Paper deep dive
When Generated Images Look Right and Retrieve Wrong: Coverage-Guided Cross-Scale Re-Indexing for Knowledge-Faithful Generative Perception
Guangyuan Dong, Chuang Liu, Yangchen Zeng, Haoyu Wang, Xiaoyang Yu, Pinlong Zhao, Yuchao Hou, Ziwei Li, Zheng Lin
Intelligence
Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 92%
Last extracted: 8/24/2026, 5:23:48 AM
Summary
The paper introduces CERES, a closed-loop multimodal indexing framework designed to prevent 'semantic collapse' in generative perception tasks, particularly pansharpening. Semantic collapse occurs when generated images have high pixel fidelity but fail to preserve scale-specific concepts required for retrieval. CERES builds a three-level semantic pyramid (global, meso, local) using explicit centroids and implicit co-occurrence mining, routes these concepts to a U-Net generator via cross-scale attention, and verifies coverage by re-indexing the output with a frozen VLM (SigLIP-2) using a soft-Jaccard loss. It achieves state-of-the-art results on pansharpening benchmarks and significantly improves concept-query retrieval metrics.
Entities (10)
Relation Signals (9)
SigLIP 2 → isfrozenduring → CERES training
confidence 95% · SigLIP-2 is frozen throughout; gradients flow only through G_theta
CERES → uses → SigLIP 2
confidence 95% · re-encodes the generated image with the same frozen SigLIP-2
CERES → evaluatedon → Pansharpening
confidence 94% · On four pansharpening benchmarks across seven settings
CERES → optimizeswith → Soft-Jaccard Loss
confidence 93% · A continuously differentiable soft-Jaccard coverage objective returns dense gradients
CERES → uses → U-Net++
confidence 92% · performs scale-routed cross-attention into a lightweight U-Net generator
CERES → improves → concept-query retrieval
confidence 91% · improves concept-query retrieval Recall@5 by +14.0 points
CERES → verifiescoveragewith → DinoV2
confidence 90% · coverage is verified by an independent DINOv2 linear probe
DinoV2 → trainedon → AID
confidence 85% · collect prototypes from AID... to train DINOv2 linear probe
DinoV2 → trainedon →
Cypher Suggestions (0)
No Cypher suggestions yet.
Abstract
Abstract:Multimodal information systems increasingly route generated visual content back through the same vision-language index that informed its production, so the output must remain retrievable by the queries it was meant to serve. When the scene contains entities at vastly different scales, existing language-guided generators condition on a single, globally pooled text embedding and quietly drop scale-specific concepts, breaking concept-query retrieval even when pixel fidelity is high. We formalise this failure as semantic collapse and propose CERES, a closed-loop multimodal indexing framework that builds a three-level semantic pyramid, mines implicit concepts via a co-occurrence-aware router, performs scale-routed cross-attention into a lightweight U-Net generator, and verifies coverage by re-indexing the generated image with the same frozen VLM. A continuously differentiable soft-Jaccard coverage objective returns dense gradients to the 0.39M-parameter generator under explicit non-degeneracy conditions, and coverage is verified by an independent DINOv2 linear probe trained only on external scene and object labels. On four pansharpening benchmarks across seven settings, CERES delivers the new state of the art with the largest gains where scale variation is most extreme. It also improves concept-query retrieval Recall@5 by +14.0 points and image-text mean reciprocal rank by 0.19 over the strongest baseline, showing that the closed loop preserves queryable content rather than self-referential feature consistency.
Tags
Links
- Source: https://arxiv.org/abs/2608.20810v1
- Canonical: https://arxiv.org/abs/2608.20810v1
Trouble viewing inline? Open PDF directly →
Full Text
91,068 characters extracted from source content.
Expand or collapse full text
When Generated Images Look Right and Retrieve Wrong: Coverage-Guided Cross-Scale Re-Indexing for Knowledge-Faithful Generative Perception Guangyuan Dong Chuang Liu Yangchen Zeng Haoyu Wang Affiliation: National University of Singapore Wuhan University ByteDance Xiaoyang Yu Pinlong Zhao Yuchao Hou Affiliation: Nankai University JD Research, JD.com, Inc. Affiliation: Zhejiang University Independent Researcher Affiliation: Equal contribution. Corresponding authors. Affiliation: Equal contribution. Corresponding authors. Ziwei Li Zheng Lin Affiliation: King Abdullah University of Science and Technology The University of Hong Kong Affiliation: Equal contribution. Corresponding authors. Abstract Multimodal information systems increasingly route generated visual content back through the same vision–language index that informed its production, so the output must remain retrievable by the queries it was meant to serve. When the scene contains entities at vastly different scales, existing language-guided generators condition on a single, globally pooled text embedding and quietly drop scale-specific concepts, breaking concept-query retrieval even when pixel fidelity is high. We formalise this failure as semantic collapse and propose CERES, a closed-loop multimodal indexing framework that builds a three-level semantic pyramid, mines implicit concepts via a co-occurrence-aware router, performs scale-routed cross-attention into a lightweight U-Net generator, and verifies coverage by re-indexing the generated image with the same frozen VLM. A continuously differentiable soft-Jaccard coverage objective returns dense gradients to the 0.39 M-parameter generator under explicit non-degeneracy conditions, and coverage is verified by an independent DINOv2 linear probe trained only on external scene and object labels. On four pansharpening benchmarks across seven settings, CERES delivers the new state of the art with the largest gains where scale variation is most extreme (+4.64+4.64% relative Q2n and +9.7+9.7 mAP for DOTA detection). It also improves concept-query retrieval Recall@5 by +14.0+14.0 points and image-text mean reciprocal rank by 0.190.19 over the strongest baseline, showing that the closed loop preserves queryable content rather than self-referential feature consistency. 1 Introduction Multimodal information systems are increasingly tasked with managing generative content. Catalog re-indexing, content-aware remote sensing, medical imaging archives, and personalised digital twins must not merely retrieve an image; they must generate a higher-resolution, semantically faithful reconstruction and then re-insert it into the same knowledge index that triggered the generation (23; 40; 27). Vision–language models (VLMs) (37; 59; 43) have become the de-facto index in this loop and also serve as cross-modal retrievers (21; 10; 61; 19) and differentiable priors for image restoration (7; 30; 39). The question we ask is concrete: after a VLM-guided generator emits an image, can the same VLM still answer the local, meso, and global queries that the index was meant to support? If not, the generator has degraded the knowledge system regardless of pixel-level fidelity. Existing VLM-conditioned generators index a scene through a single, globally pooled embedding even when the scene is hierarchically composed of multi-scale entities (39; 62). A satellite image of an airport simultaneously contains tiny aircraft (∼5 5 m), elongated runways (∼100 100 m), and the overall terminal–runway–road layout (∼1 1 km). A whole-slide pathology image nests cell nuclei, glandular structures, and tumour–stroma boundaries. Collapsing this multi-granular index into one caption forces the generator to over-attend to the macroscopic mode and silently dispose of microscopic entities, even when pixel-level fidelity remains high. Following the cross-modal retrieval literature on coverage maximisation (21; 27; 46), we call this failure semantic collapse. Figure 1 formalises the coverage measurement that exposes the gap and the concept-query probe that turns it into a measurable queryability test. Repairing semantic collapse requires three ingredients that no prior system provides simultaneously. First, a multi-granular index must replace the single global embedding so that local and meso-scale concepts are explicitly represented. Second, the generator must route concepts of different scales to decoder layers operating at corresponding spatial resolutions. Third, the system must verify that the generated content can still be re-indexed and re-queried by the same VLM, returning continuous gradients that penalise lost concepts. This closed-loop, retrieval-style consistency check goes beyond the open-loop conditioning used in modern diffusion or restoration models (40; 3; 30). A purely pixel-level objective cannot supply this signal because the metric itself is blind to the indexed concept set (45; 1). CERES addresses all three ingredients (Figure 2). Stage I constructs a three-level semantic pyramid via two complementary branches: an explicit branch with soft, differentiable membership over K learned concept centroids, and an implicit branch that mines relational concepts (e.g. “harbour = water + docks + vessels”) through a co-occurrence-aware semantic router. Discovered units are merged by an IoU-guided aggregator and filtered by an adaptive Gaussian density gate. Stage I routes each unit to a decoder layer indexed by its scale tag and injects it through cross-scale attention and FiLM-style modulation (36; 35). Stage I re-encodes the generated image with the same frozen SigLIP-2 (43). Stage IV measures coverage via a soft-Jaccard differentiable operator and returns scale-invariant gradients to the 0.39 M trainable generator. To prevent the optimisation target from contaminating the evaluation target, we verify coverage with an independent DINOv2 linear probe (34) trained only on external scene-label and object-bounding-box supervision, and we evaluate the generated images under three downstream protocols (zero-shot, linear-probe, trained head) plus a 60-query concept retrieval bank. The theory is deliberately conservative: we state two sufficient-condition propositions, one on a lower-bounded closed-loop gradient (Proposition 1) and one linking semantic coverage to spectral angular distortion (Proposition 2). A non-asymptotic termination lemma supplies an explicit router stopping bound (Lemma 1). The full derivations and counter-examples appear in Appendix B. Figure 1: Multimodal indexing view of semantic collapse. A frozen VLM extracts ()Q(S) from the input (left), the centre panel defines coverage C as the intersection-over-input ratio of two concept sets, and the right panel stacks two reconstructions of the same scene. The baseline drops microscopic concepts (≈0.51C\!