The Rescue Effect: Spatio-Semantic Early Exit
Bypasses Quantization Collapse in CLIP
May 26, 2026
Abstract
Deploying Vision–Language Models on resource-constrained hardware typically requires INT8 quantization, but in joint-embedding architectures such as CLIP this introduces a failure mode distinct from quantized CNN classifiers: activation noise
accumulated across transformer blocks perturbs the direction of the multimodal embedding, eroding the cosine alignment on which zero-shot retrieval depends. We characterize this as Quantization-Induced Representation Collapse
(QIRC) and quantify it on INT8 CLIP ViT-B/32, where the layer-wise noise-to-signal ratio grows from below \(10\%\) in shallow blocks to \(52\%\) at Layer 11. We propose
LRA-EE (Layer-wise Representation-Aware Early Exit), which bypasses noise-saturated deep layers via Spatio-Semantic Aggregation (replacing the immature shallow [CLS] with a global patch-token average), a learned multi-feature
gate (confidence, top-2 margin, spatial-activation variance), and Layer-adaptive Confidence Thresholding calibrated to each layer’s Information-to-Noise Ratio. On ImageNet-1K zero-shot classification, LRA-EE reduces FLOPs by \(13.4\%\) and improves Top-1 accuracy by \(+2.44\)%p (\(58.72\% \to 61.16\%\)) over the INT8 baseline. A four-quadrant decomposition isolates the
Rescue Effect: \(9.5\%\) of samples are correctly classified at shallow exits but lost to noise at full depth, against only \(7.1\%\) suffering the inverse. A controlled
factorial ablation confirms that depth-adaptive routing—not FP32 distillation—is the dominant source of the gain.
1 Introduction↩︎
Vision–Language Models (VLMs) such as CLIP [1], ALIGN [2], Florence [3], and EVA-CLIP [4] have catalyzed a paradigm shift in zero-shot recognition by aligning visual and textual modalities in a shared latent manifold. Their generalization, expanded by recent foundation models [5]–[7], comes at a prohibitive computational cost that exceeds the envelopes of edge accelerators such as NPUs and FPGAs. INT8 post-training quantization has emerged as the de facto compression strategy [8]–[12], compressing model weights by up to 4\(\times\) while leveraging integer SIMD pipelines for substantial latency gains [13]–[16]. Yet, the union of CLIP and aggressive quantization manifests a failure mode qualitatively distinct from quantized CNN classifiers. Whereas a quantized CNN merely confuses semantic categories—mistaking a canine for a feline—CLIP’s joint-embedding architecture is structurally more brittle: quantization noise stochastically perturbs the directionality of multimodal vectors, eroding the cosine alignment that underlies zero-shot retrieval. Layer-wise inspection on \(10{,}000\) ImageNet validation images reveals that the noise-to-signal ratio in INT8 ViT-B/32 grows monotonically from below \(10\%\) in early blocks to \(52\%\) by Layer 11—more than half of the late-stage representation contaminated by accumulated quantization residuals. We formalize this as Quantization-Induced Representation Collapse (QIRC) and contend that mitigating it requires not refinement of the deep layers, but their strategic evasion.
Conventional Early Exit (EE) frameworks [17]–[19], inherited from NLP architectures [20]–[23], route inference based on the [CLS] token aggregated at intermediate depth. In a Vision Transformer [24]–[28], the [CLS]
at shallow strata has yet to attend across the global spatial manifold; its semantic capacity is impoverished. Our measurements corroborate this: at Layer 8, a [CLS]-based head attains a meager \(21.73\%\)
accuracy—\(37.0\)%p below the INT8 full-depth baseline—rendering naive shallow exits infeasible. The path forward demands a representation strategy that recovers semantic density at shallow depth while remaining robust
under quantization.
