Well-Tuned Static Batching Policy

Mixture-of-Experts (MoE) training requires global load balance to prevent expert under-utilization and local balance for efficient expert-parallel execution. Existing distributed Quantile Balancing (QB) uses shard-dependent or approximate global quantiles, while token-independent expert biases cannot ensure microbatch-level balance. We introduce Exact Quantile Balancing (EQB), which computes exact global-batch BF16 quantiles with negligible communication, and Load-Error Injection (LEI), which injects local load errors directly into router-score gradients. On 7.5B-parameter MoEs trained for up to 500B tokens, EQB improves global balance and downstream performance over naive QB, while LEI improves local balance and outperforms the GShard loss at comparable quality.

While WhisperX accelerates speech transcription via intra-audio batching, it isolates audio segments, losing the historical context needed for coherent punctuation and terminology transcription. Conversely, standard Whisper retains context sequentially but suffers from slow inference and hallucination loops. To achieve the best of both worlds, we propose Context-Aware Interleaved Batching. By using VAD-derived segment boundaries, our algorithm stabilizes Whisper's text conditioning, allowing us to safely maintain continuous historical context across batched audio segments. As demonstrated on long-form audio benchmarks, this approach reduces Word Error Rate (WER) and improves proper noun transcription, all while maintaining high-throughput inference speeds.

In expert-parallel (EP) MoE serving, every layer synchronizes at the slowest GPU. Dispatchers balance token counts (EPLB, LPLB, UltraEP) or activated-expert counts (METRO), assuming expert time is linear in one. Measurements on two datacenter GPU generations show it is neither: below $\nstar\!\approx\!156$--$168$ tokens, HBM weight streaming dominates---cost attaches to \emph{activated replicas}, not tokens; above it, grouped GEMM rounds tokens to 128-tile $M$-tiles, so \emph{splitting} an expert adds padded compute. A max-affine profile $t=\max(a+bG,\,c+βN)$ captures both regimes. Realistic decode batches hold hot experts in the linear regime and cold in the flat \emph{simultaneously}; recorded batches show proxy dispatches differ by $1.4$--$1.6\times$ in modeled block time (p95 up to $1.7\times$), and \emph{which} proxy wins flips with the regime. We formalize per-batch dispatch as a fixed-charge makespan problem---NP-hard on two fully replicated GPUs, polynomial in degenerate limits---and present \sys{}, a makespan-aware dispatcher solving it in milliseconds off the critical path; its SGLang integration runs out-of-process and fuses dispatch with count collection into one in-graph kernel. Anchored by an 8-GPU TestbedA microbenchmark, \sys{} stays within 1% of the best fixed baseline everywhere and wins by up to $15.5\%$ where regimes mix. End-to-end on TestbedB, Qwen3-235B (inside the win region) gains $4$--$6\%$ throughput and cuts p99 latency by ${\sim}15.6\%$; DeepSeek-V3 (outside, communication-dominated) shows only mechanism cost. A phase diagram, not a universal win, is the claim: it predicts both outcomes before deployment.

A main promise of looped language models (LMs) is depth-adaptive inference. By iterating a block of shared layers a variable number of times, the model can use less compute for "easy" tokens and more for "hard" ones. However, this adaptivity breaks standard batching: tokens in the same batch now require a different number of loops, so there is no unified forward pass, making efficient inference difficult. Standard inference frameworks like vLLM schedule on the token level and cannot handle this because tokens need to be removed from the batch within the forward pass. Loop-level scheduling has been proposed as a solution, but never implemented end to end. The key challenge is that looped architectures also contain non-looped boundary stages (e.g., token embedding and LM head) that must be scheduled at different frequencies than the loop. We introduce continuous depth batching (CDB), which schedules at the granularity of individual loop iterations. CDB handles boundary stages and loop steps in separate priority queues, makes exit decisions one step ahead, and overlaps all scheduling work with GPU computation. On Ouro 1.4B and Huginn 3.5B, CDB can realize up to $99\%$ of the theoretical maximum speed-up from adaptive-depth, translating to $1.5$-$1.9\times$ higher offline throughput and $45$-$90\%$ lower normalized latency under dynamic serving load.