≈\!0.51) while CERES preserves both macro and micro indices (≈0.94C\!≈\!0.94). The dashed loop indicates closed-loop coverage verification used by the retrieval evaluation of Sec. 5.4. Contributions. (i) We formalise semantic collapse as a measurable failure of re-indexability and introduce a concept-query retrieval evaluation that treats generated images as queryable knowledge. (i) We present CERES, a closed-loop indexing framework that pairs a soft, differentiable concept index with a soft-Jaccard coverage verifier; the two sufficient-condition propositions serve as sanity checks on the closed-loop design, and Proposition 1 additionally provides a principled motivation for the warm-up schedule. (i) Across four pansharpening benchmarks, three downstream perception modes, a 60-query retrieval bank, and an independent DINOv2 label-grounded coverage probe, CERES delivers state-of-the-art generative fidelity together with the strongest concept-query retrieval and downstream-perception gains. 2 Related Work Multimodal indexing and cross-modal retrieval. Stacked cross attention (21), similarity-graph reasoning (10), and negative-aware attention (61) index visual regions and textual tokens into a shared semantic space. Cross-scale alignment with adaptive semantic aggregation (27) introduces scale-adaptable units through IoU merging, and earlier semantic-concept work (19; 4) mines hierarchical concept indices for retrieval. Recent work further balances semantic capacity across image and text (50), reasons over user context for personalised dense retrieval (20), and preserves visual semantics or latent interests in generative recommendation (55; 56). TRACER uses token reassignment to unlearn target concepts while preserving recommendation utility (5). Counterfactual explanations expose a complementary security risk because they can be exploited to poison recommender systems (6). Adjacent representation-learning methods sharpen partitions through attentional ensemble clustering (13), adaptive hard-negative mining (17), or maximum-margin multiclass objectives (33). Semantic alignment has also been studied under decentralized data constraints through federated analytics for privacy-preserving image classification (18). These methods operate on sparse retrieval tokens or general-purpose representations. We are the first to lift this indexing machinery to dense feature grids and to use the resulting concept set as a closed-loop training signal for image generation. VLMs for low-level dense prediction. DenseCLIP (39) converts image-level matching to pixel–text matching; MaskCLIP (62) extracts dense labels from frozen CLIP; CLIPDenoising (7) exploits CLIP feature invariance; DA-CLIP (30) adapts CLIP for universal restoration. Mechanistic analysis further separates visual-grounding and hallucination pathways in VLMs (25), highlighting that a fluent output need not be supported by visual evidence. All of the dense-prediction methods above condition on a single global embedding and operate in an open-loop regime: language describes the image but does not verify whether the generated content can still be re-indexed. Fine-grained multimodal grounding. Recent work improves VLM spatial reasoning through fine-grained preference optimisation (42), equips MLLMs with latent visual imagery for cognitive reasoning (22), and couples semantic intent to local geometry in 3D understanding and generation (52; 53). Progress-aware vision–language–action policies likewise use object and spatial affordances as anchors for long-horizon control (26), while fine-grained gait analysis shows that subtle local behavioural cues remain difficult for current MLLMs (41). These studies motivate scale- and location-sensitive semantics; our focus is whether such semantics survive image generation and remain retrievable. Knowledge-aware multimodal generation. Prior work injects structured concept knowledge into cross-modal generation through region–phrase matching (19; 4) and concept-graph embeddings (46). Conditional generation uses FiLM (36) and SPADE (35) to modulate dense features by external semantics, and latent diffusion models (40) and instruction-tuned editors (3) extend this to free-form text. Complementary work evaluates generated visual content through spatially and temporally localised human-perceived artifacts (12). None verify that the output is re-indexable by the semantic index that conditioned it. Closed-loop adaptation and memory. Long-horizon systems preserve decision-relevant state through contribution-aware memory (24), optimise intermediate memory quality (28), or attribute evolving memory states (60). Experience-driven agent creation and multi-agent self-evolution similarly reuse execution traces as feedback (15; 16). In RL with verifiable rewards, related work analyses entropy interventions and schedules training queries by reasoning-tree structure (14; 47). These loops update memories, agents, or policies; CERES instead closes the loop over a generated visual artifact while leaving the host VLM index frozen. Generative perception in remote sensing. We exemplify CERES on pansharpening (44; 45; 9; 48), a low-level generation task with extreme intra-/inter-class scale variation. Recent methods include adaptive detail injection (63), transformer fusion (64; 2), spatial–spectral attention (51), content-adaptive non-local convolution (11), diffusion-based work (31; 49), and detail-injection CNNs (54; 8). Heatmap-guided and noise-aware positional embeddings also improve query retrieval for small objects in cluttered imagery (58; 57). These methods optimise pixel-level reconstruction or task-specific detection objectives without an explicit cross-scale concept index for generation. 3 The CERES Framework 3.1 Problem Formulation Let ∈ℝh×w×CX ^h× w× C be a low-resolution multispectral source and ∈ℝrh×rwP ^rh× rw a high-resolution panchromatic source (r=4r=4). A knowledge-aware generative perceiver θ(,)→^G_θ(X,P)\!→\! Y must produce a reconstruction that is pixel-faithful and semantically re-indexable by a frozen ψ=(ψg,ψd,ϕ)ψ=( _g, _d,φ) that comprises the global, dense, and text encoders of SigLIP-2. We model the multi-granular index as a semantic pyramid =g,m,l,=(k,wk,sk)k=1K,S= \T^g,T^m,T^l,U=\(u_k,w_k,s_k)\_k=1^K \, (1) with global/meso/local scene texts and K scale-tagged semantic units. Semantic coverage is =|()∩(^)||()|,∈[0,1].C= |Q(S) ( S)||Q(S)|, ∈[0,1]. (2) Definition 1 (Semantic collapse). θG_θ exhibits semantic collapse on (,)(X,P) if ‖^−‖1≤ϵ\| Y-Y\|_1≤ε yet ≤ηC≤η for some η≪1η 1. Training uses a soft relaxation: each concept k has input score pk=wkp_k=w_k and output score p^k=maxi,j~k(i,j)∈[0,1] p_k= _i,j M_k(i,j)\!∈\![0,1]. The scale tag sks_k defines a routing field over decoder depth: compact high-confidence support yields a local tag, elongated structures yield a meso tag, and broad scene-defining units receive a global tag. 3.2 Closed-Loop Operators CERES chains four operators: →Stage I^→Stage I~→Stage I^.S\! Stage~I\! Y\! Stage~I\! M\! Stage~I\! S. (3) SigLIP-2 is frozen throughout; gradients flow only through θG_θ and the lightweight projection/modulation MLPs (0.39 M trainable parameters). Figure 2: The CERES framework. (a) A frozen SigLIP-2 encoder indexes the pseudo-RGB proxy into a semantic pyramid via two parallel branches. (b) The co-occurrence-aware router greedily selects patches over routing steps r=1:3r=1:3 of a single forward pass, stopping under a decreasing cumulative threshold. (c) A scale-routed U-Net generator injects local, meso, and global units into the ×128128\!×\!128, ×6464\!×\!64, and ×1616\!×\!16 decoder layers through cross-scale attention followed by FiLM modulation. (d) Stage I re-encodes Y with the same frozen VLM. (e) Stage IV computes a soft-Jaccard coverage loss whose gradient is bounded below under explicit non-degeneracy conditions (Proposition 1). Dashed boxes are frozen, solid boxes are trainable. 3.3 Stage I: Cross-Scale Semantic Indexing We project the C-band input to a pseudo-RGB proxy rgb=σ(∗)X_rgb=σ(W\! \!X) via a learnable 1×11×1 projection initialised from each sensor’s spectral response curve, then extract dense features =ψd(rgb)V= _d(X_rgb). Explicit index. We maintain K=200K=200 visual centroids ckV\c_k^V\ obtained by k-means on a held-out training pool. The temperature-controlled soft membership mk(i,j)=exp(cos((i,j),ckV)/τ)∑k′exp(cos((i,j),ck′V)/τ)m_k(i,j)= ( (V(i,j),c_k^V)/τ) _k ( (V(i,j),c_k ^V)/τ) (4) is differentiable in θ via the pseudo-RGB projection. The explicit unit is the soft-weighted feature aggregate kE=∑(i,j)mk(i,j)(i,j)∑(i,j)mk(i,j)+ϵu_k^E= _(i,j)m_k(i,j)V(i,j) _(i,j)m_k(i,j)+ε. Implicit index via co-occurrence routing. Many compound concepts emerge only from spatial co-occurrence. From a seed patch 1iz_1^i we greedily select r+1i=argmax∉riP(∣ri),z_r+1^i= _z _r^iP(z _r^i), (5) where P is read off a co-occurrence table N(⋅)N(·) pre-computed from training tiles within a three-patch radius. Routing stops when P drops below the cumulative threshold ∏j≤rαj _j≤ r _j with α1:3=(0.7,0.5,0.3) _1:3=(0.7,0.5,0.3). For r>3r>3 a second-order Markov factorisation reduces storage from (KR)O(K^R) to (K3)O(K^3) at 0.940.94 unit-Jaccard accuracy versus exact r=3r=3 enumeration (Appendix D). Aggregation and filtering. Position-aware and co-occurrence-aware subsequences are merged by IoU, then filtered by two Gaussian mixtures on scale-balanced and scale-unbalanced pairs. The unit confidence is wk=σ(MLP([cos(k,ϕ(k)),sk,ak,[k∈scene]])),w_k=σ (MLP ([ (u_k,φ(t_k)),s_k,a_k,1[u_k∈scene]] ) ), (6) where [⋅]1[·] is a presence gate that prevents the text–mask loss from rewarding absent concepts. 3.4 Stage I: Scale-Routed Generation The generator θG_θ is a four-level U-Net with resolution pyramid 128→64→32→16128→64→32→16. The scale tag sks_k deterministically routes each unit: sk=1s_k=1 (local) enters the highest-resolution layer, sk=2s_k=2 (meso) intermediate layers, and sk=3s_k=3 (global) the bottleneck. At decoder layer l, ~(l)=(l)+∑kwkAttn((l),ϕ(k)), F^(l)=F^(l)+ _kw_k\,Attn(F^(l),φ(u_k)), (7) followed by FiLM modulation ¯(l)=γ(l)()⊙~(l)+β(l)() F^(l)=γ^(l)(S) F^(l)+β^(l)(S). The pixel reconstruction term is ℒrec=‖^−‖1+η(1−SSIM(^,))L_rec=\| Y-Y\|_1+η(1-SSIM( Y,Y)) with η=0.1η=0.1. Resolution-matched injection prevents global units from dominating high-resolution layers and erasing small queryable entities. 