The Illusion of Stochasticity in LLMs

In this work, we demonstrate that reliable stochastic sampling is a fundamental yet unfulfilled requirement for Large Language Models (LLMs) operating as agents. Agentic systems are frequently required to sample from distributions, often inferred from observed data, a process which needs to be emulated by the LLM. This leads to a distinct failure point: while standard RL agents rely on external sampling mechanisms, LLMs fail to map their internal probability estimates to their stochastic outputs. Through rigorous empirical analysis across multiple model families, model sizes, prompting styles, and distributions, we demonstrate the extent of this failure. Crucially, we show that while powerful frontier models can convert provided random seeds to target distributions, their ability to sample directly from specific distributions is fundamentally flawed.

Understanding Performance Gap Between Parallel and Sequential Sampling in Large Reasoning Models

Large Reasoning Models (LRMs) have shown remarkable performance on challenging questions, such as math and coding. However, to obtain a high quality solution, one may need to sample more than once. In principal, there are two sampling strategies that can be composed to form more complex processes: sequential sampling and parallel sampling. In this paper, we first compare these two approaches with rigor, and observe, aligned with previous works, that parallel sampling seems to outperform sequential sampling even though the latter should have more representation power. To understand the underline reasons, we make three hypothesis on the reason behind this behavior: (i) parallel sampling outperforms due to the aggregator operator; (ii) sequential sampling is harmed by needing to use longer contexts; (iii) sequential sampling leads to less exploration due to conditioning on previous answers. The empirical evidence on various model families and sizes (Qwen3, DeepSeek-R1 distilled models, Gemini 2.5) and question domains (math and coding) suggests that the aggregation and context length do not seem to be the main culprit behind the performance gap. In contrast, the lack of exploration seems to play a considerably larger role, and we argue that this is one main cause for the performance gap.

Mining Generalizable Activation Functions

The choice of activation function is an active area of research, with different proposals aimed at improving optimization, while maintaining expressivity. Additionally, the activation function can significantly alter the implicit inductive bias of the architecture, controlling its non-linear behavior. In this paper, in line with previous work, we argue that evolutionary search provides a useful framework for finding new activation functions, while we also make two novel observations. The first is that modern pipelines, such as AlphaEvolve, which relies on frontier LLMs as a mutator operator, allows for a much wider and flexible search space; e.g., over all possible python functions within a certain FLOP budget, eliminating the need for manually constructed search spaces. In addition, these pipelines will be biased towards meaningful activation functions, given their ability to represent common knowledge, leading to a potentially more efficient search of the space. The second observation is that, through this framework, one can target not only performance improvements but also activation functions that encode particular inductive biases. This can be done by using performance on out-of-distribution data as a fitness function, reflecting the degree to which the architecture respects the inherent structure in the data in a manner independent of distribution shifts. We carry an empirical exploration of this proposal and show that relatively small scale synthetic datasets can be sufficient for AlphaEvolve to discover meaningful activations.

Perplexity Cannot Always Tell Right from Wrong

Perplexity -- a function measuring a model's overall level of "surprise" when encountering a particular output -- has gained significant traction in recent years, both as a loss function and as a simple-to-compute metric of model quality. Prior studies have pointed out several limitations of perplexity, often from an empirical manner. Here we leverage recent results on Transformer continuity to show in a rigorous manner how perplexity may be an unsuitable metric for model selection. Specifically, we prove that, if there is any sequence that a compact decoder-only Transformer model predicts accurately and confidently -- a necessary pre-requisite for strong generalisation -- it must imply existence of another sequence with very low perplexity, but not predicted correctly by that same model. Further, by analytically studying iso-perplexity plots, we find that perplexity will not always select for the more accurate model -- rather, any increase in model confidence must be accompanied by a commensurate rise in accuracy for the new model to be selected.