We address this gap with LRA-EE (Layer-wise Representation-Aware Early Exit), comprising (i) Spatio-Semantic Aggregation (SSA), which substitutes the [CLS] singleton with a global average over all \(196\) patch tokens; (ii) a Multi-Feature Learned Gate fusing confidence, top-2 margin, and Spatial-Activation Variance (SAV); and (iii) Layer-adaptive Confidence Thresholding (LCT) calibrated
to each block’s empirical Information-to-Noise Ratio. On ImageNet-1K, LRA-EE simultaneously trims FLOPs by \(13.38\%\) and lifts Top-1 accuracy by \(2.44\)%p over the INT8
baseline—contradicting the conventional accuracy–efficiency trade-off. We trace this paradox to the Rescue Effect: shallow exits recover \(9.5\%\) of samples that would otherwise be misclassified at full
depth, against only \(7.1\%\) lost to premature termination, yielding a \(+2.37\)%p net rescue.
1.0.0.1 Contributions.
Our principal contributions are:
We identify and quantify Quantization-Induced Representation Collapse (QIRC) in CLIP, with layer-wise evidence that quantization noise accumulates rapidly with depth and dominates the semantic signal in late blocks (§3).
We propose LRA-EE, an Early Exit framework for quantized VLMs integrating SSA, multi-feature learned gating, LCT, and a Pathological Layer Pruning rule that excludes layers with anomalous outlier-induced noise spikes (§4).
We disentangle the gain’s source through a controlled factorial ablation separating head architecture, FP32 distillation, and adaptive routing (§6.1), establishing that adaptive routing alone—without FP32 supervision—accounts for the majority of the improvement, ruling out a distillation artifact.
We formalize and mechanistically dissect the Rescue Effect via four-quadrant outcome decomposition and cosine-direction drift, showing that depth-adaptive inference under quantization yields simultaneous improvements in efficiency and accuracy (§7).
2 Related Work↩︎
2.0.0.1 Vision–Language Models and CLIP.
CLIP [1] and its descendants [2], [3], [5] established joint-embedding models as the backbone of zero-shot recognition by aligning visual and textual modalities in a shared latent manifold. Unlike CNN classifiers, CLIP’s zero-shot fidelity depends critically on the direction of multimodal embeddings in cosine space—a geometric property that, as we show, is particularly vulnerable to quantization noise accumulation across transformer depth.
2.0.0.2 Transformer Quantization.
PTQ for transformers has progressed from layer-wise static schemes [16], [29] to per-channel and learned-step variants [10], [30]. Existing CLIP compression works such as TinyCLIP [15] reduce model cost, but leave depth-wise compute fixed and do not characterize quantization-induced drift in multimodal embedding geometry. We provide a systematic layer-wise account of this interaction, identifying a structural failure mode—QIRC—that prior quantization methods neither characterize nor address.
2.0.0.3 Early Exit Mechanisms.
Early Exit was pioneered in NLP [20], [21], [31], [32] and extended to ViTs [18], [33], predominantly leveraging [CLS] entropy or confidence. However, this principle is misaligned with two properties of quantized VLMs:
(i) shallow [CLS] tokens in ViTs are semantically impoverished, and (ii) quantization noise accumulates with depth, making full-depth inference harmful for a non-trivial fraction of samples. Prior EE-only methods (BranchyNet [17], DeeBERT [20], DVT [18]) target full-precision models and do not address this failure mode, while quantization-only methods
leave depth-wise routing fixed. LRA-EE explicitly targets this intersection and, unlike prior methods, improves accuracy above the compressed full-depth baseline.
3 Motivation: Quantization-Induced Representation Collapse↩︎
3.1 Layer-wise Quantization Noise Profile↩︎
To empirically substantiate the existence of QIRC, we conducted a layer-wise dissection of an INT8-quantized ViT-B/32 CLIP encoder over 10,000 ImageNet validation images. Although only Linear-layer weights are quantized, the resulting weight perturbations introduce residual errors into the activation stream at each block, which accumulate across depth. For each transformer block \(L \in \{1,\ldots,12\}\), we compute \[\Delta_{\text{nat}}(L) = \big\| z^{\text{FP32}}_L - z^{\text{FP32}}_{L-1} \big\|_2, \quad \Delta_{\text{quant}}(L) = \big\| z^{\text{INT8}}_L - z^{\text{FP32}}_L \big\|_2,\] where \(\Delta_{\text{nat}}\) captures the natural representational evolution and \(\Delta_{\text{quant}}\) isolates the residual incurred by precision reduction.
