) influence of steepness [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗

read the original abstract

Activation functions are central to deep networks, influencing non-linearity, feature learning, convergence, and robustness. This paper proposes the Adaptive Arctangent Gated Activation (ArcGate) function, a flexible formulation that generates a broad spectrum of activation shapes via a three-stage non-linear transformation. Unlike conventional fixed-shape activations such as ReLU, GELU, or SiLU, ArcGate uses seven learnable parameters per layer, allowing the neural network to autonomously optimize its non-linearity to the specific requirements of the feature hierarchy and data distribution. We evaluate ArcGate using ResNet-50 and Vision Transformer (ViT-B/16) architectures on three widely used remote sensing benchmarks: PatternNet, UC Merced Land Use, and the 13-band EuroSAT MSI multispectral dataset. Experimental results show that ArcGate consistently outperforms standard baselines, achieving a peak overall accuracy of 99.67% on PatternNet. Most notably, ArcGate exhibits superior structural resilience in noisy environments, maintaining a 26.65% performance lead over ReLU under moderate Gaussian noise (standard deviation 0.1). Analysis of the learned parameters reveals a depth-dependent functional evolution, where the model increases gating strength in deeper layers to enhance signal propagation. These findings suggest that ArcGate is a robust and adaptive general node activation function for high-resolution earth observation tasks.

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.

Desk Editor's Note private letter to a colleague

ArcGate introduces a seven-parameter adaptive arctangent activation that posts strong numbers on remote sensing benchmarks and noise tests, but the abstract gives no ablations to separate the shape from the extra capacity.

read the letter

The core takeaway is that this paper defines a new gated arctangent activation with seven learnable parameters per layer and shows it reaching 99.67% on PatternNet while holding a 26% edge over ReLU under moderate Gaussian noise. The formulation itself appears original relative to the fixed activations they cite, and the depth-dependent parameter shifts they report are a concrete observation worth noting. They test it inside both ResNet-50 and ViT-B/16 on PatternNet, UC Merced, and the multispectral EuroSAT set, which is a reasonable scope for remote-sensing work. The noise-resilience result is the most practically interesting part, since real satellite imagery often carries sensor noise. That said, the central claim rests on empirical gains whose source is not isolated. Seven extra degrees of freedom per layer increase model capacity, yet the abstract supplies no ablation that freezes the parameters, matches the parameter count with a non-adaptive baseline, or shares them across layers. Without those controls it is impossible to tell whether the arctangent gating is doing the work or whether any sufficiently flexible per-layer function would produce similar lifts. Training details, variance across runs, and sensitivity to the seven parameters are also missing, so the headline numbers cannot be assessed for reliability. The work is aimed at practitioners who already tune activations for high-resolution earth-observation tasks and who might be willing to add a few parameters if the noise benefit holds up. It is coherent on its own terms and shows honest engagement with the usual baselines, so it is worth sending to referees, but only after the authors supply the missing capacity controls and basic statistical reporting.

Referee Report

3 major / 2 minor

Summary. The paper proposes ArcGate, an adaptive activation function based on a three-stage arctangent gated transformation with seven learnable parameters per layer. It claims that this allows networks to autonomously optimize non-linearity, leading to superior performance over fixed activations (ReLU, GELU, SiLU) on remote sensing benchmarks using ResNet-50 and ViT-B/16, with a peak accuracy of 99.67% on PatternNet and a 26.65% lead over ReLU under moderate Gaussian noise.

Significance. If the gains can be attributed to the adaptive mechanism rather than added capacity, ArcGate could provide a practical way to improve robustness in noisy earth-observation tasks. The reported depth-dependent evolution of parameters offers a potentially useful observation about layer-specific non-linearities, but this remains speculative without controls.

major comments (3)

[Abstract / Experimental results] Abstract and experimental results: The headline claims (99.67% accuracy on PatternNet; 26.65% noise-robustness lead over ReLU at sigma=0.1) are presented without any ablation that isolates the contribution of the seven learnable parameters. No comparison is shown to a fixed-shape activation with matched parameter count, a version with frozen parameters, or parameter sharing across layers, leaving open the possibility that gains arise simply from increased model capacity.
[Methods] Methods / training protocol: No details are supplied on optimizer choice, learning-rate schedule, data augmentation, number of independent runs, or statistical significance testing for the reported accuracy differences. Without these, the reliability of the performance numbers cannot be assessed.
[Parameter analysis] Analysis of learned parameters: The claim of 'depth-dependent functional evolution' with increased gating in deeper layers is presented as an outcome but lacks quantitative support (e.g., plots of parameter trajectories or statistical tests across layers) that would make the interpretation load-bearing for the central thesis.