Large language model (LLM) serving spans diverse applications with stringent service-level objectives (SLOs), often requiring GPUs to run at maximum frequencies and increasing energy consumption. Existing energy-management approaches adapt GPU frequencies only at the request or inference-phase level, overlooking operator-level differences in frequency sensitivity between Attention and feed-forward networks (FFNs). We find that the energy-optimal frequencies of Attention and FFN (A/F) differ and vary with the inference phase, workload, and system configurations. However, runtime variability and independent A/F frequency control create a large search space and high communication overhead. To address these challenges, we present AFlex, a framework that jointly optimizes resource provisioning and GPU frequency scaling for disaggregated A/F serving. AFlex introduces a global scheduler and a local operator-level dynamic voltage and frequency scaling (DVFS) controller to determine A/F resource allocations and frequencies. It further introduces an interleaved A/F pipeline with dynamic microbatch depth and adaptive request batching to reduce pipeline bubbles. We implement AFlex in SGLang and evaluate it on NVIDIA A800 GPUs using Qwen3-32B and Mixtral-8$\times$7B under production Conversation and Coding traces. \AFlex reduces energy per token by up to 49% over state-of-the-art disaggregated serving and 48% over frequency-scaling systems while satisfying TTFT and TPOT SLOs.

Fast entropic optimal transport backends reduce the cost of each Sinkhorn update, but static batches still run at full width until the slowest problem finishes. We introduce DrainSinkhorn, a verifier-gated active-packing layer for batches of independent Sinkhorn problems. It combines candidate-axis packing, a Sinkhorn-specific one-sided screen, verifier-gated retirement under the backend's configured two-sided residual check, and physical compaction of all candidate-indexed state. The EOT objective, per-instance Sinkhorn map, and stopping rule are unchanged; later kernels run only on unfinished problems. We characterize the removable work exactly. If completion depths differ within a packed window, active execution removes the padding between the static batch rectangle and the observed survival curve. A quotient nonlinear Perron-Frobenius analysis gives a local explanation for these finite-tolerance depth differences: convergence depends on the full modal spectrum and proposal alignment, not only on the slowest mode. DrainSinkhorn achieves state-of-the-art execution performance on the tested heterogeneous batched-EOT workloads within matched backend families. The complete Flash-backed OT path is 4.110x faster on MetroPT-3, 3.798x faster on ImageNet-32 feature couplings, and 1.250-1.270x faster across a five-tolerance Packer19 sweep. Independent implementations reach 2.600x on ImageNet-32 with OTT-JAX, 3.174x on A2D2 LiDAR with PyKeOps, and 1.415x on large ImageNet-32 PyKeOps couplings. End-to-end speedups remain 4.074x on MetroPT-3 and 2.786x on ImageNet-32 feature-space OT flow matching, with all reported residual, consumer-output, and training-quality checks passing.

Accurate yet low-latency depth is essential for radar-camera perception in autonomous systems. Cameras provide rich appearance but lack metric scale, whereas automotive radar offers metric range but is sparse and noisy. Many pipelines are multi-stage or depend on auxiliary annotations, increasing latency and limiting portability. We introduce JustDepth, a single-stage radar-camera depth estimator trained only with radar, camera, and single-scan LiDAR. All radar returns are aggregated into a fixed-width 1D representation, decoupling runtime from point count. A Height Fusion Block fuses modalities, a lightweight GNN propagates depth globally, and a training-only confidence decoder stabilizes learning with zero test-time cost. We mitigate stripe artifacts via simple augmentations and quantify them using the Vertical-Horizontal Gradient Ratio (VHGR). On nuScenes, compared to recent state-of-the-art methods, JustDepth maintains accuracy while reducing inference time by 39.7x and stripe artifacts by 66% as measured by VHGR.