Figure 1 suggests super-linear noise growth: the relative ratio \(\Delta_{\text{quant}}/\Delta_{\text{nat}}\) remains under \(10\%\) through shallow and mid-depth blocks, reaches the transition point around Layer 8, and rises sharply thereafter, peaking at \(52\%\) at Layer 11—with an anomalous spike at Layer 9 (MSE \(= 0.007532\), \(\sim 2\times\) its neighbors) attributable to outlier-sensitive weight kurtosis. Cosine similarity between INT8 and FP32 embeddings degrades from \(0.589\) at the input to \(0.421\) at the final layer, a \(28.5\%\) relative drop that translates directly into compromised zero-shot fidelity. These findings establish QIRC as a structural pathology: beyond a sample-dependent critical depth \(L^\star\), additional computation actively degrades the representation, motivating depth-adaptive inference that halts before noise dominance.
3.1.0.1 Scope.
Measurements use CLIP ViT-B/32 under dynamic INT8 post-training quantization. We expect the qualitative trend to hold on related backbones (ViT-L/14, SigLIP, EVA-CLIP), but a comprehensive cross-backbone sweep is left to future work.
3.2 [CLS] Immaturity and the Case for Spatial Aggregation↩︎
A naive remedy—grafting a [CLS]-based head onto an intermediate layer—is untenable: at Layer 8, a [CLS] head attains a mere \(21.73\%\) Top-1 accuracy, \(37.0\)%p below the full-depth baseline. The cause is structural: in a ViT, the [CLS] token aggregates global context only after multi-block self-attention propagates patch-level information, leaving its
shallow-depth embedding semantically impoverished. The remedy lies in harvesting the spatial manifold the [CLS] has yet to traverse: the 196 patch tokens at Layer 8, although individually local, collectively encode a dense semantic description
whose aggregate—which we term Spatio-Semantic Aggregation—rivals late-layer [CLS] fidelity while remaining shielded from late-stage quantization noise. The dimensional uniformity of ViT (constant \(197 \times
768\) across all 12 blocks) further makes it structurally amenable to layer-wise noise analysis and uniform exit-head deployment, while aligning with the systolic execution patterns of NPU and FPGA Early Exit logic; this contrasts with CNN
backbones, whose spatial resolution and channel dimensionality vary across depth.
4 Method: Layer-wise Representation-Aware Early Exit↩︎
4.1 Guiding Principle: Depth–Quality Trade-off↩︎
We characterize each transformer depth \(L\) via a representation-quality model: \[\mathcal{Q}(L) \;=\; \mathcal{R}(L) \;-\; \beta\,\mathcal{N}(L), \label{eq:quality}\tag{1}\] where \(\mathcal{R}(L)\) denotes representation richness (concave, non-decreasing) and \(\mathcal{N}(L)\) accumulated quantization noise; \(\beta \geq 0\) encodes the precision regime (\(\beta \to 0\): FP32; \(\beta\) large: INT8). When \(\mathcal{N}\) grows super-linearly with depth (§3.1), \(\mathcal{Q}\) admits a sample-dependent interior maximum \(L^\star \in \{1,\ldots,L_{\max}-1\}\). Eq. 1 serves as a conceptual organizer for three testable predictions:
Full-depth inference is suboptimal under aggressive quantization (§5.2, Table 1).
Optimal exit depth varies across samples; static truncation underperforms learned routing (§6.3, Figure 3).
Layers with anomalous \(\mathcal{N}(L)\) should be excluded even if standalone-accurate (§6.4, Figure 4).
4.2 Spatio-Semantic Aggregation (SSA)↩︎
Let \(Z_L \in \mathbb{R}^{(N+1)\times d}\) be the layer-\(L\) activation tensor with \(N=196\) patch tokens, \(d=768\),
and [CLS] as \(z_{L,0}\). SSA replaces the singleton [CLS] with a spatial aggregate: \[\mathcal{F}_{\text{SSA}}(Z_L) \;=\;
\mathrm{LayerNorm}\!\left(\frac{1}{N}\sum_{i=1}^{N} z_{L,i}\right) \;\in\; \mathbb{R}^{d}.
