Mergeable Model-Side Aggregation States for Long-Context Language Models

A known limitation of long-context language models is their increasingly unreliable performance in non-additive, set-based aggregation as context length grows. Examples include cardinality estimation, set relationships, and grouped statistics, which widely exist in logs, program outputs, tables, and multi-turn conversations. To provide the aggregation state required by these tasks, we introduce a model-side aggregation interface that maintains compact Hash-based HyperLogLog (HLL) sketch states alongside a frozen language model. While the model processes the context, an extractor maps each relevant record to a canonical identity. The identity is then hashed and updates the HLL state. These states can be merged across context segments and/or read out directly for downstream reasoning, avoiding an additional generate-execute-return cycle. We validate the proposed approach by setting the HLL state size as 2 KiB (2,048 registers), which does not increase with context length or set cardinality. In a distinct-count experiment involving one million records, the mean relative error was 1.6%. In a separate merge test, states built from as many as 256 segments produced exactly the same readout as a single pass over the same stream. On 3,969 aggregate-then-reason tasks from 174 source windows, the fixed-budget interface reached 99.2% accuracy on Gemma 4 (31B, BF16), compared with 100.0% under exact aggregation; the paired gap was 0.8 percentage points (95% window-cluster CI: 0.5-1.3 points). On a matched set of 174 items, our method improved over direct full-context reasoning by 63.2 points on Qwen and 56.3 points on Gemma. The corresponding gains over chain-of-thought (CoT) reasoning were 60.9 and 63.2 points, respectively. On a fixed 1,200-task Oolong-Synth subset, our method reached 91.1% on Qwen and 99.3% on Gemma. Code is available at https://github.com/songdc98/sketchops.

Elastic Spectral State Space Models for Budgeted Inference

Foundation models are typically trained at a fixed computational capacity, while real-world applications require deployment across platforms with different resource constraints. Current approaches usually rely on training families of model variants or model distillation, which requires additional training and supports only a pre-selected set of sizes rather than fine-grained adaptation at runtime. In this paper, we propose Elastic Spectral State Space Models (ES-SSM), which require only one-time training at full capacity, but can be directly truncated into arbitrary scales for budgeted, runtime inference without retraining. Our ES-SSM builds on Hankel spectral filtering over a state space model (SSM), coupled with a lightweight input-adaptive gate trained under randomized spectral budgets. Using a shared masked normalization rule over the ordered spectral channels, we encourage predictive capability to concentrate in low-index components, while higher-index components act primarily as refinement. We test our algorithm across long-sequence benchmarks spanning text, logic, retrieval, vision, and audio. We demonstrate that a single ES-SSM model trained once can be truncated to provide competitive performance compared with modern Transformer and SSM baselines at similar parameter scales. Furthermore, by testing under various runtime budgets, we observe smooth and stable budget-performance curves over a wide range of truncation levels.

Causality-based Subject and Task Fingerprints using fMRI Time-series Data

Recently, there has been a revived interest in system neuroscience causation models due to their unique capability to unravel complex relationships in multi-scale brain networks. In this paper, our goal is to verify the feasibility and effectiveness of using a causality-based approach for fMRI fingerprinting. Specifically, we propose an innovative method that utilizes the causal dynamics activities of the brain to identify the unique cognitive patterns of individuals (e.g., subject fingerprint) and fMRI tasks (e.g., task fingerprint). The key novelty of our approach stems from the development of a two-timescale linear state-space model to extract 'spatio-temporal' (aka causal) signatures from an individual's fMRI time series data. To the best of our knowledge, we pioneer and subsequently quantify, in this paper, the concept of 'causal fingerprint.' Our method is well-separated from other fingerprint studies as we quantify fingerprints from a cause-and-effect perspective, which are then incorporated with a modal decomposition and projection method to perform subject identification and a GNN-based (Graph Neural Network) model to perform task identification. Finally, we show that the experimental results and comparisons with non-causality-based methods demonstrate the effectiveness of the proposed methods. We visualize the obtained causal signatures and discuss their biological relevance in light of the existing understanding of brain functionalities. Collectively, our work paves the way for further studies on causal fingerprints with potential applications in both healthy controls and neurodegenerative diseases.