InfoSFT: Learn More and Forget Less with Information-Aware Token Weighting

Adel Javanmard; George Pappas; Hamed Hassani; Mahdi Sabbaghi

InfoSFT weights medium-likelihood tokens during fine-tuning to improve generalization while preserving prior capabilities.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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T0 review · grok-4.3

2026-06-30 21:43 UTC pith:KCKWBWTG

load-bearing objection InfoSFT is a one-line reweighting of the SFT loss toward medium-likelihood tokens under the base model, with the usual empirical claims but limited visible support for the core assumption. the 2 major comments →

arxiv 2605.14967 v1 pith:KCKWBWTG submitted 2026-05-14 cs.LG stat.ML

InfoSFT: Learn More and Forget Less with Information-Aware Token Weighting

Mahdi Sabbaghi , George Pappas , Adel Javanmard , Hamed Hassani This is my paper

classification cs.LG stat.ML

keywords supervised fine-tuningtoken weightingLLM generalizationcapability preservationinformation-aware lossmath reasoningcode generationchain-of-thought

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proposes InfoSFT, a weighting scheme for supervised fine-tuning that focuses learning on tokens with medium likelihood under the base model. Standard SFT applies uniform loss to all tokens, including low-likelihood ones that drive overfitting and degrade existing skills. Existing fixes filter or down-weight unlikely data and thereby suppress the very novel behaviors the training aims to teach. InfoSFT instead up-weights the medium-confidence tokens that carry the most new information without destabilizing the model. The change is a single line in the token-wise loss and yields better results on math, code, and chain-of-thought benchmarks across model families.

Core claim

InfoSFT is a principled weighting scheme for the SFT objective that concentrates learning signals on maximally informative, medium-confidence tokens—those neither overly familiar to the base model nor too unlikely to cause instability. Requiring only a one-line modification to the standard token-wise loss, it improves generalization over vanilla SFT and likelihood-weighted baselines across math, code, and chain-of-thought tasks with diverse model families, while better preserving pre-existing capabilities.

What carries the argument

Information-aware token weighting that assigns higher loss weight to tokens whose likelihood under the base model lies in an intermediate range.

Load-bearing premise

Medium-likelihood tokens are the most informative for learning new behaviors and weighting them avoids both overfitting to unlikely samples and suppression of novel behaviors.

What would settle it

A controlled experiment on a held-out math or code benchmark in which InfoSFT-trained models show no gain in task accuracy and no reduction in capability degradation compared with standard SFT would falsify the central claim.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

Better generalization on mathematical reasoning tasks than uniform or likelihood-weighted SFT.
Improved code-generation performance across model families.
Stronger retention of pre-training capabilities after adaptation.
Effective handling of chain-of-thought data without explicit filtering.
Implementation requires only a one-line change to existing training code.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same weighting logic could be tested inside preference-tuning loops such as RLHF.
If the medium-likelihood band proves robust, data curation pipelines might shift from hard filtering to soft reweighting.
Scaling the method to frontier-scale models would test whether the likelihood band remains stable as base-model competence grows.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Desk Editor's Note

InfoSFT is a one-line reweighting of the SFT loss toward medium-likelihood tokens under the base model, with the usual empirical claims but limited visible support for the core assumption.

read the letter

The main takeaway is that this paper offers a minor adjustment to supervised fine-tuning: instead of uniform token loss or filtering low-likelihood samples, it upweights tokens that sit in the middle range of the base model's probabilities. The authors argue this avoids both overfitting to outliers and the suppression of new behaviors that comes with aggressive filtering.

What is new is the specific focus on medium-confidence tokens as the sweet spot for learning signals. They contrast it with prior approaches that downweight or discard unlikely data, claiming those methods lose the very novelty the fine-tuning is meant to add. The implementation is genuinely lightweight, described as a single-line change to the token-wise loss.

The paper does a reasonable job laying out the motivation across math, code, and chain-of-thought tasks and testing on multiple model families. That breadth is better than many short empirical notes in this area. If the gains hold in the full results, it could be a practical default tweak for people running SFT.

