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arxiv: 2605.17160 · v1 · pith:LYZO6TGSnew · submitted 2026-05-16 · 💻 cs.LG · cs.AI· cs.CV

When Bits Break Recourse: Counterfactual-Faithful Quantization

Chaymae Yahyati , Ismail Lamaakal , Khalid El Makkaoui , Ibrahim Ouahbi This is my paper

Pith reviewed 2026-05-20 14:39 UTC · model grok-4.3

classification 💻 cs.LG cs.AIcs.CV
keywords quantizationalgorithmic recoursecounterfactual explanationsmodel compressionmachine learning deploymentfairnesscredit scoring
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The pith

Counterfactual-Faithful Quantization keeps recourse valid and low-cost after bit reduction while matching full-precision accuracy.

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

The paper establishes that standard quantization preserves predictive accuracy on tabular datasets yet often invalidates or inflates the cost of recourse actions that worked on the original model. It introduces Counterfactual-Faithful Quantization to jointly optimize quantizer parameters and mixed-precision bit allocation so that recourse points from the full-precision teacher remain correctly classified under a global bit budget. A margin-based argument supplies a sufficient condition under which bounded quantization perturbations transfer validity, cost, and direction stability from teacher to student. Experiments on Adult, German Credit, and COMPAS data show accuracy-matched baselines degrade recourse metrics while the proposed method improves them across bit widths.

Core claim

Quantization perturbs model outputs enough to invalidate many recourse actions that worked on the full-precision model. Counterfactual-Faithful Quantization (CFQ) solves this by jointly learning quantization parameters and bit allocations so that the quantized model still classifies the recourse points from the teacher model correctly, under a fixed total bit budget. This is supported by a sufficient condition derived from margin analysis that guarantees stability when perturbations are bounded.

What carries the argument

Counterfactual-Faithful Quantization (CFQ), which enforces the target outcome at teacher recourse points during quantizer training and mixed-precision allocation.

If this is right

  • Accuracy can stay comparable to full-precision models while validity drop and counterfactual recourse gap improve across bit budgets.
  • Recourse stability holds for the tested tabular datasets when the global bit constraint is enforced during training.
  • Mixed-precision allocation guided by counterfactual fidelity outperforms uniform accuracy-focused quantization on stability metrics.

Where Pith is reading between the lines

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

  • Deployers of quantized models in lending or criminal justice may need to adopt counterfactual-aware training to keep explanations actionable after compression.
  • The same bounded-perturbation logic could apply to other compression methods such as pruning if analogous margin conditions can be derived.
  • Future low-bit training pipelines might treat recourse metrics as first-class objectives alongside accuracy.

Load-bearing premise

The margin analysis assumes quantization perturbations remain bounded so that recourse transfers from the full-precision teacher to the quantized student.

What would settle it

Measure whether recourse actions valid on the full-precision model remain valid on the quantized version once the observed quantization error exceeds the margin bound used in the proof.

Figures

Figures reproduced from arXiv: 2605.17160 by Chaymae Yahyati, Ibrahim Ouahbi, Ismail Lamaakal, Khalid El Makkaoui.

