Class-Incremental Learning (CIL) is important in building real-world learning systems. In CLIP-based CIL, the model performs classification by comparing similarity between visual and textual embeddings obtained from template prompts, e.g., ``a photo of a [CLASS]''. This seemingly monolithic matching process can be decomposed into two conceptually distinct stages: attribute extraction and attribute aggregation. For example, a model may recognize cat using attributes such as fur texture and whiskers. When learning a new class like car, the model must extract additional attributes like wheels and adjust how they are aggregated in the shared representation space. However, since only data from the current task is available, incremental updates can bias both attribute extraction and aggregation toward new classes, leading to catastrophic forgetting. Therefore, we propose AREA for attribute extraction and aggregation for CLIP-based CIL. To stabilize extraction, we anchor class-level visual and textual attributes on the hyperspherical embedding space via principal geodesic analysis. To stabilize aggregation, we learn lightweight task-specific experts with scoring and residual refinement, regularized by a variational information bottleneck objective. During inference, we perform routing over task attribute manifolds via optimal transport for more concise prediction. Experiments on multiple benchmarks show that AREA consistently outperforms SOTA methods.
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Theory · Everything Else
We study the problem of subgroup discovery for survival analysis, where the goal is to find an interpretable subset of the data on which a Cox model is highly accurate. We examine why existing quality functions are insufficient for this problem and introduce two technical innovations: the *expected prediction entropy (EPE)*, a novel metric for evaluating survival models that predict hazard functions, and the *conditional rank statistics (CRS)*, which quantifies individual point deviation from a subgroup's survival time distribution. We study the EPE and CRS theoretically and show they address problems with existing metrics. We then introduce seven algorithms for Cox subgroup discover. Our main algorithm is based on the DDGroup framework of Izzo et al. (2023) and leverages both the EPE and CRS, allowing theoretical correctness guarantees in well-specified settings. Empirical evaluation on synthetic and real data confirms our theory, showing our methods recover ground-truth subgroups in well-specified cases and achieve better model fit than naively fitting the Cox model to the entire dataset. A case study on NASA jet engine simulation data demonstrates that discovered subgroups uncover known nonlinearities in the data and suggest design choices mirrored in practice.
We give a very general and simple framework to incorporate predictions on requests for online covering problems in a rigorous and black-box manner. Our framework turns any online algorithm with competitive ratio $\rho(k, \cdot)$ depending on $k$, the number of arriving requests, into an algorithm with competitive ratio of $\rho(\eta, \cdot)$, where $\eta$ is the prediction error. With accurate enough prediction, the resulting competitive ratio breaks through the corresponding worst-case online lower bounds, and smoothly degrades as the prediction error grows. This framework directly applies to a wide range of well-studied online covering problems such as facility location, Steiner problems, set cover, parking permit, etc., and yields improved and novel bounds.
Fair Decisions from Calibrated Scores: Achieving Optimal Classification While Satisfying Sufficiency
Social Aspects · Fairness
Binary classification based on predicted probabilities (scores) is a fundamental task in supervised machine learning. While thresholding scores is Bayes-optimal in the unconstrained setting, using a single threshold generally violates statistical group fairness constraints. Under independence (statistical parity) and separation (equalized odds), such thresholding suffices when the scores already satisfy the corresponding criterion. However, this does not extend to sufficiency: even perfectly group-calibrated scores---including true class probabilities---violate predictive parity after thresholding. In this work, we present an exact solution for optimal binary (randomized) classification under sufficiency, assuming finite sets of group-calibrated scores. We provide a geometric characterization of the feasible pairs of positive predictive value (PPV) and false omission rate (FOR) achievable by such classifiers, and use it to derive a simple post-processing algorithm that attains the optimal classifier using only group-calibrated scores and group membership. Finally, since sufficiency and separation are generally incompatible, we identify the classifier that minimizes deviation from separation subject to sufficiency, and show that it can also be obtained by our algorithm, often achieving performance comparable to the optimum.
