Hierarchical Self-Supervised Compensation (HSSC)

• Hierarchical Self-Supervised Compensation (HSSC) is a framework that uses self-supervised signals and hierarchical bias to recover missing or degraded information in representations.
• It is implemented in applications such as UniMRSeg for multi-modal segmentation, HIER for medication recommendation, and point-cloud processing with hierarchical self-distillation.
• The multi-stage design of HSSC, progressing from recovery to alignment and correction, demonstrates enhanced robustness and performance in diverse domains.

to=functions.arxiv_search เงินไทยฟรี 大发pk্রমាន { "^^^^^^^^5query5 "^^^^^^^^5\5 Self-Supervised Compensation^^^^^^^^5\5 OR ^^^^^^^^5\5 self-distillation^^^^^^^^5\5 OR ^^^^^^^^5\5 hierarchical representation^^^^^^^^5\5 OR ^^^^^^^^5\5 Emergence Exploitation^^^^^^^^5\5 "max_results": ^^^^5\5query5^^^^, "sort_by": "relevance" } to=functions.arxiv_search аанацҳауеит 红鼎ત્ન { "^^^^^^^^5query5 "(&&&^^^^5query5^^^^&&&) OR (&&&^^^^5\5^^^^&&&) OR (&&&^^^^5 OR \5^^^^&&&) OR (&&&^^^^5 OR \5^^^^&&&) OR (&&&^^^^5 OR \5^^^^&&&)", "max_results": ^^^^5\5query5^^^^, "sort_by": "relevance" } Hierarchical Self-Supervised Compensation (HSSC) denotes a class of hierarchy-aware learning strategies in which self-supervised signals are used to compensate for information that would otherwise be missing, flattened, corrupted, or weakly expressed in the base representation. In its explicit form, HSSC is the organizing principle of UniMRSeg, where a unified modality-relax segmentation network hierarchically bridges the representation gap between complete and incomplete modalities at the input, feature, and output levels (&&&^^^^5 OR \5^^^^&&&). Closely related formulations appear in medication recommendation, point-cloud understanding, generic self-supervised representation learning, and music structure modeling, where the same underlying pattern reappears: a model introduces hierarchical inductive bias and self-supervised regularization to recover structural information that standard embeddings, incomplete observations, or flat objectives do not preserve (&&&^^^^5query5^^^^&&&, &&&^^^^5\5^^^^&&&, &&&^^^^5 OR \5^^^^&&&, &&&^^^^5 OR \5^^^^&&&). This suggests that HSSC is best understood not only as a named method, but also as a broader methodological template for hierarchy-aware self-supervised correction.

^^^^5\5^^^^. Terminological scope and conceptual definition

The term Hierarchical Self-Supervised Compensation is used explicitly by UniMRSeg, which describes a unified segmentation framework that “hierarchically bridges representation gaps between complete and incomplete modalities across input, feature and output levels” (&&&^^^^5 OR \5^^^^&&&). In that formulation, “compensation” refers to progressive correction of missing-modality degradation rather than to a single auxiliary loss or a single reconstruction block.

Several other works are closely aligned in mechanism even when they do not use the same name. HIER for medication recommendation is described as a self-supervised hierarchical encoder that compensates for structural information lost by conventional one-hot code embeddings, replacing flat diagnosis/procedure representations with hierarchy-aware ones derived from ICD code trees (&&&^^^^5query5^^^^&&&). The point-cloud framework for scattered inputs does not use the term HSSC either, but its upstream masked completion branch functions as a compensation module, while hierarchical self-distillation regularizes the downstream hierarchy so that reconstructed geometry becomes semantically useful for classification and segmentation (&&&^^^^5\5^^^^&&&). HEX similarly presents a compensation mechanism for a limitation in standard self-supervised learning: it adds hierarchy-aware regularization to address not only global dimensional collapse but also local hierarchical dimensional collapse that emerges within semantic groups during training (&&&^^^^5 OR \5^^^^&&&). By contrast, self-supervised hierarchical metrical structure modeling in music is related in spirit but “not a compensation model in that explicit sense”; its hierarchical mechanism is CRF-based structured self-supervision rather than a dedicated compensation module (&&&^^^^5 OR \5^^^^&&&).

