#01Jul 23, 2026
cs.AI
MIRROR: Learning from the Other View for Multi-Modal Reasoning
Wen Ye, Yuxiao Qu, Aviral Kumar and 1 more
Unlike large language models (LLMs) that exhibit strong reasoning capabilities, vision-language models (VLMs) struggle with visual reasoning, even on geometry problems that admit equivalent text, diagram, and combined diagram+text views. We show that these views often elicit different behaviors: a model may solve a problem from text but fail on the corresponding diagram, or succeed visually while failing textually. This inconsistency suggests that different views expose complementary reasoning paths and failure modes that standard multimodal post-training does not fully exploit. To study and exploit this phenomenon, we construct ODA-Data, a high-quality paired multimodal geometry dataset with text-dominant, image-dominant, and combined image+text views of the same problems, together with splits for training and evaluating modality-dependent reasoning behaviors. We then develop Modality-Informed Reciprocal Reasoning Optimization (MIRROR), a reinforcement learning approach for improving multimodal reasoning via self supervision. For each problem, MIRROR evaluates the model under all views, selects the best-performing view as a teacher, and trains other views with a reverse-KL objective towards the teacher. Across reasoning benchmarks that evaluate on geometry problems, MIRROR improves over standard RL and yields more accurate and consistent behavior across modalities
#02Jul 23, 2026
cs.LG
Error Certificates for KV-Cache Eviction via Randomized Design
Peng Xie
Deterministic KV-cache eviction keeps the top-$k$ tokens under an importance score and deletes the rest. We prove that this design cannot know what it destroyed: evicted values can be altered so that everything the serving system retains is unchanged while the true attention-output error grows arbitrarily, so no serving-time estimator of that error is consistent. Randomized eviction restores identifiability. With a Poisson-sampled tail at known inclusion probabilities, one logit offset performs the Hájek correction inside the softmax, and a survey-sampling variance estimator over the retained set becomes a per-step error certificate with 0.97 empirical coverage at no accuracy cost. On real workloads we pre-registered seven claims and lost three: question-aware eviction at 25--50\% budgets is nearly free; output log-probability predicts failure better than the certificate; certificate-gated budget escalation adds nothing. What survives is attribution: the certificate separates cache-induced from inherent failures (AUC 0.73--0.75, against 0.47--0.54 for output confidence) and schedules recomputation better than random or confidence gating. Randomization buys attribution, not prediction.
#03Jul 23, 2026
cs.CL
Token Budget Saturation and Mechanistic Early Detection of Reasoning Non-Convergence in Chain-of-Thought Models
Renuka Oladri, Niveda Jawahar, Abdirisak Mohamed
Chain-of-thought reasoning models such as DeepSeek-R1-Distill-Qwen-7B exhibit a bimodal convergence pattern: generations either terminate within a token budget (converged) or exhaust it without reaching a conclusion (non-converged). We characterize this phenomenon empirically, showing that converged generations achieve 90.3% accuracy on AIME 1983-2024 while non-converged ones achieve only 6.6%, with an overall convergence rate of 62.0%. We then ask whether this outcome is detectable early in the thinking chain using internal model representations. Training linear probes on hidden-state activations at token positions 50-300, we find that layer-20 activations at token 150 achieve AUC 0.608 (+-0.080, 5-fold CV), reliably above chance even at token 50. Activation probes consistently outperform behavioral baselines derived from token entropy and repetition statistics. A sweep-level permutation test yields p=0.063 (100,000 permutations), consistent with a modest signal that our sample size cannot confirm at conventional thresholds. These findings suggest that convergence fate is partially encoded in intermediate representations well before the generation ends, opening a path toward early-exit inference and adaptive compute allocation.
#04Jul 23, 2026
cs.LG
Context-weighted Discrete Flow Matching
Daniil Cherniavskii, Daniel Severo, Karen Ullrich
Discrete flow matching provides a flexible framework for generative modeling on discrete structures. However, the standard factorized training objective exposes the model to targets of varying difficulty, mixing well-conditioned, predictable tokens with ambiguous, high-entropy ones. We empirically demonstrate that the uncertainty over the value of each token is closely related to the density of available context in its neighborhood. Motivated by this observation, we propose a simple modification to the underlying continuous-time Markov chain (CTMC) that incorporates local context information. Our context-weighted sampler improves generation quality with negligible computational overhead, while our scaled cross-entropy loss function reweights the training signal from different tokens and reduces generative perplexity by up to 63% on OpenWebText. Moreover, our approach matches a strong semi-autoregressive block diffusion baseline in quality while retaining the ability to perform generation in any order. These results highlight the role of local context as an important factor in discrete generative modeling and show that simple context-aware modifications can significantly improve both sampling and training efficiency.
#05Jul 23, 2026
cs.LG
Expanding Flow Maps
Sophia Tang, Pranam Chatterjee
Flow-based generative models have enabled remarkable progress in fast and controllable generation across continuous and discrete state spaces, yet existing parameterizations are constrained to fixed dimensions or fixed sequence lengths. Here, we introduce Expanding Generative Flows (EFlows), which define flows between distributions of increasing dimensionality along an expanding interpolant that grows the state by augmenting it with conditional noise. Building on this construction, we propose Expanding Flow Maps (EFMs), a new class of flow maps that distill the expanding interpolant into efficient few-step generative models. Each EFM factors the map between any two timesteps into two learnable operations: an expand operator, which augments the state space with new coordinates or tokens conditioned on the current state, and a transport map, which pushes the expanded state forward along the interpolant. Composing these operators yields a single map that jointly expands and denoises the state, recovering existing fixed-canvas flows and flow maps as the special case in which the expand operator is the identity. We further extend the framework to the discrete simplex, enabling variable-size graph generation and variable-length sequence generation. Across both continuous and discrete modalities, we establish EFlows and EFMs as a principled framework for settings in which output size is itself a learned, controllable degree of freedom.