\label{eq:ssa}\tag{2}\] Under i.i.d.residual assumptions on \(z_{L,i}\) as noisy estimates of the latent class centroid, \(\mathcal{F}_{\text{SSA}}\)’s variance shrinks as
\(\Theta(1/N)\)—a \(\sqrt{N}\)-fold noise concentration that the singleton [CLS] cannot achieve, the architectural origin of the \(+23.87\)%p
shallow-layer gain in §6.2. Each candidate \(L \in \mathcal{L}_{\text{exit}} \subseteq \{1,\ldots,11\}\) instantiates an MLP projection \(\phi_L:
\mathbb{R}^d \to \mathbb{R}^{512}\), followed by cosine similarity against the \(K=1{,}000\) text prompt embeddings to obtain \(\hat{p}_L\).
4.3 Multi-Feature Learned Gating↩︎
A learned gate \(\mathcal{G}_L:\mathbb{R}^3\to[0,1]\) takes three scalar features: Confidence \(c_L = \max_k \hat{p}_{L,k}\); Top-2 Margin \(m_L = \hat{p}_{L,(1)} - \hat{p}_{L,(2)}\), discriminating sharp from flat distributions; and Spatial-Activation Variance \(\mathrm{SAV}(Z_L) = \tfrac{1}{N}\sum_{i}\|z_{L,i} - \bar{z}_L\|_2^{2}\) with \(\bar{z}_L = \tfrac{1}{N}\sum_i z_{L,i}\), which empirically correlates inversely with quantization-robust samples. The gate is \[\mathcal{G}_L \;=\; \sigma\!\Big(w_1^{(L)} c_L + w_2^{(L)} m_L + w_3^{(L)}\,\mathrm{SAV}_L + b^{(L)}\Big),\] trained via BCE on a held-out gating split (label \(=1\) iff the layer-\(L\) exit is correct).
4.4 Layer-adaptive Confidence Thresholding (LCT)↩︎
Define the Information-to-Noise Ratio \[\mathrm{INR}(L) \;=\; \frac{\big\|\mathbb{E}_x[z_L(x)]\big\|_2^{2}}{\mathrm{Var}_x\!\big[\epsilon_L^{\text{quant}}(x)\big]}, \quad \epsilon_L^{\text{quant}}(x) = z_L^{\text{INT8}}(x) - z_L^{\text{FP32}}(x). \label{eq:inr}\tag{3}\] LCT assigns each layer a distinct threshold \(\tau_L\), jointly optimized for accuracy under a FLOPs budget: high-INR layers tolerate lower thresholds, low-INR layers demand stricter gating. A sample passing \(\tau_8 = 0.44\) at the high-INR Layer 8 exits, while the same sample at the low-INR Layer 9 (§4.5) is held.
4.5 Pathological Layer Pruning↩︎
Quantization noise grows non-uniformly: outlier-sensitive weight distributions cause anomalous spikes at certain layers. In our INT8 ViT-B/32, Layer 9’s quantization MSE (\(0.007532\)) is nearly \(2\times\) Layer 8’s (\(0.003638\)), and despite Layer 9’s higher standalone GAP-head accuracy (\(53.00\%\) vs.Layer 8’s \(47.20\%\)), its elevated noise variance destabilizes exit decisions—degrading end-to-end accuracy by up to \(3.63\)%p across \(\tau\in[0.40, 0.48]\) (§6.4). We therefore exclude any candidate with \[\mathrm{INR}(L) \;<\; \kappa\cdot\overline{\mathrm{INR}}_{\mathcal{L}_{\text{exit}}},\qquad \kappa = 0.5,\] generalizing Layer 9’s exclusion to a principled INR-driven rule. We further apply LRA-EE exclusively to the vision encoder (\(>\)90% of FLOPs), retaining the text encoder in FP16 to preserve the cross-modal semantic anchor.
