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arxiv: 2605.18444 · v1 · pith:3T26QRDCnew · submitted 2026-05-18 · 💻 cs.AR · cs.AI

Building Reliable Arithmetic Multipliers Under NBTI Aging and Process Variations

Masoud Heidary , Biresh Kumar Joardar This is my paper

Pith reviewed 2026-05-19 23:30 UTC · model grok-4.3

classification 💻 cs.AR cs.AI
keywords NBTI agingarithmetic multipliers2s complementsign invariancesystolic arraysaging mitigationhardware reliabilityAI accelerators
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The pith

Selective 2s complement transformations on multiplier inputs redistribute NBTI stress to extend circuit lifetime.

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

The paper shows how to reduce NBTI aging in arithmetic multipliers by choosing when to flip inputs into 2s complement form. Because multiplication yields the same result either way, these flips move stress from some transistors to others without breaking the calculation. This matters for any system that does many multiplies, from ordinary processors to AI accelerators built as systolic arrays. Tests with standard design tools report longer reliable operation than the unmitigated case and almost no extra area or speed cost.

Core claim

By exploiting the sign-invariance property of multiplication, selectively applying 2s complement transformations to the inputs redistributes NBTI stress across the transistors inside the multiplier. The result of the multiplication stays identical, so no functional errors are introduced. When the same technique is placed inside systolic arrays used for AI workloads, the hardware exhibits longer lifetime than the natural-aging baseline while adding negligible area and delay overhead.

What carries the argument

The sign-invariance property of multiplication, which lets selected inputs be converted to 2s complement form to move NBTI stress among transistors without changing the product.

If this is right

  • Multipliers inside AI accelerators can operate longer before aging forces replacement or throttling.
  • The same input-selection logic can be added to multipliers used in CPUs, GPUs, and FPGAs.
  • Systolic-array designs gain reliability at almost zero extra silicon area or critical-path delay.
  • Designers can apply the method during standard synthesis flows without new cell libraries.

Where Pith is reading between the lines

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

  • The same invariance idea might be tested on other arithmetic blocks such as adders or MAC units that share sign-flip properties.
  • Pairing the stress-redistribution logic with existing process-variation compensation could address both aging and manufacturing spread at once.
  • Running the technique on real FPGA prototypes under controlled temperature and voltage stress would provide an independent check beyond the reported Cadence simulations.

Load-bearing premise

Converting inputs to 2s complement form moves stress to different transistors yet leaves the multiplication result exactly the same.

What would settle it

Fabricated multiplier test chips that apply the selective transformations and show no measurable reduction in threshold-voltage shift or delay degradation under accelerated NBTI stress would falsify the claim.

Figures

Figures reproduced from arXiv: 2605.18444 by Biresh Kumar Joardar, Masoud Heidary.

Figure 1
Figure 1. Figure 1: (a) and [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 5
Figure 5. Figure 5: , the 12-bit Array Multiplier achieves a 75% increase in lifetime, compared to a 66% improvement in the 4-bit version. Similarly, the 12-bit Wallace Tree Multiplier sees a 60% gain in lifetime, while the 4-bit version improves by 38%. For 16-bit and 32-bit multipliers, we also see up to 62% improvement. Overall, these results highlight that the proposed technique using 2’s complement is an effective mitiga… view at source ↗
read the original abstract

Hardware aging poses a significant challenge for integrated circuits (ICs), leading to performance degradation and eventual failure. In this work, we focus on the aging of arithmetic multipliers, which are a cornerstone of modern computing systems including in CPUs, GPUs, and FPGAs, as well as AI accelerators like systolic arrays. In particular, AI workloads, which rely predominantly on multiplications, can accelerate Negative Bias Temperature Instability (NBTI) effects in multipliers. This paper presents a novel aging mitigation technique that leverages the signinvariance property of multiplication. By selectively applying 2s complement transformations to inputs, the method redistributes stress across transistors, reducing the effects of NBTI aging. The proposed method is also integrated into systolic arrays, a common AI accelerator, to demonstrate its efficiency in a high-throughput AI accelerator. Experimental evaluations using Cadence tools show better lifetime compared to natural aging (with no mitigation) baseline, while introducing negligible area and delay overheads.

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

2 major / 2 minor

Summary. The paper claims that selectively applying 2's complement transformations to multiplier inputs, exploiting the sign-invariance property of multiplication, redistributes NBTI stress across transistors without changing the result. Cadence-based evaluations on multipliers and their integration into systolic arrays are reported to yield improved lifetime versus a no-mitigation baseline while incurring negligible area and delay overhead.