Work	Compensation target	Hierarchical mechanism
UniMRSeg	Incomplete/corrupted modalities	Input-, feature-, and output-level compensation
HIER	Flat ICD code embeddings	Parent-child aggregation and position encoding
Joint point-cloud learning with HSD	Scattered/incomplete point clouds	Completion branch plus teacher-student hierarchy
HEX	Local hierarchical collapse in SSL	Adaptive decomposition of InfoNCE negatives
Hierarchical metrical modeling	Weakly supervised rhythmic hierarchy	Multi-layer CRF with binary regularity

A common misconception is that HSSC necessarily denotes one fixed architecture. The available literature instead supports a narrower factual claim and a broader plausible interpretation. Factually, the explicit term is attached to UniMRSeg (&&&^^^^5 OR \5^^^^&&&). A plausible implication is that the term can also serve as an umbrella description for methods that use self-supervised hierarchical structure to compensate for representational deficits of different kinds.

^^^^5 OR \5^^^^. Canonical formulation in UniMRSeg

UniMRSeg provides the clearest explicit instantiation of HSSC. It addresses multi-modal image segmentation under incomplete or corrupted modalities, where existing approaches often rely on specialized per-combination models and model-modality matching. Its stated alternative is a single unified model based on a ^^^^5 OR \5^^^^D U-Net-style encoder-decoder with a ^^^^5 OR \5^^^^D ASPP module in high-level features, trained in three stages (&&&^^^^5 OR \5^^^^&&&).

The first stage is Multi-granular Modality Reconstruction. Complete multi-modal inputs are perturbed by random modality dropout, random modality shuffle, and spatial masking. Some modalities are randomly removed with 5^^^^5query5^^^^% probability, while ensuring at least one modality remains. The remaining modalities are randomly permuted, and portions of the input are spatially masked. The reconstruction targets are normalized slices from the original complete modalities, supervised by a combination of L^^^^5\5^^^^ and SSIM. According to the paper, this stage forces the model to infer missing modality structure, learn cross-modal dependencies, and become robust to arbitrary modality-channel order (&&&^^^^5 OR \5^^^^&&&).

The second stage is modality-invariant contrastive learning. The model processes complete samples and their missing-modality counterparts, obtains multi-level encoder features, performs global average pooling, and applies NT-Xent loss at five encoder levels. Positive pairs are the complete and incomplete views of the same sample; negative pairs come from different samples. Dice supervision is retained so that the learned feature space remains segmentation-relevant rather than purely generic. This stage is designed to “implicitly compensate the feature space distance among incomplete-complete modality pairs” (&&&^^^^5 OR \5^^^^&&&).

The third stage is incomplete-modality adaptive fine-tuning. The encoder is frozen and augmented with a lightweight reverse attention adapter that explicitly compensates for weak perceptual semantics in incomplete-modality features. Feature-level and prediction-level consistency constraints then force the compensated incomplete representations and outputs to match the corresponding complete-modality ones. The paper summarizes the residual-compensation intention as

PRESERVED_PLACEHOLDER_^^^^5query5^^^^

with corrupted typesetting, but the intended meaning is explicit: the adapter learns a residual correction from incomplete to complete feature quality (&&&^^^^5 OR \5^^^^&&&).

The two consistency constraints are given as

PRESERVED_PLACEHOLDER_^^^^5\5^^^^

and

PRESERVED_PLACEHOLDER_^^^^5 OR \5^^^^

In the MRI experiments, the number of valid incomplete-modality combinations is reported as PRESERVED_PLACEHOLDER_^^^^5 OR \5^^^^ (&&&^^^^5 OR \5^^^^&&&).

The hierarchy in UniMRSeg is therefore operational rather than merely taxonomic: the model first reconstructs, then aligns, then corrects. The paper explicitly argues against collapsing these elements into a single-stage objective, reporting that the single-stage model failed to converge, plateaued early, and had fluctuating losses. In this formulation, HSSC is a staged curriculum from low-level recovery to high-level consistency (&&&^^^^5 OR \5^^^^&&&).

^^^^5 OR \5^^^^. Hierarchy restoration in medication recommendation

HIER, introduced for medication recommendation, is a self-supervised hierarchical encoder that can be read as a compensation mechanism for the loss of structural information caused by one-hot diagnosis and procedure embeddings (&&&^^^^5query5^^^^&&&). The method is motivated by the fact that diagnoses and procedures in EHRs are sparse and numerous, while standard ICD coding systems already provide an explicit taxonomy from general to specific codes. Existing medication recommenders, according to the paper, model patient-medication associations but do not adequately capture structural relations among diagnoses and procedures.