Efficient serving of diffusion large language models (dLLMs) is hindered by convergence heterogeneity: when batching multiple requests, different sequences converge at different rates, causing faster requests to stall behind slower stragglers and introducing compute bubbles and tail latency. We present BlockServe, a continuous batching framework that integrates block-grained scheduling -- immediately evicting completed requests at block boundaries -- with mixed-state execution that extends dual cache and parallel decoding to heterogeneous batches via gather-scatter indexing. Furthermore, a compute-aware admission controller expands effective batch capacity through token-budgeted refill. On Dream and LLaDA across five benchmarks, BlockServe achieves 1.9--10.6$\times$ throughput over Fast-dLLM with comparable generation quality, establishing block-grained scheduling as a foundation for high-throughput offline dLLM inference.

Inference serving systems must balance throughput and latency under bursty, heterogeneous workloads, yet the industry standard remains static batching policies that require manual tuning and cannot adapt to shifting traffic. We investigate whether reinforcement learning (RL) can learn adaptive batching and routing policies that outperform these heuristics, training REINFORCE and PPO agents on a discrete-event simulator validated against queuing theory and production traces (Azure Functions, BurstGPT). We formulate the problem as an MDP over queue state, request type and GPU availability, evaluating across standard Poisson traffic, extreme bursts, real-world traces and heterogeneous multi-GPU routing. Our central finding is a clear boundary condition for RL's value in systems problems. In single-GPU settings, a well-tuned static batching policy is already near-optimal under Poisson-like arrivals and RL offers only marginal gains (+0.1% to +1.0%). In multi-GPU heterogeneous routing, however, where fast and slow requests compete for shared resources, the agent discovers a workload-segregation policy that eliminates Head-of-Line blocking, yielding a 3.5x (348%) improvement over Round-Robin and a 48% improvement over the strongest heuristic baseline (Shortest-Queue), with 60% higher throughput and 25% lower latency while respecting SLA constraints. The policy generalizes to unseen bursty and real-world traffic despite training only on synthetic Poisson arrivals and an attention-augmented policy network converges roughly 20% faster than an MLP baseline. These results suggest RL's advantage over engineered heuristics concentrates in combinatorial, multi-resource decisions rather than single-resource temporal scheduling, a practical distinction for deciding where learned policies justify their engineering cost in production inference infrastructure.

We present AdaPrivate-TS, a differentially private contextual bandit algorithm that combines Thompson Sampling with batched zCDP composition. Our key insight is that differential privacy noise inflates the posterior covariance in a structured way: adding Gaussian noise $N(0,σ^2 I)$ to $b$ yields sampling covariance $v^2 A^{-1} + σ^2 A^{-2}$, which Thompson Sampling interprets as increased uncertainty rather than pure corruption. Under event-level privacy (protecting individual interactions) with stochastic contexts, we prove that the privacy cost is only $O(\sqrt{d}\,\log T/\sqrtρ)$, logarithmic in $T$, because parallel composition amortizes noise across batches. Additionally, we explore privacy amplification via Poisson subsampling, which can reduce effective noise at stringent privacy budgets. Experiments on synthetic and real-world datasets demonstrate: (1) AdaPrivate-TS achieves 93-99% of non-private performance at $\varepsilon \in [0.5, 5]$, outperforming UCB by 0.5-3.7% and up to 18% with tuned adaptive exploration at extreme $\varepsilon$; (2) privacy amplification provides additional 2-5% gains at low $\varepsilon$; (3) on MovieLens and Jester, AdaPrivate-TS achieves the best overall performance among event-level baselines, dominating at $\varepsilon \geq 2$; (4) under DP-SVD private features, TS's advantage over UCB grows to +11%, confirming noise-as-uncertainty is not limited to reward privacy. We provide rigorous proofs for privacy guarantees under interactive zCDP composition and comprehensive evaluation including convergence curves, 12-seed CIs, and DP-SVD feature ablation.