5 Experiments↩︎
5.1 Experimental Setup↩︎
5.1.0.1 Dataset and Backbone.
We evaluate on the ImageNet-1K validation set (50,000 images, 1,000 classes); layer-wise analyses use the canonical 10,000-image subset [18].
Zero-shot inference adopts a 5-template prompt ensemble (e.g., “a photo of a {}”, “a clear photo of a {}”). The base model is CLIP ViT-B/32 (12 transformer blocks). Quantization uses dynamic INT8 post-training quantization on Linear-layer weights of the
vision encoder via torch.ao.quantization.quantize_dynamic; the text encoder is retained in FP16 to preserve textual semantic anchors.
5.1.0.2 LRA-EE Configuration.
The exit candidate set \(\mathcal{L}_{\text{exit}} = \{8, 10, 11\}\) is determined by the Pathological Layer Pruning rule of §4.5. The SSA head is a two-layer MLP (\(768 \to 768 \to 512\), GELU), trained for 3 epochs on a 10% subset of the ImageNet-1K training split (128,117 images) with Adam (\(\text{lr}=5\times 10^{-4}\), batch size 64). Supervision combines cross-entropy on ground-truth labels with a cosine-embedding loss against the FP32 model’s text-aligned embedding—an objective we call FP32-distilled supervision. Because this introduces a potential confound between distillation and routing as sources of accuracy gain, we explicitly disentangle the two in §6.1. The learned gate is a single linear projection (\(3 \to 1\)) followed by a sigmoid, trained via BCE (\(\text{lr}=10^{-2}\)) on a held-out 5,000-image gating split disjoint from the evaluation set. Layer-specific thresholds \(\tau_L\) are selected via a 25-point grid sweep over \(\tau \in [0.20, 0.92]\). All experiments run on a single RTX 3090.
5.1.0.3 Reporting.
Top-1 accuracy and FLOPs saving are our principal metrics, with FLOPs reduction computed as \(1 - \mathbb{E}_x[L_{\text{exit}}(x)]/L_{\max}\) weighted by the per-block compute proportion of the ViT-B/32 vision encoder. We report mean \(\pm\) standard deviation across three independent runs with unconstrained seeds.
5.2 Main Results↩︎
| Method | FLOPs Saving (%) | Top-1 Acc.(%) | \(\Delta\) Acc.(%p) |
|---|---|---|---|
| Baseline (INT8 full-depth) | 0.0 | 58.72 | — |
| LRA-EE (Initial layer-wise) | 10.0 | 61.11 | +2.39 |
| LRA-EE (Layer 8 Optimized) | 13.38 \(\pm\) 0.11 | 61.16 \(\pm\) 0.06 | +2.44 |
Table 1 reports our principal results. The Initial LRA-EE configuration, trained without per-layer threshold tuning, achieves \(10.0\%\) FLOPs saving at \(61.11\%\) Top-1 (\(+2.39\)%p over the INT8 baseline). The Layer-8-Optimized variant (§5.3) extends FLOPs saving to \(13.38\%\) while marginally improving accuracy to \(61.16\%\). When combined with SmoothQuant [8], which addresses outlier-induced quantization error at the source, LRA-EE yields the strongest configuration at \(62.41\%\) Top-1 (\(+3.69\)%p over the INT8 baseline) with \(13.4\%\) FLOPs saving, indicating that the two methods address complementary components of the failure mode.
| Method | FLOPs Saving (%) | Top-1 Acc.(%) | \(\Delta\) Acc.(%p) |
|---|---|---|---|
| Baseline (INT8 full-depth) | 0.00 | 58.72 | — |
| CLS-EE [17] | 0.00 | 58.72 | +0.00 |
| PABEE [21] | 3.64 | 61.82 | +3.10 |
| AdaViT [27] | 13.50 | 59.84 | +1.12 |
| LRA-EE (Ours) | 13.38 | 61.16 | +2.44 |
Against Early Exit and adaptive-inference baselines (Table 2), CLS-EE produces no meaningful early exits, confirming the immaturity of
[CLS] tokens at shallow depths. PABEE achieves higher accuracy at a conservative operating point but only \(3.64\%\) FLOPs saving. AdaViT, re-trained with the INT8 backbone held frozen and evaluated under
matched FLOPs, achieves \(59.84\%\), outperforming the full-depth INT8 baseline but trailing LRA-EE by \(1.32\)%p. This suggests that token-level pruning alone does not address the
depth-wise noise accumulation that LRA-EE is designed to evade. LRA-EE therefore improves the accuracy–efficiency trade-off: it achieves substantially larger FLOPs saving than PABEE, while maintaining a clear accuracy advantage over matched-FLOPs adaptive
inference.
