Position Extrapolation

Looped transformers reuse a single block across iterations, raising a natural question: how far can a block trained at one depth be safely extrapolated to greater depths? We study this question for all-pairs graph connectivity, where harder graphs require longer-range information propagation. We show that under exchangeability and symmetric positive initialization, population training at depth K converges to an update rule governed by a single effective parameter that balances graph propagation against fitting structure unresolved at training depth. This trade-off creates a finite extrapolation window: too few test-time loops provide insufficient propagation, while too many eventually create false connections. We derive explicit endpoints for this window and bound the graph hardness solvable beyond training as a function of training depth and hardness. In particular, a test depth chosen solely from the training distribution can guarantee recovery on substantially harder graphs, with a certified depth gain that grows exponentially as training depth outpaces training hardness. Experiments validate the predicted windows and show how compute budget and initialization affect the optimal training depth.

Recurrent-depth Transformers reuse one block across many steps, so information needed later must survive repeated rewriting of the hidden state. A natural remedy is to keep more history. We show that, in controlled cellular-automaton tasks, making history available is not the same as making it usable. Using Rule 30, where the correct state is known at every recurrent step, we test depth extrapolation and de- layed recall, the recovery of an earlier state after further computation. CoTFormer, which caches keys and values from every earlier step, extrapolates less far and recalls less accurately than a Block Universal Transformer (BUT) that keeps only its current state. Interventions show that its retained history can pull a corrected trajectory back toward failure, and that the cache block written at the requested step is neither necessary nor sufficient for recall. We introduce LSTM-UT, which adds a small, bounded, gated cell state to the shared block. Trained to depth 12, LSTM-UT keeps 99.7% exact-row accuracy at depth 60, where BUT gets no row fully correct, and one checkpoint stays above 99.95% at depth 1,000. It also improves delayed recall over both baselines, and the advantage largely persists at near-matched parameter counts. On these tasks, a small state under learned control proved more useful than a complete but unaddressed history. In OpenWebText2 language modelling, LSTM-UT outperforms BUT and, at equal width, reaches slightly lower perplexity than CoTFormer while CoTFormer needs up to 91% more training time per step; against a parameter-matched CoTFormer, LSTM-UT comes within 0.6 perplexity.

Coupled-cluster theory defines the accuracy standard for molecular electronic-structure properties but scales too steeply for routine application, whereas density-functional theory is affordable yet systematically biased. We resolve this trade-off with a single equivariant network, HARP (Hamiltonian Read-out for Properties), that predicts an effective one-electron Hamiltonian from one inexpensive B3LYP/def2-SVP calculation and derives a broad suite of properties from it (energy, optical gap, dipole, quadrupole, polarizability, Mulliken atomic charges, and Mayer bond orders) at coupled-cluster accuracy across nine main-group elements, including the under-served phosphorus, sulfur, and chlorine chemistries. The model is trained on a new in-house dataset of multi-property labels computed at the CCSD(T) level for all nine elements. On a held-out test set, it reduces the error of every property by a factor of 3.8 to 270 relative to semi-local, hybrid, and double-hybrid DFT (referenced to composite CCSD(T)/cc-pVTZ), while adding only ~0.1 s wall time per molecule, delivering coupled-cluster-quality predictions at the cost of a single DFT calculation. Critically, deriving every property from a predicted Hamiltonian rather than pooling per-atom features builds the correct size-scaling into the model architecture: on pi-conjugated oligothiophenes it matches finite-field CCSD polarizability to ~1% and the EOM-CCSD optical gap to ~3% at the largest sizes where those references remain affordable (44 and 37 atoms, where a single CCSD field point already costs ~500x the model's entire inference) and extrapolates the corrected trends to 58-atom chains, a regime where pooling-based architectures fail by construction. Accurate extrapolation is therefore set by the model's inductive bias rather than by the training data.

Diffusion transformers (DiTs) have emerged as a dominant architecture for text-to-image generation, yet their performance drops when generating at resolutions beyond their training range. Existing training-free approaches mitigate this by modifying inference-time attention behavior, often through Rotary Position Embeddings (RoPE) extrapolation combined with attention scaling. However, these strategies apply a uniform and content-agnostic scaling across RoPE components with distinct frequency characteristics, inducing a trade-off between preserving global structure and recovering fine detail. We introduce SEGA, a training-free method that dynamically scales attention across RoPE components according to the latent's spatial-frequency structure at each denoising step. This adaptive scaling improves both structural coherence and fine-detail fidelity. Experiments show that SEGA consistently improves high-resolution synthesis across multiple target resolutions, outperforming state-of-the-art training-free baselines.

