IMC-CLINIC: Coupled Loss-Informed Newton Iterations for Clipping in Analog In-Memory Computing

Yung-Chin Chen; Chia-Yu Chen; Naveen Verma

cs.AISep 28, 2026

IMC-CLINIC: Coupled Loss-Informed Newton Iterations for Clipping in Analog In-Memory Computing

Authors: Yung-Chin Chen, Chia-Yu Chen, Naveen Verma

Organizations: Princeton University, NJ, USA · EnCharge AI, CA, USA

Abstract

Analog in-memory computing (IMC) offers a promising path toward energy-efficient large language model (LLM) inference by executing matrix multiplications (MatMul) directly within memory arrays in the analog domain. Its efficiency, however, comes with an additional source of error: limited-precision analog-to-digital converters (ADCs) quantize accumulated analog partial sums, introducing output-side error distinct from conventional activation and weight quantization at the MatMul inputs. Clipping can mitigate both operand and ADC quantization errors, but the optimal clipping factors must jointly balance activation rounding and clipping, weight rounding and clipping, and ADC quantization. Existing clipping methods, designed for digital quantization, do not explicitly optimize these coupled sources of IMC error and often rely on costly search-based calibration. We introduce IMC-CLINIC (Coupled Loss-Informed Newton Iterations for Clipping), a clipping calibration framework based on an analytical surrogate for IMC MatMul output error. The surrogate jointly models operand quantization, accumulated clipping-induced bias, and ADC quantization, enabling efficient evaluation of its gradient and approximate curvature from a small calibration set. IMC-CLINIC jointly optimizes activation and weight clipping factors using a safeguarded Newton-type method. Across multiple models and datasets, it improves average zero-shot accuracy by 6.5-11.5 percentage points over the grid search baseline while reducing calibration time by factors of 10.0-12.1. Its analytical surrogate closely tracks empirical IMC output error, and its optimizer is certified within 1% of the global optimum under the loss objective across all projections on two representative models.

Figures & tables

Panel of Figure 1 — Figure 1 : Motivation for clipping calibration in analog IMC. Clipping changes both operand quantization error and the output-referred ADC quantization error, motivating their joint optimization.

Figure 2 : Output-error analysis for LLaMA-3.2-3B across projections. Each point reports the median normalized MSE across 28 decoder layers, and shaded regions denote the 25th–75th percentiles. The first three panels isolate activation-, weight-, and ADC-induced output errors, while the final panel measures the total IMC output error directly. Lower is better.

Figure 3 : Calibration and optimization efficiency on LLaMA-3.2-3B. Left: IMC-CLINIC achieves a better WikiText-2 PPL–calibration-time trade-off than direct ADC-aware alternating search. Right: Its safeguarded Newton optimizer reaches

95\%

of the post-initialization loss improvement faster than projected gradient descent (

72

ms vs.

1.10

s median).

Appendix figures & tables23 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 4 : Empirical validation of cross-coordinate error decorrelation on LLaMA-3.2-3B. Left: Pairwise Pearson correlations between centered MAC errors for a representative output channel in the layer-13 $q$ projection. Right: Ratio of the decorrelated approximation to the exact operand MSE across decoder layers. Faint points denote individual layers, diamonds denote the median, shaded regions indicate the 25th–75th percentiles, and the dashed line denotes exact agreement.

Figure 5 : Empirical validation of the two-term second-moment approximation on LLaMA-3.2-3B. Left: Signed contributions of the six exact terms for the representative layer-13

q

projection, where the two retained terms account for

95.5\%

of the total. Right: Ratio of the retained two-term sum to the exact six-term sum across decoder layers. Faint points denote individual layers, diamonds denote the median, shaded regions indicate the 25th–75th percentiles, and the dashed line denotes exact agreement.

Figure 6 : Empirical validation of the signed-bias term on LLaMA-3.2-3B. Left: Mean signed MAC error

\mathbb{E}[\delta y_{i}]

across MAC coordinates for a representative output channel in the layer-13

q

projection. Right: Ratio of predicted to measured operand-output MSE across decoder layers, comparing the surrogate without and with

\mathcal{L}_{\mathrm{bias}}

. Faint points denote individual layers, diamonds denote the median, shaded regions indicate the 25th–75th percentiles, and the dashed line denotes exact agreement.

