arXiv subjects

Jiantao Jiao

Publications and source records attributed to Jiantao Jiao.

At least 19 recordsLinked to original sources

arXiv2026

DiscoLoop: Looping Discrete Embeddings and Continuous Hidden States for Multi-hop Reasoning

Large language models achieve strong performance on many reasoning tasks when allowed to externalize intermediate steps as Chain-of-Thought (CoT). However, many questions require the model to internalize the multi-step reasoning within a single forward pass before generating the answer. We study this challenge through two-hop reasoning, a representative task where the model must compose multiple pieces of parametric knowledge within a single forward pass. Standard non-recurrent Transformers suffer from a depth-local storage problem: facts learned in earlier layers are unavailable where second-hop retrieval happens. We found that Looped Transformers mitigate this issue by reusing the same memory, but still generalize imperfectly. We show that the remaining bottleneck is representational. In the two-hop reasoning task, the first loop often makes the correct bridge entity nearly perfectly decodable, yet the corresponding hidden state remains poorly aligned with the bridge token embedding. Surprisingly, an easy training-free realignment intervention nearly closes the generalization gap. Building upon this insight, we propose DiscoLoop, a looping architecture whose recurrence carries both a discrete embedding channel and a continuous hidden-state channel. DiscoLoop achieves near-perfect accuracy with substantially fewer training steps across symbolic and synthetic-language multi-hop reasoning tasks. When applied to real-world pretraining, DiscoLoop attains lower training loss and stronger benchmark performance than looped-transformer baselines, suggesting that the mixed-channel design transfers to practical language modeling.

cs.CL↗

arXiv2026

MLS-Bench: A Holistic and Rigorous Assessment of AI Systems on Building Better AI

Modern AI progress has been driven by ML methods that are generalizable across settings and scalable to larger regimes. As large language models demonstrate advanced capabilities in reasoning, coding, and engineering tasks, it is increasingly important to understand whether they can discover such methods rather than only apply existing ones. We introduce MLS-Bench, a benchmark for evaluating whether AI systems can invent generalizable and scalable ML methods. MLS-Bench contains 140 tasks across 12 domains, each requiring an agent to improve one targeted component of an ML system or algorithm and demonstrate that the improvement generalizes across controlled settings and scales. We find that current agents remain far from reliably surpassing human-designed methods, and that engineering-style tuning is easier for them than genuine method invention. We further study the effects of test-time scaling, adaptive compute allocation, and context provision on agents' discovery performance, together with case studies of their behavior. Our analyses suggest that the bottleneck is not only in proposing new methods, but also in the scientific insight needed to plan, validate, and scale claims about them. More search, compute, or context alone does not remove this bottleneck. We build and maintain a community platform for cumulative and comparable iteration, and release the data and code at https://mls-bench.com.

cs.LG↗

arXiv2026

Coresets Before Score Sets: Evaluation-Unsupervised Prompt Subset Selection for LLM Benchmarks

We study LLM benchmark coreset selection: selecting a small subset of prompts over multiple benchmarks whose induced model scores and rankings approximate those obtained from the full benchmark suite. In evaluation-unsupervised benchmark coreset selection (our approach), the selection algorithm uses no model evaluation outcomes, and operates on a fine granularity by producing subsets of prompts over multiple benchmarks rather than producing a sub-collection of entire benchmarks. We use submodular subset selection, and we develop and evaluate many different submodular functions for this purpose, including determinantal point process (DPP) based approaches, submodular mutual information functions, and facility location-based functions. On a new large-scale suite of 35 heterogeneous benchmarks spanning five different capability categories, 18 frontier LLMs, and over 61K prompts, we find that the facility location (FL) function operating exclusively on inexpensive semantic prompt embeddings preserves LLM scores better than twelve separate score-based and diversity-based baselines, across a range of coreset budgets. Moreover, we show our proposed objective is not limited to the evaluation-unsupervised regime: in the setting where only a handful of whole benchmarks must be selected and a large amount of model scores are available, the same objective matches or outperforms state-of-the-art baselines on the MMLU and MTEB leaderboards, while being substantially cheaper to compute. Together, our results suggest that submodularity, in general, is a strong and reliable tool for benchmark compression.