5.2.0.1 Variance and reproducibility.
The reported standard deviation reflects three independent runs with re-seeded (i) SSA head initialization and data shuffling, and (ii) gate initialization and gating-split sampling; backbone weights and the evaluation split are held fixed. FLOPs saving exhibits \(\sigma = 0.11\)%p and Top-1 accuracy \(\sigma = 0.06\)%p—the small variance reflecting the modest gate size (4 scalar parameters per layer) and the fact that backbone weights and the evaluation split remain fixed across runs.
5.3 Pareto-Frontier Analysis and Layer 8 Optimization↩︎
Figure 2 (a) traces the FLOPs–accuracy Pareto frontier across per-layer threshold settings: rather than the monotonic trade-off of conventional EE, LRA-EE ascends in both axes simultaneously across a wide threshold regime before degrading at extreme settings. The per-layer exit distribution (Figure 2 (b)) places \(10.1\%\) of samples at Layer 8, \(25.3\%\) at Layer 10, \(32.1\%\) at Layer 11, and \(32.5\%\) at full depth—reflecting the layer-adaptive policy (\(\tau_8 = 0.44\) captures easy samples shallowly, Layers 10–11 handle the intermediate regime). The resulting \(13.38\%\) FLOPs saving with marginal accuracy gain foreshadows the Rescue Effect formalized in §7.
6 Ablation Studies↩︎
| # | Configuration | Head | Supervision | Routing | FLOPs Save (%) | Top-1 Acc.(%) |
|---|---|---|---|---|---|---|
| (i) | INT8 baseline | [CLS] | — | full depth | 0.0 | 58.72 |
| (ii) | SSA-Last (hard) | SSA | hard label | full depth | 0.0 | 59.18 |
| (iii) | SSA-Last (distilled) | SSA | FP32 distill | full depth | 0.0 | 59.65 |
| (iv) | LRA-EE (hard) | SSA | hard label | adaptive | 13.38 | 60.42 |
| (v) | LRA-EE (Ours) | SSA | FP32 distill | adaptive | 13.38 | 61.16 |
6.1 Decomposing the Source of Accuracy Gain↩︎
To resolve whether the \(+2.44\)%p gain in §5.2 originates from EE’s noise-shielding mechanism or from the SSA head’s exposure to FP32 supervision, we cross-classify two design axes the main configuration entangles: head supervision (hard label vs.FP32 distillation) and routing policy (full-depth vs.LRA-EE adaptive), yielding five configurations (Table 3). All share the identical INT8 backbone, gate architecture, threshold sweep, and evaluation pipeline; configurations (ii)–(iii) attach the SSA head to the final layer only (no EE), while (iv)–(v) deploy full LRA-EE routing across \(\mathcal{L}_{\text{exit}} = \{8, 10, 11\}\).
The decomposition yields three additive contrasts. The architectural contribution—variance reduction of patch-token averaging (§4.2)—is \((ii)-(i) = +0.46\)%p; the distillation contribution is \((iii)-(ii) = +0.47\)%p, comparable in magnitude to the architectural gain but substantially smaller than the routing contribution; and the Early-Exit contribution dominates: \((iv)-(ii) = +1.24\)%p in the hard-label regime and \((v)-(iii) = +1.51\)%p in the distilled regime, accounting for roughly half the total gain on its own.
