⚡ electrical engineering

A Comparative Analysis of MLP and Kolmogorov-Arnold Networks (KAN) for Faster-than-Nyquist (FTN) Signaling Detection

This paper demonstrates that Kolmogorov-Arnold Networks (KAN) significantly outperform multilayer perceptrons (MLP) in Faster-than-Nyquist (FTN) BPSK detection, achieving an 18.6-fold lower bit error rate at 10 dB while utilizing only one-eighth of the hidden width, thereby offering a more parameter-efficient solution for handling inter-symbol interference.

Original authors: Sude Ertan, Osman Tokluoglu, Enver Cavus

Published 2026-08-04

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CC BY 4.0

Original authors: Sude Ertan, Osman Tokluoglu, Enver Cavus

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to send a secret message to a friend using a walkie-talkie, but you want to fit as many words as possible into a single minute. In the world of radio and digital communication, there is a golden rule called the "Nyquist limit." It's like a speed limit sign that says, "You can only send one symbol (a dot or a dash) every X seconds, or the signals will start to blur together." For decades, engineers have respected this limit to keep messages clear. But what if you could break the speed limit? What if you squeezed the dots and dashes closer together? This is called "Faster-than-Nyquist" (FTN) signaling. It's a clever trick to pack more data into the same amount of space, but it comes with a catch: the signals start to overlap and interfere with each other, like cars merging onto a highway too quickly.

To fix this mess, the receiver needs a super-smart detective to figure out which signal is which. The old-school detectives (called BCJR) are incredibly accurate, but they are like a giant, slow-moving tank: they need massive computing power to solve the puzzle, which is hard to fit into small, battery-powered devices. Recently, scientists have tried using "neural networks"—computer brains that learn from examples—to act as these detectives. The big question is: which type of computer brain is the best at untangling these messy signals without needing a supercomputer?

This paper dives into a head-to-head battle between two types of neural network detectives: the classic MLP (Multilayer Perceptron) and a newer, trendier model called KAN (Kolmogorov-Arnold Network). The researchers set up a massive simulation, generating nearly four million examples of these messy, overlapping signals. They taught both types of networks to identify the correct message from a window of 65 noisy samples. The goal was to see which one could spot the right signal with the fewest mistakes (Bit Error Rate) while using the least amount of "brain power" (parameters).

The results were surprising. The classic MLP detective needed a wide, bulky brain (with a hidden layer width of 32) to do a decent job. Even then, at a signal quality of 10 decibels, it made mistakes about 130 times out of a million. The KAN detective, however, was a master of efficiency. It solved the same puzzle with a tiny brain (a hidden layer width of just 4) and made mistakes only 7 times out of a million. That is a massive improvement: the KAN was 18.6 times more accurate than the MLP, despite using a hidden layer that was one-eighth the size.

The paper argues that the reason for this victory is how the two networks are built. The MLP is like a team of workers where everyone stands in a big circle and shouts their opinions at once; to get the answer right, you need a huge team. The KAN is different; it puts the "thinking" on the connections between the workers rather than the workers themselves. This allows it to handle the specific, messy overlaps of the signals much more naturally. In these simulations, the KAN didn't just beat the MLP; it reached the same level of perfection as the giant, slow "tank" detective (the BCJR), but it did it with a tiny fraction of the complexity. The authors suggest that for future devices that need to send more data with less battery and less hardware, this new "edge-based" way of thinking might be the key to unlocking faster, cleaner communication.

Technical Summary: A Comparative Analysis of MLP and Kolmogorov-Arnold Networks (KAN) for Faster-than-Nyquist (FTN) Signaling Detection

Problem Statement
Faster-than-Nyquist (FTN) signaling is a technique used to increase spectral efficiency by transmitting symbols at intervals shorter than the Nyquist limit ( $T_{FTN} = \tau T$ , where $\tau < 1$ ). While this approach boosts transmission rates (e.g., a 25% increase for $\tau=0.8$ ), it deliberately introduces deterministic inter-symbol interference (ISI). This transforms the detection problem from simple symbol-by-symbol estimation into a complex sequence-estimation task. Classical optimal detectors, such as the BCJR algorithm, can approach optimal performance but suffer from computational complexity that scales exponentially with channel memory, making them impractical for real-time or hardware-constrained receivers. Consequently, there is a need for learned detectors that can approximate the nonlinear decision regions of FTN channels with lower complexity.