LiDARs are widely used for 3D depth reconstruction, but their performance is often limited by inherent hardware constraints that impose trade-offs between range, spatial resolution, and frame rate. Many LiDAR systems typically operate at low frame rates (e.g., 5-10 Hz), prioritizing long-range sensing over responsiveness to rapid scene changes. We present NeuroLiDAR, an adaptive depth sensing framework that achieves effective frame rates of up to $\approx$66 Hz by fusing temporally sparse LiDAR data with temporally dense inputs from neuromorphic event cameras. NeuroLiDAR integrates two components: event-based keyframe detection and event-guided depth extrapolation, to dynamically adjust the sensing rate in response to scene dynamics. To evaluate our approach, we introduce ELiDAR, a dataset spanning outdoor and indoor scenarios, and show that NeuroLiDAR reduces depth reconstruction error by $\approx$29% in RMSE while achieving adaptive frame rates between 27.8-47.3 Hz. Our code and dataset are available at https://github.com/darshanakgr/neurolidar.

Streaming video understanding requires processing unbounded video streams with limited memory and computation, posing two key challenges. First, continuously constructing new and evicting old key-value(KV) caches is required for unbounded streams. Secondly, due to the high cost of collecting and training on unbounded streams, models must learn from short sequences while generalizing to long streams. Existing streaming VideoVLLMs fail to scale to unbounded video streams or focus on cache reuse strategies, leaving the impact of cache construction underexplored. In this paper, we propose Decoupled Streaming Cache(DSCache), a training-free cache construction mechanism that adapts pretrained offline models to streaming settings. DSCache maintains a cumulative past KV cache while constructing a separate instant cache on-demand, decoupled from past caches to preserve the informativeness of recent inputs. To enable position extrapolation beyond the training length, DSCache further incorporates a position-agnostic encoding strategy, ensuring KV caches to support unseen positions and preventing position overflow. Experiments on Streaming Video QA benchmarks demonstrate DSCache's state-of-the-art performance, with an average 2.5% accuracy gains over prior methods.

We study implicit reasoning, i.e. the ability to combine knowledge or rules within a single forward pass. While transformer-based large language models store substantial factual knowledge and rules, they often fail to compose this knowledge for implicit multi-hop reasoning, suggesting a lack of compositional generalization over their parametric knowledge. To address this limitation, we study recurrent-depth transformers, which enables iterative computation over the same transformer layers. We investigate two compositional generalization challenges under the implicit reasoning scenario: systematic generalization, i.e. combining knowledge that is never used for compositions during training, and depth extrapolation, i.e. generalizing from limited reasoning depth (e.g. training on up to 5-hop) to deeper compositions (e.g. 10-hop). Through controlled studies with models trained from scratch, we show that while vanilla transformers struggle with both generalization challenges, recurrent-depth transformers can effectively make such generalization. For systematic generalization, we find that this ability emerges through a three-stage grokking process, transitioning from memorization to in-distribution generalization and finally to systematic generalization, supported by mechanistic analysis. For depth extrapolation, we show that generalization beyond training depth can be unlocked by scaling inference-time recurrence, with more iterations enabling deeper reasoning. We further study how training strategies affect extrapolation, providing guidance on training recurrent-depth transformers, and identify a key limitation, overthinking, where excessive recurrence degrades predictions and limits generalization to very deep compositions.

Variational Autoencoder (VAE) encoders play a critical role in modern generative models, yet their computational cost often motivates the use of knowledge distillation or quantification to obtain compact alternatives. Existing studies typically believe that the model work better on the samples closed to their training data distribution than unseen data distribution. In this work, we report a counter-intuitive phenomenon in VAE encoder distillation: a compact encoder distilled only at low resolutions exhibits poor reconstruction performance at its native resolution, but achieves dramatically improved results when evaluated at higher, unseen input resolutions. Despite never being trained beyond $256^2$ resolution, the distilled encoder generalizes effectively to $512^2$ resolution inputs, partially inheriting the teacher model's resolution preference.We further analyze latent distributions across resolutions and find that higher-resolution inputs produce latent representations more closely aligned with the teacher's manifold. Through extensive experiments on ImageNet-256, we show that simple resolution remapping-upsampling inputs before encoding and downsampling reconstructions for evaluation-leads to substantial gains across PSNR, MSE, SSIM, LPIPS, and rFID metrics. These findings suggest that VAE encoder distillation learns resolution-consistent latent manifolds rather than resolution-specific pixel mappings. This also means that the high training cost on memory, time and high-resolution datasets are not necessary conditions for distilling a VAE with high-resolution image reconstruction capabilities. On low resolution datasets, the distillation model still could learn the detailed knowledge of the teacher model in high-resolution image reconstruction.