The encoder has two components: Relation Embedding and Position Encoding. Relation embedding recursively aggregates a code with its parent in the ICD tree,

PRESERVED_PLACEHOLDER_^^^^5 OR \5^^^^

and after $K$ layers yields

$$\mathbf{r}_v \gets \mathbf{e}_v^{K},\forall v \in \mathcal{V}.$$

This produces a representation that encodes the neighbor hierarchical structure of the code (&&&^^^^5query5^^^^&&&).

The self-supervised training objective is intended to make a code closer to its parent than to a randomly selected code: $$\mathcal{L} = -\frac{1}{N} \sum_{n=1}^{N} \left[ \log(\mathbf{r}_v \cdot \mathbf{r}_{p(v)}) + \log(\mathbf{r}_v \cdot \mathbf{r}_{rand}) \right].$$ The paper describes the intent in words rather than through an external label signal: preserve hierarchical proximity in the embedding space by learning from parent-child neighborhoods (&&&^^^^5query5^^^^&&&).

Position encoding introduces the code’s global hierarchical position. The code is decomposed into segmented digits, transformed into one-hot form, concatenated into a multi-hot vector, then projected by a linear layer followed by ReLU: $$\mathbf{s}_v = \sigma(Linear(\text{PE}_v)), \qquad \mathbf{z}_v \gets \mathbf{r}_v + \mathbf{s}_v.$$ The paper notes that ReLU keeps the projected position encoding positive, which avoids conflicts when pooling codes later. Relation embedding captures local tree structure; position encoding captures global location in the ICD hierarchy (&&&^^^^5query5^^^^&&&).

HIER is designed as a plug-in module that replaces the diagnosis/procedure embedding layer while leaving the downstream recommender unchanged. It is integrated into RETAIN, GAMENet, SafeDrug, and MoleRec, and evaluated on MIMIC-III and MIMIC-IV with an 8:^^^^5\5^^^^:^^^^5\5 train/validation/test split. The implementation uses PyHealth, runs on Ubuntu ^^^^5 OR \5 OR \5^^^^.^^^^5query5 OR \5^^^^ with an NVIDIA RTX ^^^^5 OR \5query5query5query5^^^^, searches the learning rate over $\{10^{-3}, 10^{-4}, 10^{-5}\}$, and trains for ^^^^5 OR \55^^^^ epochs. Reported evaluation metrics are Jaccard Similarity Score, F^^^^5\5^^^^-score, PRAUC, and DDI rate (&&&^^^^5query5^^^^&&&).

The main empirical pattern is consistent improvement in recommendation accuracy. On MIMIC-III, adding HIER to GAMENet improves Jaccard by 5.66%, F^^^^5\5^^^^ by ^^^^5 OR \5^^^^.8^^^^5 OR \5^^^^%, and PRAUC by ^^^^5 OR \5^^^^.7^^^^5 OR \5^^^^%. An ablation on MIMIC-III with SafeDrug shows that both components matter: w/o E/P gives Jaccard ^^^^5query5^^^^.^^^^5 OR \55 OR \5\5^^^^, F^^^^5\5^^^^ ^^^^5query5^^^^.6^^^^5\5 OR \5 OR \5^^^^, PRAUC ^^^^5query5^^^^.7^^^^5\5sort_by5 OR \5^^^^, DDI ^^^^5query5^^^^.^^^^5query5sort_by5\5query5; w/ E gives ^^^^5query5^^^^.^^^^5 OR \5^^^^668 / ^^^^5query5^^^^.6^^^^5 OR \5 OR \55^^^^ / ^^^^5query5^^^^.7^^^^5 OR \5 OR \5^^^^6 / ^^^^5query5^^^^.^^^^5query5; w/ P gives ^^^^5query5^^^^.^^^^5 OR \5sort_by5\5^^^^7 / ^^^^5query5^^^^.6^^^^5 OR \5query5 OR \5^^^^ / ^^^^5query5^^^^.7^^^^5 OR \5^^^^68 / ^^^^5query5^^^^.^^^^5query5sort_by5 OR \5^^^^7; and Ours gives ^^^^5query5^^^^.^^^^5 OR \5sort_by5 OR \55^^^^ / ^^^^5query5^^^^.6^^^^5 OR \5\5 OR \5^^^^ / ^^^^5query5^^^^.7^^^^5 OR \5query55^^^^ / ^^^^5query5^^^^.^^^^5query5 OR \5^^^^ (&&&^^^^5query5^^^^&&&). The paper attributes the relative strength of position encoding alone to its ability to encode global hierarchical position. In HSSC terms, HIER is a direct example of hierarchy-aware self-supervised compensation for flattened symbolic identifiers.

