⚡ electrical engineering

Interpretable Kolmogorov-Arnold Network Using Vertical NAND Flash Memory

This paper demonstrates an interpretable, low-power compute-in-memory implementation of Kolmogorov-Arnold networks using commercial triple-level-cell V-NAND flash memory, which achieves high prediction accuracy for multimodal gas sensing while significantly reducing energy consumption and memory requirements compared to traditional multilayer perceptrons.

Original authors: Jong-Ho Lee, Sung-Ho Park, Jonghyun Ko, Yeongheon Yang, Jiseong Im, Ryun-Han Koo, Chayeong Lee, Kangwook Choi, Hunhee Shin, Gyuweon Jung

Published 2026-07-10

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Jong-Ho Lee, Sung-Ho Park, Jonghyun Ko, Yeongheon Yang, Jiseong Im, Ryun-Han Koo, Chayeong Lee, Kangwook Choi, Hunhee Shin, Gyuweon Jung

Original paper licensed under CC BY 4.0 (https://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 have a super-smart robot brain that can solve complex puzzles, like figuring out exactly how much gas is in a room based on temperature, pressure, and smell. Usually, these robot brains are like "black boxes." You feed them data, they give you an answer, but even the people who built them can't explain how they got there. It's like asking a magician how they pulled a rabbit out of a hat, and they just say, "Magic."

This paper introduces a new kind of robot brain called a Kolmogorov-Arnold Network (or KAN for short) that doesn't hide its secrets. Instead of a black box, it's more like a transparent glass box where you can see every gear turning. But here's the twist: the researchers didn't build this brain out of fancy new computer chips. They built it using commercial V-NAND flash memory—the exact same kind of storage you find in your USB drives and smartphones, just stacked over 100 layers high.

The "Black Box" Problem vs. The "Glass Box" Solution

Most computer brains (called Multilayer Perceptrons or MLPs) work by having fixed rules for how they process information, like a factory assembly line with a set number of steps. They learn by adjusting the "weights" (how much attention to pay to each piece of data), but the rules themselves stay the same. This makes them hard to understand.

The KAN approach flips the script. Instead of fixed rules, the KAN learns the rules themselves! Imagine a factory where the machines can change their own shape to fit the job. In a KAN, the "edges" (the connections between parts of the brain) learn flexible, wiggly curves called activation functions. These curves can be shaped to look like multiplication, division, or even complex scientific formulas. Because these shapes are learned and can be written down as simple math equations, the brain becomes interpretable. You can actually read its mind and say, "Ah, I see! It figured out that gas concentration is related to pressure by dividing the two."

The Magic Trick: Turning Memory into Math

The biggest challenge was: "How do you put these wiggly, flexible math curves into a piece of memory that was only designed to store zeros and ones?"

The researchers found a clever hack using the physics of the memory itself. Inside a V-NAND chip, data is stored in tiny cells stacked vertically. When you read these cells, they act like a bottleneck. If you push two cells with opposite voltages (one going up, one going down), the electricity flowing through them creates a smooth, bell-shaped curve.

Think of it like this: Imagine two people holding a rope. If one pulls up and the other pulls down, the rope sags in the middle. The shape of that sag is a perfect "bell curve." The researchers realized they could tune the "pull" (by adjusting the voltage) to move the bell curve left or right and make it wider or narrower.

By combining several of these "bell curves" (which they call splines), they could build any wiggly math function they needed. It's like building a complex sculpture out of simple, smooth clay blobs. They took the math functions the software brain had learned, broke them down into these bell-curve pieces, and then "programmed" the memory cells to physically act out those curves.