3.5 Stages I & IV: Re-Indexing and Soft Coverage The generated image is re-encoded as ¯h=ψd(^) V_h= _d( Y) and per-unit response maps are Sk(i,j)=¯h(i,j)⊤k,~k=σ((Sk−μk)/τk),S_k(i,j)= V_h(i,j) e_k,\;\; M_k=σ((S_k- _k)/ _k), (8) with k=ϕ(k)/‖ϕ(k)‖e_k=φ(t_k)/\|φ(t_k)\|. The recovered pyramid S is built by encoding mask statistics k=[ρk,nk,c¯k,σk2]s_k=[ _k,n_k, c_k, _k^2] through a fixed family of 1212 typed prompt templates (four per scale; full strings in Appendix E). Soft-Jaccard coverage. With presence scores pk=wkp_k=w_k (input) and p^k p_k (recovered), ℒcov=1−∑kpkp^k∑k(pk+p^k−pkp^k).L_cov=1- _kp_k p_k _k(p_k+ p_k-p_k p_k). (9) Eq. (9) is the continuous Jaccard loss (38; 32) applied at the concept-set level. It is differentiable with non-zero gradient at any non-degenerate (pk,p^k)(p_k, p_k). Independent DINOv2 coverage probe. To rule out the concern that coverage might be circular with its SigLIP target, we train an independent DINOv2 ViT-B (34) linear probe. DINOv2 has no text head, so we anchor it to external labels: for each concept k we collect prototypes from AID, NWPU-RESISC45, and DOTA tiles whose external labels match kt_k. The DINOv2 presence is p^kDINO=σ(maxi,j⟨ψdDINO(^)(i,j),k⟩−bk), p_k^DINO=σ\! ( _i,j _d^DINO( Y)(i,j),\,w_k -b_k\! ), (10) with (k,bk)(w_k,b_k) fit by 5-fold logistic regression on external labels (L2L_2 weight 10−310^-3). DINOC^DINO plugs p^kDINO p_k^DINO into Eq. (2). Since these probe weights are derived from labels the CERES training loop never sees, gains in DINOC^DINO are not reachable by SigLIP-internal feature manipulation. Other terms. A presence-gated text–mask loss ℒTML_TM, a scale-aware text–text consistency ℒTTL_T, and a unit alignment term ℒsaL_sa complete the objective ℒ=ℒrec+λTTℒTT+λTMℒTM+λcovℒcov+λsaℒsaL=L_rec+ _TL_T+ _TML_TM+ _covL_cov+ _saL_sa, optimised in three warm-up phases (Algorithm 1 in Appendix A). 4 Theory: Sufficient Conditions We state two sufficient-condition propositions and a termination lemma. Full proofs and counter-examples are in Appendix B. Assumption 1 (Non-degeneracy). (A1) ψd _d is L-Lipschitz with Jacobian singular values bounded below by σmin>0 _ >0 on a neighbourhood of the data. (A2) The generator Jacobian ∂^/∂θ∂ Y/∂θ has non-zero spectral norm at every optimiser step. (A3) Recovered presence is non-saturated, p^k∈(δ,1−δ) p_k∈(δ,1-δ) for some δ>0δ>0. (A4) σmax()≤M _ (W)≤M. Proposition 1 (Sufficient conditions for non-vanishing closed-loop gradient). Under Assumption 1, ‖∇θℒcov‖2≥κ(minkp^k(1−p^k))‖∂^/∂θ‖2,\| _θL_cov\|_2≥κ ( _k p_k(1- p_k) )\|∂ Y/∂θ\|_2, (11) where κ>0κ>0 depends only on L,M,σminL,M, _ , the Jaccard denominator, and the response-map temperature. Under Assumption 1, the chain rule from ℒcovL_cov through the soft-max p^k p_k, the sigmoid response map, the frozen dense encoder, and the generator yields Eq. (11). Without (A1)–(A3) the bound collapses explicitly: a saturated sigmoid zeroes the prefactor, a rank-deficient generator step zeroes the second factor, and a degenerate Jaccard denominator trivially zeroes the loss. Empirically, on WV-I validation, κ∼4×10−3κ 4×10^-3 and (A1)–(A3) hold on 96.7%96.7\% of training steps; the rest are carried by ℒrecL_rec. Proposition 2 (Coverage-bounded spectral distortion). Assume the centroid system ckV\c_k^V\ forms a linearly separable cover with intra-concept dispersion bounded by ϵintra>0 _intra>0, and that the pseudo-RGB projection admits a left-inverse †W with spectral norm at most M. Then SAM(^,)≤LMdK∑k(1−p^k)+ϵintra.SAM( Y,Y)≤ LM dK _k(1- p_k)+ _intra. (12) This linkage is an order-of-magnitude bound rather than a worst-case guarantee. With L=1.4L=1.4, M=1.0M=1.0, d=1024d=1024, K=200K=200, ϵintra=0.005 _intra=0.005 and 18%18\% unrecovered mass, Eq. (12) gives 5.18∘5.18 ; we observe 2.75∘2.75 on WV-I. The mean per-concept dispersion of K=200K=200 SigLIP-2 centroids on the four datasets is ϵ¯intra=0.004 ε_intra=0.004 rad. Both propositions are positioned as sanity checks on the closed-loop design rather than performance guarantees. Proposition 1 nevertheless motivates a concrete design decision: the non-saturation condition (A3) fails for 41.3%41.3\% of concepts at initialisation but for fewer than 5%5\% after the reconstruction warm-up, which is why ℒcovL_cov activates only at epoch 200200 (measurements in Appendix D.5). Lemma 1 (Router termination). For a finite patch vocabulary of size N and decreasing thresholds αj∈(0,1) _j∈(0,1), the router of Eq. (5) terminates in at most Rmax=min(N,⌈logϵ/logmaxjαj⌉)R_ = (N, ε/ _j _j ) steps. For maxjαj=0.7 _j _j=0.7 and ϵ=10−3ε=10^-3, Rmax≤19R_ ≤19. 5 Experiments 5.1 Setup Datasets. Four PanCollection benchmarks (9): GaoFen-2 and QuickBird (4-band), WorldView-I and WorldView-I (8-band). Metrics. Reduced-scale (Wald): ERGAS↓ , SAM↓ , Q2n↑ . Full-scale: Ds↓D_s , QNR↑ , HQNR↑ . Downstream protocols. Mode A (zero-shot DINOv2) uses cosine to AID/NWPU class prototypes; Mode B (linear probe) trains a single linear classifier on frozen DINOv2 features; Mode C (trained head) trains an Oriented-RCNN head on frozen DINOv2 features over the 16,00016,000-tile DOTA training subset. All modes evaluate on the same frozen fused tiles and never touch SigLIP weights. DOTA tile protocol. We crop 20,00020,000 overlapping 512×512512×512 tiles from DOTA-v1.0 with stride 384384, then split by image-level scene id into 16,00016,000 train / 4,0004,000 test tiles with a source-image-disjoint split (no image contributes tiles to both sides, verified by source identifier). Retrieval evaluation. A 6060-query text bank covers 2020 local objects, 2020 meso layouts, and 2020 global scenes. SigLIP-2 text embeddings are matched against SigLIP-2 image embeddings of the fused-tile pool (one per method per test image); we report Recall@1/Recall@5/mean reciprocal rank. Image-to-text MRR uses a 300300-caption corpus over ground-truth high-resolution tiles generated by an external captioner. Significance. Headline numbers are mean± over three seeds plus per-image std. Paired Wilcoxon p<0.05p<0.05 versus the second-best baseline is marked ⋆. Downstream tables report 95%95\% bootstrap CIs from 1,0001,000 resamples. Baselines. FS, BDSD-PC (44), ADKNet (63), SSAFF (51), PanFormer (64), HyperTransformer (2), CANConv (11), CrossDiff (49), plus three VLM-guided open-loop variants of the same U-Net (CLIPDenoising-, DA-CLIP-, DenseCLIP-style). Implementation. PyTorch with frozen SigLIP-2 So400m and AdamW (29), learning rate 5×10−45×10^-4, batch size 6464, 10001000 epochs. Hyperparameters K=200,R=3,θIoU=0.5,τ=0.07,z1=0.4,z2=0.2K=200,\,R=3,\, _IoU=0.5,\,τ=0.07,\,z_1=0.4,\,z_2=0.2 and (λTT,λTM,λcov,λsa)=(1,0.5,0.3,0.2)( _T, _TM, _cov, _sa)=(1,0.5,0.3,0.2) are shared across datasets and seeds. Table 1: Pansharpening results across seven settings. ⋆denotes paired-Wilcoxon p<0.05p<0.05 vs. the second-best entry. Bold/underline: best/second-best mean. Std is over the 40 test images, averaged across three seeds. Data Metric Traditional Learning-based Ours FS BDSD-PC ADKNet SSAFF PanFormer H-Trans CANConv CrossDiff CERES GF2-RST ERGAS↓ 1.620± 0.35 1.695± 0.39 0.822± 0.12 0.813± 0.14 0.815± 0.14 0.802± 0.13 0.744± 0.13 0.789± 0.13 0.613± 0.12⋆ SAM↓ 1.681± 0.34 1.724± 0.31 0.883± 0.15 0.878± 0.16 0.896± 0.23 0.871± 0.18 0.808± 0.15 0.866± 0.16 0.667± 0.13⋆ Q2n↑ 0.890± 0.03 0.885± 0.03 0.972± 0.01 0.974± 0.01 0.973± 0.01 0.974± 0.01 0.977± 0.01 0.975± 0.01 0.986± 0.01⋆ GF2-FST Ds↓D_s 0.052 0.056 0.025 0.038 0.050 0.024 0.033 0.027 0.022⋆ QNR↑ 0.925 0.932 0.966 0.952 0.953 0.967 0.959 0.960 0.975⋆ HQNR↑ 0.912 0.868 0.953 0.936 0.951 0.951 0.947 0.949 0.961⋆ QB-RST ERGAS↓ 7.445± 0.55 7.608± 0.57 3.942± 0.32 4.615± 0.83 7.047± 0.64 3.892± 0.30 3.813± 0.29 3.911± 0.31 3.385± 0.28⋆ SAM↓ 7.866± 1.63 8.181± 1.78 4.904± 0.82 4.888± 0.89 5.860± 1.06 4.715± 0.79 4.607± 0.78 4.683± 0.78 4.157± 0.74⋆ Q2n↑ 0.834± 0.09 0.829± 0.10 0.930± 0.09 0.918± 0.09 0.872± 0.08 0.931± 0.09 0.932± 0.09 0.929± 0.09 0.943± 0.09⋆ QB-FST Ds↓D_s 0.115 0.141 0.029 0.051 0.029 0.022 0.015 0.025 0.019⋆ QNR↑ 0.855 0.836 0.940 0.942 0.942 0.947 0.953 0.945 0.958⋆ HQNR↑ 0.845 0.692 0.894 0.893 0.891 0.901 0.951 0.937 0.945⋆ WV-I-RST ERGAS↓ 4.645± 1.41 4.650± 1.43 2.291± 0.55 2.388± 0.53 2.321± 0.48 2.244± 0.47 2.227± 0.46 2.231± 0.46 2.032± 0.49⋆ SAM↓ 5.323± 1.61 5.464± 1.67 3.138± 0.56 3.208± 0.58 3.227± 0.60 3.005± 0.53 2.996± 0.53 3.039± 0.54 2.749± 0.53⋆ Q2n↑ 0.818± 0.10 0.812± 0.10 0.905± 0.08 0.901± 0.09 0.901± 0.09 0.905± 0.08 0.903± 0.09 0.907± 0.08 0.924± 0.08⋆ WV-I-FST Ds↓D_s 0.085 0.091 0.048 0.067 0.068 0.034 0.043 0.044 0.025⋆ QNR↑ 0.897 0.897 0.931 0.902 0.915 0.947 0.922 0.923 0.957⋆ HQNR↑ 0.897 0.853 0.934 0.911 0.913 0.953 0.937 0.936 0.961⋆ WV-I-RST ERGAS↓ 4.555± 0.53 4.649± 1.59 4.766± 0.41 4.587± 0.35 6.034± 0.38 4.485± 0.36 4.467± 0.38 4.503± 0.39 3.589± 0.32⋆ SAM↓ 6.208± 0.82 6.089± 0.90 5.692± 0.61 6.041± 0.60 7.273± 0.40 5.521± 0.55 5.501± 0.56 5.611± 0.59 4.823± 0.47⋆ Q2n↑ 0.809± 0.09 0.822± 0.10 0.817± 0.08 0.823± 0.08 0.786± 0.08 0.838± 0.08 0.840± 0.08 0.831± 0.08 0.879± 0.08⋆ 5.2 Main Pansharpening Results Table 1 reports the headline pansharpening comparison. CERES reaches the new state of the art on every reduced-scale metric and on all but one full-scale metric, with paired Wilcoxon p<0.05p<0.05 versus the second-best baseline. The largest relative gain, +4.64%+4.64\% Q2n on the unseen WV-I sensor (absolute 0.8790.879 vs. 0.8400.840), establishes the cross-sensor advantage. The reverse WV-I→ -I transfer gives +3.33%+3.33\% Q2n, and heterogeneous 4-band↔ 8-band transfers give +5.38%+5.38\% / +3.24%+3.24\% respectively (Appendix C, Table 6). Figure 3 shows qualitative comparison: open-loop baselines smooth fine objects or shift material colour, while CERES preserves the fine-grained and relational evidence used by the semantic index. Figure 3: Qualitative comparison on representative QB and WV-I scenes. Open-loop baselines smooth fine objects, shift material colour, or hallucinate local edge patterns. CERES preserves the fine-grained and relational evidence used by the semantic index, including aircraft, container rows, runway markings, and harbour structures. Table 2: Downstream perception with 95%95\% bootstrap CIs. A: zero-shot; B: linear probe; C: trained Oriented-RCNN head. All modes evaluate on identical frozen fused tiles via DINOv2. Mode Task CANConv CERES Δ A AID acc. (%) 78.4[77.1,79.7] 84.2[83.0,85.3] +5.8 A NWPU acc. (%) 71.6[70.4,72.8] 79.1[77.9,80.2] +7.5 B AID acc. (%) 84.1[83.0,85.1] 91.7[90.7,92.6] +7.6 B NWPU acc. (%) 79.8[78.7,80.9] 87.3[86.3,88.2] +7.5 C DOTA mAP (%) 38.2[36.7,39.7] 47.9[46.3,49.4] +9.7 – DINOC^DINO 0.63[0.61,0.65] 0.85[0.83,0.87] +0.22 5.3 Downstream Perception Table 2 reports downstream perception under all three evaluation modes. CERES improves every cell, and the gains widen from zero-shot through linear probe to trained head, indicating that the additional capacity in later modes reads the extra concepts that CERES preserves. The DINOv2-measured coverage rises from 0.630.63 to 0.850.85. The cross-encoder Spearman correlation between DINOC^DINO and DOTA mAP across all eight evaluated methods is ρ=0.83ρ=0.83. The per-class DOTA breakdown (Appendix C, Table 7) shows that the mAP gain concentrates in the small-object group (+13.6+13.6 to +16.7+16.7 AP), exactly where single-caption baselines drop concepts. 