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REVIEW 4 major objections 6 minor 34 references

Hardware Acceleration of Kolmogorov-Arnold Network (KAN) in Large-Scale Systems

T0 review · 4 major / 6 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read Kolmogorov-Arnold networks can be accelerated on RRAM compute-in-memory at tens-of-MB scale with sublinear area and power growth and under 0.23% accuracy loss.

desk verdict First large-scale KAN hardware mapping, but the headline scaling claim leans on a cross-work comparison to a stochastic-computing baseline rather than a controlled sweep. read the letter →

arxiv 2509.05937 v1 pith:DAAVDPLH submitted 2025-09-07 cs.AR

Wei-Hsing Huang , Jianwei Jia , Yuyao Kong , Faaiq Waqar , Tai-Hao Wen , Meng-Fan Chang , Shimeng Yu This is my paper · ORCID
classification cs.AR
keywords Kolmogorov-Arnoldnetworkshardwareaccelerationcompute-in-memoryRRAMB-splinequantizationtime-modulatedvoltageinputIR-dropmitigationalgorithm-hardwareco-design
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper claims that KANs can be made practical for edge deployment by co-designing quantization, input encoding, and weight placement with RRAM compute-in-memory. It introduces four techniques: a quantization scheme that aligns the B-spline knot grid to the quantization grid so all basis functions share one half-size lookup table; a hybrid voltage/time input generator that encodes multi-bit inputs in one cycle; a sparsity-aware mapping that puts frequently activated coefficients on low-IR-drop bit-line positions; and a hyperparameter search over B-spline grid size under hardware budgets. Evaluated on large recommendation models of 39 and 63 MB in a 22 nm RRAM-ACIM setup, the paper reports that parameter counts 500,000 to 807,000 times larger than earlier tiny-scale accelerators cost only 28,000 to 41,000 times more area and 51 to 94 times more power, with accuracy loss of 0.11–0.23%. If true, this removes a major obstacle to putting KAN-based models on battery-powered devices.

What carries the argument

The mechanism that carries the argument is the linear charge identity in the TM-DV-IG: Q = I[x]·W[x], where the DAC voltage levels are chosen so the RRAM cell currents stand in exact binary ratios 0:1:2:...:2^N−1 and the pulse widths are ratioed 1:2^N:2^(N+1). This makes multi-bit values accumulate as a single analog charge in one clock cycle. The supporting identities are the two quantization constraints, G·L ≤ 2^n and G·2^D ≤ 2^n, which allow every B-spline basis function B_i(x) to draw from one shared half-size lookup table and reduce the routing hardware to a small decoder pair.

What would settle it

Fabricate the input generator and a 22nm RRAM array, then measure the accumulated charge for all 256 input codes at multiple process corners and supply voltages; if adjacent charge levels overlap by more than one least-significant bit at any realistic operating corner, the linear single-cycle 8-bit MAC assumed by the scaling claim is not achievable.

Watch

Extended reading notes

Core claim

The paper's central claim is that the expensive part of KAN inference—evaluating B-spline basis functions—can be made nearly free in hardware. Two quantization constraints, G·L ≤ 2^n and G·2^D ≤ 2^n, let every basis function share one half-size lookup table and shrink the decoder and routing logic, giving a 40x average area reduction and 5.7x energy reduction over conventional quantization for grid sizes 8–64. At the circuit level, the N:1 Time-Modulated Dynamic Voltage input generator encodes an 8-bit value as a voltage amplitude times a pulse width, with the accumulated bit-line charge designed to be exactly linear in the input code, enabling single-cycle multi-bit MAC above 100 MHz. KAN s

Load-bearing premise

The accuracy and scaling claims rest on the input generator's DAC output voltages being tunable so that RRAM cell currents stand in exact ratios 0:1:2:...:2^N−1 and the accumulated charge is perfectly linear in every 8-bit input code—if that linearity cannot be held across manufacturing, supply-voltage, and temperature variations, the single-cycle multi-bit MAC and the reported accuracy loss lose their basis.

