CALR: Continuous Anchored Latent Reasoning via Render-of-Thought Compression

Zhaoyang Wei; Bowen Jiang; Yanchao Hao; Wenchao Ding; Zheng Wei; Shaocheng Wu; Zhenjun Han; Jianbin Jiao

cs.CVOct 5, 2026

CALR: Continuous Anchored Latent Reasoning via Render-of-Thought Compression

Authors: Zhaoyang Wei, Bowen Jiang, Yanchao Hao, Wenchao Ding, Zheng Wei, Shaocheng Wu, Zhenjun Han, Jianbin Jiao

Organizations: University of the Chinese Academy of Sciences · Tencent

Abstract

Visual latent reasoning compresses rendered derivations into compact intermediate states, reducing textual reasoning overhead. Existing approaches differ in how they represent these states: continuous methods avoid vocabulary constraints, whereas discrete methods improve accuracy through quantization into a finite codebook. Our analysis of representative continuous and discrete systems identifies two functional requirements: answers must rely on latent states, and those states must carry valid, problem-specific reasoning. Continuous latents influence answers despite collapsed reasoning content, whereas discrete latents retain recoverable intermediate reasoning that answer prediction largely bypasses. To address these challenges, we propose Continuous Anchored Latent Reasoning (CALR), which connects latent formation with answer use through functional anchoring. With reference latents from information-balanced compression, CALR couples latent-mediated answer supervision with derivation-level semantic anchoring: the former routes answer supervision through intermediate states, while the latter grounds their decoded content in problem-specific derivations. A parallel-to-autoregressive curriculum develops sequential reasoning by conditioning subsequent latent blocks on generated prefixes. Evaluations on five mathematical reasoning benchmarks across model families show substantial accuracy gains. Under matched budgets, CALR gains 26.0 percentage points over a comparable continuous latent reasoning method. Further analyses show that its latents support answer prediction and carry problem-specific intermediate reasoning.

Figures & tables

Figure 1: The latent handoff challenge. (a) Continuous latents can support answer prediction without carrying problem-specific reasoning. (b) Discrete latents can encode recoverable reasoning yet be bypassed by the answer model. (c) CALR couples latent reliance (C1) with derivation anchoring for reasoning capability (C2).

Figure 2: Complementary handoff failures in continuous and discrete latents. (a) Both favor the question, with higher latent attention in the continuous system. (b) Content replacement has little effect (

\Lambda_{\mathrm{content}}\approx 0

); interface disruption yields accuracy drops of

0.42

and

0.015

, respectively.

Figure 3: CALR training framework: functional anchoring followed by parallel drafting and autoregressive refinement. Purple dashed paths denote the unified internal-reader route.

Resampling	GSM8K-Aug
Resampling	Sim. (%) $\uparrow$	CE $\downarrow$
Global cross-attn.	92.8	0.183
Fixed anchors	95.3	0.158
Dynamic anchors	$\mathbf{99.1}$	$\mathbf{0.107}$

Table 5: Resampler ablations.

Appendix figures & tables5 assets

Supplementary material from the paper’s appendix.

Appendix

Setting	Parallel	Autoregressive
Reader question mask $p_{r}$	$1.0\,/\,0.5\,/\,0.3$ by epoch	0.3
Gradient gate $\alpha$	$0\rightarrow 1$ in epoch 2	$0\rightarrow 1$ over 3,000 steps
External weight $w$	$1\rightarrow 0.5$ in epoch 2	$1\rightarrow 0.5$ over 3,000 steps
Readiness checks	–	Every 500 steps; 200 problems
Reopening window	–	Steps 6,000–8,000

Appendix

Table 6: Unified-reader schedules. Epochs and steps are local to each phase.

Source	Training use	Examples
GSM8K-Aug	Resampler, reader, and producer	384,618
MATH	Resampler	11K
MathX-5M subset	Resampler	818K

Appendix

Table 7: Training data and their roles in CALR.