Figure 1
Figure 1. Figure 1: CFQ pipeline. A teacher recourse action δfp is computed on the full-precision model using a small number of projected gradient steps and is treated as a constant via stop￾gradient. The quantized model fq is trained to preserve task accuracy and to keep x + δfp a valid counterfactual under quan￾tization, while mixed-precision bit allocation and quantizer parameters are optimized under a bit budget. We do no… view at source ↗
Figure 2
Figure 2. Figure 2: Same accuracy, different recourse. Quan￾tization can shift local decision geometry: a minimal actionable recourse δ ⋆ f that flips the full-precision model may fail for the quantized model, requiring a different or larger action δ ⋆ fq even when predictive accuracy is unchanged. Quantization and mixed precision. Quantization reduces inference cost by representing weights and activations with low-bit numeri… view at source ↗
Figure 3
Figure 3. Figure 3: CFQ improves recourse validity across com￾pression regimes. Validity Drop (VD) as a function of the normalized bit budget. Lower VD indicates that full￾precision recourse actions transfer more reliably to the quantized model. CFQ consistently yields lower VD than accuracy-centric quantization baselines, with the largest gains in low-bit regimes where quantization perturbations are strongest. Relative to th… view at source ↗
Figure 4
Figure 4. Figure 4: and [PITH_FULL_IMAGE:figures/full_fig_p021_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Recourse cost inflation vs compression budget. Each panel plots CRG as a function of normalized bit budget. CRG measures the relative change in minimal recourse cost induced by quantization. CFQ consistently reduces cost inflation, indicating that quantization is less likely to increase the effort required to achieve the favorable outcome [PITH_FULL_IMAGE:figures/full_fig_p022_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Subgroup visualization for VD. Bar plot of subgroup VD for ADULT split by sex at a matched budget. VD measures whether FP32 recourse actions remain valid after quantization. CFQ reduces VD for each subgroup and improves worst-group VD, indicating more reliable transfer of recourse under compression. D.6 Subgroup (fairness-slice) reporting We report conditional VD/CRG by subgroup membership and summarize wo… view at source ↗
Figure 7
Figure 7. Figure 7: Margin diagnostics at recourse points. Empirical CDFs of the target margin evaluated at the FP32 recourse point x + δ ⋆ f . Shifting the quantized margin distribution toward larger positive values corresponds to a lower probability that quantization flips the decision at the recourse point, providing a mechanistic explanation for reductions in VD under CFQ. 1 2 3 4 5 6 7 8 2 3 4 8 Layer index Assigned bitw… view at source ↗
Figure 8
Figure 8. Figure 8: Example learned bit allocation under a fixed budget. Per-layer bitwidths selected by a standard mixed-precision baseline and by CFQ. CFQ tends to allocate higher precision to layers that most affect decision-boundary geometry near recourse points, consistent with improvements in VD/CRG at the same global BitCost. D.8 Runtime and overhead CFQ introduces an overhead due to the K-step projected-gradient teach… view at source ↗
Figure 9
Figure 9. Figure 9: Cost–robustness trade-off under deployment variability. Each point shows robust success versus mean recourse cost for ADULT. The robust solver increases robustness by optimizing against multiple sampled deployment variants, but it increases the recourse cost. CFQ shifts the trade-off by making the deployed quantized model intrinsically less sensitive at recourse points, improving robust success at near-bas… view at source ↗
Figure 10
Figure 10. Figure 10: Validity Drop on ADULT under increasingly recourse-aware quantization. Standard PTQ INT4 produces the largest recourse failure rate. Mixed-precision PTQ reduces VD by allocating bits based on factual sensitivity, but it still ignores teacher recourse points. CF-PTQ calibration lowers VD by calibrating scales and clipping thresholds on both factual and counterfactual inputs. Counterfactual sensitivity allo… view at source ↗
Figure 11
Figure 11. Figure 11: Counterfactual Recourse Gap on ADULT. CRG measures whether quantization increases the minimum action cost required to achieve the target outcome. The decreasing trend from PTQ INT4 to CF-PTQ and CFQ-QAT shows that counterfactual-aware calibration reduces the tendency of the quantized model to “move the goalpost” after deployment. This complements VD: an action may remain valid in some cases but become sig… view at source ↗
Figure 12
Figure 12. Figure 12: Cost–stability trade-off on ADULT. The horizontal axis reports relative calibration or training overhead normalized by standard PTQ. CF-PTQ occupies the middle regime between PTQ and full CFQ-QAT: it gives a substantial reduction in VD with lower cost than QAT. This figure directly motivates CF-PTQ as a practical deployment variant when full QAT is too expensive. avoiding backbone updates and QAT. Thus, C… view at source ↗
Figure 13
Figure 13. Figure 13: Layer-wise sensitivity profiles used for mixed-precision PTQ on [PITH_FULL_IMAGE:figures/full_fig_p032_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Effect of teacher PGD steps on recourse stability. Increasing the number of teacher [PITH_FULL_IMAGE:figures/full_fig_p034_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Predictive accuracy under different teacher-recoursing budgets. Accuracy is unchanged [PITH_FULL_IMAGE:figures/full_fig_p034_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Effect of teacher-action noise on VD and CRG. Both metrics increase smoothly as the [PITH_FULL_IMAGE:figures/full_fig_p035_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Training-time overhead as a function of the teacher-recoursing budget. The relative [PITH_FULL_IMAGE:figures/full_fig_p037_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Validity Drop under different action-constraint regimes. CFQ consistently reduces the [PITH_FULL_IMAGE:figures/full_fig_p040_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Counterfactual Recourse Gap under different action-constraint regimes. CFQ reduces [PITH_FULL_IMAGE:figures/full_fig_p041_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Feasible Recourse Rate of the full-precision model under different action constraints. FRR [PITH_FULL_IMAGE:figures/full_fig_p041_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: Validity Drop under distribution shift. CFQ consistently reduces recourse failure relative [PITH_FULL_IMAGE:figures/full_fig_p043_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: Counterfactual Recourse Gap under distribution shift. CFQ lowers the relative increase [PITH_FULL_IMAGE:figures/full_fig_p043_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: Subgroup Validity Drop across datasets. CFQ reduces post-quantization recourse failure [PITH_FULL_IMAGE:figures/full_fig_p045_23.png] view at source ↗
Figure 24
Figure 24. Figure 24: Subgroup Counterfactual Recourse Gap across datasets. CFQ reduces the relative increase [PITH_FULL_IMAGE:figures/full_fig_p045_24.png] view at source ↗
Figure 25
Figure 25. Figure 25: Rate–recourse curves on non-tabular datasets. Validity Drop increases as the average [PITH_FULL_IMAGE:figures/full_fig_p049_25.png] view at source ↗
Figure 26
Figure 26. Figure 26: Rate–CRG curves on non-tabular datasets. Lower bitwidths increase the relative recourse [PITH_FULL_IMAGE:figures/full_fig_p049_26.png] view at source ↗
read the original abstract