The most diagnostic comparison is \((iv)\) vs.\((i)\): a \(+1.70\)%p gain without any FP32 supervision, achieved by EE routing alone on top of an SSA head trained with hard labels. This rules out the alternative hypothesis that LRA-EE’s gain reduces to “a distilled GAP head at the final layer” and confirms that the Rescue Effect is intrinsic to depth-adaptive routing under quantization. Distillation amplifies the effect—likely by cleaning up per-layer decision boundaries—but is not its source.
6.2 [CLS] Token versus Spatio-Semantic Aggregation↩︎
Holding all other components fixed (backbone, gate, thresholds), SSA exceeds the corresponding [CLS] accuracy by \(+18\) to \(+24\)%p across all candidate layers, with the
largest gap at the shallowest viable exit (Layer 8: \(21.73\% \to 45.60\%\), \(+23.87\)%p; Layer 10: \(+18.41\)%p; Layer 11: \(+22.01\)%p). The [CLS] head’s \(21.73\%\) at Layer 8 renders shallow exit prohibitive in any single-token formulation. This ablation operationalizes the variance-reduction property
of §4.2: aggregating \(N{=}196\) patch tokens enacts a \(\sqrt{N}\)-fold concentration that the singleton [CLS] cannot achieve. Notably, SSA at
Layer 11 (\(61.40\%\)) by itself exceeds the INT8 full-depth baseline (\(58.72\%\)), indicating the spatial aggregator is itself a non-trivial source of robustness to deep-layer
quantization noise.
6.3 Heuristic versus Learned Gating↩︎
A naive confidence-only heuristic (\(c_L > \tau\)) peaks at \(60.28\%\) accuracy with \(4.7\%\) FLOPs saving, falling short of LRA-EE’s \(61.07\%\) at \(9.9\%\) saving (Figure 3). The Pareto gap widens at higher FLOPs saving regimes, confirming that confidence alone is an insufficient surrogate for representation quality under quantization. The learned gate’s incorporation of margin and SAV yields a multi-dimensional view that better discriminates noise-corrupted from genuinely refined samples—an advantage intensifying precisely at aggressive operating points.
6.4 Pathological Layer Diagnosis↩︎
Figure 4 consolidates three measurements justifying Layer 9’s exclusion: (a) activation outlier spike (\(\sim 1.6\times\) Layer 8’s maximum, signaling outlier-sensitive weight distributions that amplify quantization error disproportionately); (b) semantic drift (INT8–FP32 cosine similarity drops from \(0.9313\) at Layer 8 to \(0.9301\) at Layer 9 and \(0.9254\) at Layer 10, with Layer 9’s spike coinciding with severe exit instability); (c) routing instability (including Layer 9 in \(\mathcal{L}_{\rm exit}\) degrades end-to-end accuracy by up to \(3.63\)%p at \(\tau=0.44\)). Together these confirm that accuracy and stability are decoupled in quantized regimes: Layer 9 fails the INR criterion despite passing a naive accuracy threshold—a layer-selection principle extending beyond the specific architecture studied here.
7 Anatomy of the Rescue Effect↩︎
That a quantized model gains accuracy when computing less demands mechanistic dissection. We term this the Rescue Effect and decompose it through three analyses: a four-quadrant outcome decomposition, gate-selectivity validation, and a geometric interpretation in cosine-direction space.
7.1 Four-Quadrant Outcome Decomposition↩︎
For each of the \(10{,}000\) validation samples, we record the correctness of the LRA-EE prediction \(C_{\text{EE}}(x)\in\{0,1\}\) and the full-depth INT8 prediction \(C_{\text{full}}(x)\in\{0,1\}\), yielding four mutually exclusive quadrants (Table 4).
