SPECTRA: Pushing the KV Cache Beyond the 2-Bit Cliff via Spectral Transform Coding

Large language models (LLMs) increasingly read long inputs in the agentic era, from whole documents and codebases to conversations across many turns. Their inference memory is then dominated by the key-value (KV) cache, the stored attention keys and values of every token the model has read and generated. Because the cache grows with context length and is re-read in full at every generated token, a longer context means more GPU memory. To reduce this cost, most existing methods compress the KV cache by lowering every stored value to the same low precision, a technique known as quantization. They can push this to nearly two bits per value, but rarely further, because quality drops sharply at this 2-bit cliff: four levels are too few for the cache's outlier-heavy values, where a few large entries consume the levels and collapse the rest into noise. A natural remedy is to spend more bits on the channels (feature dimensions) that matter and fewer on the rest, but the raw cache offers no handle: its channels are strongly correlated, so none stands out as more important. Our analysis shows that this handle appears once the cache is rotated into a coordinate system computed from its own statistics, removing these correlations. There, a small fraction of channels carries almost all the information, and spending the budget on those few is far more accurate than spreading it evenly. Guided by this analysis, we develop SPECTRA, a training-free, drop-in codec that re-encodes the cache into this coordinate system and concentrates the bit budget on the channels that carry the signal. On Llama-3.1-8B and Qwen2.5-7B over long-context benchmarks, SPECTRA is near-lossless at 4x compression, competitive at 8x where uniform quantization has collapsed, and reaches up to 12x, pushing usable compression past the 2-bit cliff so the same GPU holds longer contexts and larger batches.

Perception Before Reasoning: Dynamic Latent Reasoning for Video Understanding and Question Answering

Video question answering requires models to ground language queries in visual evidence and, when necessary, reason over that evidence across time. Existing methods typically rely on long textual chain-of-thought rationales, even though many questions can be answered as soon as the relevant object, action, or frame is localized. We propose Dynamic Latent Reasoning (DyLaR), which first grounds a question in a short block of perception latents (continuous hidden states that encode query-relevant visual evidence), and then adaptively decides whether to append reasoning latents (continuous thoughts that reason over this evidence in latent space) before answering. DyLaR learns this behavior by grounding perception latents in verified visual evidence and distilling verified rationales into reasoning latents, followed by reinforcement learning that further refines when to reason. Across nine video benchmarks and four multimodal language model backbones, DyLaR improves average accuracy over same-backbone baselines while generating fewer than 20 tokens per query. On Qwen3-VL-4B, for example, DyLaR improves average accuracy over Qwen3-VL-4B-Thinking from 54.0 to 58.2 while reducing response length from 1,220.7 to 18.5 tokens per query. Ablations further show that grounded perception latents, rationale-supervised reasoning latents, and adaptive routing each improve accuracy.

Learning to Reason by Analogy via Retrieval-Augmented Reinforcement Fine-Tuning

Retrieval-augmented generation (RAG) has become a standard mechanism for grounding language models in external knowledge, yet conventional retrieval based on lexical or semantic similarity is poorly suited for complex reasoning tasks: a semantically similar problem may demand an entirely different solution strategy, while a superficially different problem may share the same underlying reasoning pattern. We propose Retrieval-Augmented Reinforcement Fine-Tuning (RA-RFT), a post-training framework that teaches language models to reason by analogy. RA-RFT uses gold-relevance distillation to train a retriever that ranks contexts by expected reasoning benefit rather than semantic overlap, and then fine-tunes the policy model via reinforcement fine-tuning methods with retrieved analogous demonstrations, so the model learns to leverage reasoning traces under verifiable outcome rewards. We further analyze the diversity of retrieved contexts and find that reasoning-aware retrieval surfaces complementary solution strategies that provide distinct reasoning scaffolds for individual problems. Across challenging mathematical reasoning benchmarks, RA-RFT consistently outperforms standard reinforcement fine-tuning methods. For example, it improves AIME 2025 average@32 accuracy by 7.1 and 2.8 points over GRPO for Qwen3-1.7B and Qwen3-4B respectively -- suggesting that reasoning-aware retrieval is a complementary axis of improvement and orthogonal to advances in reward design or training curricula.