The soft spots are the usual ones for an abstract-heavy claim. The exact definition of the medium band, the functional form of the weighting, and any ablations on the thresholds are not visible here, so it is impossible to judge whether the rule is robust or just tuned to the reported setups. The assumption that medium likelihood tokens are maximally informative rests on intuition rather than a derivation or extensive sensitivity analysis. Without error bars, run-to-run variance, or direct comparison to stronger recent baselines, the generalization and retention improvements remain assertions rather than demonstrated facts.

This is for practitioners and researchers doing LLM adaptation who already run SFT and want a low-cost way to reduce capability drop. A reader already working on token-level weighting or data selection would find the comparison useful even if the absolute gains are small.

I would send it to peer review. The idea is narrow and implementable, so referees can evaluate the experiments without much overhead, and the problem it targets is common enough that a clean negative or positive result would still be worth knowing.

Referee Report

2 major / 0 minor

Summary. The manuscript proposes InfoSFT, a one-line modification to the token-wise supervised fine-tuning (SFT) loss that reweights tokens according to their likelihood under the base model, concentrating on medium-likelihood tokens claimed to be maximally informative. It asserts that this yields better generalization than vanilla SFT or likelihood-weighted baselines on math, code, and chain-of-thought tasks across diverse model families while reducing degradation of prior capabilities.

Significance. If the empirical results hold with proper controls, the approach would supply a lightweight, training-stable alternative to filtering or regeneration methods for SFT, directly addressing the tension between acquiring novel behaviors and retaining base-model knowledge.

major comments (2)

Abstract: the central claim that InfoSFT 'demonstrably improves generalization ... across math, code, and chain-of-thought tasks with diverse model families' is presented without any equations defining the weighting function, without experimental details, tables, figures, error bars, or statistical tests, rendering the empirical assertion unsupported and unassessable.
Abstract: the key modeling assumption that 'medium-confidence tokens ... are maximally informative' is stated without derivation, ablation, or comparison to alternative weighting schemes (e.g., entropy-based or gradient-based), leaving the optimality claim without load-bearing justification.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed feedback on the abstract. We address each major comment below. Where the comments identify areas for improvement, we will revise the manuscript accordingly.

read point-by-point responses

Referee: Abstract: the central claim that InfoSFT 'demonstrably improves generalization ... across math, code, and chain-of-thought tasks with diverse model families' is presented without any equations defining the weighting function, without experimental details, tables, figures, error bars, or statistical tests, rendering the empirical assertion unsupported and unassessable.

Authors: We agree that the abstract is a high-level summary and does not contain the full supporting details. The weighting function is defined explicitly as a one-line modification in Section 3 (Equation 3), with the full experimental setup, tables, figures, and results (including multiple runs) reported in Sections 4 and 5. To make the abstract more self-contained and address the concern directly, we will revise it to briefly state the form of the weighting function and note that results are reported with standard deviations across seeds. revision: yes
Referee: Abstract: the key modeling assumption that 'medium-confidence tokens ... are maximally informative' is stated without derivation, ablation, or comparison to alternative weighting schemes (e.g., entropy-based or gradient-based), leaving the optimality claim without load-bearing justification.

Authors: The motivation for targeting medium-likelihood tokens (neither too familiar nor too unlikely) is provided in the introduction and Section 3, where we contrast it with uniform SFT and simple likelihood reweighting. The empirical results in the paper already include comparisons to likelihood-weighted baselines. To strengthen the justification, we will add a short theoretical motivation paragraph in Section 3 and include additional ablations against entropy-based weighting in the experiments. Direct comparison to gradient-based schemes is outside the current scope but can be noted as future work if space permits. revision: partial

Circularity Check

0 steps flagged

No significant circularity; empirical weighting scheme with no derivation chain

full rationale

The manuscript frames InfoSFT as a one-line empirical modification to the token-wise SFT loss that up-weights medium-likelihood tokens under the base model. No equations, derivations, fitted parameters renamed as predictions, or self-citation chains appear in the provided text. The central claim (improved generalization and capability preservation) is asserted via experimental results across tasks and models rather than reduced to any input by construction. The design choice of medium-confidence tokens is presented as a motivated heuristic, not a self-definitional or fitted-input result. This is the common honest outcome for a purely empirical proposal.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no technical details, equations, or experimental sections from which free parameters, axioms, or invented entities can be extracted.

