Post-Inference Normalization

• Post-inference normalization is a late-stage intervention that adjusts model outputs, scores, or activations to match target evaluation metrics.
• It is applied across various domains—from face recognition to transformers—by recalibrating raw scores or representations at inference time.
• This strategy improves fairness, stability, and hardware efficiency by addressing distribution shifts and aligning local and global decision criteria.

to=arxiv_search.search +天天中彩票{"^^^^^^^^15query15 normalization^^^^^^^^15\15 OR ^^^^^^^^15\15 normalization^^^^^^^^15\15 CLIP OR ^^^^^^^^15\15 score normalization^^^^^^^^15\15 face recognition OR ^^^^^^^^15\15 normalization^^^^^^^^15\15 transformers OR ^^^^^^^^15\15 example weighing^^^^^^^^15\15 batch normalization15^^^^^^^^"," to=arxiv_search.search 天天爱彩票提现json{"^^^^^^^^15query15 Mitigation of Demographic Bias in Face Recognition Using Fair Score Normalization^^^^^^^^15\15 OR all:^^^^^^^^15\15 Distribution Normalization for Contrastively Learned Vision-LLMs^^^^^^^^15\15 OR all:^^^^^^^^15\15 Normalization for Accelerating and Stabilizing Transformers^^^^^^^^15\15 OR all:^^^^^^^^15\15 Things Everyone Should Know to Improve Batch Normalization^^^^^^^^15\15 Post-inference normalization denotes a family of interventions that modify representations, scores, activations, or decoded outputs after the core model has produced them, or that restrict normalization to inference and evaluation rather than retraining. In the literature, it appears as post-comparison score shifting in face recognition, test-time distribution correction for contrastive vision–LLMs, inference-statistics blending in Batch Normalization, offline fuse-able normalization in Transformers, algebraic deferral of Softmax and LayerNorm in LLM kernels, evaluation-time homophone mapping in machine translation, post-processing of pretrained word embeddings, and posterior recalibration under a new prior in Bayesian inference (&&&^^^^15query15^^^^&&&, &&&^^^^15\15^^^^&&&, &&&^^^^15 OR \15^^^^&&&, &&&^^^^15 CLIP OR \15^^^^&&&, &&&^^^^15 face recognition OR \15^^^^&&&, &&&^^^^15 transformers OR \15^^^^&&&, &&&^^^^15 batch normalization15^^^^&&&, &&&^^^^15max_results15^^^^&&&). This suggests that the term is domain-dependent rather than a single canonical algorithm.

^^^^15\15^^^^. Scope and formal insertion points

The common structural feature is a late intervention point. In face recognition, normalization is inserted after raw similarity computation and before thresholding, so that the decision changes from PRESERVED_PLACEHOLDER_^^^^15query15^^^^ to PRESERVED_PLACEHOLDER_^^^^15\15^^^^ with PRESERVED_PLACEHOLDER_^^^^15 OR \15^^^^. In CLIP-like models, the raw dot product PRESERVED_PLACEHOLDER_^^^^15 CLIP OR \15^^^^ is replaced at test time by a mean-adjusted score. In Transformer inference, a normalization layer with fixed statistics can be fused into an adjacent linear map, or the normalization denominator can be deferred until after the linear layer. In machine translation, normalization can be applied only to the decoded hypothesis and reference before scoring. In Bayesian inference, an already computed posterior under a convenient prior can be transformed into a target posterior under a new prior without rerunning full data-dependent inference (&&&^^^^15query15^^^^&&&, &&&^^^^15\15^^^^&&&, &&&^^^^15 CLIP OR \15^^^^&&&, &&&^^^^15 transformers OR \15^^^^&&&, &&&^^^^15max_results15^^^^&&&).

These insertion points are not interchangeable. Some methods alter only the final score geometry, some restore training-time distributional information at test time, some are exact algebraic reorderings for hardware efficiency, and some are metric-side transformations. The literature therefore uses “post-inference normalization” for interventions that are unified more by timing than by mechanism.

