Distillation via sampling reasoning traces exposes closed-source frontier models to adversarial third parties who can bypass their guardrails and misappropriate their capabilities. Antidistillation methods aim to address this by poisoning reasoning traces to hinder student model learning while preserving teacher performance. However, current methods overlook detectability, both semantic and syntactic, which erodes trust in the teacher's outputs and signals the defense's presence to adversaries. We address this gap by formulating antidistillation as a Stackelberg game whose constraint set explicitly encodes detectability, and show that perturbing sparingly offers an effective, less detectable alternative to poisoning the full trace. Drawing on mechanistic interpretability, we identify thought anchors, sentences with disproportionate counterfactual influence on model outputs, as a principled sparse target: critical to reasoning yet minimally detectable. We instantiate this in TraceGuard, a training-free, black-box proof-of-concept that locates thought anchors via branching-token detection and poisons them to degrade student distillation while preserving trace coherence.
Distillation attacks create a deployment trade-off for model providers: the same outputs that make a model more useful can also make it easier to imitate. We study this trade-off through a minimax game between a utility-constrained teacher and an adaptive student. Our framework yields tractable one-sided response rules: an adaptive evaluation rule in which the student reweights high-value examples, and a teacher-side defense template that suppresses outputs most useful for distillation. From a cheap proxy for example value, we derive Product-of-Experts (PoE), a simple forward-pass-only defense that combines the teacher with a proxy student during generation. Empirically, adaptive evaluation reveals a large passive--adaptive gap: on state-of-the-art defenses, adaptive students recover substantially more capability than passive evaluation suggests on GSM8K and MATH. Under this stronger evaluation, the apparent robustness gap between expensive defenses and PoE narrows considerably, while PoE remains substantially cheaper and preserves higher-quality reasoning traces. Overall, our results suggest that strong distillation remains difficult to stop, and that progress on antidistillation should be judged against adaptive students rather than passive ones. Our code is available at: https://github.com/ysfalh/distillation-game.
Detecting unauthorized knowledge distillation from a deployed LLM API is hard because the defender controls neither the attacker's training pipeline nor the next-token logits. Existing defenses operate on the teacher's output tokens -- biasing the next-token distribution (green-list watermarks, cryptographic schemes, antidistillation sampling) or rewriting outputs after generation. Recent work shows a paraphrasing attacker can strip these signals without losing the underlying knowledge. We propose interaction-layer antidistillation watermarks, which move the trace one layer higher, into the teacher's interaction behavior: the defender wraps the teacher with a system prompt that intermittently induces a behavioral marker -- an explicit follow-up question, a low-frequency variant, or a declarative restatement. An oblivious distiller inherits the behavior, and the defender audits via black-box queries with a human-validated LLM-as-judge (Cohen's kappa = 0.84/0.78 on strong/style rubrics). Across 63 LoRA-distilled students under a Llama-3.3-70B-Instruct teacher (35,343 judged samples), behavioral watermarks transfer at 88.9% (Gemma) / 80.9% (OLMo) / 45.2% (Qwen) relative fidelity (H1, H2). Under non-adaptive DIPPER paraphrasing, robustness decomposes into a teacher-self ceiling (about 66.4%) and student-relative retention of 21-112%, with OLMo preserving the watermark above the teacher itself (H3, F-Amp). Low-density (about 20%) explicit and implicit declarative variants transfer above per-family baseline (H4, F-Style). An N=20 in-lab study (pre-registered Latin-square) shows all marker variants within 0.22 Likert step of baseline; TOST, Friedman, and Bonferroni-Wilcoxon support H5. The interaction layer is a viable design locus for antidistillation watermarking, complementary to token-, model-, and reasoning-trace-layer defenses.
Model distillation -- training on outputs from stronger third-party models -- is widely used to boost performance, but raises concerns about unfair advantages and policy violations. This motivates a fundamental question: can we detect whether a model was distilled from another? We show that, while identifying a teacher model from a student in isolation is highly challenging, it becomes tractable in a reference-based setting: given a model and an earlier-generation checkpoint from the same lineage, we can identify the teacher model used to train the later checkpoint. We introduce a distillation detection method based on reference-based membership inference. By comparing how strongly a student model preferentially aligns with outputs from different candidate teachers relative to a reference checkpoint, our method identifies the most likely teacher and detects evidence of distillation. To handle unknown distillation pipelines such as hidden prompts, we infer proxy prompt templates directly from model outputs. We additionally identify a distinctive glyph-level signal specific to o1/o3 models. Evaluating distillation detection is challenging because modern model lineages are already heavily entangled. To address this, we develop a hybrid evaluation spanning both controlled distillation experiments and real-world models. Across both settings, our approach recovers the true teacher with near-perfect accuracy in single-teacher distillation scenarios, even when the underlying distillation pipeline is largely unknown. We further introduce statistical tests for both teacher attribution and distillation detection, and extend our framework to open-world settings where no teacher is guaranteed to be present among the candidates. Applying our method to contemporary models yields new evidence regarding potential distillation relationships involving QwQ, DeepSeek-R1, and GPT-OSS.