Privileged Information Distillation for Language Models

Alexandre Lacoste; Dheeraj Vattikonda; Emiliano Penaloza; Laurent Charlin; Massimo Caccia; Nicolas Gontier

arxiv: 2602.04942 · v3 · pith:RPRTVB52new · submitted 2026-02-04 · 💻 cs.LG · cs.AI

Privileged Information Distillation for Language Models

Emiliano Penaloza , Dheeraj Vattikonda , Nicolas Gontier , Alexandre Lacoste , Laurent Charlin , Massimo Caccia This is my paper

Pith reviewed 2026-05-22 08:20 UTC · model grok-4.3

classification 💻 cs.LG cs.AI

keywords privileged information distillationlanguage model agentsaction-only supervisionjoint teacher-student trainingreinforcement learning distillationchain of thoughtmulti-turn environments

0 comments

The pith

Joint training of a PI-conditioned teacher and unconditioned student on shared weights transfers capabilities to action-only policies without exposing reasoning at inference.

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

The paper studies how to move skills learned with privileged information during training into language models that must act without that information at test time. In multi-turn agentic environments only action trajectories are typically visible while the reasoning stays hidden, which prevents standard distillation. The authors introduce π-Distill, a joint objective that trains the privileged teacher and the standard student simultaneously on the same model weights, plus On-Policy Self-Distillation that matches them through reverse KL regularization inside RL. Experiments show these methods outperform the usual pipeline of supervised fine-tuning on full chain-of-thought followed by reinforcement learning, across several benchmarks, models, and kinds of privileged information. A reader cares because this route can produce stronger agents when full reasoning traces are unavailable or too costly to collect.

Core claim

The paper claims that both π-Distill and, in some cases, OPSD effectively distill frontier agents using action-only privileged information and outperform industry standard practices of supervised finetuning followed by RL that assume access to full Chain-of-Thought supervision across multiple agentic benchmarks, models, and forms of PI.

What carries the argument

The joint teacher-student objective in π-Distill that trains a privileged-information-conditioned teacher and an unconditioned student simultaneously on the same model weights to transfer capabilities without ever observing the reasoning process at inference.

If this is right

The distilled student outperforms supervised finetuning followed by RL even when the baseline has full chain-of-thought supervision.
The approach works with action trajectories alone and does not require the reasoning process to be visible at test time.
Results hold across multiple agentic benchmarks, different model sizes, and varied forms of privileged information.
Extensive analysis identifies conditions under which joint training with π-Distill succeeds and when OPSD remains competitive.

Where Pith is reading between the lines

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

The method could reduce reliance on expensive chain-of-thought annotations when building agents for long-horizon tasks.
Similar joint-training patterns might apply in other domains where internal states are hidden but actions are observable, such as simulated control or game environments.
Extending the reverse-KL matching idea to additional regularization terms could further stabilize distillation when privileged information varies in quality.

Load-bearing premise

That simultaneous training of a PI-conditioned teacher and unconditioned student on the same model weights produces transferable representations even when the reasoning process itself is never observed at inference.

What would settle it

A controlled experiment in which the joint optimization is removed and the resulting student performs no better than a standard supervised-finetuned model without privileged information on the same agentic benchmarks.

read the original abstract

Training-time privileged information (PI) can enable language models to succeed on tasks they would otherwise fail, making it a powerful tool for reinforcement learning in hard, long-horizon settings. However, transferring capabilities learned with PI to policies that must act without it at inference time remains a fundamental challenge. We study this problem in the context of distilling frontier models for multi-turn agentic environments, which typically hide their internal reasoning and expose only action trajectories. This breaks standard distillation pipelines, since successful behavior is observable, but the reasoning process is not. For this, we introduce {\pi}-Distill, a joint teacher-student objective that trains a PI-conditioned teacher and an unconditioned student simultaneously using the same model. Additionally, we also introduce On-Policy Self-Distillation (OPSD), an alternative approach that trains using Reinforcement Learning (RL) with a reverse KL-penalty between the student and the PI-conditioned teacher. We show that both of these algorithms effectively distill frontier agents using action-only PI. Specifically, we find that {\pi}-Distill and, in some cases, OPSD, outperform industry standard practices (Supervised finetuning followed by RL) that assume access to full Chain-of-Thought supervision across multiple agentic benchmarks, models, and forms of PI. We complement our results with extensive analysis that characterizes the factors enabling effective learning with PI, focusing primarily on {\pi}-Distill and characterizing when OPSD is competitive.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

