Chi Zhang
Publications
GradCuit: Credit-Assigned Gradient Flow Enables Robust and Interpretable Test-Time Latent Reasoning
Optimization-based latent reasoning improves large language model outputs by optimizing instance-specific continuous states at test time while keeping model parameters frozen. Existing methods, however, typically connect these states to the reasoning trajectory through decoded tokens, making sequence-level credit assignment indirect and obscuring how latent updates shape subsequent reasoning. We introduce GradCuit (gradient through circuit), which inserts optimizable latent states at a selected Transformer layer between the hidden representations of the prompt and the generated continuation. Causal self-attention provides every continuation-token log-probability with a differentiable path to every preceding latent state through the remaining Transformer blocks, enabling reward-weighted gradients from the entire continuation to be assigned directly to the latents. Across five instruction-tuned backbones, three reasoning benchmarks, and two answer formats, GradCuit achieves an average accuracy of 64.5%, outperforming chain-of-thought prompting by 6.6 percentage points and the strongest competing method by 2.4 points. GradCuit also demonstrates greater robustness: across seven learning-rate settings, it consistently outperforms LatentSeek while reducing the standard deviation of accuracy from 1.53 to 0.82, and even its random-walk variant remains competitive with LatentSeek. For interpretability, token-level gradient attribution reveals that latent influence concentrates on reasoning-connector tokens, while layer analysis identifies early-to-middle Transformer layers as the most effective optimization space. By directly optimizing internal reasoning from outcome feedback, GradCuit opens a new axis of robust and interpretable test-time scaling, where LLMs adapt how they reason rather than merely regenerate, sample, or rerank outputs.
Preserve Support, Not Correspondence: Dynamic Routing for Offline Reinforcement Learning
One-step offline RL actors are attractive because they avoid backpropagating through long iterative samplers and keep inference cheap, but they still have to improve under a critic without drifting away from actions that the dataset can support. In recent one-step extraction pipelines, a strong iterative teacher provides one target action for each latent draw, and the same student output is asked to do both jobs: move toward higher Q and stay near that paired endpoint. If those two directions disagree, the loss resolves them as a compromise on that same sample, even when a nearby better action remains locally supported by the data. We propose DROL, a latent-conditioned one-step actor trained with top-1 dynamic routing. For each state, the actor samples $K$ candidate actions from a bounded latent prior, assigns each dataset action to its nearest candidate, and updates only that winner with Behavior Cloning and critic guidance. Because the routing is recomputed from the current candidate geometry, ownership of a supported region can shift across candidates over the course of learning. This gives a one-step actor room to make local improvements that pointwise extraction struggles to capture, while retaining single-pass inference at test time. On OGBench and D4RL, DROL is competitive with the one-step FQL baseline, improving many OGBench task groups while remaining strong on both AntMaze and Adroit. Project page: https://muzhancun.github.io/preprints/DROL.
The Price Reversal Phenomenon: When Cheaper Reasoning Models End Up Costing More
Developers and consumers increasingly choose reasoning language models (RLMs) based on their listed API prices. However, how accurately do these prices reflect actual inference costs? We conduct the first systematic study of this question, evaluating 8 frontier RLMs across 9 diverse tasks covering competition math, science QA, code generation, and multi-domain reasoning. We uncover the pricing reversal phenomenon: in 21.8% of model-pair comparisons, the model with a lower listed price actually incurs a higher total cost, with reversal magnitude reaching up to 28x. For example, Gemini 3 Flash's listed price is 78% cheaper than GPT-5.2's, yet its actual cost across all tasks is 22% higher. We trace the root cause to vast heterogeneity in thinking token consumption: on the same query, one model may use 900% more thinking tokens than another. In fact, removing thinking token costs reduces ranking reversals by 70% and raises the rank correlation (Kendall's $τ$ ) between price and cost rankings from 0.563 to 0.873. We further show that per-query cost prediction is fundamentally difficult: repeated runs of the same query yield thinking token variation up to 9.7x, establishing an irreducible noise floor for any predictor. Our findings demonstrate that listed API pricing is an unreliable proxy for actual cost, calling for cost-aware model selection and transparent per-request cost monitoring.