pith-pipeline@v0.9.1-grok · 5723 in / 1174 out tokens · 40490 ms · 2026-06-30T21:43:19.787533+00:00 · methodology

0 comments

read the original abstract

Supervised fine-tuning (SFT) provides the standard approach for teaching LLMs new behaviors from offline expert demonstrations. However, standard SFT uniformly fits all samples -- including those with low likelihood under the base model -- which can disproportionately drive training updates toward overfitting specific samples rather than learning the target behavior. Moreover, adapting to these unlikely samples induces substantial policy shifts that degrade prior capabilities. Existing methods mitigate this by filtering, regenerating, or down-weighting low-likelihood data. In doing so, they often suppress precisely the novel behaviors the base model has yet to learn. We propose InfoSFT, a principled weighting scheme for the SFT objective that concentrates learning signals on maximally informative, medium-confidence tokens -- those neither overly familiar to the base model nor too unlikely to cause instability. Requiring only a one-line modification to the standard token-wise loss, InfoSFT demonstrably improves generalization over vanilla SFT and likelihood-weighted baselines across math, code, and chain-of-thought tasks with diverse model families, while better preserving pre-existing capabilities.

Figures

Figures reproduced from arXiv: 2605.14967 by Adel Javanmard, George Pappas, Hamed Hassani, Mahdi Sabbaghi.

**Figure 1.** Figure 1: (left) InfoSFT assigns the highest weights to middle-confidence tokens as opposed to SFT that places the weights uniformly, and DFT that favors high-likelihood samples. (right) Shows the results for training on Science Q&A (Shenfeld et al., 2026). By sweeping over several hyper-parameters like learning-rates and epochs, we show that checkpoints of InfoSFT achieve the best curve on the new-task/prior-capabi… view at source ↗

**Figure 2.** Figure 2: (left/middle) Show pass@k with k ∈ [1, 64] for Qwen-Math-1.5B and Qwen-Math-7B trained with the three methods. InfoSFT is higher than other baselines for all k. (right) Unlike DFT, InfoSFT controls the entropy and avoids mode collapse. This randomness is crucial for any later training or alignment of the model. SFT and InfoSFT are complementary for difficult samples. In addition to the results in Section 3… view at source ↗

**Figure 3.** Figure 3: (left) On reasoning samples from OpenR1 (Open-R1, 2025) with low likelihood under the base model, SFT does better since both DFT and InfoSFT down-weight the unlikely tokens such as “<think>” and do not learn the thinking format. However, unlike DFT, InfoSFT still improves over the base model while keeping the base model’s format. However, applying 1 epoch of InfoSFT after the first epoch of SFT (which boos… view at source ↗

**Figure 4.** Figure 4: Tool-use performance vs. prior capabili [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

**Figure 5.** Figure 5: Relative performance of different models and datasets when sweeping hyper-parameter [PITH_FULL_IMAGE:figures/full_fig_p016_5.png] view at source ↗

**Figure 6.** Figure 6: Token accuracy comparisons. SFT has higher training token accuracy, but it is outperformed by [PITH_FULL_IMAGE:figures/full_fig_p017_6.png] view at source ↗

discussion (0)

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

RASFT: Rollout-Adaptive Supervised Fine-Tuning for Reasoning
cs.LG 2026-06 unverdicted novelty 6.0

RASFT is an adaptive SFT method that strengthens or relaxes expert imitation per problem based on on-policy rollout solvability and adds clipped reference-policy ratio to limit drift, reporting better results than sta...