Modern LLM training breaks a core assumption behind offline batch samplers: the true training cost of a sample is only observable after preprocessing, augmentation, templating, tokenization, and multimodal visual-token expansion. Unless one pays for a preprocessing- and augmentation-dependent length cache, batch construction is therefore blind to the quantity that determines padding, memory use, and GPU saturation. We introduce Online Dynamic Batching (ODB), a DataLoader-side drop-in system that moves batch formation to this point of accurate observability while preserving DDP step alignment. We formalize this synchronization requirement as the Distributed Group Alignment Problem and prove deadlock-free bounded termination with default join-mode identity coverage and opt-in non-join sample-quota closure. ODB requires no model, optimizer, or attention-kernel changes and is released as online-dynamic-batching with lightweight trainer adapters. Across public 2B/8B Qwen3-VL runs on UltraChat/LLaVA/ShareGPT4o, ODB improves literal emitted-sample throughput vs. fixed-batch Standard by 1.58-2.51x on single-node Full FT/LoRA and 1.71-3.78x on two-node Full FT, with Standard-comparable quality; production MM-Mix reaches 4.43x. Against GMT/BMT offline token-budget oracles, ODB is within 15% on UltraChat/LLaVA and faster on high-CV ShareGPT4o: 2.24-2.39x single-node Full FT/LoRA and 3.06-3.69x two-node Full FT. Together, ODB occupies the online/drop-in regime for high-heterogeneity LLM fine-tuning: large throughput gains at Standard-comparable quality, formal DGAP guarantees, and no length-cache precompute or kernel rewrites.

Open diffusion language models are marketed as parallel, non-autoregressive decoders, yet the order in which a shipped checkpoint actually commits its tokens is almost never measured. We instrument DiffusionGemma 26B, a masked discrete-diffusion mixture-of-experts model built on Gemma 4, hooking its sampler's accept step to record which canvas positions commit, when, and at what confidence. Across a 686-prompt, six-regime probe suite we find that its decoding is neither parallel nor block-autoregressive: it follows a partial left-to-right commit bias whose apparent strength depends almost entirely on the granularity at which you look. Order is weak token by token and strengthens smoothly as the analysis is coarsened, so the model's "block size" turns out to be an artifact of the measuring ruler rather than the architecture. The model commits in large simultaneous batches, leaving much of the within-batch order genuinely undefined rather than merely unobserved. The behaviour is regime-dependent: structured JSON is committed in essentially arbitrary order, and a position's commit confidence tracks correctness on mathematical reasoning but carries no signal on factual recall. Commitment is aggressive, finishing in a short late burst well inside the step budget, while task accuracy matches the model's autoregressive Gemma-4 sibling. Beyond these findings, our central contribution is methodological: measuring decoding order honestly demands handling trailing-EOS padding, within-regime confounding, commit non-monotonicity, block-size sensitivity, and large commit-batch ties, each of which can otherwise manufacture a decoding-order result that is not really there.

Mixed batching (MB)--interleaving prefill and decode in a single batch--has become the standard scheduling strategy for large language model (LLM) inference due to its efficiency in maximizing compute and memory utilization. However, through controlled experiments, we find that prefill-decode interference inflates MB's per-step marginal cost above that of pure decode. On the high-bandwidth H200 (4.8 TB/s), this occurs only when decode tokens exceed 80% of the batch; however, on the bandwidth-constrained RTX PRO 6000 (1.792 TB/s), this threshold plummets to just 20%. Consequently, the optimal choice between MB and exclusive batching (EB) fundamentally depends on GPU memory bandwidth, model size, and workload composition. We derive a closed-form condition for this EB-MB performance crossover, along with asymptotically optimal phase-switching thresholds and memory-safe batch sizing for EB. Optimized EB achieves up to 41.9% higher throughput on bandwidth-constrained GPUs, while MB retains its advantage on high-bandwidth hardware with larger models. Our hybrid scheduler EB+ applies this condition online to dynamically switch between EB and MB without manual intervention. Under non-stationary traffic with distribution or concurrency shifts, EB+ attains the highest or near-highest throughput in every setting, outperforming MB by up to 36.4%.