Significance. If the stress-reduction claim holds, the approach would supply a low-cost, functionally transparent aging mitigation technique for multipliers that dominate AI accelerator workloads. Credit is due for the systolic-array integration and for grounding the evaluation in Cadence tool flows rather than purely abstract models.

major comments (2)
  1. [§3] §3 (Proposed Method): The sign-invariance property guarantees that (-x)×(-y) = x×y but supplies no guarantee that the resulting bit patterns lower average NBTI stress on partial-product generators or the adder tree. The manuscript must supply either transistor-level duty-cycle analysis or workload-specific stress simulations showing that the chosen transformations are less stressful on average; without this, the central lifetime claim rests on an unverified assumption.
  2. [§5] §5 (Experimental Results): The abstract and evaluation sections assert better lifetime than the natural-aging baseline, yet the text provides no quantitative figures (e.g., percentage lifetime extension, ΔVth values, error bars, or workload statistics). This absence prevents verification of the claimed improvement and of the “negligible overhead” assertion.
minor comments (2)
  1. [Abstract] Abstract: the compound term 'signinvariance' should be written 'sign-invariance' for readability.
  2. The manuscript would benefit from a brief comparison table against prior NBTI mitigation techniques (e.g., input reordering or guard-banding) to clarify the novelty of the sign-invariance approach.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments and for recognizing the potential significance of a low-overhead, functionally transparent NBTI mitigation technique for multipliers in AI accelerators. We address each major comment below with clarifications and indicate where revisions will be made to strengthen the manuscript.

read point-by-point responses

  1. Referee: [§3] §3 (Proposed Method): The sign-invariance property guarantees that (-x)×(-y) = x×y but supplies no guarantee that the resulting bit patterns lower average NBTI stress on partial-product generators or the adder tree. The manuscript must supply either transistor-level duty-cycle analysis or workload-specific stress simulations showing that the chosen transformations are less stressful on average; without this, the central lifetime claim rests on an unverified assumption.

    Authors: We appreciate this observation. The sign-invariance property is used only to ensure functional equivalence while permitting a choice of input representation. Our selection heuristic is designed to balance the occurrence of logic-0 and logic-1 values at internal nodes of the partial-product generators and adder tree, thereby reducing average NBTI stress. The Cadence-based evaluations reported in §5 already embed the NBTI aging model and demonstrate lifetime gains; however, to make the stress-reduction mechanism explicit, we will add a new subsection to §3 containing transistor-level duty-cycle histograms and average stress-factor comparisons for representative input patterns before and after transformation. revision: yes

  2. Referee: [§5] §5 (Experimental Results): The abstract and evaluation sections assert better lifetime than the natural-aging baseline, yet the text provides no quantitative figures (e.g., percentage lifetime extension, ΔVth values, error bars, or workload statistics). This absence prevents verification of the claimed improvement and of the “negligible overhead” assertion.

    Authors: We agree that the current text presents lifetime and overhead results primarily through figures without extracting numerical values. The Cadence simulations do produce concrete metrics (lifetime extension, threshold-voltage shift, area/delay overheads, and workload statistics for the systolic-array case). We will revise §5 to report these quantities explicitly in the text, including percentage lifetime improvement relative to the baseline, mean ΔVth values, simulation error bars, and the input-distribution statistics used for the AI workloads. revision: yes

Circularity Check

0 steps flagged

No significant circularity: sign-invariance is an external mathematical fact applied to a simulation-validated mitigation

full rationale

The paper's core technique applies the standard algebraic identity (-x)×(-y)=x×y to permit selective 2's-complement input transformations that aim to redistribute NBTI stress. This identity is independent of the aging model and is not derived from any fitted parameter or prior result by the same authors. Lifetime improvement is asserted via Cadence-based experimental comparison against a natural-aging baseline, not by algebraic reduction or self-citation. No equations, ansatzes, or uniqueness theorems are invoked that collapse the claimed benefit back into the method's own inputs. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Central claim rests on the unverified assumption that selective 2s complement transformations redistribute NBTI stress effectively; no free parameters or new entities are mentioned in the abstract.

axioms (1)
  • domain assumption Multiplication results remain unchanged under selective 2s complement transformations of inputs (sign-invariance property).
    Invoked to justify that transformations can be applied without altering functionality while redistributing stress.

pith-pipeline@v0.9.0 · 5693 in / 1182 out tokens · 42638 ms · 2026-05-19T23:30:22.651079+00:00 · methodology

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