Editorial extensions

If this is right

  • B-spline evaluation, normally the hardware bottleneck of KANs, reduces to a shared half-size LUT plus a small decoder; the paper reports 40.14x average area reduction and 5.74x energy reduction versus conventional quantization for grid sizes 8–64.
  • Multi-bit MAC inputs no longer require either a high-resolution DAC or a long pulse train: combining voltage and time domains keeps operation above 100 MHz and beats pure voltage and pure PWM schemes by 3–4.1x in combined area–power–latency figure of merit for 6–8 bit inputs.
  • IR-drop, the main analog error source in large RRAM arrays, can be mitigated by input statistics rather than extra circuits: accuracy loss shrinks 2.83–5.31x as array size grows from 128 to 1024.
  • Large-scale KAN models in the tens-of-MB range are within reach of RRAM-ACIM edge accelerators: the paper demonstrates 39–63 MB recommendation models with 0.11–0.23% accuracy degradation and energy per inference of 289.6–645.9 nJ.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Because the TM-DV-IG is agnostic to what the LUT stores, the same dual-domain input generator could accelerate any piecewise or table-driven activation, not only B-splines; a test would be reusing it for learned piecewise-linear activations.
  • The reported area/power scaling ratios would presumably flatten or reverse once the shared LUT, decoder, and input generator peripherals dominate over the RRAM array; sweeping model width and grid size at fixed array size would locate that knee.
  • The paper's accuracy numbers come from a benchmark that injects measured RRAM non-ideality into a software model; a full-chip demonstration with on-chip KAN inference would be the direct confirmation of the 0.11–0.23% degradation claim.
  • The sensitivity-based grid assignment divides layers into three tiers; one could extend this to per-layer bit-width or per-layer operating mode (high-accuracy versus high-performance) selection as a joint accuracy-cost Pareto search.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper proposes an algorithm-hardware co-design approach for accelerating Kolmogorov-Arnold Networks (KAN), comprising four main techniques: Alignment-Symmetry and PowerGap hardware-aware quantization (ASP-KAN-HAQ), an N:1 Time Modulation Dynamic Voltage Input Generator (TM-DV-IG), a KAN sparsity-aware weight mapping (KAN-SAM), and a KAN-NeuroSim hyperparameter optimization framework with sensitivity-based grid assignment. The evaluation targets large-scale CF-KAN recommendation models of 39–63 MB using TSMC 22nm SPICE simulation, synthesis for area, NeuroSim for system-level metrics, and measured non-ideality statistics from previously fabricated RRAM-ACIM chips. The central claim is that compared with a tiny stochastic-computing KAN accelerator [27], parameter count grows by 500K–807K×, while area grows only 28K–41K× and power grows only 51–94×, with minimal 0.11–0.23% accuracy degradation, demonstrating scaling potential.

Significance. If the claims are fully supported, the paper would provide a useful set of circuit-level and algorithm-level techniques for KAN inference, particularly the shared-LUT quantization and the hybrid time/voltage input encoding. The work is anchored by transistor-level SPICE simulations at 22nm, synthesized area estimates, NeuroSim integration, and measured RRAM-ACIM statistics from a real chip, all of which are concrete strengths. However, the headline scaling claim is currently based on a cross-work comparison to a different architecture and technology, and the linearity premise of the TM-DV-IG is not demonstrated. The accuracy degradation numbers are also reported without a defined metric or baseline. These gaps prevent the scaling conclusion from being accepted as stated.

