LLM Inference

Large language models increasingly rely on inference-time procedures such as chain-of-thought reasoning, self-refinement, retrieval augmentation, and verifier-guided revision, yet the structure of elicited probability transformations under these procedures remains poorly understood. We study externally elicited probability assignments over candidate answers and observe recurring approximate log-ratio relationships: $$\log \tilde q_t(i) = α_t \left( \log q_t(i) + \log b_t(i) \right) + c_t,$$ where $q_t$ and $\tilde q_t$ are pre- and post-elicitation probabilities, $b_t$ is an externally constructed evidence signal, and $α_t$ is an empirical descriptor of the prompting configuration. Across 4,975 reasoning problems from GPQA Diamond, TheoremQA, MMLU-Pro, and ARC-Challenge, evaluated on multiple instruction-tuned model families, we observe approximate log-ratio relationships with mean $R^2 \approx 0.76$ over about $1.3 \times 10^5$ candidate-level observations. Coefficients vary across elicitation settings, but qualitatively similar relationships persist across evaluated conditions. Robustness analyses using alternative statistical representations, prompting configurations, held-out evaluation, and token-level log-probabilities suggest that the observed structure is not tied to one prompting procedure or probability estimation method. The main contribution is not the algebraic form itself, which is related to generalized Bayesian updating and probability-transformation frameworks, but the empirical observation that diverse inference-time prompting pipelines repeatedly exhibit reproducible log-ratio structure under controlled conditions. The framework provides a protocol-sensitive perspective for analyzing calibration, evidence amplification, uncertainty propagation, and interaction sensitivity in inference-time LLM pipelines.

Large language models have become central to many AI applications, but their growing energy consumption raises serious sustainability concerns. A key limitation in current AI deployments is the reliance on a one-size-fits-all inference strategy where most systems route every request to the same large model, regardless of task complexity, leading to substantial and unnecessary energy waste. To address this issue, we propose a context-aware model switching approach that dynamically selects an appropriate language model based on query complexity. The proposed system uses a Context-Aware Model Switching for Energy-Efficient LLM Inference that combines caching for repeated queries, rulebased complexity scoring for fast and explainable decisions, machine learning classification to capture semantic intent, and a user-adaptive component that learns from interaction patterns over time. The proposed architecture was evaluated using real conversation workloads and three open-source language models (Gemma3 1B, Gemma3 4B and Qwen3 4B) with different computational costs, measuring energy consumption (via NVML GPU power telemetry), response latency, routing accuracy, and output quality (BERTScore F1) to reflect real-world usage conditions. Experimental results show that the model switching approach can reduce energy consumption by up to 67.5% compared to always using the largest model while maintaining a response quality of 93.6%. In addition, the response time for simple queries also improved significantly by approximately 68%. These results show that model switching inference offers a practical and scalable path toward more energy-efficient and sustainable AI systems, demonstrating that significant efficiency gains can be achieved without major sacrifices in response quality.

Large language model (LLM) inference performance is increasingly bottlenecked by the memory wall. While GPUs continue to scale raw compute throughput, they struggle to deliver scalable performance for memory bandwidth bound workloads. This challenge is amplified by emerging reasoning LLM applications, where long output sequences, low arithmetic intensity, and tight latency constraints demand significantly higher memory bandwidth. As a result, system utilization drops and energy per inference rises, highlighting the need for an optimized system architecture for scalable memory bandwidth. To address these challenges we present the Reasoning Processing Unit (RPU), a chiplet-based architecture designed to address the challenges of the modern memory wall. RPU introduces: (1) A Capacity-Optimized High-Bandwidth Memory (HBM-CO) that trades capacity for lower energy and cost; (2) a scalable chiplet architecture featuring a bandwidth-first power and area provisioning design; and (3) a decoupled microarchitecture that separates memory, compute, and communication pipelines to sustain high bandwidth utilization. Simulation results show that RPU performs up to 45.3x lower latency and 18.6x higher throughput over an H100 system at ISO-TDP on Llama3-405B.