We study stochastic linear bandits under a natural combination of batching and communication constraints: the time horizon is partitioned into batches of equal size $B$, and during each batch the learner sends $B$ requested arm pulls to an agent, who then observes the corresponding $B$ rewards and responds with a single bit of feedback to the learner. For each batch, the learner specifies the 1-bit quantization rule the agent uses, which may depend on all previously received bits but not on any past rewards directly. This setting addresses a significant yet unexplored ``middle ground'' between previous models having per-round quantization only or total bit budgets only. We establish a minimax lower bound showing that $Ω(B\min\{d,\log\lvert \mathcal{A} \rvert\})$ regret is unavoidable due to the 1-bit communication bottleneck, even in the absence of noise. Combined with standard statistical limits, this yields a general lower bound of $\widetildeΩ(B\min\{d,\log\lvert \mathcal{A} \rvert\} + \sqrt{dT \min\{d,\log\lvert \mathcal{A} \rvert\}})$. We develop two phased-elimination algorithms based on $G$-optimal designs and 1-bit mean estimation. The first achieves $\widetilde{O}(dB + d\sqrt{T})$ regret, matching the lower bound up to logarithmic factors when $\lvert \mathcal{A} \rvert = \exp(Ω(d))$, and the second incorporates a safe-arm identification and warm-start procedure to obtain $\widetilde{O}(B\log\lvert \mathcal{A} \rvert + d^{3/2}\sqrt{B} + \sqrt{dT\log\lvert \mathcal{A} \rvert})$ regret, which is near-optimal in broad scaling regimes of $(\lvert \mathcal{A} \rvert, B, d, T)$. Together, our results demonstrate that a single bit of feedback per batch suffices to nearly match the minimax regret of unconstrained linear bandits in broad scaling regimes, even for batch sizes as large as $Θ(\sqrt{T})$.

Diffusion language models (dLLMs) generate text by iteratively denoising multiple token positions in parallel, offering an attractive alternative to strictly autoregressive decoding. In practice, however, block-wise dLLM inference exposes a difficult granularity trade-off: small blocks preserve local conditioning but require many denoising steps, whereas large blocks expose more parallelism but can make premature commitments and accumulate cache error. Existing acceleration methods typically choose a single block size per request, leaving the complementarity among block sizes unused. We show that block size itself is a useful branching dimension. Different block sizes induce related but non-identical KV-cache trajectories: branches often share an initial prefix, bifurcate at semantically decisive positions, and later agree on syntactically lightweight tokens. Motivated by this structure, we propose BlockBatch, a training-free online inference framework that executes multiple block-size branches for the same request inside a batched forward pass. BlockBatch coordinates these branches through confidence-gated token merging, leader-based synchronization, and periodic full-sequence refreshes that re-anchor local block updates to a globally consistent KV state. Across 3 representative dLLMs and 4 datasets, BlockBatch reduces denoising NFEs by 26.6% on average and achieves a 1.33$\times$ average end-to-end speedup over Fast-dLLM while preserving accuracy. These results identify block-size diversity as a practical and previously underexplored axis for branch-parallel dLLM inference.

Test-time training (TTT) adapts an LLM during generation by reading and updating request-owned state, such as fast weights, low-rank deltas, or streaming learner state. This breaks batched LLM serving, which assumes shared static weights: serial execution is correct but slow, while naive batching can corrupt request state. We formulate this problem as read-write TTT serving and present RW-TTT , which tags each decode step with its owner, version, and READ/WRITE effect, batches only compatible phases, and commits updates only to the owner. On one GPU with eight fast-weight InPlace-TTT streams, RW-TTT reaches 274.61 aggregate tok/s, 9.31x over sequential serving and 3.44x over per-stream replicas under the same memory budget. It preserves behavior on RULER, a long-context benchmark, and passes owner/version checks.