Reference graph

Works this paper leans on

15 extracted references · cited by 1 Pith paper

[1]

When walking at speed \( s \) km/h, the total time including coffee shop time is 4 hours
[2]

When walking at speed \( s + 2 \) km/h, the total time including coffee shop time is 2 hours and 24 minutes
[3]

Let me note that 2 hours and 24 minutes is equal to 2.4 hours

We need to find the total time when she walks at \( s + \frac{1}{2} \) km/h. Let me note that 2 hours and 24 minutes is equal to 2.4 hours. So, the total time in hours for the second case is 2.4 hours. Let’s denote: - \( s \): original speed in km/h - \( t \): time spent in the coffee shop in hours - \( d = 9 \) km: distance of the walk First, when she wa...
[4]

\( s = \frac{20}{8} = 2.5 \) km/h
[5]

the Irreducible fraction value of [the expression]

\( s = \frac{ -36 }{8 } = -4.5 \) km/h Since speed can’t be negative, we discard the negative solution. So, \( s = 2.5 \) km/h. Now, substitute \( s = 2.5 \) into equation (1) to find \( t \): \( \frac{9}{2.5} + t = 4 \) Calculate \( 9 / 2.5 \): 2.5 * 3 = 7.5, 9 -7.5 =1.5, so 9 /2.5 = 3.6 22 Thus, 3.6 + t = 4 Therefore, \( t = 4 - 3.6 = 0.4 \) hours. Conv...
[6]

3 + [something]

So the answer is 43. But let me check once again. Maybe I misread the expression. Let me write it out in order of operations. The expression is 3 + 1/(3 + 1/(3 + 1/3)). So starting from the innermost parentheses: 3 + 1/3 is 10/3. Then, 3 + 1/(10/3) is 3 + 3/10, which is 33/10. Then, adding 3 to that? Wait, hold on! Wait, the entire expression is 3 + 1 div...
[7]

[Step 1]

Compute the innermost fraction: 3 + 1/3 = 10/3. [Step 1]
[8]

Since 1/(10/3) = 3/10, so 3 + 3/10 = 33/10

Then, compute the next layer: 3 + 1/(10/3). Since 1/(10/3) = 3/10, so 3 + 3/10 = 33/10. [Step 2]
[9]

Wait, no

Then, the entire expression is 3 + 1/(33/10). Wait, no. Wait, the original expression is 3 + [1/(33/10)]. Wait, no. Wait, no. The original expression is 3 + 1/[3 + 1/(3 + 1/3)]. So after step 2, the expression is 3 + 1/(33/10). Wait, no. Wait, no. Let me think again. No, the original expression is 3 + [1 divided by (3 + 1/(3 + 1/3))]. So the denominator i...
[10]

Innermost: 3 + 1/3 = 10/3
[11]

Next layer: 3 + 1/(10/3) = 3 + 3/10 = 33/10
[12]

the Irreducible fraction value of [the expression]

Entire expression: 3 + 1/(33/10) = 3 + 10/33 = (99/33 + 10/33) = 109/33. Yes, so that’s correct. Therefore, the answer is 109/33, so m is 109 and n is 33, so m + n = 142. But wait, the problem says "the Irreducible fraction value of [the expression]". So 109/33 is already in its simplest form because 109 is a prime number. Let me check: 109 is a prime num...
[13]

Compute the innermost fraction: \[ 3 + \frac{1}{3} = \frac{9}{3} + \frac{1}{3} = \frac{10}{3} \]
[14]

Next, we use this result in the next layer of the expression: \[ 3 + \frac{1}{\frac{10}{3}} = 3 + \frac{3}{10} = \frac{30}{10} + \frac{3}{10} = \frac{33}{10} \]
[15]

Therefore, \(m = 109\) and \(n = 33\)

Finally, we use this result in the entire expression: \[ 3 + \frac{1}{\frac{33}{10}} = 3 + \frac{10}{33} = \frac{99}{33} + \frac{10}{33} = \frac{109}{33} \] The fraction \(\frac{109}{33}\) is already in its simplest form because 109 is a prime number and 33 is \(3 \times 11\). Therefore, \(m = 109\) and \(n = 33\). The value of \(m + n\) is: \[ 109 + 33 =...