As large language models (LLMs) continue to grow in size, fewer users are able to host and run models locally. This has led to increased use of third-party hosting services. However, in this setting, there is a lack of guarantees on the computation performed by the inference provider. For example, a dishonest provider may replace an expensive large model with a cheaper-to-run weaker model and return the results from the weaker model to the user. Existing tools to verify inference typically rely on methods from cryptography such as zero-knowledge proofs (ZKPs), but these add significant computational overhead, and remain infeasible for use for large models. In this work, we develop a new insight -- that given a method for performing private LLM inference, one can obtain forms of verified inference at marginal extra cost. Specifically, we propose two new protocols which leverage privacy-preserving LLM inference in order to provide guarantees over the inference that was carried out. Our approaches are cheap, requiring the addition of a few extra tokens of computation, and have little to no downstream impact. As the fastest privacy-preserving inference methods are typically faster than ZK methods, the proposed protocols also improve verification runtime. Our work provides novel insights into the connections between privacy and verifiability in LLM inference.

Most large language models (LLMs) run on external clouds: users send a prompt, pay for inference, and must trust that the remote GPU executes the LLM without any adversarial tampering. We critically ask how to achieve verifiable LLM inference, where a prover (the service) must convince a verifier (the client) that an inference was run correctly without rerunning the LLM. Existing cryptographic works are too slow at the LLM scale, while non-cryptographic ones require a strong verifier GPU. We propose TensorCommitments (TCs), a tensor-native proof-of-inference scheme. TC binds the LLM inference to a commitment, an irreversible tag that breaks under tampering, organized in our multivariate Terkle Trees. For LLaMA2, TC adds only 0.97% prover and 0.12% verifier time over inference while improving robustness to tailored attacks by up to 48% over the best prior work requiring a verifier GPU.

Large language models (LLMs) are increasingly used to generate executable outputs, JSON objects, and API calls, where a single syntax error can make the output unusable. Constrained decoding enforces validity token-by-token via masking and renormalization, but it can distort generation when the model assigns low probability mass to valid continuations, pushing decoding toward locally valid yet semantically incorrect trajectories. We propose Draft-Conditioned Constrained Decoding (DCCD), a simple two-step, training-free inference procedure that decouples semantic planning from structural enforcement: an unconstrained draft is generated first, and constrained decoding is then applied, conditioned on this draft, to guarantee validity. We analyze DCCD through a KL-projection view, showing that draft conditioning increases feasible mass and reduces the cumulative "projection tax" induced by hard constraints, with an optional best-of-$K$ draft selection. Across structured reasoning benchmarks, DCCD improves strict structured accuracy by up to +24 percentage points over standard constrained decoding (e.g., 15.2% to 39.0% on GSM8K with a 1B model), and enables smaller model pairs to match or exceed much larger constrained baselines, yielding substantial gains in parameter efficiency.

Test-time compute has emerged as a promising strategy to enhance the reasoning abilities of large language models (LLMs). However, this strategy has in turn increased how much users pay cloud-based providers offering LLM-as-a-service, since providers charge users for the amount of test-time compute they use to generate an output. In our work, we show that the market of LLM-as-a-service is socially inefficient: providers have a financial incentive to increase the amount of test-time compute, even if this increase contributes little to the quality of the outputs. To address this inefficiency, we introduce a reverse second-price auction mechanism where providers bid their offered price and (expected) quality for the opportunity to serve a user, and users pay proportionally to the marginal value generated by the winning provider relative to the second-highest bidder. To illustrate and complement our theoretical results, we conduct experiments with multiple instruct models from the $\texttt{Llama}$ and $\texttt{Qwen}$ families, as well as reasoning models distilled from $\texttt{DeepSeek-R1}$, on math and science benchmark datasets.