Quantization can preserve predictive accuracy under low-bit deployment while silently breaking algorithmic recourse: an actionable change that flips a decision before quantization may fail after quantization, or become substantially more costly. We formalize counterfactual sensitivity under quantization through validity, cost, and direction stability, and introduce two metrics: Validity Drop (VD) and Counterfactual Recourse Gap (CRG) that reveal recourse failures invisible to accuracy. We propose Counterfactual-Faithful Quantization (CFQ), which trains quantizer parameters and mixed-precision bit allocation to preserve counterfactual behavior by enforcing the target outcome at teacher recourse points under a global bit budget. A margin-based analysis gives a sufficient condition for recourse transfer under bounded quantization perturbations. Experiments on Adult, German Credit, and COMPAS show that accuracy-matched baselines can significantly degrade recourse stability, while CFQ maintains accuracy and substantially improves VD and CRG across bit budgets.

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

1 major / 3 minor

Summary. The paper formalizes how quantization can degrade algorithmic recourse (validity, cost, and direction stability of counterfactuals), introduces Validity Drop (VD) and Counterfactual Recourse Gap (CRG) metrics, proposes Counterfactual-Faithful Quantization (CFQ) that jointly optimizes quantizer parameters and mixed-precision bit allocation to enforce target outcomes at teacher recourse points under a global bit budget, supplies a margin-based sufficient condition for recourse transfer under bounded perturbations, and reports experiments on Adult, German Credit, and COMPAS showing that accuracy-matched baselines degrade recourse stability while CFQ preserves accuracy and improves VD/CRG across bit budgets.