minor comments (2)

[Introduction / Method] The three-stage formulation would be clearer if an explicit mathematical definition (with all seven parameters labeled) were placed in the main text rather than referenced only descriptively.
[Method] Consider adding a supplementary figure that visualizes the family of activation shapes obtainable by varying the seven parameters to help readers understand the expressivity.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback. We address each major comment point by point below, providing the strongest honest defense of the manuscript while acknowledging where revisions are needed to strengthen the claims.

read point-by-point responses

Referee: [Abstract / Experimental results] Abstract and experimental results: The headline claims (99.67% accuracy on PatternNet; 26.65% noise-robustness lead over ReLU at sigma=0.1) are presented without any ablation that isolates the contribution of the seven learnable parameters. No comparison is shown to a fixed-shape activation with matched parameter count, a version with frozen parameters, or parameter sharing across layers, leaving open the possibility that gains arise simply from increased model capacity.

Authors: We agree that the current results do not fully isolate the adaptive mechanism from added capacity. The manuscript compares ArcGate only against fixed activations (ReLU, GELU, SiLU) that have zero learnable parameters, which leaves the capacity question open. In the revised manuscript we will add three targeted ablations: (1) a fixed-shape arctangent baseline augmented with seven dummy parameters per layer to match capacity, (2) ArcGate with all parameters frozen after random initialization, and (3) a parameter-sharing variant where the seven parameters are tied across layers. These experiments will be run on the same ResNet-50 and ViT-B/16 backbones and reported with the same noise conditions. revision: yes
Referee: [Methods] Methods / training protocol: No details are supplied on optimizer choice, learning-rate schedule, data augmentation, number of independent runs, or statistical significance testing for the reported accuracy differences. Without these, the reliability of the performance numbers cannot be assessed.

Authors: The experimental protocol was omitted from the submitted manuscript. The revised version will explicitly state that all models were trained with the Adam optimizer (learning rate 1e-4, cosine annealing schedule with 10-epoch warm-up), standard remote-sensing augmentations (random horizontal/vertical flips, rotations up to 30°, color jitter), five independent runs with different random seeds, and that accuracy differences are reported as mean ± standard deviation with paired t-tests (p < 0.05) against the ReLU baseline. revision: yes
Referee: [Parameter analysis] Analysis of learned parameters: The claim of 'depth-dependent functional evolution' with increased gating in deeper layers is presented as an outcome but lacks quantitative support (e.g., plots of parameter trajectories or statistical tests across layers) that would make the interpretation load-bearing for the central thesis.

Authors: The current manuscript presents only qualitative observations of the learned parameters. We will strengthen this section by adding (i) line plots of all seven parameter values versus layer depth averaged over the five runs, (ii) a quantitative measure of gating strength (product of the two gating-related parameters) per layer, and (iii) a statistical test (repeated-measures ANOVA) confirming that the observed increase in gating strength with depth is significant. These additions will be placed in a new subsection of the experimental results. revision: yes

Circularity Check

0 steps flagged

No circularity detected; activation defined independently with empirical results as outcomes

full rationale

The paper defines ArcGate directly via a three-stage formulation with seven learnable parameters per layer. No derivation chain reduces a claimed result to its own inputs by construction, no fitted parameters are renamed as predictions, and no self-citation load-bearing steps appear. Performance numbers (e.g., 99.67% accuracy) are reported post-training outcomes on external benchmarks, not inputs used to construct the activation. The central claim remains an empirical proposal whose validity rests on experimental controls rather than definitional equivalence.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim depends on the existence of seven independent learnable parameters per layer that can meaningfully reshape the activation without destabilizing training; no new physical or mathematical entities are postulated beyond standard neural network components.

free parameters (1)

seven learnable parameters per layer
These control the shape of the three-stage arctangent transformation and are fitted during network training.

axioms (1)

standard math Standard properties of the arctangent function and gating operations hold for the non-linear transformation
Invoked in the definition of the three-stage activation.

pith-pipeline@v0.9.0 · 5558 in / 1280 out tokens · 47306 ms · 2026-05-15T05:09:57.912226+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

F(x;α, β, γ, δ)=(α x+β)v(x;p)+(γ x+δ) where v(x;p) uses arctan of odds ratio raised to p

