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Aug 5

State and parameter learning with PaRIS particle Gibbs

Non-linear state-space models, also known as general hidden Markov models, are ubiquitous in statistical machine learning, being the most classical generative models for serial data and sequences in general. The particle-based, rapid incremental smoother PaRIS is a sequential Monte Carlo (SMC) technique allowing for efficient online approximation of expectations of additive functionals under the smoothing distribution in these models. Such expectations appear naturally in several learning contexts, such as likelihood estimation (MLE) and Markov score climbing (MSC). PARIS has linear computational complexity, limited memory requirements and comes with non-asymptotic bounds, convergence results and stability guarantees. Still, being based on self-normalised importance sampling, the PaRIS estimator is biased. Our first contribution is to design a novel additive smoothing algorithm, the Parisian particle Gibbs PPG sampler, which can be viewed as a PaRIS algorithm driven by conditional SMC moves, resulting in bias-reduced estimates of the targeted quantities. We substantiate the PPG algorithm with theoretical results, including new bounds on bias and variance as well as deviation inequalities. Our second contribution is to apply PPG in a learning framework, covering MLE and MSC as special examples. In this context, we establish, under standard assumptions, non-asymptotic bounds highlighting the value of bias reduction and the implicit Rao--Blackwellization of PPG. These are the first non-asymptotic results of this kind in this setting. We illustrate our theoretical results with numerical experiments supporting our claims.

  • 5 authors
·
Jan 2, 2023

A Taxonomy of Event-Linked Perpetual Futures: Variant Designs Beyond the Single-Market Binary Case

Paper 1 of this research programme develops a resolution-aware risk-design framework for the simplest event-linked perpetual: a contract whose underlying tracks a single binary prediction-market probability through resolution. The instrument class is broader. Variants span conditional probabilities P(A|B), spreads p^A - p^B, weighted baskets sum w_i p^(i), derivatives on variance or entropy of the probability process, contracts on liquidity itself, perpetual-on-expiring-event roll structures, and funding-only derivatives with no settlement. Each variant inherits some framework components from the single-market binary case and requires its own design adaptations. This paper develops a formal taxonomy of seven pure-form canonical variants beyond the probability-index perpetual of Paper 1, organised along four orthogonal design axes: underlying geometry, temporal structure, settlement structure, and venue composition. The list is not exhaustive; combinations are not treated separately. For each variant we provide a precise payoff definition; an inheritance map identifying which Paper 1 components carry over, are modified, or fail; variant-specific design constraints; microstructure properties; empirical evaluability on the PMXT v2 archive; and limitations. Notable findings: the conditional variant admits a candidate non-portability proposition (denominator instability as the conditioning event becomes improbable); the spread variant requires a three-channel decomposition of resolution risk; the volatility/entropy variant avoids random binary terminal-collapse but introduces estimator-convention and entropy-decay issues; the basket variant requires multi-period jump-aware margin whose aggregation is correlation-dependent. The paper is theoretical primarily; it specifies how demonstrative time series can be constructed and provides evaluability criteria to guide future work.

  • 1 authors
·
May 10

Relax Within, Balance Across: Geometry-Guided Load Balancing for Vision-Language Mixture-of-Experts

Vision-language MoE batches contain different numbers of image and text tokens. Image resolution, image count, tiling, and prompt length all change this token mix. We call the standard token-level Switch auxiliary loss Std-Aux. Std-Aux balances only the mixed load, so large image and text load errors can cancel at one mix. On our main model, the same trained router shows more than a fivefold change in load imbalance across image resolutions. We hold the image and text load profiles fixed and derive the exact load curve as the token mix varies. The image-text load gap controls sensitivity to the token mix. Physical preprocessing can also change the conditional profiles. The fixed-profile law excludes such changes. To design a remedy, we examine the router input structure. Image and text occupy distinct regions, while visual tokens group strongly by source image. The modality boundary motivates separate image and text terms. The image boundary motivates one equal-weight routing instance per image. ReBA, or Relax Within, Balance Across, implements both choices. Across four split backbones, ReBA lowers load on every reported benchmark input while keeping mean task accuracy comparable to Std-Aux. ReBA also lowers average load over the tested range and worst physical load under resolution and tiling shifts. Code is available at https://github.com/ZiangWu-77/ReBA.

S-Bus: Automatic Read-Set Reconstruction for Multi-Agent LLM State Coordination

Concurrent LLM agents sharing mutable natural-language state produce Structural Race Conditions (SRCs): write-write and cross-shard stale-read conflicts that silently corrupt agent output. Existing multi-agent frameworks (LangGraph, CrewAI, AutoGen) provide no write-ownership semantics over shared state. We present S-Bus, an HTTP middleware whose central mechanism is a server-side DeliveryLog: a per-agent log of HTTP GET operations that automatically reconstructs each agent's read set at commit time without agent SDK changes under HTTP/1.1. The consistency property the DeliveryLog provides -- Observable-Read Isolation (ORI), a partial causal consistency over the HTTP-observable projection of the read set -- prevents structural race conditions when agents collaborate via shared shards. Three contributions: (C1) The DeliveryLog mechanism for automatic HTTP-traffic-based read-set reconstruction, with three-tier mechanised evidence: ReadSetSoundness and ORICommitSafety machine-checked in TLAPS (modulo one retained typing axiom); exhaustive TLC at N=3 (20,763,484 distinct states, zero violations); Dafny discharges 9 inductive soundness lemmas. (C2) Empirical structural-conflict prevention parity against PostgreSQL 17 SERIALIZABLE and Redis 7 WATCH/MULTI on shared-shard contention sweeps with 427,308 active HTTP-409 conflicts: zero Type-I corruptions across all three backends. (C3) ORI's operating envelope is topology-conditional: semantically neutral in dedicated-shard workloads; harmful in single-shard collaborative writing because preservation propagates concurrent contradictions. Source code: https://github.com/sajjadanwar0/sbus

