Paper List
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Developing the PsyCogMetrics™ AI Lab to Evaluate Large Language Models and Advance Cognitive Science
This paper addresses the critical gap between sophisticated LLM evaluation needs and the lack of accessible, scientifically rigorous platforms that in...
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Equivalence of approximation by networks of single- and multi-spike neurons
This paper resolves the fundamental question of whether single-spike spiking neural networks (SNNs) are inherently less expressive than multi-spike SN...
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The neuroscience of transformers
提出了Transformer架构与皮层柱微环路之间的新颖计算映射，连接了现代AI与神经科学。
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Framing local structural identifiability and observability in terms of parameter-state symmetries
This paper addresses the core challenge of systematically determining which parameters and states in a mechanistic ODE model can be uniquely inferred ...
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Leveraging Phytolith Research using Artificial Intelligence
This paper addresses the critical bottleneck in phytolith research by automating the labor-intensive manual microscopy process through a multimodal AI...
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Neural network-based encoding in free-viewing fMRI with gaze-aware models
This paper addresses the core challenge of building computationally efficient and ecologically valid brain encoding models for naturalistic vision by ...
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Scalable DNA Ternary Full Adder Enabled by a Competitive Blocking Circuit
This paper addresses the core bottleneck of carry information attenuation and limited computational scale in DNA binary adders by introducing a scalab...
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ELISA: An Interpretable Hybrid Generative AI Agent for Expression-Grounded Discovery in Single-Cell Genomics
This paper addresses the critical bottleneck of translating high-dimensional single-cell transcriptomic data into interpretable biological hypotheses ...
Covering Relations in the Poset of Combinatorial Neural Codes
Pacific Northwest National Laboratory | Florida Atlantic University
30秒速读
IN SHORT: This work addresses the core challenge of navigating the complex poset structure of neural codes to systematically test the conjecture linking convex neural codes to representable oriented matroids.
核心创新
- Methodology Provides the first complete characterization of upward covering relations in the poset P_Code of combinatorial neural codes.
- Theory Introduces a constructive method to generate all codes that cover a given neural code, based on the concept of isolated subsets within its intersection completion.
- Methodology Establishes a key lemma (Lemma 3.1) showing that a morphism between codes uniquely extends to a morphism between their intersection completions, preserving surjectivity.
主要结论
- A code C covers a code D in P_Code if and only if its intersection completion C_hat covers D_hat (Lemma 3.3).
- If C covers D, then C_hat is isomorphic to D_hat_[I] for some isolated subset I ⊆ D_hat (Theorem 3.5).
- All codes covering a given code D can be constructed via four explicit types of operations on isolated subsets of D_hat, as defined in Definition 3.9 and Table 1.
摘要: A combinatorial neural code is a subset of the power set 2[n] on [n]={1,…,n}, in which each 1≤i≤n represents a neuron and each element (codeword) represents the co-firing event of some neurons. Consider a space X⊆ℝd, simulating an animal’s environment, and a collection 𝒰={U1,…,Un} of open subsets of X. Each Ui⊆X simulates a place field which is a specific region where a place cell i is active. Then, the code of 𝒰 in X is defined as code(𝒰,X)={σ⊆[n]|⋂i∈σUi∖⋃j∉σUj≠∅}. If a neural code 𝒞=code(𝒰,X) for some X and 𝒰, we say 𝒞 has a realization of open subsets of some space X. Although every combinatorial neural code obviously has a realization by some open subsets, determining whether it has a realization by some open convex subsets remains unsolved. Many studies attempted to tackle this decision problem, but only partial results were achieved. In fact, a previous study showed that the decision problem of convex neural codes is NP-hard. Furthermore, the authors of this study conjectured that every convex neural code can be realized as a minor of a neural code arising from a representable oriented matroid, which can lead to an equivalence between convex and polytope convex neural codes. Even though this conjecture has been confirmed in dimension two, its validity in higher dimensions is still unknown. To advance the investigation of this conjecture, we provide a complete characterization of the covering relations within the poset 𝐏𝐂𝐨𝐝𝐞 of neural codes.