^^^^5 OR \5^^^^. Joint compensation and hierarchical self-distillation for point clouds

The point-cloud framework of “Joint Learning for Scattered Point Cloud Understanding with Hierarchical Self-Distillation” is described as an end-to-end system that compensates incomplete or scattered point clouds and simultaneously identifies them through a hierarchy-aware downstream network (&&&^^^^5\5^^^^&&&). The paper does not use the name HSSC, but it is described as conceptually very close: the upstream completion branch is the compensation module, and the downstream hierarchical self-distillation mechanism makes that compensation semantically effective.

The overall cascade is

PRESERVED_PLACEHOLDER_^^^^5\5query5^^^^

where PRESERVED_PLACEHOLDER_^^^^5\5\5^^^^ is a masked autoencoder-like completion model and PRESERVED_PLACEHOLDER_^^^^5\5 OR \5^^^^ is a hierarchy-based recognition or segmentation network (&&&^^^^5\5^^^^&&&). To generate scattered inputs, the method uses farthest point sampling (FPS) to choose sparse patch centroids and kNN to gather local neighborhoods. The compensation objective is a bidirectional Chamfer distance,

PRESERVED_PLACEHOLDER_^^^^5\5 OR \5^^^^

which reconstructs the incomplete point cloud into a completed shape PRESERVED_PLACEHOLDER_^^^^5\5 OR \5^^^^ for downstream use (&&&^^^^5\5^^^^&&&).

The distinctive element is hierarchical self-distillation (HSD). Multiple classification heads are attached to features from different scales. The deepest classifier, with the largest perceptual field of local kernels and the longest code length, acts as the teacher; the intermediate classifiers act as students. The paper states that the goal is not merely to aggregate multi-scale features, but to let the deepest classifier “provide additional regularization to intermediate ones” (&&&^^^^5\5^^^^&&&).

The information-theoretic HSD objective is written as

PRESERVED_PLACEHOLDER_^^^^5\55^^^^

and the full joint objective as

PRESERVED_PLACEHOLDER_^^^^5\5^^^^6

with PRESERVED_PLACEHOLDER_^^^^5\5^^^^7, PRESERVED_PLACEHOLDER_^^^^5\5^^^^8, and PRESERVED_PLACEHOLDER_^^^^5\5^^^^9. The paper also notes that deeply supervised nets are a special case when PRESERVED_PLACEHOLDER_^^^^5 OR \5query5^^^^, at which point the teacher-student term vanishes (&&&^^^^5\5^^^^&&&).

This distinction matters. Classic deep supervision independently constrains multiple scales; HSD adds explicit teacher-student coupling across scales through PRESERVED_PLACEHOLDER_^^^^5 OR \5\5^^^^. The paper argues that this is especially useful for irregular, sparse, or partially observed point clouds because shallow scales may overfit to noisy local cues, whereas the deepest scale contains more global semantic structure (&&&^^^^5\5^^^^&&&).