cs.AI↗

arXiv2026

DiPOD: Diffusion Policy Optimization without Drifting Apart

RL post-training has become increasingly pivotal for improving diffusion policies, but existing diffusion policy-gradient methods are often unstable and cannot achieve reliable policy improvement. We identify the cause as the double-drift phenomenon: optimizing a variational surrogate can let the ELBO separate from the true log-likelihood, which then makes the resulting proxy policy gradient misaligned with the true policy gradient of expected return. We propose \textbf{DiPOD}, a diffusion policy optimization framework that maintains tight-bound behavior throughout training by interleaving self-distillation with policy-improving gradient updates. This leads to a simple and practical algorithm: augmenting each diffusion policy-gradient update with an on-policy ELBO regularizer. Across diffusion language model post-training and continuous-control diffusion policies, DiPOD substantially stabilizes training and reaches higher rewards than previous methods.

cs.LG↗

arXiv2026

Transformers Provably Learn to Internalize Chain-of-Thought

Chain-of-Thought (CoT) prompting substantially improves the sample efficiency of transformers, reducing the complexity of tasks like parity learning from exponential to polynomial in the input length. However, generating explicit reasoning steps at inference is computationally expensive. Implicit Chain-of-Thought (ICoT) has emerged as a promising empirical remedy that trains models to internalize intermediate steps within their hidden states, but its theoretical foundations remain poorly understood. We give the first theoretical analysis of ICoT, proving that an $L$-layer transformer trained under our proposed Log-ICoT curriculum learns $k$-parity with $\mathsf{poly}(n)$ samples and $L = \log_2 k$ training stages. This matches the sample efficiency of explicit CoT while eliminating its inference overhead, and extends prior one-layer parity guarantees to multi-layer architectures. Compared to standard ICoT, which removes thinking tokens one at a time, Log-ICoT removes them in geometric chunks, reducing the number of stages from linear in $k$ to logarithmic. Experiments on multi-layer transformers confirm the theory and visualize how reasoning is progressively absorbed into deeper layers.

cs.LG↗

arXiv2026

PivotRL: High Accuracy Agentic Post-Training at Low Compute Cost

Post-training for long-horizon agentic tasks has a tension between compute efficiency and generalization. While supervised fine-tuning (SFT) is compute efficient, it often suffers from out-of-domain (OOD) degradation. Conversely, end-to-end reinforcement learning (E2E RL) preserves OOD capabilities, but incurs high compute costs due to many turns of on-policy rollout. We introduce PivotRL, a novel framework that operates on existing SFT trajectories to combine the compute efficiency of SFT with the OOD accuracy of E2E RL. PivotRL relies on two key mechanisms: first, it executes local, on-policy rollouts and filters for pivots: informative intermediate turns where sampled actions exhibit high variance in outcomes; second, it utilizes rewards for functional-equivalent actions rather than demanding strict string matching with the SFT data demonstration. We theoretically show that these mechanisms incentivize strong learning signals with high natural gradient norm, while maximally preserving policy probability ordering on actions unrelated to training tasks. In comparison to standard SFT on identical data, we demonstrate that PivotRL achieves +4.17% higher in-domain accuracy on average across four agentic domains, and +10.04% higher OOD accuracy in non-agentic tasks. Notably, on agentic coding tasks, PivotRL achieves competitive accuracy with E2E RL with 4x fewer rollout turns. PivotRL is adopted by NVIDIA's Nemotron-3-Super-120B-A12B, acting as the workhorse in production-scale agentic post-training.

cs.AI↗

arXiv2026

Emergence of Superposition: Unveiling the Training Dynamics of Chain of Continuous Thought

Previous work shows that the chain of continuous thought (continuous CoT) improves the reasoning capability of large language models (LLMs) by enabling implicit parallel thinking, and a subsequent work provided theoretical insight by showing that a two-layer transformer equipped with continuous CoT can efficiently solve directed graph reachability by maintaining a superposition of multiple reasoning traces in the continuous thought. However, it remains unclear how the superposition mechanism is naturally learned from gradient-based training methods. To fill this gap, we theoretically analyze the training dynamics of a simplified two-layer transformer on the directed graph reachability problem to unveil how the superposition mechanism emerges during training in two training stages -- (i) a thought-generation stage that autoregressively expands the continuous thought, and (ii) a prediction stage that converts the thought into the final answer. Our analysis reveals that during training using continuous thought, the index-matching logit, an important quantity which reflects the strength of the model's local search ability, will first increase and then remain bounded under mild assumptions. The bounded index-matching logit effectively balances exploration and exploitation during the reasoning process: the model will exploit local problem structures to identify plausible search traces, and assign comparable weights to multiple such traces to explore when it is uncertain about which solution is correct, which results in superposition. Our experimental results tracking the growth of logits further validate our theory.