^^^^15 OR \15^^^^. Post-comparison normalization in biometric decision systems

In face recognition, post-inference normalization is formalized most explicitly as a post-comparison transformation of similarity scores. The pipeline is face detection/alignment PRESERVED_PLACEHOLDER_^^^^15 face recognition OR \15^^^^ embedding extraction PRESERVED_PLACEHOLDER_^^^^15 transformers OR \15^^^^ PRESERVED_PLACEHOLDER_^^^^15 batch normalization15^^^^ similarity computation PRESERVED_PLACEHOLDER_^^^^15max_results15^^^^ PRESERVED_PLACEHOLDER_^^^^15sort_by15^^^^ decision PRESERVED_PLACEHOLDER_^^^^15relevance15^^^^, and the normalization block is inserted after the similarity score and before thresholding. In the reported experiments, the raw comparator is cosine similarity,

PRESERVED_PLACEHOLDER_^^^^15\15query15^^^^

The proposed method clusters the embedding space by k-means, forms cluster-specific genuine and impostor score sets, estimates a local threshold PRESERVED_PLACEHOLDER_^^^^15\15\15^^^^ for each cluster at target false match rate PRESERVED_PLACEHOLDER_^^^^15\15 OR \15^^^^, and compares these thresholds to a global threshold PRESERVED_PLACEHOLDER_^^^^15\15 CLIP OR \15^^^^. For a pair PRESERVED_PLACEHOLDER_^^^^15\15 face recognition OR \15^^^^, with cluster-specific thresholds PRESERVED_PLACEHOLDER_^^^^15\15 transformers OR \15^^^^ and PRESERVED_PLACEHOLDER_^^^^15\15 batch normalization15^^^^, the normalized score is

PRESERVED_PLACEHOLDER_^^^^15\15max_results15^^^^

followed by the global decision rule PRESERVED_PLACEHOLDER_^^^^15\15sort_by15^^^^ (&&&^^^^15query15^^^^&&&).

The stated rationale is individual fairness: “treat similar individuals similarly.” Similarity is operationalized by proximity in embedding space via k-means clustering, and local thresholds are intended to ensure that nearby embeddings face similar decision conditions without using demographic labels. This differs from z-norm, t-norm, s-norm, and as-norm, which standardize scores by mean and variance statistics rather than aligning local operating thresholds to a global operating point.

Empirically, the method was evaluated on Adience, ColorFeret, and Morph under subject-disjoint ^^^^15 transformers OR \15^^^^-fold cross-validation with FaceNet and VGGFace embeddings and cosine similarity. Reported results include bias reduction of up to ^^^^15sort_by15 OR \15^^^^.^^^^15max_results15^^^^% for gender on Adience with FaceNet at PRESERVED_PLACEHOLDER_^^^^15\15relevance15^^^^, ethnic-bias reduction by ^^^^15\15max_results15^^^^.^^^^15 face recognition OR \15^^^^–^^^^15 CLIP OR \15 OR \15^^^^.^^^^15sort_by15^^^^% in several settings, overall FNMR improvements of up to ^^^^15 transformers OR \15 CLIP OR \15^^^^.^^^^15 OR \15^^^^% at PRESERVED_PLACEHOLDER_^^^^15 OR \15query15^^^^ on Morph with FaceNet, and up to ^^^^15sort_by15 OR \15^^^^.^^^^15relevance15^^^^% at PRESERVED_PLACEHOLDER_^^^^15 OR \15\15^^^^ on Morph with VGGFace. The method also adapts subgroup performance asymmetrically: underperforming classes can improve strongly, while overperforming classes are “gently adjusted for fairness.” Sensitivity analysis reported stable behavior around PRESERVED_PLACEHOLDER_^^^^15 OR \15 OR \15^^^^, with degradation at very large PRESERVED_PLACEHOLDER_^^^^15 OR \15 CLIP OR \15^^^^ due to unreliable threshold estimates in small clusters (&&&^^^^15query15^^^^&&&).

^^^^15 CLIP OR \15^^^^. Distributional normalization of representations and similarities

A second line of work treats post-inference normalization as a correction to the representation geometry used at test time. For contrastively trained vision–LLMs, the central claim is that ordinary test-time dot-product scoring is only a zeroth-order approximation to the InfoNCE objective, because it ignores the negative-sample distribution present during training. Distribution Normalization (DN) approximates the mean image and text representations of the unlabeled test pool, PRESERVED_PLACEHOLDER_^^^^15 OR \15 face recognition OR \15^^^^ and PRESERVED_PLACEHOLDER_^^^^15 OR \15 transformers OR \15^^^^, and uses the first-order similarity

PRESERVED_PLACEHOLDER_^^^^15 OR \15 batch normalization15^^^^

This is training-free, requires no fine-tuning, and is used for retrieval, zero-shot classification, and caption evaluation. The paper also defines a robustness variant,