major comments (4)
  1. [Abstract; §4D, Fig. 19] The central scaling claim compares the proposed large-scale CF-KAN designs (39/63 MB) to [27], a tiny stochastic-computing KAN accelerator with a different architectural principle and technology. This is not a controlled scaling experiment: the observed 500K–807K× parameter growth against 28K–41K× area and 51–94× power growth could reflect [27]'s bitstream-generation overhead and larger per-parameter peripherals rather than any property of the proposed architecture. To support the 'scaling potential' claim, the authors should evaluate the same ASP-KAN-HAQ/TM-DV-IG/RRAM-ACIM flow at a small scale (e.g., the 279–2232-parameter knot-theory model in [24]) and at the large scale, and report area/power breakdowns and per-parameter metrics. As written, the abstract's headline ratios are not a valid scaling law.
  2. [§3.2, TM-DV-IG; §4B] The linear-input assumption is load-bearing: the paragraph states that DAC voltages can be chosen so that I[0]:I[1]:...:I[2^N−1] = 0:1:2:...:2^N−1, yielding a perfectly linear charge Q. This requires the MOSFET transfer function to be pre-distorted over the entire 8-bit range, which is not a generic property and is sensitive to PVT variations. The paper provides no transistor-level DC curves, Monte Carlo results, or measured prototype data for this transfer function; §4B reports only FOM comparisons against voltage/PWM schemes, not the linearity error or its effect on MAC accuracy. Without this evidence, the single-cycle multi-bit MAC accuracy claim is unsupported.
  3. [§4C/§4D, Figs. 18–19] Accuracy degradation is reported as '0.23%' and '0.11%' without defining the metric: percentage of what (test accuracy, RMSE, NDCG?) and relative to which software baseline? The software baseline accuracy is not given, so the reader cannot judge whether 0.11–0.23% is small. Likewise, Fig. 18 reports 'accuracy enhancements' of 2.83× to 5.31× without absolute accuracy numbers or a definition of the baseline. These omissions directly affect the paper's 'minimal accuracy degradation' claim.
  4. [§3.1, Eqs. (4)–(6)] The alignment/PowerGap constraints in Eqs. (4)–(6) require G·L (or G·2^D) ≤ 2^n. For the representative G=5 and for the evaluated G=7, 15, 30, 60 with n=8, these bounds are not equalities: e.g., G=15 gives at most 240 quantization levels, not 256. The paper does not explain how the full 8-bit input range [0,255] is represented, nor how effective input precision is affected. If inputs are rescaled to [0, G·L−1], the claimed 8-bit precision is not actually maintained. This is load-bearing for the ASP-KAN-HAQ accuracy/area tradeoffs reported in §4A.
minor comments (6)
  1. [Abstract vs. §5] The abstract reports power growth of '51× to 94×', while the conclusion reports '51× to 97×'. Please reconcile.
  2. [§4B] The text says 'corresponding to 22, 24, 26, and 28 distinct WL pulses' — this should be 2^2, 2^4, 2^6, and 2^8.
  3. [Fig. 9 caption vs. §3.2] The caption refers to '(b) 3-3 bit input vector' and '(c) 4-4 bit input vector', while the text describes TD-A as N=3 and TD-P as N=4. The notation should be aligned.
  4. [Eqs. (4)–(6)] The equations are typeset with garbled symbols (e.g., '2௡'); please use proper superscripts and define L, D, and LD explicitly.
  5. [Algorithm 2, line 4] The sensitivity formula uses x_{i,j} and M_i without definition; clarify what variable is being differentiated and how the expectation is computed.
  6. [§3.2] The module is referred to as both PM-TCL and PM-TCM; use a single acronym consistently.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the core derivations are constraint-based hardware optimizations and hardware-aware simulations using externally measured chip statistics; the scaling claim is an external benchmark comparison, not a reduction to the paper's own inputs.

full rationale

The paper's main claimed contributions are: (1) ASP-KAN-HAQ, which derives LUT sharing and decoder/MUX reduction from the explicit alignment/power-of-two constraints in Eqs. (4)-(6); (2) TM-DV-IG, which is proposed as a circuit design whose linearity is an explicit design target ('By carefully designing the DAC output voltages ... current ratios satisfy ...'), not a predicted outcome; (3) KAN-SAM, whose mapping is computed from training-set statistics and compared against a uniform baseline under the same error model; and (4) KAN-NeuroSim, which uses non-ideality statistics from a previously fabricated TSMC 22nm RRAM-ACIM chip [13]. The chip statistics are external measured data from prior work by the same group; per the review rules this is real evidence and does not constitute circularity. Accuracy degradation figures (0.11%-0.23%) are obtained by injecting those measured MAC error rates into PyTorch CF-KAN models, i.e., hardware-aware simulation, not a fitted parameter renamed as a prediction. The abstract's scaling ratios (500K-807K parameter increase vs. 28K-41K area and 51x-94x power increase) compare the proposed large-scale CF-KAN-1/CF-KAN-2 designs to the tiny stochastic-computing SCKAN accelerator [27]. This is an uncontrolled cross-architecture comparison and a fairness/experimental-design concern, not a circular derivation: the ratios are arithmetic comparisons of two independent implementations and do not reduce to any equation in this paper. No uniqueness theorem or ansatz is imported from self-citations; [24] is prior small-scale work and [28][29] are simulator tools. Therefore, no specific circular step can be quoted, and the paper's central claims have independent content beyond their inputs. Score 1 reflects the presence of minor self-citations that are not load-bearing.