Conformal Certification of Reasoning Trace Prefixes

Language model reasoning traces are rarely all-or-nothing; they frequently contain valid intermediate steps before a critical error occurs. Existing uncertainty quantification methods typically certify final answers or entire responses, failing to provide statistical guarantees for the proportion of a sequential trace that can be safely retained. To address this, we introduce CROP (Conformal Reasoning Output Prefixes), a verifier-agnostic calibration procedure for clean-prefix certification. Given any step-level risk proxy, CROP selects a calibrated threshold and returns the longest contiguous prefix whose step risk proxies remain below it, routing the uncertified suffix for downstream review or repair. Assuming exchangeability, CROP rigorously controls the marginal probability that the returned prefix contains an annotated error. Across six process-labeled reasoning datasets, we demonstrate that standard step-level metrics such as AUROC do not fully capture prefix utility, suggesting verifiers should instead be evaluated by certified prefix length. Furthermore, CROP balances over- and under-withholding, improving downstream repair accuracy by preserving valid intermediate reasoning while discarding misleading suffixes. Ultimately, this work positions prefix certification as a rigorous, practical bridge between process supervision, abstention, and repair.

LT2: Linear-Time Looped Transformers

Looped Transformers (LT) have emerged as a powerful architecture by iterating their layers multiple times before decoding the final token. However, pairing them with full attention retains quadratic complexity, making them computationally expensive and slow. We introduce LT2 (Linear-Time Looped Transformers), a family of looped architectures that replace quadratic softmax attention with subquadratic, linear-time attention. We study two variants: LT2-linear with linear attention and LT2-sparse with sparse attention. We find that looping uniquely synergizes with these variants: it enables iterative memory refinement in linear attention and progressively expands the effective receptive field in sparse attention. We formalize these benefits theoretically and demonstrate consistent empirical gains across controlled recall, state-tracking, and language modeling tasks. We then explore LT2-hybrid, which combines different attention variants in a looped setting. Two variants are especially promising: LT2-hybrid (GDN+DSA), which interleaves linear and sparse attention to maximize efficiency and matches the standard looped transformer's quality at fully linear-time cost; and LT2-hybrid (Full+GDN), which interleaves GDN with a small fraction of full attention layers to maximize quality, surpassing the standard looped transformer in both performance and efficiency. We also show how to convert a pre-trained LT into an LT2-hybrid model. With about 1B tokens of training, our converted model, Ouro-hybrid-1.4B, outperforms industry-level 1B models and is competitive with industry-level 4B models while retaining the speed benefits of linear-time attention. Together, these results show a clear path toward making looped transformers more scalable and advancing efficient, capable small language models.

BenchCAD: A Comprehensive, Industry-Standard Benchmark for Programmatic CAD

Industrial Computer-Aided Design (CAD) code generation requires models to produce executable parametric programs from visual or textual inputs. Beyond recognizing the outer shape of a part, this task involves understanding its 3D structure, inferring engineering parameters, and choosing CAD operations that reflect how the part would be designed and manufactured. Despite the promise of Multimodal large language models (MLLMs) for this task, they are rarely evaluated on whether these capabilities jointly hold in realistic industrial CAD settings. We present BenchCAD, a unified benchmark for industrial CAD reasoning. BenchCAD contains 17,900 execution-verified CadQuery programs across 106 industrial part families, including bevel gears, compression springs, twist drills, and other reusable engineering designs. It evaluates models through visual question answering, code question answering, image-to-code generation, and instruction-guided code editing, enabling fine-grained analysis across perception, parametric abstraction, and executable program synthesis. Across 10+ frontier models, BenchCAD shows that current systems often recover coarse outer geometry but fail to produce faithful parametric CAD programs. Common failures include missing fine 3D structure, misinterpreting industrial design parameters, and replacing essential operations such as sweeps, lofts, and twist-extrudes with simpler sketch-and-extrude patterns. Fine-tuning and reinforcement learning improve in-distribution performance, but generalization to unseen part families remains limited. These results position BenchCAD as a benchmark for measuring and improving the industrial readiness of multimodal CAD automation.