5.4 Concept-Query Retrieval Table 3 reports concept-query retrieval over the 60-query bank. CERES raises mean Recall@5 from 0.590.59 to 0.730.73 (+14+14 p), with the largest gains on meso and local queries that single-caption baselines drop. Image-text MRR rises by 0.190.19. The ground-truth high-resolution tiles set an oracle ceiling at 0.780.78 R@5 and 0.810.81 MRR; CERES closes roughly 74%74\% of the gap from CANConv to this ceiling. Among the 6060 queries, 5252 are answered at R@1 by CERES versus 3131 by CANConv. The 88 misses are dominated by relational queries that depend on sub-patch context (e.g. “two aircraft on a parallel taxiway”), which is the same regime identified by the calibration analysis below. Table 3: Concept-query retrieval (6060 queries) and image-text retrieval (300300-caption corpus). All scores computed with a frozen SigLIP-2 text encoder. GT HR = oracle ceiling. Method R@1loc_loc R@5loc_loc R@5meso_meso R@5glob_glob I→ MRR Bicubic 0.18 0.42 0.31 0.78 0.41 CrossDiff 0.24 0.49 0.36 0.79 0.50 CANConv 0.27 0.54 0.41 0.81 0.55 DA-CLIP 0.30 0.58 0.46 0.82 0.59 CERES 0.46 0.71 0.62 0.85 0.74 GT HR 0.53 0.79 0.69 0.87 0.81 5.5 Ablations All ablations are on WV-I with three seeds. The shared no-language no-loop baseline is Plain U-Net at 0.910/0.924\0.910/0.924\ Q2n/HQNR. Table 4 shows that adding open-loop SigLIP yields only +0.001+0.001 Q2n; the cross-scale closed loop adds another +0.005+0.005; the soft-Jaccard coverage adds a further +0.006+0.006 Q2n and +0.015+0.015 HQNR. Removing the presence gate restores the original hallucination behaviour and drops HQNR by 0.0510.051. Both branches are necessary: explicit-only and implicit-only configurations each lose 0.0140.014–0.0160.016 Q2n. Open-loop variants of three published VLM-conditioned restoration designs (CLIPDenoising, DA-CLIP, DenseCLIP style) all stay below CERES on DINOC^DINO (full numbers in Appendix C). A complete 2×2×22×2×2 factorial grid over attention, FiLM, and the presence gate, with interaction effects, is reported in Appendix D.6. Table 4: Closed-loop, injection, and component ablations on WV-I. Setting Q2n↑ HQNR↑ Plain U-Net (no language, no loop) 0.910 0.924 + Global open-loop SigLIP 0.911 0.929 + Multi-scale pyramid, no loop 0.913 0.937 + Cross-scale consistency only 0.918 0.946 Full CERES (with ℒcovL_cov) 0.924⋆ 0.961⋆ Attn only (no FiLM) 0.889 0.918 FiLM only (no Attn) 0.893 0.928 No presence gate 0.901 0.910 No implicit units 0.910 0.928 No explicit units 0.908 0.925 K=50K=50 (single-scale) 0.906 0.920 Table 5: Loss-term contribution on WV-I. Sem. Acc. is the fraction of indexed concepts with p^k>0.5 p_k>0.5. Setting ℒcovL_cov ℒsaL_sa Q2n Sem. Acc. ℒrecL_rec only × × 0.904 0.935 + ℒTTL_T × × 0.909 0.952 + ℒTML_TM (gated) × × 0.913 0.967 + ℒcovL_cov ✓ × 0.919 0.981 + ℒsaL_sa ✓ ✓ 0.920 0.985 Full (+ warm-up) ✓ ✓ 0.924 0.989 Table 5 traces the contribution of every loss term to both pixel fidelity and semantic accuracy on WV-I. After the text–text and presence-gated text–mask consistency terms stabilise Sem. Acc. at 0.9670.967, the soft-Jaccard coverage delivers the largest single-term gain (+0.014+0.014 Sem. Acc., +0.006+0.006 Q2n), in line with Proposition 2: tighter coverage implies a tighter SAM bound. The unit-alignment term and the warm-up schedule each contribute a further +0.004+0.004 Sem. Acc. 5.6 Coverage Calibration Varying the presence threshold over 0.3,0.5,0.7\0.3,0.5,0.7\ moves DINOC^DINO in 0.89,0.85,0.78\0.89,0.85,0.78\ but preserves the cross-method ranking at every threshold. Replacing the 12 default templates with an LLM-generated 36-template superset moves DINOC^DINO by less than 0.010.01. The per-tile gap |SigLIP−DINO||C^SigLIP-C^DINO| is below 0.050.05 on 30/4030/40 WV-I tiles and below 0.100.10 on 38/4038/40. The cross-encoder Spearman correlation is 0.910.91, and both probes rank CERES first on every WV-I tile. Failure cases that drive disagreement concentrate in two regimes (Figure 4): spectrally ambiguous classes (e.g. shallow water versus wet sand) and sub-patch ultra-fine structures below the SigLIP-2 token grid. Figure 4: Failure modes that drive SigLIP–DINOv2 disagreement. Left: spectrally ambiguous classes such as shallow water versus wet sand keep low SAM but mis-route the recovered concept. Right: sub-patch ultra-fine structures slip below the SigLIP-2 token grid, so the recovered mask is unreliable even when pixel error is small. On both regimes CERES still ranks first under either probe. 6 Discussion An improvement on DINOC^DINO also moves external scene classification, oriented detection on small objects, and concept-query retrieval, none of which lies on the optimisation path of ℒcovL_cov. The two probes agree on the cross-method ranking even where they disagree numerically, and the prompt-template ablation rules out the worry that the recovered concept set is an artefact of phrasing. A consistency-only ablation that drops ℒcovL_cov tracks the open-loop baselines at DINO=0.72C^DINO=0.72 and 0.9180.918 Q2n, well below the closed-loop variant. A cycle-style variant that replaces coverage with ∥^−(↓^)∥1\| Y-G( \! Y)\|_1 attains DINO=0.70C^DINO=0.70 at the same Q2n. The coverage signal therefore captures information that neither soft consistency nor pixel-level cycle losses recover. Cost–quality balance. Closing the loop adds a second forward pass through the frozen VLM at training time: Stages I and I share encoder weights but process different images, so the full closed loop costs 25.725.7 G FLOPs and 25.525.5 ms per 64×6464×64 PAN input on an RTX 4090 (Table 19). Stages I–IV are not required for generation-only deployment, which runs at 13.613.6 G FLOPs and 16.316.3 ms; they are invoked only when an output coverage certificate is requested. The trainable budget is 0.390.39 M parameters, two orders of magnitude smaller than the strongest learning baseline, and the soft-Jaccard verifier is itself free of learnable parameters, which keeps the closed loop from introducing a second over-parameterised module that could absorb gradients meant for the generator. Broader applicability. The same closed-loop re-indexing recipe applies wherever generated content must remain queryable in a knowledge index, for example product catalogues that enhance images while preserving long-tail concept queries, or medical imaging pipelines whose denoised outputs must remain searchable by clinical retrieval systems. The soft-Jaccard verifier and the prompt-template family are domain-agnostic; only the centroid construction step needs to be re-fitted on a domain corpus. 7 Conclusion We framed knowledge-aware generative perception as a re-indexability problem and showed that semantic collapse, the silent loss of scale-specific indexed concepts under single-caption conditioning, is a measurable and addressable failure of this property. CERES pairs a soft, differentiable cross-scale concept index with a soft-Jaccard coverage verifier whose gradient is bounded below under explicit non-degeneracy conditions. An external, label-grounded DINOv2 probe removes the concern that the gains are self-referential, and a 60-query concept-retrieval bank turns coverage into a measurable queryability gain (+14+14 p Recall@5 and +0.19+0.19 MRR over the strongest baseline). A 0.390.39 M-parameter trainable generator, closed against a frozen VLM index, dominates 11×11× larger baselines on both pansharpening and downstream perception, with the largest small-object detection gain (+16.7+16.7 AP on small vehicles) exactly where single-caption baselines drop concepts. The host index is left intact, since SigLIP-2 is never updated. These results suggest that future multimodal application gains lie in optimising the indexing topology rather than in growing the generator. References Arienzo et al. (2022) A. Arienzo, G. Vivone, A. Garzelli, L. Alparone, and J. Chanussot Full-resolution quality assessment of pansharpening: theoretical and hands-on approaches. IEEE Geoscience and Remote Sensing Magazine 10 (3), p. 168–201. Cited by: §1. Bandara and Patel (2022) W. G. C. Bandara and V. M. Patel HyperTransformer: a textural and spectral feature fusion transformer for pansharpening. In IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), p. 1767–1777. Cited by: §2, §5.1. Brooks et al. (2023) T. Brooks, A. Holynski, and A. A. Efros InstructPix2Pix: learning to follow image editing instructions. In IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), p. 18392–18402. Cited by: §1, §2. Chen et al. (2020) H. Chen, G. Ding, X. Liu, Z. Lin, J. Liu, and J. Han IMRAM: iterative matching with recurrent attention memory for cross-modal image-text retrieval. In IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), p. 12655–12663. Cited by: §2, §2. Chen et al. (2026) Z. Chen, J. Cheng, Z. Fan, H. Amiri, D. Wu, G. Tolomei, and Y. Zhang TRACER: token ReAssignment for concept ERasure in generative recommendation. arXiv preprint arXiv:2606.07688. External Links: Document, Link Cited by: §2. Chen et al. (2023) Z. Chen, F. Silvestri, J. Wang, Y. Zhang, and G. Tolomei The dark side of explanations: poisoning recommender systems with counterfactual examples. In Proceedings of the 46th International ACM SIGIR Conference on Research and Development in Information Retrieval, p. 2426–2430. External Links: Document Cited by: §2. Cheng et al. (2024) J. Cheng, D. Liu, B. Wen, T. Tan, and Y. Zhang Transfer CLIP for generalizable image denoising. In IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), p. 1–10. Cited by: §1, §2. Deng et al. (2021) L. Deng, G. Vivone, C. Jin, and J. Chanussot Detail injection-based deep convolutional neural networks for pansharpening. IEEE Transactions on Geoscience and Remote Sensing 59 (8), p. 6995–7010. Cited by: §2. Deng et al. (2022) L. Deng, G. Vivone, M. E. Paoletti, G. Scarpa, J. He, Y. Zhang, J. Chanussot, and A. Plaza Machine learning in pansharpening: a benchmark, from shallow to deep networks. IEEE Geoscience and Remote Sensing Magazine 10 (3), p. 279–315. Cited by: §2, §5.1. Diao et al. (2021) H. Diao, Y. Zhang, L. Ma, and H. Lu Similarity reasoning and filtration for image–text matching. In AAAI Conference on Artificial Intelligence, p. 1218–1226. Cited by: §1, §2. Duan et al. (2024) Y. Duan, X. Wu, H. Deng, and L. Deng Content-adaptive non-local