Hyperparameter	Stage I: Representation	Stage I: Readout	Stage II: Drafting	Stage II: Refinement
Training data	Rendered chains (Appendix B.2 )	GSM8K-Aug 385K	GSM8K-Aug 385K	GSM8K-Aug 385K
Optimizer / LR schedule	AdamW / cosine	AdamW / cosine	AdamW / cosine	AdamW / cosine
Peak learning rate	$10^{-4}$	$10^{-4}$	$10^{-4}$	$10^{-4}$
Warm-up steps	300	200	360	360
Steps (epochs)	12,000 ( $\approx 1$ )	6,000 (2)	18,000 (3)	18,000 (3)
Global batch size	128	128	64	64

Appendix

Table 8: Per-stage training configurations. Rows marked “unified” apply only to unified CALR; the decoupled form uses the same shared settings with

\alpha=0

w=1

, and no internal reader.

System	Question attention	Latent attention	Latent/question gradient ratio
RoT	$0.51$	$0.33$	$1.12$
DLR-SFT	$0.72$	$0.05$	$0.13$

Appendix

Table 9: Answer-stage attention and gradient measurements.

Condition	Metric	Set 1	Set 2
Feedback substitution + suffix regeneration	Expected	75.0	80.0
Reader-input substitution only	Expected	0.8	0.8
Same intermediate, different answer	Orig.	87.5	82.5

Appendix

Table 17: Intermediate-state substitution on two disjoint sets of 120 problems each. Expected denotes the percentage of outputs matching

y_{\mathrm{exp}}

; Orig. denotes accuracy against the original answer

y

. Regeneration retains the original first two blocks at readout. All values are percentages.

Explore similar work

Why Struggle with Continuous Latents? Interpretable Discrete Latent Reasoning via Rendered Compression
Jun 29, 2026Shuochen Chang, Qingyang Liu, Shaobo Wang +8Efficient Latent Reasoning Intermediate Latent States
Shanghai Jiao Tong University · Tongji University
Selective Latent Thinking: Adaptive Compression of LLM Reasoning Chains
May 25, 2026Hui Xie, Jie Liu, Ziyue Qiao +1Latent Thoughts Chain-of-Thought Reasoning
Eindhoven University of Technology, Netherlands · School of Computing and Information Technology, Great Bay University, China
Latent Recurrent Thoughts: Recurrent Refinement of Proposed Latents for Reasoning with Frozen LLMs
Sep 1, 2026Zhaoliang Chen, Jie FuLatent Thoughts Chain-of-Thought Reasoning
Emory University · IQuest Research

Jun 29, 2026, cs.CLJ/K move · Enter open · S save

Why Struggle with Continuous Latents? Interpretable Discrete Latent Reasoning via Rendered Compression

Shuochen Chang, Qingyang Liu, Shaobo Wang, Bingjie Gao+7

Shanghai Jiao Tong University · Tongji University

Efficient Latent Reasoning Intermediate Latent States Latent Variable Chain-of-Thought Reasoning Data Compression Methods

Open paper AskPDF arXiv

Large language models achieve high reasoning performance via explicit chain-of-thought and reinforcement learning, but require long output sequences and extended inference time. Latent reasoning reduces this cost by shifting computation into a latent space; however, continuous latent methods are hard to train, suffering from unstable and uninterpretable reasoning trajectories. We argue these issues stem from a misalignment between continuous-space reasoning and discrete symbolic supervision, as continuous states lack explicit anchors for step-by-step alignment. To resolve this, we propose \textbf{Discrete Latent Reasoning~(DLR)}, the first method that converts continuous latent states into explicit discrete tokens. Inspired by render-based compression, we render textual chains of thought into images, extract visual features, and construct a discrete latent vocabulary via clustering-based fine-tuning. Expanding the vocabulary and output head enables standard autoregressive modeling over both natural language and latent tokens, supporting pretraining alignment, SFT, and RL. Experiments on five reasoning benchmarks and two model series~(Qwen3-VL and LLaMA-3) confirm that \textbf{DLR} outperforms prior latent reasoning baselines with up to \textbf{20

\times

compression}. Furthermore, the learned latent trajectories retain an interpretable semantic structure. Overall, discrete latent tokens provide a controllable and interpretable basis for efficient latent reasoning.

Abstract

Explore similar work

Why Struggle with Continuous Latents? Interpretable Discrete Latent Reasoning via Rendered Compression

Selective Latent Thinking: Adaptive Compression of LLM Reasoning Chains

Latent Recurrent Thoughts: Recurrent Refinement of Proposed Latents for Reasoning with Frozen LLMs