Figure 7 : Empirical validation of operand–ADC error decorrelation on LLaMA-3.2-3B. Left: Operand-induced output error versus the additional ADC error for the representative layer-13

q

projection, with Pearson correlation

r=-0.001

. Right: Pearson correlation across all 28 decoder layers and projection types. Faint points denote individual layers, diamonds denote the median, shaded regions indicate the 25th–75th percentiles, and the dashed line denotes zero correlation.

Figure 8 : PSD regions of the full surrogate Hessian for the $q$ , $o$ , $up$ , and $down$ projections in decoder block 13 of LLaMA-3.2-3B. Blue points are sampled clipping-factor configurations with $\lambda_{\min}>0$ , gray points have $\lambda_{\min}<0$ , and the red surface marks the $\lambda_{\min}=0$ boundary. The insets show the optimization trajectories (black dashed lines) from initialization (blue circles) to the calibrated solutions (red stars); both endpoints lie in the PSD region in all four projections.

Property	LLaMA-3.2-3B	Qwen3-4B
Single connected PSD component	196/196 projs	252/252 projs
Initialization in PSD component	196/196 projs	252/252 projs
Calibrated solution in PSD component	196/196 projs	252/252 projs
Accepted trajectory remains in PSD component	196/196 projs	252/252 projs

Appendix

Table 2 : Full-Hessian PSD-region validation across all projections of LLaMA-3.2-3B and Qwen3-4B. Entries report the number of projections satisfying each property.

Figure 9 : Relative mismatch between the analytical surrogate and empirically measured MatMul output MSE for LLaMA-3.2-3B at the calibrated solutions. Points denote individual layers, solid lines show the median across all 28 layers, and shaded regions indicate the 25th–75th percentiles. Each panel reports the indicated error component across projection types.

Panel of Figure 10 — Figure 10 : Output-error analysis for the three additional models. Each subfigure shows normalized MSE from activation quantization, weight quantization, and ADC quantization, followed by the total IMC output error across projection types. Points report the median across decoder layers, and shaded bands show the interquartile range. Lower is better.

Figure 11 : Clipping factors for LLaMA-3.2-3B under the default 9-bit ADC configuration. Results are shown for the upper activation factor

\gamma

, lower activation factor

\beta

, and weight factor

\alpha

across projection types. Markers denote the mean across decoder layers, and shaded regions indicate

\pm 1

standard deviation. A clipping factor of

1

corresponds to no clipping.

Model	Method	PPL ( $\downarrow$ )	Wino	OBQA	PIQA	ARC-C	BoolQ	ARC-E	Hella	Avg. ( $\uparrow$ )	Calib. Time ( $\downarrow$ )
LLaMA-3.2-3B	No clipping	175.70	0.515	0.268	0.533	0.241	0.527	0.293	0.310	0.384	–
	W/A grid search	19.12	0.566	0.294	0.672	0.317	0.515	0.528	0.525	0.488	32.9 min
	IMC-CLINIC	12.27	0.622	0.368	0.722	0.367	0.665	0.630	0.651	0.575	3.3 min
	W8A8 no-IMC	7.82	0.698	0.402	0.778	0.464	0.745	0.723	0.740	0.650	–
	FP16 baseline	7.81	0.694	0.408	0.781	0.462	0.742	0.721	0.741	0.650	–
LLaMA-3.1-8B	No clipping	127.28	0.460	0.274	0.572	0.263	0.489	0.363	0.357	0.397	–

Appendix

Table 3 : Full WikiText-2 perplexity (PPL), seven-task zero-shot accuracy, and calibration time across models and inference configurations. Avg. is the unweighted mean task accuracy; a dash indicates that calibration time is unavailable or inapplicable.

ADC bits	Method	PPL ( $\downarrow$ )	Wino	OBQA	PIQA	ARC-C	BoolQ	ARC-E	Hella	Avg. ( $\uparrow$ )
8	No clipping	29717.68	0.502	0.294	0.505	0.271	0.412	0.256	0.262	0.358
	W/A grid search	1572.10	0.510	0.262	0.504	0.268	0.395	0.259	0.263	0.352
	IMC-CLINIC	42.63	0.530	0.244	0.585	0.242	0.531	0.402	0.376	0.416
9 ∗	No clipping	175.70	0.515	0.268	0.533	0.241	0.527	0.293	0.310	0.384
	W/A grid search	19.12	0.566	0.294	0.672	0.317	0.515	0.528	0.525	0.488
	IMC-CLINIC	12.27	0.622	0.368	0.722	0.367	0.665	0.630	0.651	0.575

Appendix

Table 4 : LLaMA-3.2-3B results across ADC precision.