We argue that the dominant paradigm of AI evaluation, which focuses on autonomous superhuman performance and so an implicit goal of replacing humans, is guiding AI development in the wrong direction. Instead, the AI community should pivot to evaluating the performance of human–AI teams. We argue that this collaborative shift in evaluation will foster AI systems that act as true complements to human capabilities and therefore lead to far better societal outcomes than the current process.
We investigate the fundamental optimization question of minimizing a \emph{target} function $f(x)$, whose gradients are expensive to compute or have limited availability, given access to some \emph{auxiliary} side function $h(x)$ whose gradients are cheap or more available. This formulation captures many settings of practical relevance, such as i) re-using batches in SGD, ii) transfer learning, iii) federated learning, iv) training with compressed models/dropout, etcetera. We propose two generic new algorithms that apply in all these settings; we also prove that we can benefit from this framework under the Hessian similarity assumption between the target and side information. A benefit is obtained when this similarity measure is small; we also show a potential benefit from stochasticity when the auxiliary noise is correlated with that of the target function.
Reinforcement Learning · Everything Else
Most multi-objective reinforcement learning (MORL) methods either condition on a fixed preference weight $w$ or consider episodic robustness where an adversary selects a single $w$ per episode. We study a time-consistent robustness model with reactive preferences: after each transition, an opponent chooses the next weight $w_{t+1}$ after observing $s_{t+1}$, and incurs a switching cost $\lambda D_\Phi(w_{t+1}\mid w_t)$ based on a Bregman divergence. This yields a Bellman–Isaacs recursion with an inner weight minimization at every backup. We prove the induced operator is a contraction and derive a Bellman-residual certificate that turns approximation error into a uniform bound on robust performance. We develop practical solvers in both tabular and deep settings using Bregman-prox inner updates and a stabilized fixed-point iteration. To evaluate robustness without optimistic critic reuse, we introduce BR-$K$, testing policies against $K$ independently trained best-response preference adversaries. Across MO-Gymnasium benchmarks, our approach consistently improves WRR under strong step-wise opponents over preference-conditioned baselines while keeping DRIFT smoothly controllable via $\lambda$.
Reinforcement Learning · Policy Search
Non-Markovian dynamics are commonly found in real-world environments due to long-range dependencies, partial observability, and memory effects. The Bellman equation that is the central pillar of Reinforcement learning (RL) becomes only approximately valid under Non-Markovian. Existing work often focus on practical algorithm designs and offer limited theoretical treatment to address key questions, such as what dynamics are indeed capturable by the Bellman framework and how to inspire new algorithm classes with optimal approximations. In this paper, we present a novel topological viewpoint on temporal-difference (TD) based RL. We show that TD errors can be viewed as 1-cochain in the topological space of state transitions, while Markov dynamics are then interpreted as topological integrability. This novel view enables us to obtain a Hodge-type decomposition of TD errors into an integrable component and a topological residual, through a Bellman–de Rham projection. We further propose HodgeFlow Policy Search (HFPS) by fitting a {potential network} to minimize the non-integrable projection residual in RL, achieving stability/sensitivity guarantees. In numerical evaluations, HFPS is shown to significantly improve RL performance under non-Markovian.
Reinforcement Learning · Planning
We introduce a recursive AlphaZero style Monte--Carlo tree search algorithm, "RMCTS". It first generates the search tree using prior policies, and then recursively re-estimates action values by using the regularized optimal posterior policies from ``Monte--Carlo tree search as regularized policy optimization'' (Grill et al., 2020) at each node of the search tree, starting from the leaves and working back up to the root. We find that RMCTS matches or exceeds the quality of AlphaZero's MCTS-UCB in a tiny fraction of the time.