Safety evaluations of language models often treat serving configuration as fixed background infrastructure, but batch condition is an untested treatment variable whenever the same prompt may be evaluated alone, in a synchronized batch, or inside a continuous-batching scheduler. We synthesize four artifact-backed studies into a paired testing protocol: Study A combines local discovery, scorer-corrected adjudication, and true-batching confirmation; Study B tests cross-model generalization; Study C tests continuous-batch composition; and Study D runs a batch-invariant-kernel ablation. The local test finds safety-label changes more often than capability-label changes (0.51% vs. 0.14%), but adjudication of 63 candidate rows leaves only 17 genuine behavioral flips, implying a corrected full-set rate of 0.16%. The 15-model extension finds no detectable universal safety-over-capability skew: flips are near parity (0.94x), alignment type has no detectable association ($p=0.942$, $η^2=0.033$), and output instability is the strongest tested fragility screen ($r=0.909$, bootstrap 95% CI [0.65, 0.97]). In the targeted kernel ablation, standard vLLM reproduces 22/55 label flips on current score-flip candidates, while enabling VLLM_BATCH_INVARIANT=1 reduces the same test to 0/55 flips; the composition test separately finds no aggregate effect at 4.7pp sensitivity. The testing recommendation is exact-stack validation: evaluate refusal at the served batch setting, pair safety prompts with capability controls, and report low-rate directional flips separately from aggregate null effects.

We present MuJoCoUni, a downstream MuJoCo distribution for online robot learning and batched physics evaluation. Alongside the open-loop batched trajectory generation already provided by upstream mujoco.rollout, MuJoCoUni supplies runtime primitives for stateful environment execution. The target workloads need high-throughput parallel execution while retaining upstream CPU MuJoCo semantics for models, sensors, contact, and constraints. Its core object, BatchEnvPool, is a C++/pybind11 executor that owns per-environment mjModel copies, per-thread mjData workers, and an internal thread pool. It provides final-state-only short stepping, sparse reset, reset-lifecycle domain randomization, batched sensor forward evaluation without advancing dynamics, and batched Jacobian and height-field queries. The implementation is confined to the Python binding layer; MuJoCo's solver, contact model, integrator, and core source tree retain upstream semantics. This report describes the BatchEnvPool API, implementation boundary, relationship to rollout, and the validation and benchmark scripts shipped with the open-source mujoco-uni package, which is installed with \texttt{pip install mujoco-uni}.

Preconditioned optimizers are central to language model training, but their stochastic update rules are usually treated as direct approximations to population preconditioned descent. We show that this view misses two finite-sample biases. First, the gradient and preconditioner are typically estimated from the same minibatch, introducing gradient--preconditioner coupling bias. Second, even when the preconditioner estimate is unbiased, its inverse or inverse-root is generally biased because inversion is nonlinear. We propose a single-batch bias-correction framework that addresses both effects: cross-fitted preconditioning estimates the numerator and preconditioner from independent microbatch groups, while variance-corrected inversion uses microbatch variability to subtract the leading delta-method bias term. The framework applies to diagonal moment, diagonal curvature, and matrix preconditioning methods, instantiated in AdamW, Sophia, and Shampoo. Bias correction reduces held-out pretraining loss on Qwen2.5-0.5B by $0.15$, $0.07$, and $0.11$ nats, respectively; the effects on mixed-quality pretraining and downstream instruction tuning are consistently neutral-to-positive. Together, these results establish bias correction as a practical mechanism for reducing finite-sample update bias and improving the performance of preconditioned optimizers.

