One Spectrum, Two Resources: Data-Memory Scaling in Autoregressive Prediction · Research brief

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What you would change

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Compare against

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Run the baseline and the proposed change on identical inputs. Keep other settings fixed and repeat paired runs to expose variation.
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What to measure

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When to keep it

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abstract indexedPaperraft next step

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Abstract-level screening only. Risks and infrastructure may not have been evaluated. This recommendation is not a reproduced result.

minimum test setup: not reported
published evidence setup: not reported
source-linked claims: 0 of 1
exposure checks: 0 of 8

Why it was shortlisted

The technical change, research area, and reason it entered the archive.

recommendation: watch
research area: other
technical change: Data-memory scaling law for autoregressive prediction
published: 2026-09-11

This is a theoretical scaling-law result without an actionable method, so it is relevant background for capacity planning but not something a constrained-infrastructure team can adopt or benchmark now.

Central equations

Original equations, typeset for reading. Paperraft explanations connect the mechanism, its aim, and the evidence.

For the bounded-logit value experiment,

ℜ^{*}_{value} (n, B) ≍_{R} Φ_{μ} (n^{- 1}) + Φ_{μ} (τ_{B}) .

equation (3.3) · §3 The Energy-per-Coordinate Spectrum: Minimax Risk and Identifiability · proposed method

Let $q_{i} > 0$ , $\sum_{i} q_{i} < \infty$ , and let $μ$ , $Φ_{μ}$ , and $τ_{B}$ be defined above. Then

𝒮_{q} ​ (n) : = \sum_{i} \min {q_{i}, n^{- 1}} = Φ_{μ} ​ (n^{- 1}),

equation (3.1) · §3 The Energy-per-Coordinate Spectrum: Minimax Risk and Identifiability · metric

Let $q_{i} > 0$ , $\sum_{i} q_{i} < \infty$ , and let $μ$ , $Φ_{μ}$ , and $τ_{B}$ be defined above. Then

D_{q} ​ (B) : = inf_{\begin{matrix} b_{i} \geq 0 \\ \sum_{i} b_{i} \leq B \end{matrix}} \sum_{i} q_{i} ​ 2^{- 2 ​ b_{i}} = Φ_{μ} ​ (τ_{B}) .

equation (3.2) · §3 The Energy-per-Coordinate Spectrum: Minimax Risk and Identifiability · metric

equations from arXiv HTML · fetched 2026-09-30

Claims and evidence

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claim 01Paperraft inference
Read the brief interpretation
The paper does not propose a deployable technique; it proves a minimax law linking dataset size and learned-state memory through a single predictive-energy spectrum, replacing heuristic capacity-data sizing rules with a theoretical curve. It costs nothing to adopt directly but offers no implementation, serving path, or quantified efficiency gain; the weight-only quantization section is an examination of existing pretrained models, not a new compression method. The law's assumptions (positive-entropy autoregressive retrieval source, optimal bit allocation, two-sided arithmetic bounds) may not hold for real pretraining workloads, so its exponents may not transfer to production model sizing decisions.
This is a Paperraft inference. It is not pinned to a verified PDF passage.
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Exposure map

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quality

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compute and memory

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latency

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Are startup time, typical response time, and slow requests measured separately?

operations

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software compatibility

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Does the implementation support your model, runtime, and hardware?

security

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data and training

Still unknown

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reproducibility

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Questions to guide your next reading.

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What to inspect

Which assumptions does the proposed method need, and where might your workload violate them?

Plan a fair comparison

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Questions for adoption

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Inside the paper

Preview the first 3 pages of the original PDF. Click the stack to turn the page.

The downloadable skill includes SKILL.md and evidence.json, with recorded findings and unanswered checks. TRY-IT.md adds a product test plan and a blank results sheet.

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Provisional research brief updated 2026-10-18. Paperraft has not reproduced this experiment.