Reinforcement Learning · Online
In this paper, we study the private and robust alignment of language models from a theoretical perspective by establishing upper bounds on the suboptimality gap in both offline and online settings. We consider preference labels subject to privacy constraints and/or adversarial corruption, and analyze two distinct interplays between them: privacy-first and corruption-first. For the privacy-only setting, we show that log loss with an MLE-style algorithm achieves near-optimal rates, in contrast to conventional wisdom. For the joint privacy-and-corruption setting, we first demonstrate that existing offline algorithms in fact provide stronger guarantees---simultaneously in terms of corruption level and privacy parameters---than previously known, which further yields improved bounds in the corruption-only regime. In addition, we also present the first set of results for private and robust online alignment. Our results are enabled by new uniform convergence guarantees for log loss and square loss under privacy and corruption, which we believe have broad applicability across learning theory and statistics.
Reinforcement Learning · Online
Online reinforcement learning in non-episodic, finite-horizon MDPs remains underexplored and is challenged by the need to estimate returns to a fixed terminal time. Existing infinite-horizon methods, which often rely on discounted contraction, do not naturally account for this fixed-horizon structure. We introduce a modified Q-function: rather than targeting the full-horizon, we learn a K-step lookahead Q-function that truncates planning to the next K steps. To further improve sample efficiency, we introduce a thresholding mechanism: actions are selected only when their estimated K-step lookahead value exceeds a time-varying threshold. We provide an efficient tabular learning algorithm for this novel objective, proving it achieves fast finite-sample convergence: it achieves minimax optimal constant regret for $K=1$ and $\mathcal{O}(\max((K-1),C_{K-1})\sqrt{SAT\log(T)})$ regret for any $K \geq 2$. We numerically evaluate the performance of our algorithm under the objective of maximizing reward. Our implementation adaptively increases K over time, balancing lookahead depth against estimation variance. Empirical results demonstrate superior cumulative rewards over state-of-the-art tabular RL methods across synthetic MDPs and RL environments: JumpRiverswim, FrozenLake and AnyTrading.
Deep Learning · Theory
Softmax attention is a central component of transformer architectures, yet its nonlinear structure poses significant challenges for theoretical analysis. We develop a unified, measure-based framework for studying single-layer softmax attention under both finite and infinite prompts. For i.i.d. Gaussian inputs, we lean on the fact that the softmax operator converges in the infinite-prompt limit to a linear operator acting on the underlying input-token measure. Building on this insight, we establish non-asymptotic concentration bounds for the output and gradient of softmax attention, quantifying how rapidly the finite-prompt model approaches its infinite-prompt counterpart, and prove that this concentration remains stable along the entire training trajectory in general in-context learning settings with sub-Gaussian tokens. In the case of in-context linear regression, we use the tractable infinite-prompt dynamics to analyze training at finite prompt length. Our results allow optimization analyses developed for linear attention to transfer directly to softmax attention when prompts are sufficiently long, showing that large-prompt softmax attention inherits the analytical structure of its linear counterpart. This, in turn, provides a principled and broadly applicable toolkit for studying the training dynamics and statistical behavior of softmax attention layers in large prompt regimes.
Reinforcement Learning · Online
While the "Scaling Laws" have driven massive success in Computer Vision and NLP through large-scale training with massive batch sizes, Reinforcement Learning (RL) has largely failed to benefit from this paradigm. In RL, increasing batch sizes beyond a modest threshold often leads to diminishing returns or performance degradation due to the inherent non-stationarity of the data distribution. In this paper, we challenge the prevailing static view of batch sizes in RL by observing that the degree of non-stationarity is not constant: early training involves rapid behavioral shifts requiring small batches for plasticity, whereas late training approaches a quasi-stationary regime where large batches are essential for high-precision convergence. To leverage this insight, we propose Adaptive Batch Scaling (ABS), a simple yet effective framework that dynamically adjusts the effective batch size based on the stability of the learning process. We introduce Behavioral Divergence, a novel metric that quantifies non-stationarity by measuring action-level shifts between policy updates, and use it to scale the batch size inversely to the policy's volatility. By integrating ABS with the Parallelised Q-Network (PQN) algorithm, we demonstrate on the ALE benchmark that our method synergizes early-stage model plasticity with late-stage accurate and stable convergence. Our empirical results show that ABS not only yields substantial performance improvements over static baselines but also successfully scales to larger network architectures, offering a foundational step toward bridging the scaling gap between RL and supervised learning.