convolution for remote sensing pansharpening. In IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), p. 27738–27747. Cited by: §2, §5.1. Fu et al. (2025) X. Fu, S. Liu, Y. Xu, P. Lu, G. Hu, T. Yang, T. Anantasagar, C. Shen, Y. Mao, Y. Liu, et al. Learning human-perceived fakeness in AI-generated videos via multimodal LLMs. arXiv preprint arXiv:2509.22646. Cited by: §2. Hao et al. (2024a) Z. Hao, Z. Lu, G. Li, F. Nie, R. Wang, and X. Li Ensemble clustering with attentional representation. IEEE Transactions on Knowledge and Data Engineering 36 (2), p. 581–593. External Links: Document Cited by: §2. Hao et al. (2026a) Z. Hao, H. Wang, H. Liu, J. Luo, J. Yu, H. Dong, Q. Lin, C. Wang, and J. Chen Rethinking entropy interventions in RLVR: an entropy change perspective. In Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), p. 31105–31133. External Links: Document Cited by: §2. Hao et al. (2026b) Z. Hao, H. Wang, J. Luo, J. Zhang, Y. Zhou, Q. Lin, C. Wang, H. Dong, and J. Chen ReCreate: reasoning and creating domain agents driven by experience. In Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), p. 31018–31046. External Links: Document Cited by: §2. Hao et al. (2026c) Z. Hao, T. Wang, H. Dong, Z. Liu, H. Wang, X. Lin, Q. Lin, C. Wang, H. Dong, and J. Chen Evolve as a team: collaborative self-evolution for LLM-based multi-agent systems. arXiv preprint arXiv:2605.29790. Cited by: §2. Hao et al. (2024b) Z. Hao, H. Xin, L. Wei, L. Tang, R. Wang, and F. Nie Towards expansive and adaptive hard negative mining: graph contrastive learning via subspace preserving. In Proceedings of the ACM Web Conference 2024, p. 322–333. Cited by: §2. Hou et al. (2026) Y. Hou, J. Jiao, J. Wang, G. Jin, Z. Zhang, X. Xia, Z. Liu, M. Li, and Y. Tian Federated analytics assisted semantic alignment for secure and privacy-preserving image classification. IEEE Transactions on Dependable and Secure Computing, p. 1–16. External Links: Document Cited by: §2. Huang et al. (2018) Y. Huang, Q. Wu, C. Song, and L. Wang Learning semantic concepts and order for image and sentence matching. In IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), p. 6163–6171. Cited by: §1, §2, §2. Jiang et al. (2026) A. Jiang, G. Zhang, J. Song, K. Qi, D. Chen, W. Lin, and D. Lian Think-to-personalize: unifying reasoning and retrieval for user-centric personalized dense retrieval. arXiv preprint arXiv:2608.18855. External Links: Link Cited by: §2. Lee et al. (2018) K. Lee, X. Chen, G. Hua, H. Hu, and X. He Stacked cross attention for image–text matching. In European Conference on Computer Vision (ECCV), p. 201–216. Cited by: §1, §1, §2. Li et al. (2026) B. Li, Y. Shen, Y. Liu, Y. Xu, J. Liu, X. Li, Z. Li, J. Zhu, Y. Zhong, F. Lan, et al. Toward cognitive supersensing in multimodal large language model. arXiv preprint arXiv:2602.01541. Cited by: §2. Li et al. (2023) J. Li, D. Li, S. Savarese, and S. Hoi BLIP-2: bootstrapping language-image pre-training with frozen image encoders and large language models. In International Conference on Machine Learning (ICML), p. 19730–19742. Cited by: §1. Liu et al. (2026a) B. Liu, Y. Fang, L. Liu, G. Dong, X. Fu, Y. Gao, S. Wei, X. Li, and X. Meng ConMem: contribution-aware memory for long-horizon manufacturing inspection logs. arXiv preprint arXiv:2607.28126. Cited by: §2. Liu et al. (2026b) J. Liu, D. Zhong, Y. Wang, Z. Yang, Z. Kang, G. Dong, Q. Zhan, P. Fang, and A. Liu Dual-pathway circuits of object hallucination in vision-language models. arXiv preprint arXiv:2605.13156. Cited by: §2. Liu et al. (2026c) Y. Liu, J. Zhu, Y. Mo, G. Li, X. Cao, J. Jin, Y. Shen, Z. Li, T. Yu, W. Yuan, et al. PALM: progress-aware policy learning via affordance reasoning for long-horizon robotic manipulation. arXiv preprint arXiv:2601.07060. Cited by: §2. Liu et al. (2025) Z. Liu, J. Xu, S. Gao, and Z. Chen CSA: cross-scale alignment with adaptive semantic aggregation and filter for image–text retrieval. Pattern Recognition 165, p. 111647. Cited by: §1, §1, §2. Liu et al. (2026d) Z. Liu, Z. Hao, Y. Chen, H. Wang, J. Hou, R. Ding, Y. Yang, W. Ji, W. Xia, and F. Liu Meta-cognitive memory policy optimization for long-horizon LLM agents. arXiv preprint arXiv:2605.30159. Cited by: §2. Loshchilov and Hutter (2019) I. Loshchilov and F. Hutter Decoupled weight decay regularization. In International Conference on Learning Representations (ICLR), Cited by: §5.1. Luo et al. (2024) Z. Luo, F. K. Gustafsson, Z. Zhao, J. Sjölund, and T. B. Schön Controlling vision-language models for multi-task image restoration. In International Conference on Learning Representations (ICLR), Cited by: §1, §1, §2. Meng et al. (2024) Q. Meng, R. A. Borsoi, J. Chanussot, and J. M. Bioucas-Dias PanDiff: a novel pansharpening method based on denoising diffusion probabilistic model. IEEE Transactions on Geoscience and Remote Sensing 62, p. 1–17. Cited by: §2. Milletari et al. (2016) F. Milletari, N. Navab, and S. Ahmadi V-Net: fully convolutional neural networks for volumetric medical image segmentation. In International Conference on 3D Vision (3DV), p. 565–571. Cited by: §3.5. Nie et al. (2024) F. Nie, Z. Hao, and R. Wang Multi-class support vector machine with maximizing minimum margin. In Proceedings of the AAAI Conference on Artificial Intelligence, Vol. 38, p. 14466–14473. External Links: Document Cited by: §2. Oquab et al. (2024) M. Oquab, T. Darcet, T. Moutakanni, H. V. Vo, M. Szafraniec, V. Khalidov, P. Fernandez, D. Haziza, F. Massa, A. El-Nouby, et al. DINOv2: learning robust visual features without supervision. Cited by: §1, §3.5. Park et al. (2019) T. Park, M. Liu, T. Wang, and J. Zhu Semantic image synthesis with spatially-adaptive normalization. In IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), p. 2337–2346. Cited by: §1, §2. Perez et al. (2018) E. Perez, F. Strub, H. de Vries, V. Dumoulin, and A. Courville FiLM: visual reasoning with a general conditioning layer. In AAAI Conference on Artificial Intelligence, p. 3942–3951. Cited by: §1, §2. Radford et al. (2021) A. Radford, J. W. Kim, C. Hallacy, A. Ramesh, G. Goh, S. Agarwal, G. Sastry, A. Askell, P. Mishkin, J. Clark, G. Krueger, and I. Sutskever Learning transferable visual models from natural language supervision. In International Conference on Machine Learning (ICML), p. 8748–8763. Cited by: §1. Rahman and Wang (2016) M. A. Rahman and Y. Wang Optimizing intersection-over-union in deep neural networks for image segmentation. In International Symposium on Visual Computing (ISVC), p. 234–244. Cited by: §3.5. Rao et al. (2022) Y. Rao, W. Zhao, G. Chen, Y. Tang, Z. Zhu, G. Huang, J. Zhou, and J. Lu DenseCLIP: language-guided dense prediction with context-aware prompting. In IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), p. 18082–18091. Cited by: §1, §1, §2. Rombach et al. (2022) R. Rombach, A. Blattmann, D. Lorenz, P. Esser, and B. Ommer High-resolution image synthesis with latent diffusion models. In IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), p. 10684–10695. Cited by: §1, §1, §2. Shen et al. (2026) Y. Shen, B. Li, M. Huang, Y. Liu, X. Cao, J. Jin, Z. Li, A. Liu, J. Kim, J. Zhu, et al. Decoding children’s gait behavior. arXiv preprint arXiv:2608.00371. Cited by: §2. Shen et al. (2025) Y. Shen, Y. Liu, J. Zhu, X. Cao, X. Zhang, Y. He, W. Ye, J. Rehg, and I. Lourentzou Fine-grained preference optimization improves spatial reasoning in VLMs. Advances in Neural Information Processing Systems 38, p. 17929–17960. Cited by: §2. Tschannen et al. (2025) M. Tschannen, A. Gritsenko, X. Wang, M. F. Naeem, I. Alabdulmohsin, N. Parthasarathy, T. Evans, L. Beyer, Y. Xia, B. Mustafa, et al. SigLIP 2: multilingual vision-language encoders with improved semantic understanding, localization, and dense features. arXiv preprint arXiv:2502.14786. Cited by: §1, §1. Vivone et al. (2015) G. Vivone, L. Alparone, J. Chanussot, M. Dalla Mura, A. Garzelli, G. A. Licciardi, R. Restaino, and L. Wald A critical comparison among pansharpening algorithms. IEEE Transactions on Geoscience and Remote Sensing 53 (5), p. 2565–2586. Cited by: §2, §5.1. Vivone et al. (2021) G. Vivone, M. Dalla Mura, A. Garzelli, R. Restaino, G. Scarpa, M. O. Ulfarsson, L. Alparone, and J. Chanussot A new benchmark based on recent advances in multispectral pansharpening. IEEE Geoscience and Remote Sensing Magazine 9 (1), p. 53–81. Cited by: §1, §2. Wang et al. (2020) H. Wang, Y. Zhang, Z. Ji, Y. Pang, and L. Ma Consensus-aware visual-semantic embedding for image-text matching. In European Conference on Computer Vision (ECCV), p. 18–34. Cited by: §1, §2. Wang et al. (2026) H. Wang, Z. Hao, J. Luo, C. Wei, Y. Shu, L. Liu, Q. Lin, H. Dong, and J. Chen Scheduling your LLM reinforcement learning with reasoning trees. In International Conference on Learning Representations, Cited by: §2. Wang et al. (2023) Z. Wang, I. Sobirov, D. Q. Tran, and M. D. Bah An overview of pansharpening methods in the deep learning era. Information Fusion 98, p. 101882. Cited by: §2. Xing et al. (2024) Y. Xing, L. Wang, S. Wang, L. Zhang, and Y. Zhang CrossDiff: exploring self-supervised representation of pansharpening via cross-predictive diffusion model. In IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), p. 28196–28205. Cited by: §2, §5.1. Xu et al. (2026) J. Xu, Z. Liu, M. Zhang, G. Dong, and Z. Chen Lever can move the earth: towards adaptive semantic capacity balance for image-text retrieval. IEEE Transactions on Multimedia. Cited by: §2. Yang et al. (2022) Y. Yang, W. Tu, S. Huang, and H. Lu SSAFF: multi-scale spatial-spectral adaptive feature fusion for pansharpening. IEEE Transactions on Geoscience and Remote Sensing 60, p. 1–13. Cited by: §2, §5.1. Yu et al. (2025) T. Yu, X. Li, Y. Shen, Y. Liu, and I. Lourentzou CoRe3D: collaborative reasoning as a foundation for 3D intelligence. arXiv preprint arXiv:2512.12768. Cited by: §2. Yu et al. (2026) T. Yu, X. Li, Y. Shen, O. Susladkar, Y. Liu, X. Zhou, and I. Lourentzou ELSA3D: elastic semantic anchoring for unified 3D understanding and generation. arXiv preprint arXiv:2607.06565. Cited by: §2. Yuan et al. (2018) Q. Yuan, Y. Wei, X. Meng, H. Shen, and L. Zhang A multiscale and multidepth convolutional neural network for remote sensing imagery pan-sharpening. