Platonic Projection Structures: Operator-Induced Observability in Representation Learning

We characterize observability in representation learning through Platonic Projection Structures (PPS), an operator-theoretic framework for analyzing representation accessibility under partial observation. Rather than treating observable outputs as direct reflections of latent representations, PPS models observation through a self-adjoint positive semidefinite operator acting on a latent representation space. A system is represented as a triple $(H, Π, O)$, where $H$ is a latent representation space, $Π\succeq 0$ is an observation operator, and $O(v)=\langle v,Πv\rangle$ defines an induced scalar observable. Observability is characterized by the quotient geometry $H/\ker(Π)$, representing equivalence classes of latent states indistinguishable under observation. We show that quantum measurement and representation inference under linear observation models share this operator-theoretic structure while differing in the algebraic properties of their observation operators; the correspondence is structural rather than physical. Representation transfer and knowledge distillation can likewise be interpreted as approximate preservation of observable geometry through $ΦΠ_T \approx Π_S Φ$. PPS also reveals a structural limitation of output-based interpretability: latent components in $\ker(Π)$ are inaccessible from induced observables, imposing intrinsic constraints on attribution and explanation methods. Controlled empirical validations demonstrate kernel-invariant observability, projection-induced attribution gaps, and rank-controlled observable geometry in latent representation spaces. PPS thus provides an explicit characterization of observability through operator-induced quotient geometry and a unified perspective on representation accessibility, interpretability, and projection-mediated inference.

BianQue: Balancing the Questioning and Suggestion Ability of Health LLMs with Multi-turn Health Conversations Polished by ChatGPT

Large language models (LLMs) have performed well in providing general and extensive health suggestions in single-turn conversations, exemplified by systems such as ChatGPT, ChatGLM, ChatDoctor, DoctorGLM, and etc. However, the limited information provided by users during single turn results in inadequate personalization and targeting of the generated suggestions, which requires users to independently select the useful part. It is mainly caused by the missing ability to engage in multi-turn questioning. In real-world medical consultations, doctors usually employ a series of iterative inquiries to comprehend the patient's condition thoroughly, enabling them to provide effective and personalized suggestions subsequently, which can be defined as chain of questioning (CoQ) for LLMs. To improve the CoQ of LLMs, we propose BianQue, a ChatGLM-based LLM finetuned with the self-constructed health conversation dataset BianQueCorpus that is consist of multiple turns of questioning and health suggestions polished by ChatGPT. Experimental results demonstrate that the proposed BianQue can simultaneously balance the capabilities of both questioning and health suggestions, which will help promote the research and application of LLMs in the field of proactive health.