Fake-Score Perspective & Dual Potentials

• The paper introduces the fake-score perspective, a method for classifying model steps as causally functional or decorative, quantified via the True Thinking Score (TTS).
• It details the use of dual potentials, which steer model activations by contrasting high and low TTS steps, enabling controlled engagement or suppression of specific computations.
• Experimental results demonstrate that activating dual potentials significantly flips outputs in LLMs and enhances video diffusion performance, improving interpretability, safety, and training efficiency.

A fake-score perspective provides a unifying diagnostic and optimization lens for evaluating model outputs, reasoning steps, or generated samples in terms of whether they are genuinely functional, causally relevant, or merely decorative—across domains as diverse as Chain-of-Thought (CoT) prompting in LLMs and score-based video diffusion distillation. Dual potentials refer to paired steering directions or objectives derived from this lens, mechanistically controlling whether a model engages with, or ignores, specific computational steps or representation errors.

1. Formalization of the Fake-Score Perspective

The fake-score concept originates as a binary/ternary classification proxy for model trustworthiness and causal utility. In settings where explicit likelihoods or confidence scores are unavailable or unreliable, fake-score is instantiated, for instance, as the correctness of a model’s output classification (e.g., “real” vs “fake” news) or the causal impact of a specific step in a computation pipeline (Sallami et al., 2024, Zhao et al., 28 Oct 2025).

For CoT in LLMs, the formal True Thinking Score (TTS) is proposed as:

$$\text{TTS}(s) = \frac{1}{2}\big(|\mathbb{E}[Y \mid \text{do}(X=1),C=1] - \mathbb{E}[Y \mid \text{do}(X=0),C=1]| + |\mathbb{E}[Y \mid \text{do}(X=1),C=0] - \mathbb{E}[Y \mid \text{do}(X=0),C=0]|\big)$$

where $X$ toggles inclusion/perturbation of step $s$, $C$ controls context integrity, and $Y$ is outcome indicator for correctness. In score-based generative distillation, fake-score refers to the student’s score-network output $S_{fake}$, which is iteratively matched to the unavailable true or teacher score $S_{real}$ (Wu et al., 28 May 2026).

The central epistemic aim is to distinguish steps or samples that are causally determinant (“true-thinking” or “genuine”) from those that are merely presentational (“decorative” or “artifactual”), quantifying the impact of interventions either via TTS or tracking residuals.

2. Mechanistic Role of Dual Potentials

Dual potentials are paired mechanisms in model latent space or optimization objectives, designed to selectively modulate internal engagement with candidate steps or corrections. In LLMs, a difference-of-means direction in the hidden state at layer $\ell$,

$$v_{TrueThinking}^\ell = \mu_{TT}^\ell - \mu_{DT}^\ell$$

is extracted by contrasting high-TTS (“true-thinking”) and low-TTS (“decorative”) step activations (Zhao et al., 28 Oct 2025). At inference, activation steering is applied as $$\bar{h}^\ell = h^\ell + \lambda v_{TrueThinking}^\ell$$ with $X$0 positive (“Engagement Test”) or negative (“Disengagement Test”), forcing the model to amplify or suppress the impact of a step. In video diffusion distillation, dual potentials manifest as loss terms—Negative-Residual (NR) and Residual-Contraction (RC)—that implement opposing outer- and inner-loop pulls for distribution matching and tracking.

3. Methodologies Across Domains

Table: Manifestations of Fake-Score and Dual Potentials

Domain	Fake-Score Instance	Dual Potentials/Steering
LLM Chain-of-Thought	TTS, correctness delta	Latent steering via $X$1
Video Diffusion Dist.	Student–teacher score error	NR (outer), RC (inner) potentials
News Detection	Correctness in classif.	N/A (implicit, not mechanistic)

In LLM reasoning, each CoT step is probed for causal relevance by perturbing it and monitoring impact on model predictions. Steps are classified and hidden-space steering directions are empirically validated by forcing answer-flips or restoration via vector addition/subtraction.

In SGMD, the tracking residual $X$2 is central. The NR potential $X$3 corrects the outer loop by pulling $X$4 toward $X$5, while the RC potential $X$6 contracts the error in the fake-score. The generator and student score network are updated with distinct gradients, enabling faster and more stable optimization (Wu et al., 28 May 2026).

4. Experimental Observations and Results

In LLMs on the AIME dataset (Qwen-2.5), TTS is extremely right-skewed: mean ≈ 0.03, only 2.3% of CoT steps with TTS ≥ 0.7, and most “aha” moments in output text—ostensibly self-verification—are decorative (TTS ≪ 0.01) and causally irrelevant. Activating $X$7 on typically ignored steps flips answers 50–70% of the time; $X$8 restores correctness comparably (Zhao et al., 28 Oct 2025).

In SGMD, compared to DMD2, fewer fake-score updates per iteration (1 vs 5) yields roughly 3× speedup (77.5s vs 255s/iter), while preserving or improving Fréchet Video Distance (FVD) and substantially enhancing motion dynamics (DynDeg from 80.56 to 93.06). Human studies showed preference for SGMD outputs in motion and overall quality (Wu et al., 28 May 2026).

5. Implications for Trust, Safety, and Optimization

The fake-score perspective exposes a gap between surface-level output and true internal computation. In LLMs, many reasoning steps are decorative, undermining the use of Chain-of-Thought outputs for interpretability and safety—inspection of CoT does not guarantee faithful internal reasoning. Mechanistic dual-potential interventions allow for diagnostic tests (engagement/disengagement) and, in principle, finer control over a model’s reliance on specific reasoning steps.

In video diffusion, decoupling tracking and distribution matching with dual potentials allows the fake-score to lag, yet recover, reducing computational overhead and avoiding the pitfalls of mode-seeking conservatism (common in reverse-KL objectives). This suggests improved sample quality, reduced degeneracy, and increased training efficiency (Wu et al., 28 May 2026).

6. Extensions and Broader Significance

The framework unifies diagnostic and interventional control across supervised, self-supervised, and generative settings. The universality of the TrueThinking direction for LLMs across datasets (AMC, AIME, MATH) suggests the presence of generic latent mechanisms for thought engagement. Token pruning based on TTS (“TokenSkip”) and reward design for high-TTS steps are plausible training targets for efficient and trustworthy reasoning (Zhao et al., 28 Oct 2025).

SGMD’s design demonstrates that fake-score-guided objectives, when paired with suitable dual potentials, improve alignment of student generators with teacher dynamics in high-dimensional, high-variance regimes (e.g., complex video motion), challenging the primacy of generator-centered optimization.

Overall, the fake-score perspective and its associated dual potentials provide a rigorously grounded, intervention-compatible approach for diagnosing and manipulating the causal structure of complex AI systems—spanning interpretability, safety, and training efficiency.