Reinforcement Learning · Online
Standard practice across domains from robotics to language is to first pretrain a policy on a large-scale demonstration dataset, and then finetune this policy, typically with reinforcement learning (RL), in order to improve performance on deployment domains. This finetuning step has proved critical in achieving human or super-human performance, yet while much attention has been given to developing more effective finetuning algorithms, little attention has been given to ensuring the pretrained policy is an effective initialization for RL finetuning. In this work we seek to understand how the pretrained policy affects finetuning performance, and how to pretrain policies in order to ensure they are effective initializations for finetuning. We first show theoretically that standard behavioral cloning (BC) can fail to ensure coverage over the demonstrator's actions, a minimal condition necessary for effective RL finetuning. We then show that if, instead of exactly fitting the observed demonstrations, we train a policy to model the posterior distribution of the demonstrator's behavior given the demonstration dataset, we do obtain a policy that ensures coverage over the demonstrator's actions, enabling more effective finetuning. Furthermore, this policy achieves this while ensuring pretrained performance is no worse than that of the BC policy. We then show this approach is practically implementable with modern generative models and leads to significantly improved RL finetuning performance on both realistic robotic control benchmarks and real-world robotic manipulation tasks, as compared to standard behavioral cloning.
From Interaction Trajectories to Prompt Rules: Credit Assignment for Multi-Agent Prompt Optimization
Reinforcement Learning · Multi-agent
Large language model (LLM)-based multi-agent systems commonly rely on natural-language prompts to specify agent behavior, yet optimizing these prompts remains challenging when agent roles and interaction structures are fixed by design. In such systems, behaviors emerge over long, noisy interaction trajectories, making it difficult to determine which prompt components are responsible for success or failure. As a result, outcome-level feedback alone is insufficient, while existing prompt optimization methods typically rely on final task scores or global prompt rewrites, limiting their ability to exploit trajectory evidence or support the localized updates. We propose Trajectory-based Rule Credit Estimation (TRUCE), a framework for prompt optimization in multi-agent systems that explicitly addresses this credit assignment challenge. TRUCE performs trajectory-aware attribution by linking outcome feedback to informative sub-trajectories and translating the resulting credit signals into unit-level edits over prompt-defined behavioral rules. By preserving agent roles and interaction structures, TRUCE enables prompt refinement through localized updates aggregated across tasks. Experiments on multiple benchmarks demonstrate that TRUCE consistently improves task performance and efficiency over competitive baselines.
Reinforcement Learning · Multi-agent
Controlling partial differential equations (PDEs) with learning-based policies remains fundamentally limited by fixed-dimensional representations: policies trained for a specific sensor, actuator, or agent configuration typically fail when the configuration changes. This limitation is particularly severe in multi-agent PDE control, where policies do not scale across population sizes without retraining. We address this challenge by reformulating PDE control as an operator learning problem that maps state fields to continuous control functions and trains them end-to-end through differentiable PDE solvers, yielding policies that naturally adapt to varying sensor and actuator configurations. Remarkably, policies trained on small swarms exhibit cardinality invariance, allowing for zero-shot transfer to significantly larger populations as well as robustness to partial agent failure. This scalability arises from agents sharing a common policy and coordinating through their physical environment, which produces an emergent self-normalization effect. To explain this phenomenon, we provide a theorem grounded in mean-field theory demonstrating that policy gradients computed from finite-agent systems converge to those of a continuous control limit. Empirically, we validate the framework on tracking, stabilization, and density transport across linear, nonlinear, chaotic, and turbulent PDEs.