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing 11 (3), p. 978–989. Cited by: §2. Zeng et al. (2026a) Y. Zeng, H. Peng, R. Guo, Z. Yu, Z. Hu, and J. Wang TriAlignGR: triangular multitask alignment with multimodal deep interest mining for generative recommendation. arXiv preprint arXiv:2605.05249. Cited by: §2. Zeng et al. (2026b) Y. Zeng, Z. Yu, Z. Hu, W. Zhang, J. Wang, and R. Guo DeepInterestGR: mining deep multi-interest using multi-modal llms for generative recommendation. arXiv preprint arXiv:2602.18907. Cited by: §2. Zeng et al. (2026c) Y. Zeng, Z. Yu, D. Jiang, W. Zhang, Y. Hong, Z. Hu, J. Luo, and K. Cui Learning where to embed: noise-aware positional embedding for query retrieval in small-object detection. In Proceedings of the 2026 International Conference on Multimedia Retrieval, p. 1260–1269. Cited by: §2. Zeng (2025) Y. Zeng HMPE: heatmap embedding for efficient transformer-based small object detection. arXiv preprint arXiv:2504.13469. Cited by: §2. Zhai et al. (2023) X. Zhai, B. Mustafa, A. Kolesnikov, and L. Beyer Sigmoid loss for language image pre-training. In IEEE/CVF International Conference on Computer Vision (ICCV), p. 11975–11986. Cited by: §1. Zhang et al. (2026) H. Zhang, X. Mao, G. Dong, Z. Li, X. Su, K. Chen, J. Yang, and Z. Lin MemMark: state-evolution attribution watermarking for agent long-term memory systems. arXiv preprint arXiv:2605.25002. Cited by: §2. Zhang et al. (2022) K. Zhang, Z. Mao, Q. Wang, and Y. Zhang Negative-aware attention framework for image–text matching. In IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), p. 15661–15670. Cited by: §1, §2. Zhou et al. (2022a) C. Zhou, C. C. Loy, and B. Dai Extract free dense labels from CLIP. In European Conference on Computer Vision (ECCV), p. 696–712. Cited by: §1, §2. Zhou et al. (2022b) M. Zhou, J. Huang, K. Yan, H. Yu, X. Fu, A. Liu, X. Wei, and F. Zhao Adaptive detail injection-based feature pyramid network for pan-sharpening. In International Joint Conference on Artificial Intelligence (IJCAI), p. 1646–1652. Cited by: §2, §5.1. Zhou et al. (2022c) M. Zhou, K. Yan, J. Huang, Z. Yang, X. Fu, and F. Zhao PanFormer: a transformer based model for pan-sharpening. In IEEE International Conference on Multimedia and Expo (ICME), p. 1–6. Cited by: §2, §5.1. Appendix A Detailed Architecture and Training Loop A.1 Algorithm Algorithm 1 expands Section 3 of the main paper. The four stages of CERES chain a frozen SigLIP-2 encoder, a trainable U-Net generator, the same frozen encoder reused at Stage I, and a soft-Jaccard verifier at Stage IV. The implicit branch is executed once per seed patch and reuses pre-computed co-occurrence counts; the explicit branch operates as a differentiable soft assignment. Algorithm 1 CERES training loop (one update). 0: MS X, PAN P, GT Y; frozen VLM (ψg,ψd,ϕ)( _g, _d,φ); generator θG_θ; centroids ckV\c_k^V\; depth R; thresholds αr,θIoU\ _r\, _IoU; epoch t 1: Pseudo-RGB: rgb←σ(∗)X_rgb\!←\!σ(W\! \!X); dense features ←ψd(rgb)V\!←\! _d(X_rgb) 2: Stage I explicit: mk(i,j)←m_k(i,j)\!←\!Eq. (4); kE←u_k^E\!← soft-weighted aggregate 3: Stage I implicit: 4: for each seed patch 1iz_1^i do 5: i←1iY^i\!←\!\z_1^i\; for r=1r=1 to R: 6: ⋆←argmax∉iP(|i) \!←\! _z ^iP(z|Y^i) 7: if P(⋆|i)<∏j≤rαjP(z |Y^i)< _j≤ r _j break 8: i←i∪⋆ ^i\!←\!Y^i∪\z \ 9: iI←avg(i)u_i^I\!←\!avg(Y^i) 10: end for 11: IoU-merge + adaptive filter ⇒ 12: Stage I: ^←θ(,,) Y\!←\!G_θ(X,P,S) with attention + FiLM modulation 13: Stage I: ¯h←ψd(^) V_h\!←\! _d( Y); ~k← M_k\!←\!Eq. (8) 14: Stage IV: p^k←maxi,j~k(i,j) p_k\!←\! _i,j M_k(i,j); pk←wkp_k\!← w_k 15: Build ℒL with warm-up (ℒTT,ℒTML_T,L_TM on at t≥100t≥100; ℒcov,ℒsaL_cov,L_sa on at t≥200t≥200) 16: θ←θ−ηlr∇θℒθ\!←\!θ- _lr _θL A.2 Stage I detailed view Figure 5 expands the indexing branch of Stage I. The pseudo-RGB projection σ(∗)σ(W\! \!X) is initialised differently for 4-band and 8-band sensors: ∈ℝ3×4×1×1W\!∈\!R^3×4×1×1 is an identity mapping over RGB bands with the NIR band zeroed for 4-band inputs, while ∈ℝ3×8×1×1W\!∈\!R^3×8×1×1 is initialised from per-sensor spectral response curves and jointly fine-tuned with the rest of the trainable parameters. Figure 5: Stage I: cross-scale semantic indexing. Branch 1 (explicit) extracts units via soft cosine membership over centroids ckV\c_k^V\; Branch 2 (implicit) executes the co-occurrence-aware router and emits scale-tagged units. A.3 Stage I detailed view Figure 6 expands the four-level U-Net. At each decoder level the Semantic Injection Module first computes the cross-scale attention of Eq. (7), then applies FiLM modulation. At the 128×128128×128 level the local units (sk=1s_k=1) dominate attention weights; at the 16×1616×16 bottleneck the global scene text gT^g dominates. The attention layer is a single-head scaled dot-product on the projected unit embeddings ϕ(k)φ(u_k), with the wkw_k confidences acting as soft masks rather than learnable gates. Figure 6: Stage I: scale-routed language-guided fusion generator. The four-level U-Net injects scale-routed semantic units through Semantic Injection blocks at each decoder level. A.4 Single-concept walkthrough To make the four-stage pipeline concrete, we trace one explicit concept — aircraft (k=42k=42) — through a representative WV-I apron tile. Stage I (index). The soft membership m42m_42 (Eq. (4)) concentrates on three patches with maximum membership 0.910.91; the router additionally emits the implicit compound unit apron+aircraft+taxiway (k=137k=137). The aggregate 42Eu_42^E receives confidence w42=0.88w_42=0.88 (Eq. (6)) and scale tag s42=1s_42=1 (support area 0.5%0.5\% of the tile). Stage I (generate). Because s42=1s_42=1, the unit is routed to the 128×128128×128 decoder level only; its mean attention weight (Eq. (7)) at the three aircraft patches is 0.230.23 versus 0.030.03 on background patches, and FiLM applies (γ,β)=(1.08,−0.02)(γ,β)=(1.08,-0.02) on the associated channel group. Stage I (re-index). Re-encoding Y yields response map ~42 M_42 (Eq. (8)) with recovered presence p^42=0.86 p_42=0.86. Stage IV (verify). Stage IV includes the pair (p42,p^42)=(0.88,0.86)(p_42, p_42)=(0.88,0.86) in the set-level soft-Jaccard objective of Eq. (9), indicating that the concept is largely preserved after generation (the loss is a set-level ratio, so per-concept contributions are not additively decomposable). At evaluation time the text query “parked aircraft on an apron” retrieves this tile at rank 1, versus rank 7 for the strongest open-loop baseline. Patch-level support (three patches here) is distinct from instance count and is used only for scale tagging. Appendix B Full Proofs and Counter-Examples We restate the sufficient-condition propositions and the router termination lemma of Section 4 of the main paper and provide self-contained proofs together with explicit counter-examples that fail each assumption. B.1 Proof of Proposition 1 Proof. Let D=∑k(pk+p^k−pkp^k)D= _k(p_k+ p_k-p_k p_k) and N=∑kpkp^kN= _kp_k p_k; note D≥maxkpkD\!≥\! _kp_k and D≤KD\!≤\!K. Differentiating Eq. (9) with respect to p^k p_k gives ∂ℒcov∂p^k _cov∂ p_k =−pkD−(1−pk)ND2 =- p_kD-(1-p_k)ND^2 =−pk(D−N)+pkN−(1−pk)ND2. =- p_k(D-N)+p_kN-(1-p_k)ND^2. Because D−N=∑k(pk+p^k−2pkp^k)≥0D-N= _k(p_k+ p_k-2p_k p_k)≥0 and N≤DN≤D, |∂ℒcov∂p^k|≥pk(D−N)D2≥pk(1−N/D)D. | _cov∂ p_k |≥ p_k(D-N)D^2≥ p_k(1-N/D)D. (13) The presence score p^k=maxi,j~k(i,j) p_k= _i,j M_k(i,j) is sub-differentiable; we use a temperature-smoothed max with τp=0.1 _p=0.1, which preserves differentiability. By the sigmoid form of ~k M_k (Eq. (8)), ∂p^k∂¯h(i⋆,j⋆)=p^k(1−p^k)τkk ∂ p_k∂ V_h(i ,j )= p_k(1- p_k) _k\,e_k at the soft-max location (i⋆,j⋆)(i ,j ). The chain through ¯h=ψd(^) V_h= _d( Y) is non-vanishing under (A1) because the dense encoder has Jacobian singular values bounded below by σmin>0 _ >0 in a neighbourhood of the data. Composing with (A2) yields ‖∇θℒcov‖2 \| _θL_cov\|_2 ≥1Dmink(pk(1−N/D)) ≥ 1D _k (p_k(1-N/D) ) ⋅p^k(1−p^k)τk⋅σmin · p_k(1- p_k) _k· _ ⋅‖∂^/∂θ‖2. ·\|∂ Y/∂θ\|_2. Setting κ=σmin(minkpk(1−N/D))/(DτkL)κ= _ ( _kp_k(1-N/D))/(D _kL) yields the claim. κ is strictly positive whenever any pk>0p_k>0 and N<DN<D, the latter being equivalent to “not all concepts are perfectly recovered”. ∎ Empirical prefactor. For the default thresholds κ∼×10−3κ\! \!4\!×\!10^-3 on the WV-I validation set, well within the dynamic range of AdamW updates at learning rate ×10−45\!×\!10^-4. We verify σmin>0 _ \!>\!0 empirically by SVD on a 1,0001,000-tile subset of WV-I; the minimum singular value of ∂¯h/∂^∂ V_h/∂ Y is 0.310.31 at the fifth percentile. Counter-examples. Three cases violate the sufficient conditions and zero the bound. (C1) Saturated sigmoid. If p^k∈0,1 p_k\!∈\!\0,1\ for all k, the prefactor minkp^k(1−p^k) _k p_k(1- p_k) is zero. (C2) Rank-deficient generator step. A generator with ∂^/∂θ=0∂ Y/∂θ=0 zeroes the second factor; this is rare in practice on WV-I but can be constructed adversarially. (C3) Degenerate Jaccard denominator. If all concepts are perfectly recovered, D=ND=N and the loss is identically zero. In all three cases the pixel reconstruction loss ℒrecL_rec still contributes a non-zero gradient. B.2 Proof of Proposition 2 Proof. By definition SAM(^,)=1HW∑i,jarccos^i,j⊤i,j‖^i,j‖⋅‖i,j‖.SAM( Y,Y)= 1HW _i,j y_i,j y_i,j\| y_i,j\|·\|y_i,j\|. For unit-norm vectors and small angles arccos(⊤)≤‖−‖2 (a b)\!≤\!\|a-b\|_2, so SAM≤‖^−‖2SAM\!≤\!E\,\| y-y\|_2. Linear separability ensures that every GT spectrum i,jy_i,j lies within ϵintra _intra (in raw spectral space) of its assigned centroid after applying †W , i.e. ‖i,j−†ck⋆V‖2≤ϵintra\|y_i,j-W c_k ^V\|_2\!≤\! _intra. For the prediction, if p^k⋆=1 p_k =1 the prediction lies within the same concept; otherwise by Lipschitz continuity of ψd _d the spectrum moves by at most LMd/K⋅(1−p^k⋆)LM d/K·(1- p_k ) on average. Summing over the K concepts gives the bound. ∎ Numerical illustration. With L=1.4L=1.4 (empirical Lipschitz constant of SigLIP-2 ViT-B dense features, measured on 5,0005,000 WV-I patches by finite differences), M=1.0M=1.0, d=1024d=1024, K=200K=200, ϵintra=0.005 _intra=0.005 rad and ∑k(1−p^k)=0.18K _k(1- p_k)=0.18K, the bound gives SAM≤5.18∘SAM\!≤\!5.18 . The observed SAM on WV-I is 2.75∘2.75 , so the bound is non-vacuous. When the proposition fails. The linear separability assumption is not innocuous. The mean per-concept dispersion ϵ¯intra ε_intra is 0.0040.004 rad on GF2, 0.0060.006 on QB, 0.0050.005 on WV-I, and 0.0110.011 on the cross-sensor WV-I split. Linear separability is satisfied on 98.4%98.4\% of held-out tiles via a logistic-regression test on the visual centroids. On WV-I the residual ϵintra _intra is larger and the bound correspondingly looser. B.3 Proof of Lemma 1 Proof. The cumulative threshold ∏j≤rαj _j≤ r _j is upper-bounded by (maxjαj)r( _j _j)^r and the maximum conditional co-occurrence probability is at most 11. Routing therefore terminates whenever (maxjαj)r≤ϵ( _j _j)^r\!≤\!ε, i.e. when r≥logϵ/logmaxjαjr\!≥\! ε/ _j _j. The vocabulary bound r≤Nr≤N is tight because at every accepted step at least one patch leaves the residual pool. For α=0.7,ϵ=10−3α=0.7,ε=10^-3, log0.710−3≈19.36 _0.710^-3\!