Significance. If the empirical gains hold under the stated conditions, the work identifies a practically relevant failure mode for quantized models in recourse-sensitive applications and supplies a targeted mitigation that does not sacrifice predictive accuracy. The introduction of VD and CRG provides concrete, falsifiable ways to measure the phenomenon beyond accuracy, and the margin analysis offers a starting point for theoretical guarantees. The experiments across three standard datasets strengthen the case that the issue is not isolated.

major comments (1)
  1. [Margin-based analysis (abstract and §4)] Margin-based analysis (abstract and §4): the sufficient condition for validity/cost/direction stability requires quantization perturbations to remain strictly smaller than the decision margin at each teacher recourse point. For the 4-bit regime tested, worst-case ||q(x)-x|| can exceed typical margins on Adult/German Credit/COMPAS near boundaries or in low-bit regions; when this occurs the formal transfer guarantee does not apply, so the reported VD/CRG improvements rest on the empirical objective rather than the stated analysis. The manuscript should either verify the bound holds on the evaluated points or qualify the analysis as applying only above a minimum bit-width.
minor comments (3)
  1. [Results] Results section: report dataset-specific numerical values for VD and CRG (with standard deviations over runs) rather than qualitative statements of 'substantial improvement'; include the exact bit-allocation schedules chosen by CFQ versus baselines.
  2. [Method] Notation: define the teacher recourse point generation procedure and the precise form of the CFQ loss (including how the global bit budget is enforced) before the margin analysis; the current abstract-level description leaves the optimization target ambiguous.
  3. [Experiments] Figure clarity: ensure recourse stability plots distinguish between validity drop and cost/direction components; add a table summarizing per-dataset accuracy, VD, and CRG at each bit-width for direct comparison.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback and for highlighting the distinction between the sufficient condition in our margin analysis and the empirical performance of CFQ. We address the major comment below and have prepared revisions to qualify the analysis appropriately while preserving the core contributions.

read point-by-point responses

  1. Referee: Margin-based analysis (abstract and §4): the sufficient condition for validity/cost/direction stability requires quantization perturbations to remain strictly smaller than the decision margin at each teacher recourse point. For the 4-bit regime tested, worst-case ||q(x)-x|| can exceed typical margins on Adult/German Credit/COMPAS near boundaries or in low-bit regions; when this occurs the formal transfer guarantee does not apply, so the reported VD/CRG improvements rest on the empirical objective rather than the stated analysis. The manuscript should either verify the bound holds on the evaluated points or qualify the analysis as applying only above a minimum bit-width.

    Authors: We agree that the margin-based result is a sufficient (not necessary) condition and that, for 4-bit quantization, the worst-case perturbation norm can exceed the decision margin at some recourse points near boundaries. In such cases the formal transfer guarantee does not apply, and the reported gains in VD and CRG are attributable to the joint optimization objective that directly enforces the teacher recourse outcome under the global bit budget. We will revise the abstract and §4 to explicitly qualify the analysis as holding only when the quantization perturbation bound is strictly smaller than the margin at each evaluated recourse point. We will also add a short discussion (with illustrative margin-versus-error estimates on the three datasets) clarifying the bit-width regimes in which the sufficient condition is expected to be satisfied. This change does not alter the empirical claims or the practical utility of CFQ. revision: yes

Circularity Check

0 steps flagged

No circularity: optimization targets external teacher recourse points and metrics are independently defined

full rationale

The paper defines CFQ as training quantizer parameters and bit allocation to enforce the target outcome specifically at recourse points obtained from a separate full-precision teacher model, under a global bit budget. Validity Drop (VD) and Counterfactual Recourse Gap (CRG) are defined directly from the stability of validity, cost, and direction between teacher and student models. The margin-based analysis supplies only a sufficient condition under an explicit bounded-perturbation assumption and is not used to derive the training objective or the reported empirical gains. No step reduces a claimed result to a self-fit, self-citation chain, or renaming of the input; the central experimental comparison against accuracy-matched baselines therefore remains independent of the method's own outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the existence of a bounded quantization perturbation and on the availability of reliable teacher recourse points; both are domain assumptions rather than derived quantities.

axioms (1)
  • domain assumption Quantization perturbations remain bounded
    Invoked by the margin-based sufficient condition for recourse transfer

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