I demonstrate that large language models can infer ethnicity from names with accuracy exceeding that of Bayesian Improved Surname Geocoding (BISG) without additional training data, enabling inference outside the United States and to contextually appropriate classification categories. Using stratified samples from Florida and North Carolina voter files with self-reported race, LLM-based classification achieves up to 84.7% accuracy, outperforming BISG (68.2%) on balanced samples. I test six models including Gemini 3 Flash, GPT-4o, and open-source alternatives such as DeepSeek v3.2 and GLM-4.7. Enabling extended reasoning can improve accuracy by 1-3 percentage points, though effects vary across contexts; including metadata such as party registration reaches 86.7%. LLM classification also reduces the income bias inherent in BISG, where minorities in wealthier neighborhoods are systematically misclassified as White. I further validate using Lebanese voter registration with religious sect (64.3% accuracy), Indian MPs from reserved constituencies (99.2%), and Indian land records with caste classification (74.0%). Aggregate validation across India, Uganda, Nepal, Armenia, Chile, and Costa Rica using original full-count voter rolls demonstrates that the method recovers known population distributions where naming conventions are distinctive. For large-scale applications, small transformer models fine-tuned on LLM labels exceed BISG accuracy while enabling local deployment at no cost.

Optimizing the performance of large language models (LLMs) on large-scale AI training and inference systems requires a scalable and expressive mechanism to model distributed workload execution. Such modeling is essential for pre-deployment system-level optimizations (e.g., parallelization strategies) and hardware design-space explorations. While recent efforts have proposed collecting execution traces from real systems, access to large-scale infrastructure remains limited to major cloud providers. Moreover, traces capturing execution on a specific platform cannot be easily adapted to study alternate software and/or hardware configurations, especially at scale. We introduce STAGE, a framework that synthesizes high-fidelity execution graphs to accurately model distributed AI workloads (including LLMs and MoEs). STAGE supports a comprehensive set of parallelization strategies, allowing users to systematically explore a wide spectrum of model architectures and system configurations. STAGE demonstrates its scalability by synthesizing high-fidelity LLM traces spanning over 128K GPUs, while preserving tensorlevel accuracy in compute, memory, and communication. STAGE is publicy available at https://github.com/astra-sim/stage

LLM inference often generates a batch of candidates for a prompt and selects one via strategies like majority voting or Best-of- N (BoN). For difficult tasks, this single-shot selection often underperforms. Consequently, evaluations commonly report Pass@$k$: the agent may submit up to $k$ responses, and only the best of them is used when computing regret. Motivated by this, we study inference scaling in the more general Pass@$k$ inference setting, and prove that neither majority voting nor BoN exhibits the desirable scaling with $k$ and the sampling budget $N$. Combining the advantages of majority voting and BoN, we propose a new inference strategy called Best-of-Majority (BoM), with a pivotal step that restricts the candidates to the responses with high frequency in the $N$ samples before selecting the top-$k$ rewards. We prove that when the sampling budget is $N=\tildeΩ(C^*)$, the regret of BoM is $O(ε_{\mathrm{opt}}+\sqrt{ε_{\mathrm{RM}}^2C^*/k})$, where $C^*$ is the coverage coefficient, $ε_{\mathrm{RM}}$ is the estimation error of the reward model, and $ε_{\mathrm{opt}}$ is the estimation error of reward at the optimal response. We further establish a matching lower bound, certifying that our algorithm is minimax optimal. Beyond optimality, BoM has a key advantage: unlike majority voting and BoN, its performance does not degrade when increasing $N$. Experimental results of inference on math problems show BoM outperforming both majority voting and BoN.

Understanding how large language models (LLMs) internally represent and process their predictions is central to detecting uncertainty and preventing hallucinations. While several studies have shown that models encode uncertainty in their hidden states, it is underexplored how this affects the way they process such hidden states. In this work, we demonstrate that the dynamics of output token probabilities across layers for certain and uncertain outputs are largely aligned, revealing that uncertainty does not seem to affect inference dynamics. Specifically, we use the Tuned Lens, a variant of the Logit Lens, to analyze the layer-wise probability trajectories of final prediction tokens across 11 datasets and 5 models. Using incorrect predictions as those with higher epistemic uncertainty, our results show aligned trajectories for certain and uncertain predictions that both observe abrupt increases in confidence at similar layers. We balance this finding by showing evidence that more competent models may learn to process uncertainty differently. Our findings challenge the feasibility of leveraging simplistic methods for detecting uncertainty at inference. More broadly, our work demonstrates how interpretability methods may be used to investigate the way uncertainty affects inference.