IMC rows	Method	PPL ( $\downarrow$ )	Wino	OBQA	PIQA	ARC-C	BoolQ	ARC-E	Hella	Avg. ( $\uparrow$ )
128	No clipping	10.36	0.627	0.404	0.737	0.419	0.647	0.660	0.696	0.599
	W/A grid search	9.39	0.669	0.400	0.751	0.406	0.657	0.677	0.699	0.608
	IMC-CLINIC	9.04	0.680	0.408	0.749	0.434	0.706	0.692	0.712	0.626
256	No clipping	15.86	0.564	0.326	0.681	0.331	0.518	0.528	0.593	0.506
	W/A grid search	11.42	0.647	0.358	0.742	0.398	0.607	0.657	0.661	0.581
	IMC-CLINIC	10.03	0.648	0.384	0.744	0.401	0.654	0.660	0.688	0.597

Appendix

Table 5 : LLaMA-3.2-3B results across IMC row counts.

IMC columns	Method	PPL ( $\downarrow$ )	Wino	OBQA	PIQA	ARC-C	BoolQ	ARC-E	Hella	Avg. ( $\uparrow$ )
8	No clipping	175.32	0.505	0.228	0.542	0.223	0.538	0.299	0.311	0.378
	W/A grid search	19.12	0.565	0.296	0.672	0.317	0.515	0.529	0.525	0.488
	IMC-CLINIC	12.27	0.622	0.368	0.722	0.367	0.665	0.630	0.651	0.575
16	No clipping	175.32	0.504	0.228	0.542	0.223	0.538	0.299	0.311	0.378
	W/A grid search	19.12	0.565	0.296	0.672	0.317	0.515	0.529	0.525	0.488
	IMC-CLINIC	12.27	0.622	0.368	0.722	0.367	0.665	0.630	0.651	0.575

Appendix

Table 6 : LLaMA-3.2-3B results across IMC column counts.

Noise (LSB)	Method	PPL ( $\downarrow$ )	Wino	OBQA	PIQA	ARC-C	BoolQ	ARC-E	Hella	Avg. ( $\uparrow$ )
0 ∗	No clipping	175.70	0.515	0.268	0.533	0.241	0.527	0.293	0.310	0.384
	W/A grid search	19.12	0.566	0.294	0.672	0.317	0.515	0.528	0.525	0.488
	IMC-CLINIC	12.27	0.622	0.368	0.722	0.367	0.665	0.630	0.651	0.575
0.1	No clipping	288.45	0.514	0.256	0.503	0.242	0.478	0.294	0.287	0.368
	W/A grid search	21.70	0.552	0.300	0.599	0.299	0.536	0.485	0.490	0.466
	IMC-CLINIC	12.58	0.614	0.352	0.679	0.345	0.643	0.601	0.636	0.553

Appendix

Table 7 : LLaMA-3.2-3B robustness to analog noise.

Samples	Method	PPL ( $\downarrow$ )	Wino	OBQA	PIQA	ARC-C	BoolQ	ARC-E	Hella	Avg. ( $\uparrow$ )	Calib. Time ( $\downarrow$ )
8 ∗	W/A grid search	19.12	0.566	0.294	0.672	0.317	0.515	0.528	0.525	0.488	32.9 min
	IMC-CLINIC	12.27	0.622	0.368	0.722	0.367	0.665	0.630	0.651	0.575	3.4 min
16	W/A grid search	N/E	N/E	N/E	N/E	N/E	N/E	N/E	N/E	N/E	$>60$ min (T/O)
	IMC-CLINIC	12.21	0.631	0.350	0.716	0.373	0.623	0.642	0.654	0.570	3.9 min
32	W/A grid search	N/E	N/E	N/E	N/E	N/E	N/E	N/E	N/E	N/E	$>60$ min (T/O)
	IMC-CLINIC	12.31	0.631	0.370	0.723	0.384	0.650	0.654	0.641	0.579	5.0 min

Appendix

Table 8 : LLaMA-3.2-3B results across calibration-set sizes. N/E indicates metrics not evaluated because calibration timed out; T/O marks a run exceeding the 60-minute limit.