≈\!19.36, so Rmax≤19R_ ≤19. ∎ Appendix C Cross-Sensor and Per-Class Results C.1 Bidirectional cross-sensor Q2n Table 6 reports the bidirectional cross-sensor pansharpening Q2n complementing the WV-I→ -I result in the main paper. CERES improves all four directions over the strongest baseline by +3.24+3.24% to +5.38+5.38%, with the largest relative gain on the heterogeneous 4-band→ 8-band transfer. Table 6: Bidirectional cross-sensor Q2n. Direction Best baseline CERES WV-I → WV-I 0.840 (CANConv) 0.879 (+4.64%) WV-I → WV-I 0.872 (CANConv) 0.901 (+3.33%) QB → WV-I (4→ 8) 0.781 (CANConv) 0.823 (+5.38%) WV-I → QB (8→ 4) 0.864 (CANConv) 0.892 (+3.24%) C.2 Per-class DOTA AP Table 7 reports the full 15-class oriented-object detection AP on the 4,0004,000-tile DOTA test split. The Oriented-RCNN head is trained on frozen DINOv2 features of the fused tiles for each pansharpening method under the identical hyperparameter recipe (Sec. E). CERES improves every class versus all baselines, and the gain monotonically tracks median oriented-box area: small classes gain +13.6+13.6 to +16.7+16.7 AP, medium classes +8.1+8.1 to +9.3+9.3, and large classes +5.3+5.3 to +5.6+5.6. Table 7: Per-class DOTA AP on the 4,0004,000-tile test split. SV: small vehicle, LV: large vehicle, PL: plane, HC: helicopter, SH: ship, TC: tennis-court, BC: basketball-court, ST: storage-tank, BR: bridge, RA: roundabout, HA: harbor, SP: swimming-pool, SBF: soccer-ball-field, BD: baseball-diamond, GTF: ground-track-field. Class ADKNet CrossDiff CANConv CERES Δ Small (median area <1,500<\!1,500 px2) SV 22.4 27.1 28.6 45.3 +16.7 PL 31.8 36.4 37.2 51.8 +14.6 SH 26.7 31.0 32.5 47.0 +14.5 HC 24.1 28.7 29.8 43.7 +13.9 TC 31.5 36.2 33.9 47.5 +13.6 Medium (1,5001,500–8,0008,000 px2) LV 33.2 38.9 39.4 48.7 +9.3 BC 36.4 39.5 41.2 50.1 +8.9 ST 35.5 40.0 39.8 48.4 +8.6 BR 37.8 41.4 40.9 49.0 +8.1 RA 36.6 40.8 41.2 50.3 +9.1 Large (>8,000>\!8,000 px2) HA 39.7 42.2 43.0 48.4 +5.4 SP 36.8 41.0 41.5 47.0 +5.5 SBF 38.6 41.7 41.9 47.5 +5.6 BD 38.5 41.9 42.3 47.8 +5.5 GTF 39.4 42.0 41.3 46.6 +5.3 mAP 33.9 37.8 38.2 47.9 +9.7 C.3 VLM-guided open-loop comparison Table 8 compares CERES to three open-loop adaptations of established VLM-conditioned restoration designs to pansharpening. None closes the loop; the closed-loop design of CERES delivers the largest gain on independent DINOv2 coverage. Table 8: VLM-guided open-loop baselines. Only CERES closes the loop. Baseline Q2n HQNR DINOC^DINO CLIPDenoising-style global cond. 0.912 0.931 0.66 DA-CLIP-style controller cond. 0.915 0.934 0.69 DenseCLIP-style dense cond. 0.917 0.938 0.72 CERES (closed-loop) 0.924 0.961 0.85 C.4 Independent DINOv2 coverage breakdown Table 9 decomposes DINOC^DINO into explicit (object-like) and implicit (relational) subsets across the four datasets. Implicit relational concepts are the hardest: the strongest baseline recovers 0.760.76 of explicit but only 0.450.45 of implicit concepts on WV-I, explaining why pixel fidelity can saturate yet downstream detection remains low. CERES narrows the gap to 0.91/0.790.91/0.79; the cross-sensor WV-I number remains the lowest because sensor response differences distort relational water–dock–vessel relations more than object-like primitives. Table 9: Per-dataset DINOv2 coverage decomposition. Dataset Explicit Implicit Overall GF2 0.95 0.86 0.91 QB 0.93 0.83 0.89 WV-I 0.91 0.79 0.85 WV-I (cross-sensor) 0.87 0.75 0.82 Best baseline (WV-I) 0.76 0.45 0.63 Appendix D Extra Ablations D.1 Vocabulary size Table 10 reports Q2n sensitivity to the centroid vocabulary K. Performance climbs quickly from K=50K=50 to K=100K=100, plateaus through K=250K=250, then degrades for K>300K>300 as the centroid system over-fragments. The 8-band datasets benefit from a larger K than the 4-band ones. Table 10: Q2n sensitivity to vocabulary size K. K GF2 QB WV-I WV-I 50 0.978 0.937 0.906 0.853 100 0.983 0.941 0.914 0.864 200 0.986 0.943 0.924 0.879 400 0.985 0.942 0.925 0.876 D.2 Routing depth Table 11 shows that R=3R=3 saturates on 8-band datasets and R=2R=2 already saturates on 4-band ones. Doubling R from 33 to 55 raises overall coverage by only +0.004+0.004 at twice the lookup cost. Table 11: Q2n vs. routing depth R. Bold = default. R GF2 QB WV-I WV-I 1 0.982 0.938 0.919 0.863 2 0.986 0.943 0.922 0.872 3 0.986 0.943 0.924 0.879 4 0.985 0.942 0.924 0.878 D.3 Markov approximation audit The chain-rule approximation N(1,…,r+1)≈N(1,…,r)⋅P(r+1|r,r−1)N(z_1,…,z_r+1)\!≈\!N(z_1,…,z_r)\!·\!P(z_r+1|z_r,z_r-1) replaces an (KR)O(K^R) tensor with an (K3)O(K^3) surrogate. Measured on WV-I, the routing accuracy under the exact R=3R=3 enumeration versus the Markov approximation has unit-Jaccard similarity 0.940.94 at depth 3 and 0.860.86 at depth 4, while storage drops from 1.41.4 TB to 3232 MB. D.4 Threshold sensitivity Varying the presence threshold for hard coverage over 0.3,0.5,0.7\0.3,0.5,0.7\ moves DINOC^DINO in 0.89,0.85,0.78\0.89,0.85,0.78\ but preserves the cross-method ranking at every threshold. Decreasing θIoU _IoU from 0.50.5 to 0.30.3 produces fragmented units that hurt Sem. Acc. by 0.0180.018. Decreasing the cumulative thresholds to (0.6,0.4,0.2)(0.6,0.4,0.2) admits more candidate patches but adds 1.7%1.7\% false-positive concepts. D.5 Convergence and scale-tag distribution The three-phase warm-up (Algorithm 1) avoids optimisation interference: Phase 1 (epochs 00–100100) stabilises ℒrecL_rec to 0.9040.904 Q2n; Phase 2 (100100–200200) turns on ℒTT,ℒTML_T,L_TM and reaches 0.9130.913; Phase 3 (200200–10001000) activates ℒcovL_cov and ℒsaL_sa and converges to 0.9240.924. Warm-up is dictated by Proposition 1. The saturation condition (A3) is directly measurable: at initialisation, 41.3%41.3\% of recovered presences satisfy p^k∉(0.05,0.95) p_k∉(0.05,0.95); after Phase 1 this drops to 11.8%11.8\%, and after Phase 2 to 4.6%4.6\%. Activating ℒcovL_cov from epoch 00 instead of epoch 200200 lowers final Q2n to 0.9170.917 (−0.007-0.007) and produces unstable early training, with the gradient-norm ratio ‖∇ℒcov‖/‖∇ℒrec‖\| _cov\|/\| _rec\| collapsing below 10−410^-4 on 38%38\% of Phase-1 steps, consistent with the prefactor collapse that Proposition 1 identifies under saturation. These measurements provide a principled motivation for delaying the coverage loss until recovered presences are largely non-saturated; we present the warm-up as a theory-informed design choice rather than a consequence uniquely determined by the proposition. Table 12 confirms that the scale-tag distribution responds to inherent scene complexity rather than a fixed prior: 8-band datasets allocate more weight to global units. Table 12: Scale-tag distribution across datasets (%). Dataset Local Meso Global GF2 52.3 31.4 16.3 QB 48.7 33.1 18.2 WV-I 38.5 36.2 25.3 WV-I 36.1 37.8 26.1 D.6 Joint factorial ablation of the injection mechanism Table 13 reports the complete 2×2×22×2×2 factorial grid over cross-scale attention (A), FiLM modulation (F), and the presence gate (G) on WV-I (three seeds; all other components fixed to the full configuration). The four rows shared with Table 4 match exactly. Three effects emerge. (i) Attention and FiLM are strongly super-additive: the mean A×F interaction on Q2n is +0.053+0.053, and either mechanism alone falls below the no-injection baseline, because unnormalised semantic injection (attention without FiLM’s channel re-scaling) or affine modulation of un-attended features (FiLM without attention’s spatial selection) perturbs decoder feature statistics. (i) The presence gate contributes mainly to HQNR (+0.026+0.026 mean main effect), consistent with its role of suppressing rewards for absent concepts. (i) The three-way interaction on HQNR is positive (+0.016+0.016): the gate is most valuable exactly when both injection mechanisms are active, because joint injection amplifies hallucinated concepts that the gate then suppresses. Table 13: Full 2×2×22×2×2 factorial over attention (A), FiLM (F), and presence gate (G) on WV-I (three seeds). A F G Q2n↑ HQNR↑ × × × 0.908 0.919 × × ✓ 0.911 0.927 ✓ × × 0.874 0.896 × ✓ × 0.882 0.907 ✓ × ✓ 0.889 0.918 × ✓ ✓ 0.893 0.928 ✓ ✓ × 0.901 0.910 ✓ ✓ ✓ 0.924 0.961 D.7 Language-causality ablation The venue-relevant question is whether the language pathway is causally load-bearing or merely a descriptive interface over a vision pipeline. We therefore run a single-variable intervention: all five settings retain the identical CERES architecture and visual pathway — the same generator, injection modules, and router — and differ only in the text-anchor set supplied to Stages I–IV. Each setting is retrained from scratch under the identical schedule with the same three seeds (WV-I); this is a training-time intervention, not an inference-time substitution on shared checkpoints. The settings are: correct anchors (full CERES); paraphrased anchors (every prompt replaced by an LLM paraphrase before encoding); a generic global caption whose embedding replaces all K anchors; zeroed anchors (image-only: the anchor is set to the zero vector with the normalisation in Eq. (8) skipped, which nulls the injection pathway and leaves the text-dependent losses ℒTT,ℒTM,ℒcov,ℒsaL_T,L_TM,L_cov,L_sa without gradient signal, so training reduces to ℒrecL_rec); and shuffled anchors (the assignment k↔ke_k\! \!k is randomly permuted, so the correspondence is actively mismatched while every embedding is still a valid concept anchor). Results are in Table 14. Table 14: Single-variable intervention on the language pathway (WV-I, 3 seeds; architecture and visual pathway identical in all rows). Anchor setting Q2n DINOC^DINO R@5loc_loc R@5meso_meso R@5glob_glob MRR Correct (full CERES) 0.924 0.85 0.71 0.62 0.85 0.74 Paraphrased 0.923 0.84 0.70 0.61 0.85 0.73 Generic caption 0.913 0.68 0.55 0.44 0.83 0.57 Zeroed (image-only) 0.912 0.62 0.52 0.40 0.81 0.54 Shuffled 0.914 0.60 0.45 0.38 0.80 0.49 Pixel metrics vary by at most 0.0120.012 Q2n across the five settings, whereas local/meso retrieval and coverage decrease substantially when the language–concept correspondence is removed, coarsened to a single caption, or deliberately mismatched. Shuffled anchors yield lower R@5loc_loc than zeroed anchors (0.450.45 vs. 0.520.52), while global-query performance changes only modestly (0.800.80–0.850.85) and paraphrasing has little effect. Because the architecture and visual pathway are held fixed, these controlled interventions show that text anchors are causally load-bearing for local- and meso-scale re-indexability within CERES on WV-I, rather than serving as a merely descriptive interface over a vision pipeline; the effect is tied to the anchor–concept correspondence rather than to surface phrasing. D.8 Joint sensitivity of K, τ, and template count Table 15 crosses the centroid vocabulary K with the membership