PRESERVED_PLACEHOLDER_^^^^15 OR \15max_results15^^^^

The reported gains include approximately ^^^^15\15^^^^.^^^^15\15 average top-^^^^15\15^^^^ recall improvement in cross-modal retrieval across CLIP, TCL, and ALBEF, average +^^^^15 face recognition OR \15^^^^.^^^^15 face recognition OR \15^^^^% Acc@^^^^15\15^^^^ across six zero-shot classification datasets, and caption-evaluation improvements such as Flickr^^^^15sort_by15^^^^k-Expert PRESERVED_PLACEHOLDER_^^^^15 OR \15sort_by15^^^^ increasing from ^^^^15 transformers OR \15\15^^^^.^^^^15 face recognition OR \15^^^^ to ^^^^15 transformers OR \15 face recognition OR \15^^^^.^^^^15 CLIP OR \15^^^^. Using ^^^^15\15query15query15^^^^ unlabeled samples for mean estimation caused at most a ^^^^15query15^^^^.^^^^15 OR \15^^^^% accuracy drop relative to the full test-set mean, with an average drop of ^^^^15query15^^^^.^^^^15query15relevance15 (&&&^^^^15\15^^^^&&&).

A related post-processing usage appears in pretrained word embeddings. Variance Normalization (PVN) mean-centers embeddings, performs PCA, and shrinks the leading PRESERVED_PLACEHOLDER_^^^^15 OR \15relevance15^^^^ principal components so that their post-processed standard deviation equals PRESERVED_PLACEHOLDER_^^^^15 CLIP OR \15query15^^^^ rather than removing them outright:

PRESERVED_PLACEHOLDER_^^^^15 CLIP OR \15\15^^^^

Dynamic Embedding (PDE) complements this by learning an orthogonal dynamic subspace from ordered contexts. The integrated PVN+PDE representation improved SGNS on multiple benchmarks, including WS-^^^^15 CLIP OR \15 transformers OR \15 CLIP OR \15^^^^ from ^^^^15 batch normalization15 transformers OR \15^^^^.^^^^15max_results15^^^^ to ^^^^15 batch normalization15relevance15^^^^.^^^^15query15^^^^, Verb-^^^^15\15 face recognition OR \15 CLIP OR \15^^^^ from ^^^^15 CLIP OR \15 transformers OR \15^^^^.^^^^15query15^^^^ to ^^^^15 face recognition OR \15 face recognition OR \15^^^^.^^^^15\15^^^^, Google analogy from ^^^^15 transformers OR \15relevance15^^^^.^^^^15 batch normalization15^^^^ to ^^^^15 batch normalization15 OR \15^^^^.^^^^15sort_by15^^^^, and MSR from ^^^^15 transformers OR \15\15^^^^.^^^^15query15^^^^ to ^^^^15 transformers OR \15 CLIP OR \15^^^^.^^^^15max_results15^^^^. PVN alone improved the weighted-average word-similarity score from ^^^^15 face recognition OR \15max_results15^^^^.^^^^15sort_by15^^^^ to ^^^^15 transformers OR \15query15^^^^.^^^^15 CLIP OR \15^^^^ and IMDb accuracy from ^^^^15sort_by15query15^^^^.^^^^15relevance15 OR \15^^^^ to ^^^^15sort_by15 batch normalization15^^^^.^^^^15query15 CLIP OR \15^^^^ in the SGNS setting (&&&^^^^15 batch normalization15^^^^&&&).

These two examples share the idea that a pretrained similarity space can be made more faithful to the optimization geometry or the latent structure of the data by a post hoc transform. They differ, however, in their statistics: DN uses test-pool first moments to approximate negatives, whereas PVN reshapes the principal-component variance profile of a static vocabulary-wide embedding cloud.

