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"scenario": "A product assistant retrieves plausible documents but gives unsupported answers.",
"change": "Change one retrieval or ranking step while keeping the document snapshot fixed.",
"baseline": "Your current retrieval pipeline with identical questions and answer model.",
"steps": [
"Locate the paper's implementation and check its license, model support, data needs, and hardware requirements. Stop here if you cannot obtain the required artifacts.",
"Save a small set of representative product tasks and expected outcomes. Keep evaluation tasks out of any training or tuning, and choose quality and cost limits before running.",
"Run the baseline and the proposed change on identical inputs. Keep other settings fixed and repeat paired runs to expose variation.",
"Save per-task outputs, failures, timings, and all usage costs. Review regressions before expanding the test."
],
"measure": "Supported answers, retrieval misses, correct abstentions, index cost, and response latency.",
"decision": "Keep the change only if it meets your preselected quality and latency limits and improves the metric you care about after setup and operating costs. Otherwise retain the baseline. This is an exploration plan, not a validated recommendation."
},
"builder_review": null,
"arxiv_id": "2608.04234",
"title": "Multimodal Alignment Through Joint Kernel Entropic Gromov--Wasserstein Optimal Transport",
"summary": "Replaces labeled-pair cross-modal fine-tuning with post-hoc alignment of pretrained encoder embeddings using quadratic optimal transport. A low-rank kernel approximation and alternating variational solver add implementation and computational cost, although working on embeddings allows a CPU or small GPU. Weak unimodal encoders or incompatible within-modality similarity structures can undermine the method, which preserves geometry already present in the embeddings.",
"rationale": "Worth a bounded test for cross-modal retrieval with few paired examples, but requires a nontrivial optimal-transport solver rather than direct adoption.",
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"anchor": "S2.E1",
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"section": "2 Joint Kernel Gromov–Wasserstein Optimal Transport",
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"latex": "S_{\\epsilon}(\\{\\mu^{i}\\}_{i=1}^{M},\\nu)\\coloneqq\\inf_{\\begin{subarray}{c}\\pi^{i}\\in\\Gamma(\\mu^{i},\\nu)\\\\\ni\\in[M]\\end{subarray}}\\Bigg\\{ \\sum_{i,j=1}^{M}\\int_{\\mathcal{X}^{i}\\times\\mathcal{Z}}\\int_{\\mathcal{X}^{j}\\times\\mathcal{Z}}K(x,x^{\\prime})\\|z-z^{\\prime}\\|^{2}\\,d\\pi^{i}(x,z)\\,d\\pi^{j}(x^{\\prime},z^{\\prime}) \\\\ +\\epsilon\\sum_{i=1}^{M}D_{\\mathrm{KL}}\\!\\left(\\pi^{i}\\,\\middle\\|\\,\\mu^{i}\\otimes\\nu\\right)\\Bigg\\}.",
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"context": "Motivated by the kernel-weighted pairwise penalty shown above, we define our JK-EGW objective as",
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"latex": "S^{R}_{\\epsilon}(\\{\\mu^{i}\\}_{i=1}^{M},\\nu)\\coloneqq\\inf_{\\begin{subarray}{c}\\pi^{i}\\in\\Gamma(\\mu^{i},\\nu)\\\\\ni\\in[M]\\end{subarray}}\\Bigg\\{ \\sum_{i,j=1}^{M}\\int_{\\mathcal{X}^{i}\\times\\mathcal{Z}}\\int_{\\mathcal{X}^{j}\\times\\mathcal{Z}}\\Phi_{R}(x)^{\\top}\\Phi_{R}(x^{\\prime})\\|z-z^{\\prime}\\|^{2}\\,d\\pi^{i}(x,z)\\,d\\pi^{j}(x^{\\prime},z^{\\prime}) \\\\ +\\epsilon\\sum_{i=1}^{M}D_{\\mathrm{KL}}\\!\\left(\\pi^{i}\\,\\middle\\|\\,\\mu^{i}\\otimes\\nu\\right)\\Bigg\\}.",
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"context": "Fix a truncation rank . Under Assumption 2.2, the finite-rank term separates the dependence of the kernel on and . We can thus introduce a rank- JK-EGW objective by replacing by its rank- approximation,",
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},
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"section": "2 Joint Kernel Gromov–Wasserstein Optimal Transport",
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"latex": "\\inf_{\\pi}\\iint\\bigl|c_{\\mathcal{X}}(x,x^{\\prime})-c_{\\mathcal{Z}}(z,z^{\\prime})\\bigr|^{2}\\,d\\pi(x,z)\\,d\\pi(x^{\\prime},z^{\\prime}).",
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"context": "Specifically, the standard quadratic GWOT aligns distributions by comparing pairwise relational structures in different spaces. One specifies relational functions and on the source and target spaces, and seeks a coupling whose paired samples minimize the relational difference in aggregate,",
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