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    "story_id": "mp-2026-08-13-014",
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    "headline": "The Machine Can Carry Its Own Gradient",
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    "dek": "A unifying theory specifies when a physical computing system can generate the adjoint field needed to train itself on-device.",
    "summary": "A unifying theory specifies when a physical computing system can generate the adjoint field needed to train itself on-device.",
    "body_text": "The work derives sufficient conditions for formally exact physical gradients. Linear systems may tolerate damping or gain when reciprocity is preserved, while nonlinear trajectory systems require reciprocity of the linearized dynamics and a time-reversal mirror. The framework recovers several previously separate physical-learning schemes and extends through a broader intertwining condition to some non-reciprocal systems. It is a theoretical synthesis and construction guide, not a single new hardware demonstration.",
    "why_it_matters": "A unifying theory specifies when a physical computing system can generate the adjoint field needed to train itself on-device.",
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      "It is a theoretical synthesis and construction guide, not a single new hardware demonstration."
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    "first_published_at": "2026-08-13T09:00:00.000-04:00",
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    "tags": [
      "physical computing",
      "backpropagation",
      "photonics",
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      "title": "arXiv preprint 2608.11585",
      "publisher": "arXiv",
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      "published_at": "2026-08-11T22:53:39.000-04:00",
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    "title": "The Machine Can Carry Its Own Gradient",
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