cs.LG↗

arXiv2026

Towards Anytime-Valid Statistical Watermarking

The proliferation of Large Language Models (LLMs) necessitates efficient mechanisms to distinguish machine-generated content from human text. While statistical watermarking has emerged as a promising solution, existing methods suffer from two critical limitations: the lack of a principled approach for selecting sampling distributions and the reliance on fixed-horizon hypothesis testing, which precludes valid early stopping. In this paper, we bridge this gap by developing the first e-value-based watermarking framework, Anchored E-Watermarking, that unifies optimal sampling with anytime-valid inference. Unlike traditional approaches where optional stopping invalidates Type-I error guarantees, our framework enables valid, anytime-inference by constructing a test supermartingale for the detection process. By leveraging an anchor distribution to approximate the target model, we characterize the optimal e-value with respect to the worst-case log-growth rate and derive the optimal expected stopping time. Our theoretical claims are substantiated by simulations and evaluations on established benchmarks, showing that our framework can significantly enhance sample efficiency, reducing the average token budget required for detection by 13-15% relative to state-of-the-art baselines.

cs.LG↗

arXiv2026

dUltra: Ultra-Fast Diffusion Language Models via Reinforcement Learning

Masked diffusion language models (MDLMs) offer the potential for parallel token generation, but most open-source MDLMs decode fewer than 5 tokens per model forward pass even with sophisticated sampling strategies, limiting their parallel generation potential. Existing acceleration methods either rely on fixed confidence-based heuristics or use distillation-based approaches that finetune MDLMs on trajectories generated by a base model, which can become off-policy during finetuning and restrict performance to the quality of the base model's samples. We propose \texttt{dUltra}, an on-policy reinforcement learning framework based on Group Relative Policy Optimization (GRPO) that learns unmasking strategies for efficient parallel decoding. dUltra introduces an unmasking planner head that predicts per-token unmasking likelihoods under independent Bernoulli distributions. We jointly optimize the base diffusion LLM and the unmasking order planner using reward signals combining verifiable reward, distillation reward, and the number of unmasking steps. Across mathematical reasoning and code generation tasks, dUltra achieves superior accuracy-efficiency trade-offs compared to state-of-the-art heuristic (Fast-dLLM) and distillation baselines (d3LLM, dParallel), demonstrating that learned unmasking trajectories through on-policy RL enable better exploitation of parallel generation in MDLMs. Code and checkpoints are released at https://github.com/chinsengi/dUltra-os.

cs.LG↗

arXiv2026

Generalization or Hallucination? Understanding Out-of-Context Reasoning in Transformers

Large language models (LLMs) can acquire new knowledge through fine-tuning, but this process exhibits a puzzling duality: models can generalize remarkably from new facts, yet are also prone to hallucinating incorrect information. However, the reasons for this phenomenon remain poorly understood. In this work, we argue that both behaviors stem from a single mechanism known as out-of-context reasoning (OCR): the ability to deduce implications by associating concepts, even those without a causal link. Our experiments across five prominent LLMs confirm that OCR indeed drives both generalization and hallucination, depending on whether the associated concepts are causally related. To build a rigorous theoretical understanding of this phenomenon, we then formalize OCR as a synthetic factual recall task. We empirically show that a one-layer single-head attention-only transformer with factorized output and value matrices can learn to solve this task, while a model with combined weights cannot, highlighting the crucial role of matrix factorization. Our theoretical analysis shows that the OCR capability can be attributed to the implicit bias of gradient descent, which favors solutions that minimize the nuclear norm of the combined output-value matrix. This mathematical structure explains why the model learns to associate facts and implications with high sample efficiency, regardless of whether the correlation is causal or merely spurious. Ultimately, our work provides a theoretical foundation for understanding the OCR phenomenon, offering a new lens for analyzing and mitigating undesirable behaviors from knowledge injection.

cs.CL↗

arXiv2025

From Bits to Rounds: Parallel Decoding with Exploration for Diffusion Language Models

Diffusion Language Models (DLMs) have recently emerged as a strong alternative to autoregressive language models (LMs). DLMs offer comparable accuracy with faster inference speed via parallel decoding. However, standard DLM decoding strategies relying on high-confidence tokens encounter an inherent information-theoretic bottleneck that restricts decoding progress and ultimately slows generation. We demonstrate both theoretically and empirically that prioritizing high-confidence tokens is inherently inefficient. High-probability tokens carry negligible information and strictly relying on them limits the effective progress made in each decoding round. We prove that the number of decoding rounds must grow linearly with the sample's total information (negative log-likelihood) and inversely with the per-round information budget, establishing a bits-to-rounds principle. We also propose Explore-Then-Exploit (ETE), a training-free decoding strategy that maximizes information throughput and decoding efficiency. ETE combines cross-block decoding with targeted exploration of high-uncertainty tokens to reshape the conditional distribution and trigger cascades of confident predictions. Experiments verify our theoretical bounds and demonstrate that ETE consistently reduces the required number of decoding rounds compared to confidence-only baselines without compromising generation quality.