temperature τ on WV-I. Within each K column, τ moves Q2n by at most 0.0030.003; the K effect saturates at K≥200K≥200, consistent with Table 10. Growing the verifier template family from 44 to 3636 templates moves DINOC^DINO from 0.820.82 to 0.850.85 with a plateau at 1212: 4,8,12,24,36\4,8,12,24,36\ templates give DINO=0.82,0.84,0.85,0.85,0.85C^DINO=\0.82,0.84,0.85,0.85,0.85\ and mean Recall@5 0.69,0.72,0.73,0.73,0.73\0.69,0.72,0.73,0.73,0.73\. The default (K=200,τ=0.07CLOSE(K=200,τ=0.07, 1212 templates)) sits on a broad plateau rather than a tuned peak. Table 15: Q2n on WV-I for the K×τK×τ grid. τ τ\; \;K 100 200 400 0.05 0.911 0.921 0.922 0.07 0.914 0.924 0.925 0.10 0.912 0.922 0.923 D.9 Centroid quality and dataset-bias robustness Seed variance. Across 1010 k-means restarts (fixed data, different seeds), WV-I Q2n varies by 0.924±0.0010.924± 0.001, DINOC^DINO by 0.850±0.0040.850± 0.004, and mean Recall@5 by 0.730±0.0060.730± 0.006: centroid stochasticity is negligible relative to the method-to-method gaps in Table 1. Initialisation. k-means++, random initialisation, and spherical k-means give Q2n 0.924/0.922/0.9250.924/0.922/0.925 and DINOC^DINO 0.85/0.84/0.850.85/0.84/0.85. Biased centroid pools. Re-fitting the K=200K=200 centroids on deliberately biased pools (Table 16) degrades pixel metrics by at most 0.0080.008 Q2n, but coverage and retrieval degrade selectively: concepts absent from the pool lose −0.09-0.09 Recall@5 on average, while concepts present in the pool lose only −0.01-0.01. Dataset bias therefore maps to a localised, diagnosable coverage loss on the missing concept families rather than a global failure. Pool size. Pools of 55k/20/20k/80/80k patches give DINO=0.83/0.85/0.85C^DINO=0.83/0.85/0.85. Table 16: Centroid-pool bias on WV-I. Centroid pool Q2n DINOC^DINO R@5 Balanced (default, 20k) 0.924 0.85 0.73 Urban-only 0.918 0.82 0.70 Rural-only 0.916 0.80 0.68 Maritime-only 0.917 0.81 0.69 Appendix E Prompt Templates, DOTA Protocol, Reproducibility E.1 Prompt template family The verifier of Stage I/IV maps mask statistics k=[ρk,nk,c¯k,σk2]s_k=[ _k,n_k, c_k, _k^2] to a fixed family of 1212 typed prompt templates, four per scale tag. The templates are parameter-free, shared across datasets, and never tuned per sensor (Table 17). Each template instantiates the component count nkn_k, area ratio ρk⋅100% _k·100\%, centroid c¯k c_k and dispersion σk2 _k^2, then is encoded by ϕφ. Table 17: The 12 prompt templates of the verifier. Global (sk=3s_k=3). “a wide-area scene of top-3 concepts” “a landscape dominated by concept with ρ⋅100%ρ·100\% coverage” “an urban / rural mosaic of concept and concept” “a scene whose principal layout is concept” Meso (sk=2s_k=2). “a q-scale region with nkn_k concept instances covering ρ⋅100%ρ·100\%” “a layout with concept adjacent to concept” “a corridor of concept arranged along the c¯k c_k direction” “a cluster of concept with dispersion σk2 _k^2” Local (sk=1s_k=1). “nkn_k instances of concept with mean activation M¯k M_k” “small concept located near c¯k c_k” “nkn_k compact concept occupying ρ⋅100%ρ·100\% of the tile” “a fine-grained concept with dispersion σk2 _k^2” A prompt-template ablation in the main paper that replaces these 1212 templates with an LLM-generated 3636-template superset moves DINOC^DINO by less than 0.010.01, indicating that the recovered concept set is robust to prompt phrasing. E.2 DOTA tile protocol We crop 20,00020,000 overlapping 512×512512×512 tiles (stride 384384) from DOTA-v1.0 and split by source image identifier into 16,00016,000 training tiles and 4,0004,000 test tiles. The split is source-image-disjoint: no source image contributes tiles to both sides, so train–test leakage through spatial overlap is impossible; we verify by hashing the source identifier set. The Oriented-RCNN head follows MMRotate defaults: two RoI heads with rotated bounding-box regression, AdamW with learning rate ×10−55\!×\!10^-5, batch size 44, 2424 epochs, random rotation augmentation, and standard DOTA mAP evaluation. E.3 Coverage probe construction For each concept k with text prompt kt_k we collect a prototype set kP_k of DINOv2 ViT-B dense features from AID, NWPU-RESISC45, and DOTA crops whose external labels match kt_k. The negative set kN_k is sampled class-balanced from non-matching labels. We fit (k,bk)(w_k,b_k) by 5-fold logistic regression with L2L_2 weight 10−310^-3 on k∪kP_k _k, and the probe is frozen for all downstream evaluations. E.4 Hyperparameters Table 18 summarises every hyperparameter used. None is tuned per sensor; the same configuration is shared across the four datasets and three seeds. Table 18: Hyperparameters shared across all datasets and seeds. Component Value Centroid count K 200200 Router depth R 33 Routing thresholds (α1,α2,α3)( _1, _2, _3) (0.7,0.5,0.3)(0.7,0.5,0.3) IoU threshold θIoU _IoU 0.50.5 Membership temperature τ 0.070.07 Filter quantiles (z1,z2)(z_1,z_2) (0.4,0.2)(0.4,0.2) Loss weights (1.0,0.5,0.3,0.2)(1.0,0.5,0.3,0.2) Optimiser AdamW Learning rate 5×10−45×10^-4 Batch size 6464 Epochs (with halving every 200200) 10001000 Centroid k-means seed / restarts 4242 / 1010 Co-occurrence radius (patches) 33 E.5 Per-module compute cost Table 19 reports per-module compute on a single 64×6464×64 PAN input on an RTX 4090. The frozen SigLIP-2 forward pass dominates inference time but is amortised across retrieval and tagging in any host knowledge system that already deploys a VLM. Peak allocated CUDA memory during training (AMP/fp16, batch 6464, 64×6464×64 PAN inputs, AdamW states and gradients included) is 11.411.4 GB, decomposed disjointly into 6.86.8 GB of Stage-I frozen-VLM activations, 2.12.1 GB of additional Stage-I re-encoding activations, and 2.52.5 GB for the lightweight path, optimiser states, and buffers. Stages I–IV are used during training and are not required for generation-only deployment (peak 1.91.9 GB, batch 11); they are invoked only when an output coverage certificate is requested, which adds one encoder pass and 0.60.6 GB transiently. Peak allocated CUDA memory during training (AMP/fp16, batch 6464, 64×6464×64 PAN inputs, AdamW states and gradients included) is 11.411.4 GB, decomposed disjointly into 6.86.8 GB of Stage-I frozen-VLM activations, 2.12.1 GB of additional Stage-I re-encoding activations, and 2.52.5 GB for the lightweight path, optimiser states, and buffers. Stages I–IV are used during training and are not required for generation-only deployment (peak 1.91.9 GB, batch 11); they are invoked only when an output coverage certificate is requested, which adds one encoder pass and 0.60.6 GB transiently. Table 19: Per-image cost decomposition (64×6464×64 PAN, RTX 4090). Module Params FLOPs Time (ms) SigLIP-2 (frozen) 400 M 12.1 G 8.2 Pseudo-RGB projection 0.01 M 0.003 G 0.1 Explicit branch 0.05 M 0.12 G 0.8 Implicit router – 0.09 G 2.4 Adaptive filter 0.03 M 0.04 G 0.5 U-Net generator 0.28 M 1.23 G 4.3 Stage I re-encode 400 M 12.1 G 8.2 Soft-Jaccard verifier – 0.06 G 1.0 Non-VLM lightweight path 0.39 M 1.54 G 9.1 Generation-only (Stages I–I) 400.4 M 13.58 G 16.3 Full closed loop (Stages I–IV) 400.4 M 25.74 G 25.5 The non-VLM lightweight path row aggregates all non-VLM modules; it includes the parameter-free router and verifier, and 0.390.39 M is its trainable parameter count. Parameter sharing and compute sharing are distinct: the frozen encoder’s parameters are counted once (Stages I and I share weights), but its two forward passes process different images (input versus generated output), so both passes are counted in the FLOPs and latency of the full closed loop. Figure 7: Explicit and implicit unit activations from Stage I on a WV-I scene. Each row shows the membership map of a single unit overlaid on the input tile. Implicit units (right) span relational structures invisible to single-scale conditioning. E.6 Unit activations Figure 7 visualises representative explicit and implicit unit activations on a WV-I scene. Explicit units form compact, high-confidence supports over object-like primitives. Implicit units span elongated or compound layouts such as runway–apron corridors and harbour–dock–vessel relations. The median support area is 0.6%0.6\% for sk=1s_k=1, 4.3%4.3\% for sk=2s_k=2, and 24.7%24.7\% for sk=3s_k=3. Each row corresponds to a single unit at one of the three scale tags (sk=1/2/3s_k=1/2/3); the soft membership column shows the differentiable presence mass mk(i,j)m_k(i,j) and the recovered mask column shows the verifier response ~k M_k after re-encoding the generated image. The residual column highlights pixels where the recovered mask disagrees with the input membership and is the signal that ℒcovL_cov minimises during training. Appendix F Cross-Domain Pilot: Histopathology Super-Resolution The introduction motivates semantic collapse with whole-slide pathology, whose concept hierarchy (cell nuclei → glandular structures → tumour–stroma layout) mirrors the local/meso/global pyramid. To test whether the CERES recipe transfers beyond remote sensing, we run a deliberately small pilot on 4×4× histopathology super-resolution. Setup. We extract 8,0008,000 training and 1,0001,000 test 256×256256×256 tiles at 0.5μ0.5\, /px from Camelyon16 whole-slide images, downsampling to 2μ2\, /px inputs. Following the recipe in Sec. 3, only the K=200K=200 centroids are re-fitted (on 2020k pathology patches); every hyperparameter of Table 18 — τ, R, α1:3 _1:3, θIoU _IoU, loss weights, warm-up schedule — is reused unchanged. Prompt templates keep their schema with domain nouns (e.g. “nkn_k instances of mitotic figure”). The independent probe is a DINOv2 linear probe fit on PCam tumour/normal and NCT-CRC-HE-100K tissue-type labels, never seen in training. A 3030-query bank covers 1010 cellular, 1010 glandular, and 1010 tissue-level queries. Table 20: Histopathology 4×4× SR pilot (Camelyon16 test tiles). Method PSNR↑ SSIM↑ DINO↑C^DINO\! R@5↑ Bicubic 27.8 0.86 0.58 0.44 SwinIR-light 31.2 0.91 0.66 0.55 Open-loop SigLIP U-Net 31.4 0.91 0.70 0.58 CERES (closed-loop) 31.6 0.92 0.83 0.71 Results. Table 20 reproduces the remote-sensing pattern: pixel metrics are nearly saturated across learning-based methods (31.431.4 vs. 31.631.6 PSNR), yet closed-loop coverage verification lifts label-grounded coverage from 0.700.70 to 0.830.83 and mean Recall@5 from 0.580.58 to 0.710.71 (+13+13 p). The gain concentrates on cellular-scale queries (→0.580.40\!→\!0.58 R@5), the pathology analogue of the small-object result of Table 7. The pilot is small and uses a single organ site, so we do not claim clinical validity; its role is to show that the closed-loop recipe, with unchanged hyperparameters and only re-fitted centroids, is not specific to satellite imagery.