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Linear memory capacity depends on retrieval: $n\log n$ for top-1, $n$ for listwise

By PulseAugur Editorial · [2 sources] ·

Researchers have analyzed the capacity limits of linear associative memory, finding that the retrieval criterion significantly impacts how many associations can be stored. For top-1 retrieval, where a signal must outperform all others, the memory size scales as $d^2 \asymp n \log n$. When considering listwise retrieval, which allows the correct target to be among a controlled list of strong candidates, the capacity scales quadratically as $d^2 \asymp n$. This work introduces the Tail-Average Margin (TAM) criterion to formalize listwise retrieval and develops an asymptotic theory for its performance. AI

IMPACT Provides theoretical insights into the capacity limits of memory systems, relevant for designing future AI architectures.

RANK_REASON This is a research paper detailing theoretical findings on associative memory capacity.

Read on arXiv stat.ML →

AI-generated summary · Google Gemini · from 2 sources. How we write summaries →

Linear memory capacity depends on retrieval: $n\log n$ for top-1, $n$ for listwise

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COVERAGE [2]

  1. arXiv cs.LG TIER_1 English(EN) · Nicholas Barnfield, Juno Kim, Eshaan Nichani, Jason D. Lee, Yue M. Lu ·

    Sharp Capacity Thresholds in Linear Associative Memory: From Winner-Take-All to Listwise Retrieval

    arXiv:2605.05189v1 Announce Type: cross Abstract: How many key-value associations can a $d\times d$ linear memory store? We show that the answer depends not only on the $d^2$ degrees of freedom in the memory matrix, but also on the retrieval criterion. In an isotropic Gaussian mo…

  2. arXiv stat.ML TIER_1 English(EN) · Yue M. Lu ·

    Sharp Capacity Thresholds in Linear Associative Memory: From Winner-Take-All to Listwise Retrieval

    How many key-value associations can a $d\times d$ linear memory store? We show that the answer depends not only on the $d^2$ degrees of freedom in the memory matrix, but also on the retrieval criterion. In an isotropic Gaussian model for the stored pairs, we show that top-1 retri…

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