cs.LG↗

arXiv2025

Information-driven design of imaging systems

Imaging systems have traditionally been designed to mimic the human eye and produce visually interpretable measurements. Modern imaging systems, however, process raw measurements computationally before or instead of human viewing. As a result, the information content of raw measurements matters more than their visual interpretability. Despite the importance of measurement information content, current approaches for evaluating imaging system performance do not quantify it: they instead either use alternative metrics that assess specific aspects of measurement quality or assess measurements indirectly with performance on secondary tasks. We developed the theoretical foundations and a practical method to directly quantify mutual information between noisy measurements and unknown objects. By fitting probabilistic models to measurements and their noise characteristics, our method estimates information by upper bounding its true value. By applying gradient-based optimization to these estimates, we also developed a technique for designing imaging systems called Information-Driven Encoder Analysis Learning (IDEAL). Our information estimates accurately captured system performance differences across four imaging domains (color photography, radio astronomy, lensless imaging, and microscopy). Systems designed with IDEAL matched the performance of those designed with end-to-end optimization, the prevailing approach that jointly optimizes hardware and image processing algorithms. These results establish mutual information as a universal performance metric for imaging systems that enables both computationally efficient design optimization and evaluation in real-world conditions. A video summarizing this work can be found at: https://waller-lab.github.io/EncodingInformationWebsite/

physics.optics↗

arXiv2025

Reasoning by Superposition: A Theoretical Perspective on Chain of Continuous Thought

Large Language Models (LLMs) have demonstrated remarkable performance in many applications, including challenging reasoning problems via chain-of-thoughts (CoTs) techniques that generate ``thinking tokens'' before answering the questions. While existing theoretical works demonstrate that CoTs with discrete tokens boost the capability of LLMs, recent work on continuous CoTs lacks a theoretical understanding of why it outperforms discrete counterparts in various reasoning tasks such as directed graph reachability, a fundamental graph reasoning problem that includes many practical domain applications as special cases. In this paper, we prove that a two-layer transformer with $D$ steps of continuous CoTs can solve the directed graph reachability problem, where $D$ is the diameter of the graph, while the best known result of constant-depth transformers with discrete CoTs requires $O(n^2)$ decoding steps where $n$ is the number of vertices ($D<n$). In our construction, each continuous thought vector is a superposition state that encodes multiple search frontiers simultaneously (i.e., parallel breadth-first search (BFS)), while discrete CoTs must choose a single path sampled from the superposition state, which leads to sequential search that requires many more steps and may be trapped into local solutions. We also performed extensive experiments to verify that our theoretical construction aligns well with the empirical solution obtained via training dynamics. Notably, encoding of multiple search frontiers as a superposition state automatically emerges in training continuous CoTs, without explicit supervision to guide the model to explore multiple paths simultaneously.

cs.LG↗

arXiv2025

GSM-Agent: Understanding Agentic Reasoning Using Controllable Environments

As LLMs are increasingly deployed as agents, agentic reasoning - the ability to combine tool use, especially search, and reasoning - becomes a critical skill. However, it is hard to disentangle agentic reasoning when evaluated in complex environments and tasks. Current agent benchmarks often mix agentic reasoning with challenging math reasoning, expert-level knowledge, and other advanced capabilities. To fill this gap, we build a novel benchmark, GSM-Agent, where an LLM agent is required to solve grade-school-level reasoning problems, but is only presented with the question in the prompt without the premises that contain the necessary information to solve the task, and needs to proactively collect that information using tools. Although the original tasks are grade-school math problems, we observe that even frontier models like GPT-5 only achieve 67% accuracy. To understand and analyze the agentic reasoning patterns, we propose the concept of agentic reasoning graph: cluster the environment's document embeddings into nodes, and map each tool call to its nearest node to build a reasoning path. Surprisingly, we identify that the ability to revisit a previously visited node, widely taken as a crucial pattern in static reasoning, is often missing for agentic reasoning for many models. Based on the insight, we propose a tool-augmented test-time scaling method to improve LLM's agentic reasoning performance by adding tools to encourage models to revisit. We expect our benchmark and the agentic reasoning framework to aid future studies of understanding and pushing the boundaries of agentic reasoning.

cs.AI↗

arXiv2025

Token Assorted: Mixing Latent and Text Tokens for Improved Language Model Reasoning