Assumptions & free parameters 5 free parameters · 5 assumptions · 2 invented entities

The central claim rests on a small set of designed parameters (alpha, beta, percentiles, N) whose values are mostly undisclosed, on the transferability of error statistics from a prior chip, and on the asserted linearizability of the input generator. The methods are precise equations and pseudocode, but the hardware realization depends on engineering assumptions not validated by a fabricated prototype.

free parameters (5)
  • alpha (KAN-SAM criticality weight)
    Algorithm 1 line 22: C_w[i] = alpha*J[i] + beta*S[i]*J[i]; alpha and beta are called tunable but no values are given or swept. They control the trade-off between expected contribution and stability, and the reported accuracy improvements depend on this choice.
  • beta (KAN-SAM stability weight)
    Same as alpha; beta = 1 - alpha implicitly (the text states alpha+beta=1). No value or tuning procedure is reported.
  • epsilon (CV numerical guard)
    Algorithm 1 line 19: epsilon in the coefficient-of-variation denominator to avoid divide-by-zero; value not specified, assumed small positive constant.
  • sensitivity percentiles (33%/67%) in Algorithm 2 = 67th and 33rd percentiles
    Algorithm 2 lines 7-8: thresholds for classifying high/medium/low sensitivity layers are chosen by hand without sensitivity analysis.
  • N (TM-DV-IG bit-resolution mode) = N=4 (TD-P), N=3 (TD-A)
    Section 3.2: N is a design parameter selected for high-performance vs high-accuracy modes; the choice is application-driven and not derived from first principles. It directly controls the number of voltage levels and charge resolution.
assumptions (5)
  • domain assumption Uniform node distribution of KAN B-splines allows a single shared LUT across all basis functions.
    Section 3.1 and Fig. 7: the shared SH-LUT depends on the B(X) shape being identical across knot intervals. This is true for uniform knot spacing, which is the standard KAN grid, but it is a modeling assumption about the KAN training framework.
  • ad hoc to paper The DAC output voltages can be chosen so that MOSFET currents satisfy a precise linear ratio I[0]:I[1]:... = 0:1:2:..., making charge Q linear in the input.
    Section 3.2: 'By carefully designing the DAC output voltages ... such that the current ratios satisfy...' This is asserted, not derived or shown with transistor-level data. The nonlinear MOSFET transfer curve makes this nontrivial, and the paper does not demonstrate the pre-distortion or its robustness across PVT.
  • domain assumption The measured non-ideality statistics from the prior TSMC 22nm RRAM-ACIM chip [13] transfer to the proposed KAN accelerator's arrays.
    Section 4C: 'we refer to TSMC's 22 nm RRAM-ACIM chip measurement results [13] of the single BL IR drop effect...' and use these error rates to train/evaluate the CF-KAN models. The array sizes differ (128-1024), and [13] is a different macro design, so the error statistics are assumed to be representative.
  • domain assumption The training-set activation statistics (Phase A of Algorithm 1) are representative of inference-time distributions.
    Algorithm 1 phases A-C: KAN-SAM places weights based on activation probability, mean magnitude, and coefficient of variation computed on D_train. If deployment distribution shifts, the mapping may be suboptimal.
  • standard math B-spline basis functions are non-negative, so Algorithm 1's b>=0 holds.
    Algorithm 1 line 5: 'Spline/LUT; b>=0'. Standard B-spline basis functions are indeed non-negative. This is standard math.
invented entities (2)
  • N:1 Time Modulation Dynamic Voltage Input Generator (TM-DV-IG)
    purpose: Encodes multi-bit B(X) LUT values as WL pulses that combine voltage amplitude and time width to achieve linear charge accumulation in ACIM, replacing pure voltage or pure PWM schemes.
    Introduced in Section 3.2. Validated only via SPICE simulation at 22nm; no fabricated silicon or measured silicon data for this specific generator. Its linearity depends on an asserted DAC pre-distortion.
  • Sharable-Hemi LUT (SH-LUT)
    purpose: A shared, half-capacity lookup table enabled by Alignment-Symmetry quantization, reducing LUT memory for B-spline evaluation.
    Section 3.1: the SH-LUT is an architectural invention; its area and energy savings are estimated by synthesis and simulation, not measured on silicon.