The Proof: Doing Math and Sensing Gas

To prove this wasn't just a theory, they tested it in two ways:

The Math Test: They taught the software brain to do multiplication and division. Then, they transferred those specific math rules to the memory chip. When they tested the chip, it performed these operations with incredible accuracy, matching the software almost perfectly. The paper shows that the hardware output tracks the ideal software results with a correlation of 0.9737 for multiplication and 0.9906 for division. This means the memory chip didn't just guess; it physically recreated the math.
The Gas Test: They used the brain to figure out the concentration of two different gases (NO₂ and H₂S) mixed together, while also accounting for changes in temperature and pressure. This is a tough job because the sensors get confused when conditions change.
- The KAN brain figured out a simple, physical rule: To find the gas amount, you divide the gas sensor reading by the pressure reading. This makes perfect physical sense (like how a balloon expands when pressure drops).
- The hardware brain used this rule to predict the gas levels in 256 different test conditions (combinations of 4 temperatures, 4 pressures, and 4 gas levels). It got the answers right, even when the gases were mixed in tricky ways.

Why This Matters: Speed, Size, and Energy

The most exciting part is how efficient this is. Because the KAN learns the actual shape of the math (the curves) instead of using thousands of fixed, rigid steps, it needs way fewer parts to do the job.

Memory Savings: To solve the gas puzzle, the KAN needed only 250 memory cells. A traditional brain (MLP) needed 2,070 cells for a simple version, and up to 4,896 cells for a more complex one. That's a massive reduction.
Energy Savings: Because it uses fewer cells, it uses less power. The paper measured that the KAN used 94% less energy just for the reading part of the calculation compared to a standard one-layer brain.

What It's Not (Yet)

It's important to know what this paper doesn't claim. The researchers didn't say this solves every problem in the world.

They didn't test it on massive, complex datasets like recognizing millions of cat photos. They stuck to math and gas sensing to prove the concept works.
The accuracy depends on how well they could approximate the math curves using the memory cells. It's an approximation, not a perfect, infinite-precision digital calculation.
They didn't claim this is a finished product ready for your phone tomorrow. They showed it works on a specific, unmodified commercial chip, but there's still work to be done to make the circuits around it even better.

The Bottom Line

This paper shows that we can turn the memory in our devices into a brain that not only predicts the future but also explains why. By using the natural physics of V-NAND flash memory to build "math curves" out of electricity, they created a system that is small, super energy-efficient, and transparent. It's a step toward a future where our devices can learn from the world around them—like sensing gas leaks or weather changes—and tell us the rules they discovered, all while using a tiny fraction of the battery power.

Technical Summary: Interpretable Kolmogorov-Arnold Network Using Vertical NAND Flash Memory

Problem Statement
The rapid expansion of artificial intelligence has created a critical demand for hardware capable of executing neural network inference with high energy efficiency and scalability. Conventional von Neumann architectures struggle with the "memory wall," where costly data movement between separated memory and processing units hinders performance, particularly in sensor-rich applications like autonomous robotics. While Compute-in-Memory (CIM) using Vertical NAND (V-NAND) flash memory offers a promising solution due to its high density, maturity, and low read power, current neural network implementations on such hardware face two significant limitations:

Lack of Interpretability: Most hardware neural networks utilize Multi-Layer Perceptrons (MLPs) with fixed node-wise activation functions and entangled linear weights. This "black-box" nature obscures the physical relationships between inputs and outputs, which is detrimental to scientific applications where understanding the underlying mechanism is as crucial as prediction accuracy.
Hardware Inefficiency for Flexible Functions: Emerging architectures like Kolmogorov-Arnold Networks (KANs) offer superior interpretability by learning non-linear activation functions (AFs) on network edges rather than fixing them on nodes. However, translating these flexible, spline-based edge functions into hardware is challenging. Conventional digital implementations require significant area and energy overhead, and existing memory platforms are not naturally optimized for evaluating diverse, learned non-linear functions.

Methodology
The authors propose a novel hardware implementation of KANs using commercial triple-level-cell (TLC) V-NAND flash memory without modifying the device structure. The core methodology involves mapping the mathematical basis functions of software-trained KANs to the intrinsic analog physics of V-NAND strings.