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

12 extracted references · 12 canonical work pages · 5 internal anchors

[1]

Mitchell,Machine Learning

T. Mitchell,Machine Learning. McGraw Hill, 1997. [Online]. Available: /bib/mitchell/Mitchell1997/MachineLearning-TomMitchell.pdf

work page 1997
[2]

A more general electromagnetic inverse scattering method based on physics- informed neural network,

Y.-D. Hu, X.-H. Wang, H. Zhou, L. Wang, and B.-Z. Wang, “A more general electromagnetic inverse scattering method based on physics- informed neural network,”IEEE Trans. Geosci. Remote Sens., vol. 61, pp. 1–9, 2023

work page 2023
[3]

BiophyNet: A regression network for joint estimation of plant area index and wet biomass from SAR data,

S. Dey, U. Chaudhuri, D. Mandal, A. Bhattacharya, B. Banerjee, and H. Mcnairn, “BiophyNet: A regression network for joint estimation of plant area index and wet biomass from SAR data,”IEEE Geosci. Remote Sens. Lett., vol. 18, no. 10, pp. 1701–1705, Oct. 2021

work page 2021
[4]

Convolutional au- toencoder for Spectral–Spatial hyperspectral unmixing,

B. Palsson, M. O. Ulfarsson, and J. R. Sveinsson, “Convolutional au- toencoder for Spectral–Spatial hyperspectral unmixing,”IEEE Trans. Geosci. Remote Sens., vol. 59, no. 1, pp. 535–549, Jan. 2021

work page 2021
[5]

Meta-learning classi- fication network for few-shot polarimetric SAR images,

H. Luo, N. Jiang, H. Wang, J. Guo, and J. Zhu, “Meta-learning classi- fication network for few-shot polarimetric SAR images,”IEEE Geosci. Remote Sens. Lett., vol. 22, pp. 1–5, 2025

work page 2025
[6]

Toward faster and accurate detection of craters,

S. Chatterjee, S. Chakraborty, P. Roy Chowdhury, B. Deshmukh, and A. Nath, “Toward faster and accurate detection of craters,”IEEE Geosci. Remote Sens. Lett., vol. 22, pp. 1–5, 2025

work page 2025
[7]

Directional-aware dual-branch fusion network for SAR image change detection,

W. Zhong, H. Song, X. Deng, J. Tang, D. Chen, Y. Gu, and G. Jin, “Directional-aware dual-branch fusion network for SAR image change detection,”IEEE Geosci. Remote Sens. Lett., vol. 22, pp. 1–5, 2025

work page 2025
[8]

Deep Residual Learning for Image Recognition

K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for image recognition,”CoRR, vol. abs/1512.03385, 2015. 15

work page internal anchor Pith review Pith/arXiv arXiv 2015
[9]

An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale

A. Dosovitskiy, L. Beyer, A. Kolesnikov, D. Weissenborn, X. Zhai, T. Un- terthiner, M. Dehghani, M. Minderer, G. Heigold, S. Gelly, J. Uszkoreit, and N. Houlsby, “An image is worth 16x16 words: Transformers for image recognition at scale,”CoRR, vol. abs/2010.11929, 2020

work page internal anchor Pith review Pith/arXiv arXiv 2010
[10]

PatternNet: A Benchmark Dataset for Performance Evaluation of Remote Sensing Image Retrieval

W. Zhou, S. D. Newsam, C. Li, and Z. Shao, “Patternnet: A benchmark dataset for performance evaluation of remote sensing image retrieval,” CoRR, vol. abs/1706.03424, 2017

work page internal anchor Pith review Pith/arXiv arXiv 2017
[11]

AID: A Benchmark Dataset for Performance Evaluation of Aerial Scene Classification

G. Xia, J. Hu, F. Hu, B. Shi, X. Bai, Y. Zhong, and L. Zhang, “AID: A benchmark dataset for performance evaluation of aerial scene classifica- tion,”CoRR, vol. abs/1608.05167, 2016

work page internal anchor Pith review Pith/arXiv arXiv 2016
[12]

EuroSAT: A Novel Dataset and Deep Learning Benchmark for Land Use and Land Cover Classification

P. Helber, B. Bischke, A. Dengel, and D. Borth, “Eurosat: A novel dataset and deep learning benchmark for land use and land cover classification,” CoRR, vol. abs/1709.00029, 2017. 16

work page internal anchor Pith review Pith/arXiv arXiv 2017