| Outcome | # Samples | Proportion (%) |
|---|---|---|
| Both correct (EE \(✔\), Full \(✔\)) | 5,162 | 51.6 |
| Rescue (EE \(✔\), Full \(\times\)) | 947 | 9.5 |
| Loss (EE \(\times\), Full \(✔\)) | 710 | 7.1 |
| Both incorrect (EE \(\times\), Full \(\times\)) | 3,181 | 31.8 |
| Net Gain (Rescue \(-\) Loss) | +237 | +2.37 (%p) |
The diagonal cells (\(83.4\%\)) are indifferent to the exit policy; the off-diagonal cells expose the paradox. The Rescue cell (\(947\) samples) captures cases where full-depth inference is overcome by accumulated noise that perturbs the embedding off-axis, while the early-exit prediction terminates before noise dominance and retains correct cosine alignment; the Loss cell (\(710\)) captures the inverse—deep-layer refinement net of noise would have corrected an erroneous shallow prediction, but the gate prematurely committed. We formalize this as the Rescue Margin: \[\Delta_{\text{Rescue}} \;=\; \mathbb{E}_x\!\left[\mathbb{1}\{C_{\text{EE}}{=}1, C_{\text{full}}{=}0\}\right] \;-\; \mathbb{E}_x\!\left[\mathbb{1}\{C_{\text{EE}}{=}0, C_{\text{full}}{=}1\}\right]. \label{eq:rescue}\tag{4}\] For our setup, \(\Delta_{\text{Rescue}} = +2.37\%\text{p}\) (\(947 - 710\)), close to the headline \(+2.44\)%p gain (Table 1); the small gap reflects subset choice, run averaging, and rounding. Class-level analysis further supports the cosine-drift interpretation: visually ambiguous categories such as canoe and admiral concentrate the rescued samples, consistent with their embeddings lying closest to angular decision boundaries.
7.2 Gate Selectivity Validation↩︎
Under the diagnostic operating point for the rescue analysis, the gate’s selectivity is unambiguous: early-exited samples (\(75.7\%\)) achieve \(68.81\%\) accuracy versus \(37.00\%\) for the full-inference group (\(24.3\%\))—a \(31.81\)%p gap that rules out random selection. The full-inference group’s below-baseline accuracy (\(37.00\%\) vs.\(58.72\%\)) is consistent with the Rescue Effect’s mechanism: these are the most ambiguous samples, for which neither shallow nor deep inference excels.
7.3 Mechanistic Interpretation: Cosine-Direction Drift↩︎
In CLIP, classification reduces to cosine similarity between an image embedding and \(1{,}000\) class-prompt embeddings. Each transformer block applies a residual update \[z_{L+1} \;=\; z_L \;+\; f_L(z_L) \;+\; \epsilon_L^{\text{quant}}, \label{eq:11}\tag{5}\] with \(\epsilon_L^{\text{quant}}\) the per-block quantization residual. Over \(12\) blocks, residuals accumulate as \(\sum_{L}\epsilon_L^{\text{quant}}\), a random walk whose direction may diverge from the semantic update \(\sum f_L\). For samples whose initial cosine alignment is large but marginal—near the angular decision boundary between top-1 and top-2 classes—even small angular drift suffices to flip the prediction. Early Exit truncates this walk at a depth where the signal-to-drift ratio remains favorable; the \(947\) rescued samples are those whose cosine geometry is most fragile to deep-layer drift. The asymmetry \(\text{Rescue} > \text{Loss}\) follows directly: \(\mathcal{N}(L)\)’s super-linear growth (§3.1) ensures that beyond the crossover point, additional computation is on average destructive—an interior maximum of \(\mathcal{Q}(L)\) (§4.1) that LRA-EE locates sample-adaptively. The asymmetry thus reflects a structural property of the quantized model rather than a sampling artifact: beyond the crossover depth, the noise term of equation 5 dominates the semantic update on average, and no static threshold can replicate this sample-adaptive localization.
8 Conclusion↩︎
LRA-EE bypasses Quantization-Induced Representation Collapse in CLIP via Spatio-Semantic Aggregation, Layer-adaptive Confidence Thresholding, and Pathological Layer Pruning. It trims \(13.38\%\) of FLOPs while lifting Top-1 accuracy by \(+2.44\)%p, a result traced to the Rescue Effect, wherein depth-adaptive routing preserves cosine alignment for samples most fragile to accumulated quantization noise. The factorial ablation confirms that this gain is intrinsic to adaptive routing and not an artifact of FP32 distillation.
References↩︎
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