Physical Spline Generation: The authors exploit the series-connected nature of cells within a V-NAND string. By applying complementary word-line (WL) biases to two series-connected cells, a bell-shaped current response is generated at the bit-line. This response acts as a physical "spline primitive."
Tunability: The center position and width of these splines are tuned by programming the threshold voltages ( $V_{th}$ ) of the two cells using Incremental-Step-Pulse Programming (ISPP). This allows the creation of a library of spline components distributed across the input window.
Function Approximation: Software-trained edge-wise activation functions (represented as linear combinations of B-spline basis functions) are approximated in hardware as weighted sums of these measured V-NAND spline responses. Both positive and negative contributions are handled via subtraction circuits within the neuron logic.
Inference Process: During inference, the system applies complementary read voltages ( $V_{Input}$ and $2 - V_{Input}$ ) to selected WLs. The resulting currents from multiple splines are summed in parallel on the bit-lines, effectively evaluating the entire layer of the KAN in a single read operation.
Application: The framework is validated first on fundamental arithmetic operations (multiplication and division) and then applied to a multimodal gas sensing task involving gas, temperature, and pressure data.

Key Contributions

First Hardware KAN on Commercial Memory: The work demonstrates the first physical realization of a KAN on a mature, unmodified commercial V-NAND flash platform (SK hynix, >100 stacked layers), bridging the gap between interpretable machine learning algorithms and practical CIM hardware.
Analog-to-Algorithm Mapping: It establishes a direct mapping between the mathematical spline basis functions of KANs and the intrinsic analog current-voltage characteristics of V-NAND strings, avoiding the need for complex digital logic to evaluate non-linear functions.
Interpretability Preservation: Unlike traditional MLP hardware, this approach preserves the ability to inspect, symbolize, and understand the learned functional relationships, translating them into physically meaningful operations (e.g., division, multiplication).
Efficiency Gains: The method achieves comparable prediction accuracy to MLPs while utilizing significantly fewer memory cells, leading to substantial reductions in inference energy.

Results

Arithmetic Validation: The hardware successfully reproduced symbolic multiplication and division operations extracted from software KANs. The measured outputs closely tracked ideal software targets, with $R^2$ values of 0.9737 for multiplication and 0.9906 for division. This confirmed that the spline summation approach can accurately transfer learned edge functions to hardware.
Multimodal Gas Sensing: In a mixed-gas environment (NO $_2$ and H $_2$ S) with varying temperature and pressure, the V-NAND KAN successfully predicted gas concentrations. The network identified a compact, physically meaningful functional relationship, specifically a division operation between gas sensor output and pressure, reflecting the underlying sensing physics.
Hardware Efficiency Comparison: Compared to 1-, 2-, and 3-layer MLP implementations trained on the same dataset:
- Cell Count: The KAN required only 250 V-NAND cells, whereas the MLPs required between 2,070 and 4,896 cells.
- Energy: The read-operation energy per inference was reduced by 94% compared to a one-layer MLP. This reduction is attributed to the compactness of the KAN representation, which minimizes the number of active read operations and peripheral circuit activity.

Significance and Claims
The paper claims that commercial V-NAND flash memory is a practical platform for interpretable, low-power CIM hardware that can both predict and explain. The significance lies in the dual achievement of:

Scientific Utility: By revealing the functional structure of learned mappings (e.g., identifying that gas concentration scales inversely with pressure), the hardware serves as a tool for functional discovery, not just a black-box predictor.
System Efficiency: The compactness of the KAN architecture, when mapped to V-NAND splines, directly translates to reduced memory footprint and energy consumption, making it highly suitable for in-sensor computing in power-constrained physical AI systems.

The authors note that while the current implementation relies on approximating analytical functions with measured splines and focuses on compact, physically structured tasks, it establishes a foundational route for future low-power in-sensor computing that integrates prediction with explanation.