Agentic Discovery with Active Hypothesis Exploration for Visual Recognition

We introduce HypoExplore, an agentic framework that formulates neural architecture discovery for visual recognition as a hypothesis-driven scientific inquiry. Given a human-specified high-level research direction, HypoExplore ideates, implements, evaluates, and improves neural architectures through evolutionary branching. New hypotheses are created using a large language model by selecting a parent hypothesis to build upon, guided by a dual strategy that balances exploiting validated principles with resolving uncertain ones. Our proposed framework maintains a Trajectory Tree that records the lineage of all proposed architectures, and a Hypothesis Memory Bank that actively tracks confidence scores acquired through experimental evidence. After each experiment, multiple feedback agents analyze the results from different perspectives and consolidate their findings into hypothesis confidence updates. Our framework is tested on discovering lightweight vision architectures on CIFAR-10, with the best achieving 94.11% accuracy evolved from a root node baseline that starts at 18.91%, and generalizes to CIFAR-100 and Tiny-ImageNet. We further demonstrate applicability to a specialized domain by conducting independent architecture discovery runs on MedMNIST, which yield a state-of-the-art performance. We show that hypothesis confidence scores grow increasingly predictive as evidence accumulates, and that the learned principles transfer across independent evolutionary lineages, suggesting that HypoExplore not only discovers stronger architectures, but can help build a genuine understanding of the design space.

PRISM: A Dual View of LLM Reasoning through Semantic Flow and Latent Computation

Large language models (LLMs) solve complex problems by generating multi-step reasoning traces. Yet these traces are typically analyzed from only one of two perspectives: the sequence of tokens across different reasoning steps in the generated text, or the hidden-state vectors across model layers within one step. We introduce PRISM (Probabilistic Reasoning Inspection through Semantic and Implicit Modeling), a framework and diagnostic tool for jointly analyzing both levels, providing a unified view of how reasoning evolves across steps and layers. Across multiple reasoning models and benchmarks, PRISM uncovers systematic patterns in the reasoning process, showing that failed trajectories are more likely to become trapped in unproductive verification loops and further diverge into distinct modes such as overthinking and premature commitment, which behave differently once a candidate answer is reached. It further reveals how prompting reshapes reasoning behavior beyond aggregate accuracy by altering both semantic transitions and internal computational patterns. By modeling reasoning trajectories as structured processes, PRISM makes these behaviors observable and analyzable rather than relying solely on final-task accuracy. Taken together, these insights position PRISM as a practical tool for analyzing and diagnosing reasoning processes in LLMs.

GR-SAP: Generative Replay for Safety Alignment Preservation during Fine-Tuning

Recent studies show that the safety alignment of large language models (LLMs) can be easily compromised even by seemingly non-adversarial fine-tuning. To preserve safety alignment during fine-tuning, a widely used strategy is to jointly optimize safety and task objectives by mixing in the original alignment data, which is typically inaccessible even for open-weight LLMs. Inspired by generative replay in continual learning, we propose Generative Replay for Safety Alignment Preservation (GR-SAP), a unified framework that synthesizes domain-specific alignment data from LLMs and integrate them during downstream adaption to preserve safety alignment. Theoretical and empirical analyses demonstrate this synthetic data serves as a reliable proxy for the original alignment data. Experiments across various models and downstream tasks show that GR-SAP substantially mitigates fine-tuning-induced safety degradation while maintaining comparable downstream performance. Our code is available at https://github.com/chili-lab/gr-sap.

Spherical Steering: Geometry-Aware Activation Rotation for Language Models

Inference-time steering has emerged as a promising paradigm for controlling language models (LMs) without the cost of retraining. However, standard approaches typically rely on activation addition, a geometric operation that inevitably alters the magnitude of hidden representations. This raises concerns about representation collapse and degradation of open-ended generation capabilities. In this work, we explore Spherical Steering, a training-free primitive that resolves this trade-off through activation rotation. Rather than shifting activations with a fixed vector, our method rotates them along a geodesic toward a target direction, guiding the activation toward the target concept while preserving the integrity of the signal. To further enhance adaptivity, we incorporate a confidence gate that dynamically modulates steering strength based on input uncertainty. Extensive experiments across multiple-choice benchmarks demonstrate that Spherical Steering significantly outperforms addition-based baselines (notably by +10% on TruthfulQA, COPA, and Storycloze), while simultaneously maintaining the model's general open-ended generation quality. This work highlights the value of geometric consistency, suggesting that norm-preserving rotation is a robust and effective primitive for precise inference-time control.