2026

[1] [1]

When walking at speed \( s \) km/h, the total time including coffee shop time is 4 hours

[2] [2]

When walking at speed \( s + 2 \) km/h, the total time including coffee shop time is 2 hours and 24 minutes

[3] [3]

Let me note that 2 hours and 24 minutes is equal to 2.4 hours

We need to find the total time when she walks at \( s + \frac{1}{2} \) km/h. Let me note that 2 hours and 24 minutes is equal to 2.4 hours. So, the total time in hours for the second case is 2.4 hours. Let’s denote: - \( s \): original speed in km/h - \( t \): time spent in the coffee shop in hours - \( d = 9 \) km: distance of the walk First, when she wa...

[4] [4]

\( s = \frac{20}{8} = 2.5 \) km/h

[5] [5]

the Irreducible fraction value of [the expression]

\( s = \frac{ -36 }{8 } = -4.5 \) km/h Since speed can’t be negative, we discard the negative solution. So, \( s = 2.5 \) km/h. Now, substitute \( s = 2.5 \) into equation (1) to find \( t \): \( \frac{9}{2.5} + t = 4 \) Calculate \( 9 / 2.5 \): 2.5 * 3 = 7.5, 9 -7.5 =1.5, so 9 /2.5 = 3.6 22 Thus, 3.6 + t = 4 Therefore, \( t = 4 - 3.6 = 0.4 \) hours. Conv...

[6] [6]

3 + [something]

So the answer is 43. But let me check once again. Maybe I misread the expression. Let me write it out in order of operations. The expression is 3 + 1/(3 + 1/(3 + 1/3)). So starting from the innermost parentheses: 3 + 1/3 is 10/3. Then, 3 + 1/(10/3) is 3 + 3/10, which is 33/10. Then, adding 3 to that? Wait, hold on! Wait, the entire expression is 3 + 1 div...

[7] [7]

[Step 1]

Compute the innermost fraction: 3 + 1/3 = 10/3. [Step 1]

[8] [8]

Since 1/(10/3) = 3/10, so 3 + 3/10 = 33/10

Then, compute the next layer: 3 + 1/(10/3). Since 1/(10/3) = 3/10, so 3 + 3/10 = 33/10. [Step 2]

[9] [9]

Wait, no

Then, the entire expression is 3 + 1/(33/10). Wait, no. Wait, the original expression is 3 + [1/(33/10)]. Wait, no. Wait, no. The original expression is 3 + 1/[3 + 1/(3 + 1/3)]. So after step 2, the expression is 3 + 1/(33/10). Wait, no. Wait, no. Let me think again. No, the original expression is 3 + [1 divided by (3 + 1/(3 + 1/3))]. So the denominator i...

[10] [10]

Innermost: 3 + 1/3 = 10/3

[11] [11]

Next layer: 3 + 1/(10/3) = 3 + 3/10 = 33/10

[12] [12]

the Irreducible fraction value of [the expression]

Entire expression: 3 + 1/(33/10) = 3 + 10/33 = (99/33 + 10/33) = 109/33. Yes, so that’s correct. Therefore, the answer is 109/33, so m is 109 and n is 33, so m + n = 142. But wait, the problem says "the Irreducible fraction value of [the expression]". So 109/33 is already in its simplest form because 109 is a prime number. Let me check: 109 is a prime num...

[13] [13]

Compute the innermost fraction: \[ 3 + \frac{1}{3} = \frac{9}{3} + \frac{1}{3} = \frac{10}{3} \]

[14] [14]

Next, we use this result in the next layer of the expression: \[ 3 + \frac{1}{\frac{10}{3}} = 3 + \frac{3}{10} = \frac{30}{10} + \frac{3}{10} = \frac{33}{10} \]

[15] [15]

Therefore, \(m = 109\) and \(n = 33\)

Finally, we use this result in the entire expression: \[ 3 + \frac{1}{\frac{33}{10}} = 3 + \frac{10}{33} = \frac{99}{33} + \frac{10}{33} = \frac{109}{33} \] The fraction \(\frac{109}{33}\) is already in its simplest form because 109 is a prime number and 33 is \(3 \times 11\). Therefore, \(m = 109\) and \(n = 33\). The value of \(m + n\) is: \[ 109 + 33 =...

2026