Methodology
The study conducts a systematic, direct comparison between two neural network architectures for FTN Binary Phase-Shift Keying (BPSK) detection under Additive White Gaussian Noise (AWGN):

Multilayer Perceptron (MLP): A standard baseline where nonlinearity is applied at node activations (hidden layers). The authors performed a "width sweep" across hidden layer sizes $\{8, 16, 32, 64, 128, 256\}$ to identify the optimal configuration.
Kolmogorov-Arnold Network (KAN): An architecture based on the Kolmogorov-Arnold representation theorem, where nonlinearity is placed on the edges via learnable B-spline functions rather than at nodes. Two configurations ( $w4\_g5$ and $w8\_g3$ ) were evaluated.

Experimental Setup

Dataset: A large-scale Monte Carlo dataset comprising nearly 4 million labeled windows (3,999,936 total) was generated.
Parameters: The study focused on a time-packing factor of $\tau = 0.8$ and Signal-to-Noise Ratio (SNR) values ranging from 7 to 10 dB.
Input Representation: Detectors operate on a 65-sample received window centered on the target symbol ( $r_k = [r_{k-32}, \dots, r_{k+32}]^T$ ).
Training: Both models utilized Binary Cross-Entropy loss and the Adam optimizer.
Comparison Baselines: Performance was measured against a hard-decision FTN baseline and the optimal BCJR reference.

Key Contributions

Dataset Creation: Generation of a large-scale, labeled FTN-BPSK dataset specifically for $\tau=0.8$ and SNR 7–10 dB.
Systematic Comparison: A controlled evaluation of KAN versus MLP under identical conditions (same window size, dataset split, and SNR values) to determine which model more efficiently represents FTN decision boundaries.
Efficiency Analysis: Evaluation of Bit Error Rate (BER) performance relative to model complexity (parameter count and hidden width).
Performance Benchmarking: Demonstration of KAN's ability to approach BCJR reference performance without the associated sequence-estimation complexity.

Results

Performance: The selected KAN configuration (hidden width 4, spline grid size 5) consistently outperformed the best MLP configuration (hidden width 32) across all SNR values.
- At 10 dB SNR, the MLP achieved a BER of $1.3 \times 10^{-4}$ .
- The KAN achieved a BER of $7.0 \times 10^{-6}$ , matching the BCJR reference.
- This represents an 18.6-fold improvement in BER for KAN over MLP at 10 dB.
Parameter Efficiency:
- The best MLP used 2,145 parameters (hidden width 32).
- The selected KAN used approximately 3,920 parameters (hidden width 4).
- Despite the KAN having roughly 1.83 times more raw parameters, it utilized a hidden layer width that was only 1/8th of the MLP's width.
- The authors define a parameter efficiency metric ( $\eta$ ) as the ratio of BER improvement to parameter increase, calculating a value of approximately 10.2, indicating KAN provides significantly more performance gain per unit of parameter increase.
SNR Scaling: The performance gap widened as SNR increased. While the MLP approached saturation at higher SNRs, the KAN continued to decrease its error rate, suggesting it models the fine-grained decision boundaries of the ISI channel more completely.

Significance and Claims
The paper claims that the KAN architecture offers a "qualitative and fundamental superiority" over MLPs for FTN detection due to its structural alignment with the communication channel. Specifically:

Edge-Based Modeling: By placing learnable spline functions on edges, KANs can model the effect of each input component independently, capturing the local, structured interactions of ISI more effectively than the shared node activations of MLPs.
Compact Representation: KANs can form a meaningful feature space with a hidden width as low as 1/8th of what an MLP requires, making them highly attractive for embedded or resource-constrained hardware where memory footprint and inference latency are critical.
Optimal Convergence: The study demonstrates that a data-driven KAN approach can converge to the optimal BCJR solution without requiring computationally expensive sequence-estimation algorithms.

The authors conclude that KANs represent a strong alternative to dense MLP baselines for communication problems where parameter sensitivity and energy efficiency are paramount. Future work is planned to investigate KAN performance in multipath fading channels and on real-time hardware platforms, as well as its generalization to different time-packing factors and higher-order modulations.

Technical Summary: A Comparative Analysis of MLP and Kolmogorov-Arnold Networks (KAN) for Faster-than-Nyquist (FTN) Signaling Detection

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