^^^^15 face recognition OR \15^^^^. Inference statistics, batch independence, and hardware-oriented fusion

Several works reinterpret post-inference normalization as a correction to inference-time statistics or as a way to remove runtime statistics altogether. In Batch Normalization, standard inference uses frozen moving averages, whereas training uses statistics that include the current example. “Inference Example Weighing” corrects this discrepancy by blending current-example moments with stored running moments:

PRESERVED_PLACEHOLDER_^^^^15 CLIP OR \15 OR \15^^^^

The resulting normalization is purely an inference-time change and requires no retraining. Reported results include up to ^^^^15query15^^^^.^^^^15 batch normalization15^^^^% top-^^^^15\15^^^^ and ^^^^15query15^^^^.^^^^15\15 batch normalization15^^^^% top-^^^^15 transformers OR \15^^^^ improvement on ImageNet with ResNet-^^^^15\15 transformers OR \15 OR \15^^^^, and a CIFAR-^^^^15\15query15query15^^^^ non-i.i.d. batch result of ^^^^15 face recognition OR \15query15^^^^.^^^^15\15^^^^% accuracy with standard BN versus ^^^^15 batch normalization15 OR \15^^^^.^^^^15 OR \15^^^^% with Inference Example Weighing; Ghost BN plus PRESERVED_PLACEHOLDER_^^^^15 CLIP OR \15 CLIP OR \15^^^^ reached up to ^^^^15max_results15 OR \15^^^^.^^^^15 OR \15^^^^% (&&&^^^^15 OR \15^^^^&&&).

Proxy Normalization addresses a different issue: the failure modes of batch-independent normalization. It normalizes post-activations using proxy statistics derived from a per-channel Gaussian random variable,

PRESERVED_PLACEHOLDER_^^^^15 CLIP OR \15 face recognition OR \15^^^^

typically with PRESERVED_PLACEHOLDER_^^^^15 CLIP OR \15 transformers OR \15^^^^. Combined with Layer Normalization or Group Normalization, it emulates Batch Normalization without batch dependence. On ImageNet, GN+PN matched or exceeded BN across several architectures; for example, RN^^^^15 transformers OR \15query15^^^^ yielded BN ^^^^15max_results15 batch normalization15^^^^.^^^^15 CLIP OR \15^^^^/^^^^15max_results15 transformers OR \15^^^^.^^^^15sort_by15^^^^ and GN+PN ^^^^15max_results15 batch normalization15^^^^.^^^^15 CLIP OR \15^^^^/^^^^15max_results15 batch normalization15^^^^.^^^^15max_results15^^^^, while EN-B^^^^15 OR \15^^^^ with group convolution yielded BN ^^^^15max_results15relevance15^^^^.^^^^15 transformers OR \15^^^^/^^^^15max_results15relevance15^^^^. and GN+PN ^^^^15max_results15relevance15^^^^.^^^^15 CLIP OR \15^^^^/^^^^15sort_by15query15^^^^. (&&&^^^^15\15sort_by15^^^^&&&).

In Transformers, Unified Normalization removes per-token inference statistics by fixing normalization statistics offline and fusing the normalizer into adjacent linear layers. With inference-time statistics PRESERVED_PLACEHOLDER_^^^^15 CLIP OR \15 batch normalization15^^^^, the normalized affine can be absorbed into the next projection by

PRESERVED_PLACEHOLDER_^^^^15 CLIP OR \15max_results15^^^^

UN uses only second-moment statistics in the forward pass, geometric-mean smoothing of recent variances, arithmetic averaging plus momentum in the backward pass, and an adaptive outlier filtration rule. On GPU inference, Swin-T on ImageNet-^^^^15\15^^^^K showed ^^^^15\15max_results15^^^^.^^^^15max_results15 memory reduction and ^^^^15 CLIP OR \15\15^^^^.^^^^15 OR \15^^^^% throughput improvement, and Mask R-CNN on COCO showed ^^^^15 batch normalization15^^^^.^^^^15\15^^^^% memory reduction and ^^^^15 OR \15 face recognition OR \15^^^^.^^^^15 OR \15^^^^% throughput improvement, while maintaining near-LN performance (&&&^^^^15 CLIP OR \15^^^^&&&).

A hardware-oriented variant, also called Post-Inference Normalization, defers collective normalization until after the following linear layer when the normalization factor is a per-row or per-sample scalar. For attention,

PRESERVED_PLACEHOLDER_^^^^15 CLIP OR \15sort_by15^^^^

so the numerator-times-values and the denominator can be computed in parallel, followed by a cheap row-wise division. For LayerNorm,

PRESERVED_PLACEHOLDER_^^^^15 CLIP OR \15relevance15^^^^

which enables concurrent execution of the matmul and the reductions for PRESERVED_PLACEHOLDER_^^^^15 face recognition OR \15query15^^^^ and PRESERVED_PLACEHOLDER_^^^^15 face recognition OR \15\15^^^^. On the d-Matrix Corsair AI accelerator, this reordering yielded approximately ^^^^15 OR \15query15^^^^% end-to-end latency reduction in autoregressive inference on Llama ^^^^15 OR \15^^^^/^^^^15 CLIP OR \15^^^^ families, with no accuracy degradation (&&&^^^^15 face recognition OR \15^^^^&&&).