π-Distill and OPSD give a joint-training way to move privileged reasoning into action-only student policies, but the abstract leaves the size and robustness of the gains unclear.

read the letter

The main point is that this paper introduces π-Distill, which trains a PI-conditioned teacher and an unconditioned student at the same time on shared weights, and OPSD, which adds an on-policy reverse-KL RL term to match the student to the teacher. Both target the setting where only action trajectories are available at inference for multi-turn agents. The authors claim these beat the usual SFT followed by RL pipeline that relies on full CoT supervision, and they add some analysis of when PI helps learning. That framing of the distillation problem for hidden-reasoning agents is the clearest new angle here. It directly tackles a constraint that shows up when you try to compress frontier agents without exposing their internal steps. If the joint objective really transfers capability without needing separate models or full traces, it could simplify some training setups. The soft spots sit mostly in the evidence. The abstract reports outperformance across benchmarks and models but gives no numbers, effect sizes, or description of baseline tuning and statistical checks. That makes it hard to tell whether the gains come from the new objectives or from differences in optimization or capacity during training. The shared weights in π-Distill also leave open the possibility that gradients or hidden states from the PI path continue to influence the student even after the conditioning is removed at test time. The stress-test note flags this exact risk, and without explicit checks that the student representations stay independent of the PI features, the transfer claim rests on weaker ground. This is the sort of work that matters to groups building and deploying agentic language models who need to reduce inference cost without losing too much performance. It has enough of a concrete algorithmic proposal and a timely problem to deserve a serious referee, though the review should focus on experimental controls, ablations, and direct tests for leakage. I would send it out for peer review rather than desk reject.

Referee Report

3 major / 2 minor

Summary. The paper introduces π-Distill, a joint teacher-student objective that simultaneously trains a PI-conditioned teacher and an unconditioned student on shared model weights, along with OPSD, an RL approach using reverse KL penalty to the PI-conditioned teacher. It claims these methods distill effective action-only policies from frontier agents in multi-turn environments, outperforming standard SFT followed by RL (which uses full CoT supervision) across multiple agentic benchmarks, models, and PI types, while providing analysis of factors enabling PI-based learning.

Significance. If the empirical results hold and the student policies operate without implicit reliance on privileged information at inference, this would be a notable contribution to distilling deployable agentic language models. It offers practical techniques for leveraging rich training-time signals in long-horizon settings where reasoning traces are unavailable at test time, potentially improving efficiency over full-supervision baselines.

major comments (3)

[§3] §3 (π-Distill description): the joint optimization on shared weights between the PI-conditioned teacher and unconditioned student risks implicit leakage via gradients or hidden-state updates. No verification is provided (e.g., probing student representations for residual PI dependence or ablation isolating the joint-training component) to confirm that inference-time behavior depends solely on observable actions, which is load-bearing for the central distillation claim.
[§5] §5 (Experimental results): outperformance over SFT+RL baselines is reported on agentic benchmarks, but without details on run counts, statistical significance, variance, or controls for hyperparameter tuning and compute parity, it is unclear whether gains are robust or attributable to the proposed methods rather than baseline weaknesses.
[Analysis] Analysis section: while factors enabling effective PI learning are characterized, no explicit tests for representation independence (such as mutual information between student activations and PI features or performance under attempted PI reconstruction) are described, leaving the 'action-only' transfer unverified.

minor comments (2)

[Abstract] Abstract: the claim of outperformance 'across multiple agentic benchmarks' would benefit from naming the specific benchmarks and models for immediate clarity.
[Methods] Notation: ensure π-Distill and OPSD are introduced with explicit mathematical objectives early in the methods section to aid readability.