Modern Large Foundation Model (LFM) training has transformed the data pipeline from a static ingestion layer into a dynamic component that must co-evolve with the training process. Existing systems are ill-equipped: colocated dataloaders offer no failure isolation, while message queue-based disaggregated dataloaders operate on a record/offset abstraction that cannot express the batch-level semantics required by distributed training. We present BatchWeave, an object-store-native training data plane for distributed LFM training. BatchWeave uses versioned manifests and conditional object writes to coordinate batch publication, recovery, and lifecycle management. First, it introduces the Transactional Global Batch (TGB), which builds on versioned-manifest ACID storage semantics and extends them with training-specific consistency, including atomic all-rank batch visibility, a globally ordered step sequence, checkpoint-aligned lifecycle management, and end-to-end exactly-once recovery. Second, it realizes recovery and retention directly in the storage layer, by durably persisting producer state through the commit protocol and tying reclamation to distributed checkpoint state. Third, its Decentralized Adaptive Commit (DAC) algorithm sustains stable ingestion throughput as the manifest grows, without any inter-producer communication. Evaluations on large-scale multimodal pre-training and SFT workloads using 64 GPUs show that BatchWeave outperforms colocated dataloader throughput while providing full failure isolation, outperforms Apache Kafka in ingestion throughput, and achieves lower consumer read latency than Kafka.

The expansion of Artificial Intelligence-generated content service requires diffusion model serving to simultaneously achieve high throughput and low task end-to-end (E2E) latency. However, existing continuous batching methods suffer from severe resource contention during UNet-VAE concurrency, leading to latency spikes. Furthermore, concurrent multi-task scheduling entails a trade-off between UNet throughput and VAE latency across varying scheduling strategies. To address these, we propose SynerDiff, an efficient continuous batching system built on intra-inter level synergy. At the intra-concurrency level, SynerDiff alleviates resource contention by pruning component-specific resource bottlenecks via VAE Chunking and Adaptive Skip-CFG. At the inter-concurrency level, leveraging components' differential sensitivity to scheduling granularities, a threshold-aware scheduler plans concurrent sequences and tunes intra-concurrency decisions to minimize VAE latency while maintaining UNet within high-throughput threshold. Additionally, a feedback controller dynamically adjusts this threshold based on queue loads to boost system capacity ceiling. Experimental results show that, SynerDiff improves throughput by 1.6$\times$ and decreases both average E2E and P99 tail latencies by up to 78.7%, compared to benchmarks while guaranteeing high image fidelity.

Black-Box Variational Inference (BBVI) typically relies on Stochastic Gradient Descent (SGD) to optimize the Evidence Lower Bound (ELBO). However, the stochastic gradients in BBVI inherently exhibit unbounded variance, violating standard assumptions and instead satisfying the weaker Blum-Gladyshev (BG) condition, where variance grows quadratically with distance from the optimum. In this paper, we bridge the gap between stochastic optimization theory and the practical instances of BBVI. Focusing on the broad elliptic location-scale family of parameterized distributions, we offer two main contributions. First, we prove the existence of an ELBO solution, a foundational property usually assumed a priori in the literature. Second, we establish comprehensive convergence guarantees spanning finite-time and asymptotic regimes for Minibatch Projected SGD (PSGD) equipped with dynamic batching and preconditioning under the BG condition. Our theoretical framework demonstrates that dynamic batching combined with preconditioning systematically enables rigorous guarantees even in complex settings. We illustrate our theoretical findings with numerical results, highlighting the efficacy of our approach for modern inference tasks.