Empirically, the framework is evaluated on ModelNet^^^^5 OR \5query5^^^^, ScanObjectNN, and ShapeNetPart. For incomplete/scattered ModelNet^^^^5 OR \5query5^^^^, the best reported table entries are Our PRESERVED_PLACEHOLDER_^^^^5 OR \5 OR \5^^^^ (PointNet++-HSD) with 9^^^^5query5^^^^.8 OA / 87.7 mAcc / ^^^^5 OR \5 OR \5^^^^.^^^^5\5query5^^^^ CD for PRESERVED_PLACEHOLDER_^^^^5 OR \5 OR \5^^^^, 89.9 / 86.6 / ^^^^5 OR \5^^^^7.79 for PRESERVED_PLACEHOLDER_^^^^5 OR \5 OR \5^^^^, and 8^^^^5 OR \5^^^^.9 / 76.9 / ^^^^5 OR \5^^^^9.^^^^5\5query5^^^^ for PRESERVED_PLACEHOLDER_^^^^5 OR \55^^^^. On ScanObjectNN PB_T5^^^^5query5^^^^_RS with background, PointMLP-HSD reaches 8^^^^5 OR \5^^^^.7 OA / 8^^^^5query5^^^^.8 mAcc / ^^^^5\5^^^^6.^^^^5 OR \55^^^^ CD. On ShapeNetPart, PointMLP-HSD obtains 8^^^^5 OR \5^^^^.5 mIoU / 8^^^^5query5^^^^.^^^^5 OR \5^^^^ cIOU / ^^^^5 OR \5 OR \5^^^^.^^^^5\5 OR \5^^^^ CD (&&&^^^^5\5^^^^&&&). These results support the paper’s claim that compensation and hierarchical distillation should not be separated into purely geometric reconstruction on one side and purely semantic recognition on the other.

5. Related self-supervised hierarchical regularization in SSL and music

HEX extends the compensation idea to generic self-supervised representation learning. Its starting point is that standard SSL methods typically combine an invariance term with a regularization term to prevent global dimensional collapse, but do not account for the local collapse that emerges within hierarchical semantic clusters during training (&&&^^^^5 OR \5^^^^&&&). The paper argues that samples from the same higher-level semantic group exhibit stronger local collapse than the batch as a whole, and therefore require additional hierarchy-aware regularization.

To address this, HEX modifies the InfoNCE denominator by decomposing negatives into hierarchical negatives PRESERVED_PLACEHOLDER_^^^^5 OR \5^^^^6 and regular negatives. The thresholded criterion for determining whether a sample belongs to the hierarchical subset is

PRESERVED_PLACEHOLDER_^^^^5 OR \5^^^^7

with the adaptive threshold

PRESERVED_PLACEHOLDER_^^^^5 OR \5^^^^8

This threshold is computed from the cosine similarity distribution in the batch and is said to decrease over training as hierarchical structure emerges more clearly (&&&^^^^5 OR \5^^^^&&&). The method is presented as framework-agnostic and is integrated into SimCLR, NNCLR, All^^^^5 OR \5^^^^One, VicReg, and Barlow Twins. Reported representative gains include SimCLR on CIFAR-^^^^5\5query5query5^^^^: 6^^^^5 OR \5^^^^.^^^^5 OR \5^^^^6 ^^^^^^^^5\5 67.56, NNCLR on CIFAR-^^^^5\5query5query5^^^^: 7^^^^5query5^^^^.7^^^^5 OR \5^^^^ ^^^^^^^^5\5 7^^^^5\5^^^^.55, SimCLR on ImageNet-^^^^5\5query5query5^^^^: 8^^^^5query5^^^^.^^^^5 OR \5query5^^^^ ^^^^^^^^5\5 8^^^^5\5^^^^.78, and NNCLR on full ImageNet linear evaluation: 6^^^^5 OR \5^^^^.^^^^5 OR \5^^^^7 ^^^^^^^^5\5 65.96. The abstract states up to 5.6% relative improvement on ImageNet with ^^^^5\5query5query5^^^^ epochs of training (&&&^^^^5 OR \5^^^^&&&). In HSSC terms, HEX compensates for a mismatch between the geometry assumed by standard SSL objectives and the hierarchical geometry that actually emerges during training.

Self-supervised hierarchical metrical structure modeling in music provides a contrasting case. The method predicts an 8-layer hierarchical metrical tree from beat to section level using a Temporal Convolutional Network (TCN) and a CRF over latent hierarchical states, trained without hierarchical metrical labels except for beats used for quantization and alignment (&&&^^^^5 OR \5^^^^&&&). For symbolic multi-track input, track outputs are combined via a softmax-weighted average,

PRESERVED_PLACEHOLDER_^^^^5 OR \5^^^^9

The key inductive bias is binary metrical regularity, namely that a level-PRESERVED_PLACEHOLDER_^^^^5 OR \5query5^^^^ unit should contain exactly ^^^^5 OR \5^^^^ level-PRESERVED_PLACEHOLDER_^^^^5 OR \5\5^^^^ units. The model uses an unsupervised CRF loss and, for multi-track MIDI, a consistency loss that encourages aligned tracks to share the same latent hierarchical state sequence (&&&^^^^5 OR \5^^^^&&&).

