Daily research notes14 min read

Predicting mixtures, identifying gains

Meta Models · Limits of data curation · Reading LoRA

Two main readings, two briefs, and three version watches recovered in the overlapping window: predicting experiments from training records and separating acceleration from persistent curation gains. The classic is LoRA and its factorized gradients.

Scaling lawsData mixingPost-training
Daily classic · 2022LoRA
Main readingRelevant methods and experiments read; not reproduced

Treat mixture experiments as numeric regression

Meta Models: Models that Model Learning
Peihang Li · Ziming Liu
First submitted 2026-10-27 · v1 · Recovered in the overlapping window

Building on parametric scaling curves (Kaplan, 2020; Chinchilla, 2022), this paper supplies configurations q, progress t, and historical losses to frozen TabPFN. Mixture proportions are configuration fields.[1]

The prediction target; context updates do not train weights [1]
R={(qi,tij,Lij)}i,j,L^(q,t)=fθ(q,t∣R)\mathcal R=\{(q_i,t_{ij},L_{ij})\}_{i,j},\qquad \widehat L(q,t)=f_\theta(q,t\mid\mathcal R)
Evaluation designTabPFNBaseline
Delphi: 3,737 runs; 24 held-out groups; mean Spearman ρ0.967XGBoost 0.875

Leaving out five-domain mixtures individually, MAE is about 20%–40% below the best evaluated parametric law at four model sizes; laws win on two-domain mixtures and some RedPajama settings.[1]

Main readingRelevant methods and experiments read; not reproduced

Reaching it faster, or reaching a better endpoint?

Advancement or Acceleration? How Data Curation Improves LLM Training
Jiaxing Wang · Zicheng Zhang · Deping Xiang · Jin Xu · Yong Li · Chao Liu · Pengzhang Liu · Qixia Jiang
First submitted 2026-10-27 · v1 · Recovered in the overlapping window

The paper analyzes growing sample budgets in teacher–student perceptrons and distinguishes the effects empirically in LLMs. If the population training objective equals target loss and the baseline is globally optimal, reallocation cannot beat that optimum; finite-budget acceleration remains possible.[2]

Population optimality without shift; not a nonconvex training guarantee [2]
θ0∈arg⁡min⁡θLtar(θ)⟹Ltar(θ(w))≥Ltar(θ0)\theta_0\in\arg\min_\theta L_{\rm tar}(\theta)\quad\Longrightarrow\quad L_{\rm tar}(\theta(w))\ge L_{\rm tar}(\theta_0)
Domain-level diagnostic; training loss is measured on seen examples [2]
Δ=∑k∣w^kLtark(θ0)−wkLtraink(θ0)∣\Delta=\sum_k\left|\widehat w_k L^k_{\rm tar}(\theta_0)-w_k L^k_{\rm train}(\theta_0)\right|
160M GPT / SlimPajama; 40K steps, five runsUniform PPLTANDEM PPL
Near-zero gap: Δ=0.0719.7119.66
Limited data: Δ=0.6428.6026.02
Held-out CC target: Δ=1.2649.1940.24
BriefBased on the abstract

Sources and diversity at small data scale

Specialization, Diversity, and Scaling in Child-Scale Language Models
Steven Y. Feng · Michael C. Frank
First submitted 2026-10-27 · v1 · Recovered in the overlapping window

Based on the abstract: small GPT-2 models use BabyView home-recording transcripts and synthetic TinyDialogues, varying quantity, source, and diversity of child environments. Multiple children improve pooled held-out language prediction, without equally clear grammatical-benchmark gains; one loss does not represent every capability.[3]

BriefBased on the abstract

Effective critical exponents for grokking

Scaling and Renormalization in Neural Networks: An Effective Renormalization-Group Description of Grokking
Min Chen · Junqi Wang · Zeguan Wu · Wenhao Huang · Junyu Liu
First submitted 2026-10-26 · v1 · Recovered in the overlapping window

Based on the abstract: in two-layer modular-addition networks, a second-order loss expansion in per-neuron norms defines couplings, followed by Fiedler ordering and coarse-graining to estimate critical exponents. This concerns scaling of ML generalization transitions, rather than a universal model–data–compute budget power law.[4]

Version watchAbstract and version metadata; differences unverified

Exact Unlearning of Finetuning Data via Model Merging at Scale

Exact Unlearning of Finetuning Data via Model Merging at Scale
Kevin Kuo · Amrith Setlur · Kartik Srinivas · Aditi Raghunathan · Virginia Smith
First submitted 2025-04-06; updated 2026-10-27 · v2