  • 1 authors
·
May 15 1

ScatterPrism: convergence for generative simulation and inverse problems in particle and nuclear physics

High-fidelity simulations and complex inverse problems, such as detector modeling and unfolding, are computationally intensive bottlenecks across subatomic physics, yet essential for accurate physical interpretation. While Conditional Flow Matching (CFM) offers a robust acceleration approach, we demonstrate its standard training loss is fundamentally misleading. Specifically, utilizing a Jefferson Lab Nuclear Physics (NP) kinematic dataset (γp to ρ^0 p to π^+π^- p), we expose that CFM loss plateaus prematurely, obscuring ongoing physical refinement. To verify this disconnect is a dataset-agnostic pathology, we introduce ScatterPrism, an efficient generative surrogate evaluated against both the NP data and synthetic stress tests modeling challenging 1D distribution topologies. Coupling these benchmarks, we establish that physics-informed metrics continue improving long after standard loss converges. Consequently, we propose a multi-metric diagnostic protocol to ensure true kinematic fidelity without data memorization. Driven by NP challenges relevant to the forthcoming Electron-Ion Collider (EIC), this unified machinery has strong potential to extend to High-Energy Physics (HEP) applications, such as jet modeling. Furthermore, the framework holds promise for broader domains requiring rigorous generative reliability, including medical imaging, astrophysics, and quantitative finance.

  • 6 authors
·
Jun 4

Demystifying the Token Dynamics of Deep Selective State Space Models

Selective state space models (SSM), such as Mamba, have gained prominence for their effectiveness in modeling sequential data. Despite their outstanding empirical performance, a comprehensive theoretical understanding of deep selective SSM remains elusive, hindering their further development and adoption for applications that need high fidelity. In this paper, we investigate the dynamical properties of tokens in a pre-trained Mamba model. In particular, we derive the dynamical system governing the continuous-time limit of the Mamba model and characterize the asymptotic behavior of its solutions. In the one-dimensional case, we prove that only one of the following two scenarios happens: either all tokens converge to zero, or all tokens diverge to infinity. We provide criteria based on model parameters to determine when each scenario occurs. For the convergent scenario, we empirically verify that this scenario negatively impacts the model's performance. For the divergent scenario, we prove that different tokens will diverge to infinity at different rates, thereby contributing unequally to the updates during model training. Based on these investigations, we propose two refinements for the model: excluding the convergent scenario and reordering tokens based on their importance scores, both aimed at improving practical performance. Our experimental results validate these refinements, offering insights into enhancing Mamba's effectiveness in real-world applications.

  • 4 authors
·
Oct 4, 2024

Power-SMC: Low-Latency Sequence-Level Power Sampling for Training-Free LLM Reasoning

Many recent reasoning gains in large language models can be explained as distribution sharpening: biasing generation toward high-likelihood trajectories already supported by the pretrained model, rather than modifying its weights. A natural formalization is the sequence-level power distribution π_α(ymid x)propto p_θ(ymid x)^α (α>1), which concentrates mass on whole sequences instead of adjusting token-level temperature. Prior work shows that Metropolis--Hastings (MH) sampling from this distribution recovers strong reasoning performance, but at order-of-magnitude inference slowdowns. We introduce Power-SMC, a training-free Sequential Monte Carlo scheme that targets the same objective while remaining close to standard decoding latency. Power-SMC advances a small particle set in parallel, corrects importance weights token-by-token, and resamples when necessary, all within a single GPU-friendly batched decode. We prove that temperature τ=1/α is the unique prefix-only proposal minimizing incremental weight variance, interpret residual instability via prefix-conditioned Rényi entropies, and introduce an exponent-bridging schedule that improves particle stability without altering the target. On MATH500, Power-SMC matches or exceeds MH power sampling while reducing latency from 16--28times to 1.4--3.3times over baseline decoding. The code is available at https://github.com/ArminAzizi98/Power-SMC.

  • 5 authors
·
Mar 22

Optimizing Mario Adventures in a Constrained Environment

This project proposes and compares a new way to optimise Super Mario Bros. (SMB) environment where the control is in hand of two approaches, namely, Genetic Algorithm (MarioGA) and NeuroEvolution (MarioNE). Not only we learn playing SMB using these techniques, but also optimise it with constrains of collection of coins and finishing levels. Firstly, we formalise the SMB agent to maximize the total value of collected coins (reward) and maximising the total distance traveled (reward) in order to finish the level faster (time penalty) for both the algorithms. Secondly, we study MarioGA and its evaluation function (fitness criteria) including its representation methods, crossover used, mutation operator formalism, selection method used, MarioGA loop, and few other parameters. Thirdly, MarioNE is applied on SMB where a population of ANNs with random weights is generated, and these networks control Marios actions in the game. Fourth, SMB is further constrained to complete the task within the specified time, rebirths (deaths) within the limit, and performs actions or moves within the maximum allowed moves, while seeking to maximize the total coin value collected. This ensures an efficient way of finishing SMB levels. Finally, we provide a fivefold comparative analysis by plotting fitness plots, ability to finish different levels of world 1, and domain adaptation (transfer learning) of the trained models.

  • 1 authors
·
Dec 14, 2023