On-device inference offers privacy, offline use, and instant response, but consumer hardware restricts large language models (LLMs) to low throughput and capability. To overcome this challenge, we present prima.cpp, a distributed on-device inference system that runs 30-70B LLMs on consumer home clusters with mixed CPUs/GPUs, insufficient RAM/VRAM, slow disks, Wi-Fi links, and heterogeneous OSs. We introduce pipelined-ring parallelism (PRP) to overlap disk I/O with compute and communication, and address the prefetch-release conflict in mmap-based offloading. We further propose Halda, a heterogeneity-aware scheduler that co-optimizes per-device CPU/GPU workloads and device selection under RAM/VRAM constraints. On four consumer home devices, a 70B model reaches 674 ms/token TPOT with <6% memory pressure, and a 32B model with speculative decoding achieves 26 tokens/s. Compared with llama.cpp, exo, and dllama, our proposed prima.cpp achieves 5-17 times lower TPOT, supports fine-grained model sizes from 8B to 70B, ensures broader cross-OS and quantization compatibility, and remains OOM-free, while also being Wi-Fi tolerant, privacy-preserving, and hardware-independent. The code is available at https://github.com/OpenCPIL/prima.cpp.

This is a book about large language models. As indicated by the title, it primarily focuses on foundational concepts rather than comprehensive coverage of all cutting-edge technologies. The book is structured into six main chapters, each exploring a key area: pre-training, generative models, prompting, alignment, inference, and reasoning. It is intended for college students, professionals, and practitioners in natural language processing and related fields, and can serve as a reference for anyone interested in large language models.

LLMs are increasingly used world-wide from daily tasks to agentic systems and data analytics, requiring significant GPU resources. While LLM inference systems are capable of serving millions of requests from multiple users, they often lack theoretical models to determine whether they achieve the performance upper bounds of underlying hardware resources. Beyond online workload serving, merely analyzing existing systems-or developing yet another one-is both GPU-intensive and labor-intensive. This paper provides a comprehensive survey of LLM inference systems, focusing on their cache management policies and availability. We then show that simulations can be an effective tool to save GPU hours in the development and analysis phase of inference systems, revealing useful insights for developing better inference techniques, unlike how existing studies used simulations to find the best parameters inside a given system. Finally, we provide theoretical tools to estimate the optimal performance and formulate new ideas. Based on the theoretical analysis, especially on the cache management in LLM inference, we propose a simple yet effective cache replacement policy that can be easily plugged into existing preemptive schedulers and systems. We show that such a simple policy inspired from database systems can substantially save GPU hours in actual inference systems on online workloads. We share our experience submitting a journal paper to a database venue in November 2025 for anyone considering a similar path.

Large Language Models (LLMs) are increasingly being employed for downstream tasks such as tabular classification, where predictions can directly influence individuals in high-stakes domain such as hiring, education and criminal justice. As the adoption of LLMs for such decision making tasks continues to grow, ensuring fairness in their predictions becomes increasingly important. Existing approaches to ensure fairness in tabular data, typically process test instances independently, limiting the models awareness of the demographic composition and predictions of other instances, which is particularly important for reasoning about group-level fairness. To address this limitation, we propose FABLE (FAir Batch-based LLM framEwork) for tabular classification, a batch-based framework that jointly processes multiple test instances, enabling LLMs to reason over demographic information and prediction outcomes within a batch. To mitigate positional bias introduced by batch processing, the framework generates multiple shuffled versions of each batch and aggregates the resulting predictions through voting. We evaluate FABLE on three tabular classification datasets using three popular LLMs and four prompting configurations spanning zero-shot, few-shot, direct, and self-reflective prompting. Experimental results demonstrate that incorporating demographic information and explicit fairness constraints enable LLMs to achieve substantial fairness improvements across diverse datasets and fairness notions, highlighting their potential as fairness reasoners for tabular classification and promoting more equitable and accountable decision-making.