^^^^15 transformers OR \15^^^^. The limits of forward-only normalization

Not all inference-only normalization improves learning. In excitatory–inhibitory networks trained on Fashion-MNIST with per-sample luminance shifts, inhibition-mediated normalization of forward activations alone did not improve learning performance. The paper defines this setting as “normalization applied only during inference” in the sense that inhibitory computations normalize excitatory activity in the forward pass but are detached from the task loss, so the back-propagated error is unchanged. The central claim is that the gains associated with LayerNorm arise primarily because normalization reshapes the error signals during backpropagation rather than merely stabilizing activations (&&&^^^^15 OR \15\15^^^^&&&).

The LayerNorm gradient transform is

PRESERVED_PLACEHOLDER_^^^^15 face recognition OR \15 OR \15^^^^

and the paper calls its explicit use “GradNorm.” Adding GradNorm to inhibitory normalization restored the benefits seen with standard LayerNorm. Moreover, centering alone was the critical component: accuracy with centering only was statistically indistinguishable from LN at PRESERVED_PLACEHOLDER_^^^^15 face recognition OR \15 CLIP OR \15^^^^ and PRESERVED_PLACEHOLDER_^^^^15 face recognition OR \15 face recognition OR \15^^^^ under Mann–Whitney PRESERVED_PLACEHOLDER_^^^^15 face recognition OR \15 transformers OR \15^^^^ tests with PRESERVED_PLACEHOLDER_^^^^15 face recognition OR \15 batch normalization15^^^^ and PRESERVED_PLACEHOLDER_^^^^15 face recognition OR \15max_results15^^^^, and a lateral inhibitory mean-centering mechanism performed comparably to explicit centering and full GradNorm. This section of the literature therefore argues against a common misconception: a forward-pass normalization applied only at inference, or during training without affecting the backward pass, does not by itself inherit the optimization benefits of LayerNorm (&&&^^^^15 OR \15\15^^^^&&&).

^^^^15 batch normalization15^^^^. Output-space and posterior-space post-processing

In machine translation for Ge’ez-script languages, post-inference normalization is an evaluation-time mapping applied to the model prediction and the reference, not to the training data. Let PRESERVED_PLACEHOLDER_^^^^15 face recognition OR \15sort_by15^^^^ be a language-specific homophone map. After decoding, the hypothesis and reference are transformed as PRESERVED_PLACEHOLDER_^^^^15 face recognition OR \15relevance15^^^^ and PRESERVED_PLACEHOLDER_^^^^15 transformers OR \15query15^^^^, punctuation is removed, and BLEU and ChrF are computed on the normalized strings. The motivation is that homophone normalization at training time imposes an implicit standard and can harm orthographic coverage and cross-lingual transfer, whereas post-inference normalization preserves the original training distribution while reducing purely orthographic mismatches in automatic evaluation. Reported gains include +^^^^15query15^^^^.^^^^15 OR \15 face recognition OR \15^^^^ BLEU and +^^^^15query15^^^^.^^^^15 OR \15relevance15^^^^ ChrF for an Amharic Transformer, +^^^^15query15^^^^.^^^^15 batch normalization15relevance15^^^^ BLEU and +^^^^15query15^^^^.^^^^15 batch normalization15 CLIP OR \15^^^^ ChrF for NLLB-^^^^15 batch normalization15query15query15^^^^M with HSL-style post-inference normalization, and up to +^^^^15\15^^^^.^^^^15query15 CLIP OR \15^^^^ BLEU when applied to an external baseline trained without normalization. The paper also states that normalization should remain evaluation-only or user-optional, because in Tigrinya and Ge’ez the same character collapses can alter meaning or reduce readability (&&&^^^^15 transformers OR \15^^^^&&&).