The paper is explicit that this is “closer to hierarchical structured self-supervision than to a dedicated compensation network.” That distinction is important. The model is highly relevant to the self-supervised and hierarchical parts of HSSC, but it does not define compensation as an explicit corrective module. It also illustrates a second misconception: self-supervised does not necessarily mean fully label-free. Training uses beat labels only, and ^^^^5\5^^^^ annotated song is required for post-training global offset calibration (&&&^^^^5 OR \5^^^^&&&).

6. Empirical patterns, limitations, and interpretive boundaries

Across these works, several recurring empirical patterns are directly supported by the reported results. First, hierarchy-aware self-supervision is repeatedly used as a plug-in or add-on mechanism rather than as a full replacement for the downstream task model. HIER replaces the diagnosis/procedure embedding layer while preserving the rest of each recommender backbone (&&&^^^^5query5^^^^&&&). HEX is designed as a framework-agnostic addition to multiple SSL families (&&&^^^^5 OR \5^^^^&&&). The point-cloud framework allows replacement of the upstream completion module, and the authors report that replacing SnowflakeNet with PMP-Net++ improves the downstream joint model further (&&&^^^^5\5^^^^&&&). UniMRSeg likewise emphasizes unified parameter sharing rather than an ensemble of per-modality subset models (&&&^^^^5 OR \5^^^^&&&).

Second, the hierarchical signal can be either explicit or emergent. In HIER, the hierarchy is explicit in the ICD taxonomy (&&&^^^^5query5^^^^&&&). In the music model, the hierarchy is enforced by binary metrical regularity and CRF transitions (&&&^^^^5 OR \5^^^^&&&). In UniMRSeg, the hierarchy is architectural and staged across input, feature, and output levels (&&&^^^^5 OR \5^^^^&&&). In HEX, by contrast, the hierarchy is not given by labels during training but emerges in the representation space and is detected through the cosine-similarity distribution (&&&^^^^5 OR \5^^^^&&&). This suggests that HSSC is not tied to a particular source of hierarchy.

Third, the compensated quantity differs by domain. UniMRSeg compensates incomplete modalities; HIER compensates representational flatness; the point-cloud framework compensates geometric incompleteness; HEX compensates local hierarchical collapse; and the music model compensates, in a weaker and more indirect sense, for the absence of hierarchical labels through structured inductive bias (&&&^^^^5 OR \5^^^^&&&, &&&^^^^5query5^^^^&&&, &&&^^^^5\5^^^^&&&, &&&^^^^5 OR \5^^^^&&&, &&&^^^^5 OR \5^^^^&&&). A plausible implication is that “compensation” in HSSC is best interpreted functionally: the method supplies information that the original representation, observation process, or loss function does not adequately encode.

The limitations are equally domain-specific. UniMRSeg reports that single-stage optimization of reconstruction, contrastive learning, segmentation, and adapter correction failed to converge and plateaued early, motivating its strict three-stage design (&&&^^^^5 OR \5^^^^&&&). HIER improves accuracy consistently, but the DDI rate is not its explicit training target and therefore does not always decrease (&&&^^^^5query5^^^^&&&). The point-cloud method requires point-order alignment for segmentation because metrics such as per-point accuracy and mIoU need correspondence to ground truth (&&&^^^^5\5^^^^&&&). The music model assumes binary metrical regularity, ignores non-binary meters such as ^^^^5 OR \5^^^^/^^^^5 OR \5^^^^ or 6/8, performs poorly at the highest hypermetric layer, and requires beat labels plus post hoc calibration (&&&^^^^5 OR \5^^^^&&&). HEX is sensitive to the threshold schedule, and its ablations show that the threshold mechanism is central rather than incidental (&&&^^^^5 OR \5^^^^&&&).

The literature therefore supports a disciplined interpretation. HSSC is a precise named framework in UniMRSeg and a strong conceptual analogue in several other recent methods. What unifies these methods is not a shared backbone, but a recurring design principle: self-supervised objectives are organized hierarchically so that they compensate for missing structure, degraded observations, or objective mismatch that flat supervision or flat representations leave unresolved.