Seq. length	Method	PPL ( $\downarrow$ )	Wino	OBQA	PIQA	ARC-C	BoolQ	ARC-E	Hella	Avg. ( $\uparrow$ )	Calib. Time ( $\downarrow$ )
512	W/A grid search	17.72	0.548	0.302	0.671	0.317	0.523	0.529	0.539	0.490	10.9 min
	IMC-CLINIC	12.26	0.611	0.368	0.713	0.376	0.630	0.648	0.651	0.571	3.0 min
1024	W/A grid search	18.46	0.586	0.310	0.655	0.300	0.497	0.530	0.539	0.488	18.4 min
	IMC-CLINIC	12.20	0.638	0.372	0.731	0.386	0.660	0.653	0.645	0.584	3.1 min
2048 ∗	W/A grid search	19.12	0.566	0.294	0.672	0.317	0.515	0.528	0.525	0.488	32.9 min
	IMC-CLINIC	12.27	0.622	0.368	0.722	0.367	0.665	0.630	0.651	0.575	3.4 min

Appendix

Table 9 : LLaMA-3.2-3B results across calibration sequence lengths.

Domain	Method	PPL ( $\downarrow$ )	Wino	OBQA	PIQA	ARC-C	BoolQ	ARC-E	Hella	Avg. ( $\uparrow$ )
WikiText-2 ∗	W/A grid search	19.12	0.566	0.294	0.672	0.317	0.515	0.528	0.525	0.488
	IMC-CLINIC	12.27	0.622	0.368	0.722	0.367	0.665	0.630	0.651	0.575
C4	W/A grid search	17.73	0.568	0.316	0.676	0.306	0.542	0.546	0.559	0.502
	IMC-CLINIC	12.32	0.627	0.376	0.720	0.381	0.642	0.643	0.646	0.576
Pile	W/A grid search	17.88	0.566	0.316	0.655	0.331	0.553	0.555	0.552	0.504
	IMC-CLINIC	12.31	0.623	0.362	0.729	0.373	0.685	0.647	0.652	0.581

Appendix

Table 10 : LLaMA-3.2-3B results across calibration domains.

Figure 12 : Optimization convergence of IMC-CLINIC on LLaMA-3.2-3B. Left: Surrogate loss versus accepted Newton iteration for decoder block 13, normalized by the loss at the selected initialization,

\mathcal{L}^{(t)}/\mathcal{L}^{(0)}

. Right: Number of accepted Newton iterations at optimizer return across all 28 decoder blocks. Faint points denote individual decoder blocks, diamonds denote the median, and vertical ranges indicate the 25th–75th percentiles.

Method	Joint W/A	Signed bias	ADC term	PPL ( $\downarrow$ )
IMC-CLINIC	✓	✓	✓	12.27
w/o ADC term	✓	✓		127.91
w/o signed-bias term	✓		✓	12.76
Independent W/A		✓	✓	15.80

Appendix

Table 11 : Method ablations on LLaMA-3.2-3B under the 9-bit ADC setting. All variants use the same default initialization, and ADC quantization remains enabled during inference.

Method	PPL ( $\downarrow$ )	Wino	OBQA	PIQA	ARC-C	BoolQ	ARC-E	Hella	Avg. ( $\uparrow$ )
IMC-CLINIC + per-channel $\alpha$	12.02	0.617	0.370	0.721	0.393	0.668	0.649	0.650	0.581
IMC-CLINIC (shared scalar $\alpha$ )	12.27	0.622	0.368	0.722	0.367	0.665	0.630	0.651	0.575

Appendix

Table 12 : LLaMA-3.2-3B results across weight-clipping granularities.

Method	PPL ( $\downarrow$ )	Wino	OBQA	PIQA	ARC-C	BoolQ	ARC-E	Hella	Avg. ( $\uparrow$ )
IMC-CLINIC +EF-weighted loss	11.88	0.619	0.364	0.716	0.370	0.622	0.631	0.657	0.568
IMC-CLINIC (unweighted loss)	12.27	0.622	0.368	0.722	0.367	0.665	0.630	0.651	0.575

Appendix

Table 13 : LLaMA-3.2-3B results with empirical-Fisher weighting for input-divergent projections.

Figure 13 : Branch-and-bound procedure for validating global $1\%$ -optimality of the calibrated clipping factors under the surrogate objective.

Model	Q	K	V	O	Gate	Up	Down	Total	Median Time
LLaMA-3.2-3B	28/28	28/28	28/28	28/28	28/28	28/28	28/28	196/196	16.88 min
Qwen3-4B	36/36	36/36	36/36	36/36	36/36	36/36	36/36	252/252	18.58 min

Appendix

Table 14 : Optimality-validation results. Each entry under a projection type reports the number of projection-level clipping solutions certified to be within

1\%

of the global minimum of the calibration objective. Validation time is the median wall-clock time per projection and is incurred only for the optimality check, not during clipping calibration.

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