Large Language Models (LLMs) excel at reasoning and planning when trained on chainof-thought (CoT) data, where the step-by-step thought process is explicitly outlined by text tokens. However, this results in lengthy inputs where many words support textual coherence rather than core reasoning information, and processing these inputs consumes substantial computation resources. In this work, we propose a hybrid representation of the reasoning process, where we partially abstract away the initial reasoning steps using latent discrete tokens generated by VQ-VAE, significantly reducing the length of reasoning traces. We explore the use of latent trace abstractions in two scenarios: 1) training the model from scratch for the Keys-Finding Maze problem, 2) fine-tuning LLMs on this hybrid data with an extended vocabulary including unseen latent tokens, for both logical and mathematical reasoning problems. To facilitate effective learning, we introduce a simple training procedure that randomly mixes latent and text tokens, which enables fast adaptation to new latent tokens. Our approach consistently outperforms the baselines methods in various benchmarks.

cs.CL↗

arXiv2025

Sample Complexity and Representation Ability of Test-time Scaling Paradigms

Test-time scaling paradigms have significantly advanced the capabilities of large language models (LLMs) on complex tasks. Despite their empirical success, theoretical understanding of the sample efficiency of various test-time strategies -- such as self-consistency, best-of-$n$, and self-correction -- remains limited. In this work, we first establish a separation result between two repeated sampling strategies: self-consistency requires $Θ(1/Δ^2)$ samples to produce the correct answer, while best-of-$n$ only needs $Θ(1/Δ)$, where $Δ< 1$ denotes the probability gap between the correct and second most likely answers. Next, we present an expressiveness result for the self-correction approach with verifier feedback: it enables Transformers to simulate online learning over a pool of experts at test time. Therefore, a single Transformer architecture can provably solve multiple tasks without prior knowledge of the specific task associated with a user query, extending the representation theory of Transformers from single-task to multi-task settings. Finally, we empirically validate our theoretical results, demonstrating the practical effectiveness of self-correction methods.

cs.LG↗

arXiv2025

How Do LLMs Perform Two-Hop Reasoning in Context?

``Socrates is human. All humans are mortal. Therefore, Socrates is mortal.'' This form of argument illustrates a typical pattern of two-hop reasoning. Formally, two-hop reasoning refers to the process of inferring a conclusion by making two logical steps, each connecting adjacent concepts, such that the final conclusion depends on the integration of both steps. It is one of the most fundamental components of human reasoning and plays a crucial role in both formal logic and everyday decision-making. Despite recent progress in large language models (LLMs), we surprisingly find that they can fail at solving simple two-hop reasoning problems when distractors are present. We observe on a synthetic dataset that pre-trained LLMs often resort to random guessing among all plausible conclusions. However, after few steps of fine-tuning, models achieve near-perfect accuracy and exhibit strong length generalization. To understand the underlying mechanisms, we train a 3-layer Transformer from scratch on a synthetic two-hop reasoning task and reverse-engineer its internal information flow. We observe a clear progression in the attention logits throughout training. This pictures a sharp phase transition from an initial stage of random guessing to the emergence of a structured sequential query mechanism, where the model first retrieves the preceding and the bridge concepts in the early layers and then uses them to infer the final answer. Finally, we show that these dynamics can be captured by a minimal three-parameter attention-only network.

cs.CL↗

arXiv2025

Toward a Theory of Tokenization in LLMs

While there has been a large body of research attempting to circumvent tokenization for language modeling (Clark et al., 2022; Xue et al., 2022), the current consensus is that it is a necessary initial step for designing state-of-the-art performant language models. In this paper, we investigate tokenization from a theoretical point of view by studying the behavior of transformers on simple data generating processes. When trained on data drawn from certain simple $k^{\text{th}}$-order Markov processes for $k > 1$, transformers exhibit a surprising phenomenon - in the absence of tokenization, they empirically fail to learn the right distribution and predict characters according to a unigram model (Makkuva et al., 2024). With the addition of tokenization, however, we empirically observe that transformers break through this barrier and are able to model the probabilities of sequences drawn from the source near-optimally, achieving small cross-entropy loss. With this observation as starting point, we study the end-to-end cross-entropy loss achieved by transformers with and without tokenization. With the appropriate tokenization, we show that even the simplest unigram models (over tokens) learnt by transformers are able to model the probability of sequences drawn from $k^{\text{th}}$-order Markov sources near optimally. Our analysis provides a justification for the use of tokenization in practice through studying the behavior of transformers on Markovian data.

cs.CL↗