Simulated Author's Rebuttal

3 responses · 0 unresolved

Thank you for the constructive feedback on our manuscript. We appreciate the referee's focus on the potential for implicit leakage in π-Distill, the need for greater experimental rigor, and explicit verification of action-only transfer. We address each major comment below and outline planned revisions to strengthen the paper.

read point-by-point responses

Referee: [§3] §3 (π-Distill description): the joint optimization on shared weights between the PI-conditioned teacher and unconditioned student risks implicit leakage via gradients or hidden-state updates. No verification is provided (e.g., probing student representations for residual PI dependence or ablation isolating the joint-training component) to confirm that inference-time behavior depends solely on observable actions, which is load-bearing for the central distillation claim.

Authors: We thank the referee for identifying this critical point. The π-Distill objective is designed such that the student component receives no PI input and is optimized to match the teacher's action distribution on observable trajectories only. However, we acknowledge that shared weights introduce a plausible pathway for gradient-based leakage that is not directly ruled out in the current analysis. To address this, we will add an ablation that isolates the joint-training component (comparing against separately trained teacher and student) as well as probing experiments on student activations for residual dependence on PI features. These additions will be included in the revised manuscript to provide direct evidence that inference-time behavior depends solely on observable actions. revision: yes
Referee: [§5] §5 (Experimental results): outperformance over SFT+RL baselines is reported on agentic benchmarks, but without details on run counts, statistical significance, variance, or controls for hyperparameter tuning and compute parity, it is unclear whether gains are robust or attributable to the proposed methods rather than baseline weaknesses.

Authors: We agree that additional experimental details are necessary to establish robustness. The original manuscript reports results across multiple agentic benchmarks, models, and PI types, but does not include run counts, variance estimates, or formal significance testing. In the revision we will expand §5 and the appendix to report the number of independent runs, standard deviations, statistical significance (e.g., paired t-tests against baselines), and explicit controls for hyperparameter search effort and total compute to ensure fair comparison. This will clarify that observed gains are attributable to the proposed methods. revision: yes
Referee: [Analysis] Analysis section: while factors enabling effective PI learning are characterized, no explicit tests for representation independence (such as mutual information between student activations and PI features or performance under attempted PI reconstruction) are described, leaving the 'action-only' transfer unverified.

Authors: Our analysis section characterizes several factors (PI type, horizon length, model capacity) that correlate with successful distillation under action-only inference. While these results provide indirect support for representation independence, we concede that direct tests such as mutual-information estimation between student activations and PI features or reconstruction attacks are absent. We will add these explicit independence checks to the analysis section in the revised version to more rigorously verify that the student has not retained implicit access to privileged information. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical algorithms evaluated against external baselines

full rationale

The paper introduces π-Distill and OPSD as joint training or RL-based distillation methods and supports its claims through direct experimental comparisons on agentic benchmarks against standard SFT+RL baselines that use full CoT supervision. No equations, derivations, or first-principles results are presented that reduce reported performance gains to quantities defined by the paper's own fitted parameters or self-citations. The work remains self-contained via observable action trajectories and external benchmarks, with no load-bearing steps that collapse by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The central claims rest on standard assumptions in RL distillation (e.g., that policy gradients and KL penalties can transfer latent capabilities) plus the empirical claim that action trajectories suffice as supervision. No new physical or mathematical axioms are introduced.

pith-pipeline@v0.9.0 · 5806 in / 1115 out tokens · 35361 ms · 2026-05-22T08:20:52.649847+00:00 · methodology

discussion (0)

Forward citations

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