Reinforcement Learning · Deep RL
Policies learned via continuous actor-critic methods often exhibit erratic, high-frequency oscillations, making them unsuitable for physical deployment. Current approaches attempt to enforce smoothness by directly regularizing the policy's output. We argue that this approach treats the symptom rather than the cause. In this work, we theoretically establish that policy non-smoothness is fundamentally governed by the differential geometry of the critic. By applying implicit differentiation to the actor-critic objective, we prove that the sensitivity of the optimal policy is bounded by the ratio of the Q-function's mixed-partial derivative (noise sensitivity) to its action-space curvature (signal distinctness). To empirically validate this theoretical insight, we introduce PAVE (Policy-Aware Value-field Equalization), a critic-centric regularization framework that treats the critic as a scalar field and stabilizes its induced action-gradient field. PAVE rectifies the learning signal by minimizing the Q-gradient volatility while preserving local curvature. Experimental results demonstrate that PAVE achieves smoothness and robustness comparable to policy-side smoothness regularization methods, while maintaining competitive task performance, without modifying the actor.
General Machine Learning · Evaluation
Evaluations of generative models are now ubiquitous, and their outcomes critically shape public and scientific expectations of AI's capabilities. Yet skepticism about their reliability continues to grow. How can we know that a reported accuracy genuinely reflects a model’s underlying performance? Although benchmark results are often presented as direct measurements of capability, in practice they are inferences: treating a score as evidence of capability already presupposes a theory of what it means to be capable at a task. We argue that AI evaluations should instead be framed as inference tasks grounded on an explicit theory of capability. While this perspective is standard in fields like psychometrics, it remains underdeveloped in AI evaluation, where core assumptions are often left *implicit*. As a proof-of-concept, we empirically show that reported performance can depend strongly on the evaluator’s modeling assumptions, underscoring the need for transparent, theory-driven evaluation practices. We conclude by offering practical guidelines for rigorously designing evaluations built on explicit theories of capability.
Applications · Robotics
Video generation models offer a promising imagination mechanism for robot manipulation by predicting long-horizon future observations, but effectively exploiting these imagined futures for action execution remains challenging. Existing approaches either condition policies on predicted frames or directly decode generated videos into actions, both suffering from a mismatch between visual realism and control relevance. As a result, predicted observations emphasize perceptual fidelity rather than action-centric causes of state transitions, leading to indirect and unstable control. To address this gap, we propose MoLA (Mixture of Latent Actions), a control-oriented interface that transforms imagined future videos into executable representations. Instead of passing predicted frames directly to the policy, MoLA leverages multiple pretrained inverse dynamics models to infer a mixture of latent actions implied by generated visual transitions. These modality-aware inverse dynamics models capture complementary semantic, depth, and flow cues, providing a structured and physically grounded action representation that bridges video imagination and policy execution. We evaluate our approach on simulated benchmarks (LIBERO, CALVIN, and LIBERO-Plus) and real-world robot manipulation tasks, achieving consistent gains in task success, temporal consistency, and generalization. Code will be released.
Reinforcement Learning · Deep RL
Optimizing Conditional Value-at-risk (CVaR) using policy gradient (a.k.a CVaR-PG) faces significant challenges of sample inefficiency. This inefficiency stems from the fact that it focuses on tail-end performance and overlooks many sampled trajectories. We address this problem by augmenting CVaR with an expected quantile term. Quantile optimization admits a dynamic programming formulation that leverages all sampled data, thus improves sample efficiency. This does not alter the CVaR objective since CVaR corresponds to the expectation of quantile over the tail. Empirical results in domains with verifiable risk-averse behavior show that our algorithm within the Markovian policy class substantially improves upon CVaR-PG and consistently outperforms other existing methods.