Batch processes are inherently transient and typically nonlinear, motivating nonlinear model predictive control (NMPC). However, adopting NMPC is hindered by the cost and unavailability of dynamic models. Thus, we propose to use Gaussian Processes (GP) in a model-learning NMPC scheme (GP-MLMPC) for batch processes. We initialize the GP-MLMPC using data from a single initial trajectory, e.g., from a PI controller. We iteratively apply the NMPC embedded with GPs to run batches and update the GP with new observations from each iteration, thereby achieving batch-wise improvements. Using uncertainty quantification from the GPs, we formulate chance constraints to enforce safe operation to the required confidence levels. We demonstrate our approach in \textit{silico} on a semi-batch polymerization reactor for tracking and economic objectives over durations of two hours, and the reactor temperature is constrained in a range of $\pm2^\circ C$ around its setpoint. After only four batch iterations, tracking error from the GP-MLMPC scheme converged to a reduction of $83\%$, compared to the initial trajectory. Furthermore, under an economic objective, the GP-MLMPC resulted in a 17-fold increase in final product mass by iteration 8, compared to the initial trajectory. In both cases, the resulting GP-MLMPC performance is on par with the full-model NMPC, which shows that the optimal controller can be learned by the approach. By collecting samples around the optimal trajectory, the GP-MLMPC remains sample-efficient across iterations and achieves quick convergence. Thus, the proposed GP-MLMPC scheme presents a promising data-efficient approach for the control of nonlinear batch processes without mechanistic knowledge.

Batch Normalization (BN) is a cornerstone of deep learning, yet it fundamentally breaks down in micro-batch regimes (e.g., 3D medical imaging) and non-IID Federated Learning. Removing BN from deep architectures, however, often leads to catastrophic training failures such as vanishing gradients and dying channels. We identify that standard activation functions, like Swish and ReLU, exacerbate this instability in BN-free networks due to their non-zero-centered nature, which causes compounding activation mean-shifts as network depth increases. In this technical communication, we propose Zero-Centered Swish (ZC-Swish), a drop-in activation function parameterized to dynamically anchor activation means near zero. Through targeted stress-testing on BN-free convolutional networks at depths 8, 16, and 32, we demonstrate that while standard Swish collapses to near-random performance at depth 16 and beyond, ZC-Swish maintains stable layer-wise activation dynamics and achieves the highest test accuracy at depth 16 (51.5%) with seed 42. ZC-Swish thus provides a robust, parameter-efficient solution for stabilizing deep networks in memory-constrained and privacy-preserving applications where traditional normalization is unviable.

Recent research in geospatial machine learning demonstrates that models pretrained with self-supervised learning on Earth observation data can perform well on downstream tasks with limited labeled data. However, most benchmark datasets have few data modalities and poor global representation, limiting the ability to evaluate multimodal pretrained models at global scales. In order to fill this gap, we introduce MMEarth-Bench, a collection of five new environmental tasks with 12 modalities, globally distributed data, and both random and geographic test splits. We benchmark a diverse set of pretrained models and find that while (multimodal) pretraining tends to improve model robustness in limited data settings, geographic generalization abilities remain poor. Moreover, a simple randomly initialized multimodal model is competitive given enough labeled data. Although data is abundant, models can currently only make use of the modalities on which they were pretrained. To solve this problem, we propose using all the modalities available at test time as auxiliary tasks for test-time adaptation. Our model-agnostic method for test-time training with multimodal reconstruction (TTT-MMR) can improve performance across all models and tasks on both test splits. Furthermore, geographic batching leads to a good trade-off between regularization and specialization during TTT, which is especially beneficial for long-tail distributions. Our dataset, code, and visualization tool are linked on the project page: lgordon99.github.io/mmearth-bench.

A fundamental problem in machine learning is understanding the effect of early stopping on the parameters obtained and the generalization capabilities of the model. Even for linear models, the effect is not fully understood for arbitrary learning rates and data. In this paper, we analyze the dynamics of discrete full batch gradient descent for linear regression. With minimal distributional assumptions, we characterize the trajectory of the parameters and the expected excess risk. Using this characterization, we show that when training with any learning rate schedule and finite time horizon, the early stopped solution is equivalent to the minimum norm solution for a generalized ridge regression problem. We also prove that early stopping is beneficial for generic data with arbitrary spectrum and for a wide variety of learning rate schedules. We provide an estimate for the optimal stopping time and empirically demonstrate the accuracy of our estimate.