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Cite this review

Pith. "Pith review of Hardware Acceleration of Kolmogorov-Arnold Network (KAN) in Large-Scale Systems." pith.science (2026). https://pith.science/paper/DAAVDPLH

@misc{pith2026250905937,
  author       = {Pith},
  title        = {Pith review of: Hardware Acceleration of Kolmogorov-Arnold Network (KAN) in Large-Scale Systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DAAVDPLH}},
  note         = {Machine review of arXiv:2509.05937}
}
read the original abstract

Recent developments have introduced Kolmogorov-Arnold Networks (KAN), an innovative architectural paradigm capable of replicating conventional deep neural network (DNN) capabilities while utilizing significantly reduced parameter counts through the employment of parameterized B-spline functions with trainable coefficients. Nevertheless, the B-spline functional components inherent to KAN architectures introduce distinct hardware acceleration complexities. While B-spline function evaluation can be accomplished through look-up table (LUT) implementations that directly encode functional mappings, thus minimizing computational overhead, such approaches continue to demand considerable circuit infrastructure, including LUTs, multiplexers, decoders, and related components. This work presents an algorithm-hardware co-design approach for KAN acceleration. At the algorithmic level, techniques include Alignment-Symmetry and PowerGap KAN hardware aware quantization, KAN sparsity aware mapping strategy, and circuit-level techniques include N:1 Time Modulation Dynamic Voltage input generator with analog-compute-in-memory (ACIM) circuits. This work conducts evaluations on large-scale KAN networks to validate the proposed methodologies. Non-ideality factors, including partial sum deviations from process variations, have been evaluated with statistics measured from the TSMC 22nm RRAM-ACIM prototype chips. Utilizing optimally determined KAN hyperparameters in conjunction with circuit optimizations fabricated at the 22nm technology node, despite the parameter count for large-scale tasks in this work increasing by 500Kx to 807Kx compared to tiny-scale tasks in previous work, the area overhead increases by only 28Kx to 41Kx, with power consumption rising by merely 51x to 94x, while accuracy degradation remains minimal at 0.11% to 0.23%, demonstrating the scaling potential of our proposed architecture.

Figures

Figures reproduced from arXiv: 2509.05937 by the authors.

Figure 1
Figure 1. Introduction of KAN and its potential for parameter reduction. This work was supported in part by the PRISM, one of the SRC/DARPA JUMP 2.0 centers. Wei-Hsing Huang, Jianwei Jia, Yuyao Kong, Faaiq Waqar, and Shimeng Yu are with the School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332 USA (Corresponding author. E-mail: shimeng.yu@ece.gatech.edu). Wei-Hsing Huang and Jianwei… view at source ↗
Figure 3
Figure 3. HW efficient Alignment-Symmetry KAN Quantization for LUTs optimization [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 5
Figure 5. Hardware architecture with Alignment-Symmetry and PowerGap KAN hardware aware quantization [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figures from the paper (10 more)
Figure 8
Figure 8. Figure 8: N:1 Time Modulation Dynamic Voltage input generator for ACIM [PITH_FULL_IMAGE:figures/full_fig_p006_8.png]
Figure 6
Figure 6. Figure 6: The hardware architecture with efficient LUT retrieval process [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]
Figure 7
Figure 7. Figure 7: The hardware architecture with efficient LUT retrieval process [PITH_FULL_IMAGE:figures/full_fig_p006_7.png]
Figure 10
Figure 10. Figure 10: KAN sparsity-aware weight mapping [PITH_FULL_IMAGE:figures/full_fig_p007_10.png]
Figure 14
Figure 14. Figure 14: Fig.14 [PITH_FULL_IMAGE:figures/full_fig_p009_14.png]
Figure 15
Figure 15. Figure 15: Fig.15 [PITH_FULL_IMAGE:figures/full_fig_p009_15.png]
Figure 13
Figure 13. Figure 13: Comparison of Normalized Energy Consumption between proposed ASP-KAN-HAQ and conventional method based on Post-Training Quantization [29] using NVIDIA's TensorRT framework [PITH_FULL_IMAGE:figures/full_fig_p009_13.png]
Figure 16
Figure 16. Figure 16: Fig.16 [PITH_FULL_IMAGE:figures/full_fig_p010_16.png]
Figure 17
Figure 17. Figure 17: Fig.17 [PITH_FULL_IMAGE:figures/full_fig_p010_17.png]
Figure 19
Figure 19. Figure 19: Comparison of proposed KAN accelerator with previous work across small-scale and large-scale computational tasks [PITH_FULL_IMAGE:figures/full_fig_p010_19.png]

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Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.