A probabilistic analogue appears in Bayesian inference under the name “prior swapping.” If PRESERVED_PLACEHOLDER_^^^^15 transformers OR \15\15^^^^ is the posterior under a convenient false prior PRESERVED_PLACEHOLDER_^^^^15 transformers OR \15 OR \15^^^^ and PRESERVED_PLACEHOLDER_^^^^15 transformers OR \15 CLIP OR \15^^^^ is a target prior, then

PRESERVED_PLACEHOLDER_^^^^15 transformers OR \15 face recognition OR \15^^^^

The paper defines a prior-swap density

PRESERVED_PLACEHOLDER_^^^^15 transformers OR \15 transformers OR \15^^^^

where PRESERVED_PLACEHOLDER_^^^^15 transformers OR \15 batch normalization15^^^^ is an exact or approximate false-posterior density available at PRESERVED_PLACEHOLDER_^^^^15 transformers OR \15max_results15^^^^ evaluation cost with respect to data size. Sampling from PRESERVED_PLACEHOLDER_^^^^15 transformers OR \15sort_by15^^^^ yields exact target-posterior samples when PRESERVED_PLACEHOLDER_^^^^15 transformers OR \15relevance15^^^^, and approximate samples otherwise; semiparametric corrections are then used to recover consistency. The paper’s central negative result is that naive importance sampling from the false posterior often fails when the target prior is heavier-tailed or otherwise dissimilar, whereas prior swapping provides bounded-ratio finite-variance guarantees for the proposed proxy family and a mean-square consistency rate of order PRESERVED_PLACEHOLDER_^^^^15 batch normalization15query15^^^^ for the semiparametric correction (&&&^^^^15max_results15^^^^&&&).

^^^^15max_results15^^^^. Cross-cutting properties and limitations

Taken together, these papers suggest that post-inference normalization is most effective when the extra statistics can be estimated cheaply and are aligned with the quantity that actually governs downstream behavior. In face recognition, that quantity is the local decision threshold rather than the raw cosine score distribution. In CLIP-like models, it is the negative-sample context missing from dot-product inference. In BatchNorm and Transformer normalization, it is the mismatch between training-time and inference-time statistics, or the hardware cost of recomputing them online. In Ge’ez-script MT, it is the mismatch between orthographic variation and exact-string evaluation. In prior swapping, it is the discrepancy between a convenient inference prior and the prior of actual interest (&&&^^^^15query15^^^^&&&, &&&^^^^15\15^^^^&&&, &&&^^^^15 OR \15^^^^&&&, &&&^^^^15 CLIP OR \15^^^^&&&, &&&^^^^15 transformers OR \15^^^^&&&, &&&^^^^15max_results15^^^^&&&).

The literature is equally explicit about failure modes. Cluster-wise fair score normalization requires enough genuine and impostor scores per cluster, and very large PRESERVED_PLACEHOLDER_^^^^15 batch normalization15\15^^^^ can produce unreliable thresholds; one reported failure case involved ColorFeret VGGFace with unequal cluster sizes. DN can be unstable under severe distribution shift, which motivated DN*. Inference Example Weighing requires validation-time tuning of PRESERVED_PLACEHOLDER_^^^^15 batch normalization15 OR \15^^^^, and overly large PRESERVED_PLACEHOLDER_^^^^15 batch normalization15 CLIP OR \15^^^^ can overfit noisy current-example statistics. UN requires adaptive outlier filtration for stable Transformer training, and the hardware deferral of Softmax or LayerNorm is valid only when the normalization factor commutes with the following linear map. Aggressive homophone normalization such as HSL can collapse meaningful distinctions. Forward-only normalization without gradient transformation may stabilize activations but leave learning unchanged. Prior swapping requires support overlap between target and false priors and inherits the usual high-dimensional difficulty of semiparametric correction (&&&^^^^15query15^^^^&&&, &&&^^^^15\15^^^^&&&, &&&^^^^15 OR \15^^^^&&&, &&&^^^^15 CLIP OR \15^^^^&&&, &&&^^^^15 face recognition OR \15^^^^&&&, &&&^^^^15 transformers OR \15^^^^&&&, &&&^^^^15 OR \15\15^^^^&&&, &&&^^^^15max_results15^^^^&&&).

A final distinction is between exact and approximate post-inference normalization. Some methods are exact algebraic reorderings, such as the deferral of Softmax and LayerNorm after a linear layer. Some are exact inference-time substitutions with fixed statistics, as in fused offline normalization. Others are explicitly approximate but principled: DN is presented as a first-order approximation to InfoNCE, PVN as targeted variance shrinkage rather than whitening, and prior swapping as exact only when the false posterior is known exactly. This suggests that “post-inference normalization” is best understood not as a single normalization family, but as a general design strategy: postpone normalization to the latest stage at which sufficient local, population, or structural information is available, provided that the postponement preserves the intended objective, decision rule, or semantics.