Aditi Raghunathan subscription: v2 is available. Based on its current abstract, SIFT-Masks combines a global sign constraint and local masks for model merging and exact unlearning. The v1→v2 content changes have not been checked; current claims are not treated as newly established results.[7]

Version watchAbstract and version metadata; differences unverified

Momentum in large-batch training: Polyak enlarges the critical batch size, Nesterov improves data efficiency

Momentum in large-batch training: Polyak enlarges the critical batch size, Nesterov improves data efficiency
Jia-Nan Wang · Zixun Huang · Kairui Li · Zilin Wang · Lei Wu
First submitted 2026-09-02; updated 2026-10-27 · v3

Lei Wu subscription and scaling: v3 is available. Current Comments mention revised proofs and added neural-network experiments. Without a v2→v3 comparison, these additions cannot all be assigned to v3; earlier critical-batch conclusions are not reported as new.[8]

Version watchAbstract and version metadata; differences unverified

Scaling Reasoning Efficiently via Relaxed On-Policy Distillation

Scaling Reasoning Efficiently via Relaxed On-Policy Distillation
Jongwoo Ko · Sara Abdali · Young Jin Kim · Tianyi Chen · Pashmina Cameron
First submitted 2026-03-11; updated 2026-10-27 · v2

v2 is available. Its current abstract describes REOPOLD controlling where, how strongly, and when teacher feedback acts, with extensions to test-time scaling. Version differences remain unchecked; the abstract’s sample-efficiency maximum is not attributed to this update.[9]

Historical classicParameterization, initialization, and rank experiments read; gradient formulas are explanatory derivations, not paper theorems

Low rank also changes the optimization path

LoRA: Low-Rank Adaptation of Large Language Models
Edward J. Hu · Yelong Shen · Phillip Wallis · Zeyuan Allen-Zhu · Yuanzhi Li · Shean Wang · Lu Wang · Weizhu Chen
First submitted 2021-06-17; v2 (2021-10-16), §§4, 7 and appendix rank experiments
ICLR 2022 · Important historical work on parameter-efficient adaptation (DBLP checked 2026-10-29) ↗

Full fine-tuning stores all parameters per task; adapters (2019) add layers. Following low-intrinsic-dimension adaptation (2020), LoRA freezes pretrained weights and learns a low-rank increment that can be merged for deployment.[5][6]

Paper parameterization; W₀ is frozen [5]
W=W0+sBA,s=α/r,B∈Rd×r, A∈Rr×k,r≪min⁡(d,k)W=W_0+sBA,\quad s=\alpha/r,\quad B\in\mathbb R^{d\times r},\ A\in\mathbb R^{r\times k},\quad r\ll\min(d,k)
Per-matrix parameter count and representation constraint [5]
#(A,B)=r(d+k),rank⁡(W−W0)≤r\#(A,B)=r(d+k),\qquad \operatorname{rank}(W-W_0)\le r

Let G denote the loss gradient with respect to the effective weight. The following uses the chain rule and a first-order expansion of simultaneous SGD. The paper uses Adam, so this recurrence does not directly describe its experiments.

Explanatory derivation; not a paper theorem
∇BL=sGA⊤,∇AL=sB⊤G\nabla_B L=sGA^\top,\qquad\nabla_A L=sB^\top G
Induced matrix update under simultaneous SGD; factors set left/right preconditioning
ΔW=−ηs2(GA⊤A+BB⊤G)+O(η2)\Delta W=-\eta s^2(GA^\top A+BB^\top G)+O(\eta^2)
Paper initialization; first-step SGD consequence
B0=0,A0∼N:∇AL∣0=0,ΔW0=−ηs2G0A0⊤A0B_0=0,\quad A_0\sim\mathcal N:\qquad \nabla_A L|_0=0,\quad\Delta W_0=-\eta s^2G_0A_0^\top A_0

READ THE ORIGINALS

Original sources

  1. Meta Models: Models that Model Learning
  2. Advancement or Acceleration? How Data Curation Improves LLM Training
  3. Specialization, Diversity, and Scaling in Child-Scale Language Models
  4. Scaling and Renormalization in Neural Networks: An Effective Renormalization-Group Description of Grokking
  5. LoRA · v2 full text
  6. DBLP · ICLR 2022 record
  7. Exact Unlearning of Finetuning Data via Model Merging at Scale · version record
  8. Momentum in large-batch training: Polyak enlarges the critical batch size, Nesterov improves data efficiency · version record
  9. Scaling Reasoning Efficiently via Relaxed On-Policy Distillation · version record
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2026-10-26 08:53 — 2026-10-29 08:53 · America/New_York

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