MS-SSM: A Multi-Scale State Space Model for Efficient Sequence Modeling

State-space models (SSMs) have recently attention as an efficient alternative to computationally expensive attention-based models for sequence modeling. They rely on linear recurrences to integrate information over time, enabling fast inference, parallelizable training, and control over recurrence stability. However, traditional SSMs often suffer from limited effective memory, requiring larger state sizes for improved recall. Moreover, existing SSMs struggle to capture multi-scale dependencies, which are essential for modeling complex structures in time series, images, and natural language. This paper introduces a multi-scale SSM framework that addresses these limitations by representing sequence dynamics across multiple resolution and processing each resolution with specialized state-space dynamics. By capturing both fine-grained, high-frequency patterns and coarse, global trends, MS-SSM enhances memory efficiency and long-range modeling. We further introduce an input-dependent scale-mixer, enabling dynamic information fusion across resolutions. The proposed approach significantly improves sequence modeling, particularly in long-range and hierarchical tasks, while maintaining computational efficiency. Extensive experiments on benchmarks, including Long Range Arena, hierarchical reasoning, time series classification, and image recognition, demonstrate that MS-SSM consistently outperforms prior SSM-based models, highlighting the benefits of multi-resolution processing in state-space architectures.

Fine-Tuned In-Context Learners for Efficient Adaptation

When adapting large language models (LLMs) to a specific downstream task, two primary approaches are commonly employed: (1) prompt engineering, often with in-context few-shot learning, leveraging the model's inherent generalization abilities, and (2) fine-tuning on task-specific data, directly optimizing the model's parameters. While prompt-based methods excel in few-shot scenarios, their effectiveness often plateaus as more data becomes available. Conversely, fine-tuning scales well with data but may underperform when training examples are scarce. We investigate a unified approach that bridges these two paradigms by incorporating in-context learning directly into the fine-tuning process. Specifically, we fine-tune the model on task-specific data augmented with in-context examples, mimicking the structure of k-shot prompts. This approach, while requiring per-task fine-tuning, combines the sample efficiency of in-context learning with the performance gains of fine-tuning, leading to a method that consistently matches and often significantly exceeds both these baselines. To perform hyperparameter selection in the low-data regime, we propose to use prequential evaluation, which eliminates the need for expensive cross-validation and leverages all available data for training while simultaneously providing a robust validation signal. We conduct an extensive empirical study to determine which adaptation paradigm - fine-tuning, in-context learning, or our proposed unified approach offers the best predictive performance on a concrete data downstream-tasks.

What Can Grokking Teach Us About Learning Under Nonstationarity?

In continual learning problems, it is often necessary to overwrite components of a neural network's learned representation in response to changes in the data stream; however, neural networks often exhibit \primacy bias, whereby early training data hinders the network's ability to generalize on later tasks. While feature-learning dynamics of nonstationary learning problems are not well studied, the emergence of feature-learning dynamics is known to drive the phenomenon of grokking, wherein neural networks initially memorize their training data and only later exhibit perfect generalization. This work conjectures that the same feature-learning dynamics which facilitate generalization in grokking also underlie the ability to overwrite previous learned features as well, and methods which accelerate grokking by facilitating feature-learning dynamics are promising candidates for addressing primacy bias in non-stationary learning problems. We then propose a straightforward method to induce feature-learning dynamics as needed throughout training by increasing the effective learning rate, i.e. the ratio between parameter and update norms. We show that this approach both facilitates feature-learning and improves generalization in a variety of settings, including grokking, warm-starting neural network training, and reinforcement learning tasks.

Optimizers Qualitatively Alter Solutions And We Should Leverage This

Due to the nonlinear nature of Deep Neural Networks (DNNs), one can not guarantee convergence to a unique global minimum of the loss when using optimizers relying only on local information, such as SGD. Indeed, this was a primary source of skepticism regarding the feasibility of DNNs in the early days of the field. The past decades of progress in deep learning have revealed this skepticism to be misplaced, and a large body of empirical evidence shows that sufficiently large DNNs following standard training protocols exhibit well-behaved optimization dynamics that converge to performant solutions. This success has biased the community to use convex optimization as a mental model for learning, leading to a focus on training efficiency, either in terms of required iteration, FLOPs or wall-clock time, when improving optimizers. We argue that, while this perspective has proven extremely fruitful, another perspective specific to DNNs has received considerably less attention: the optimizer not only influences the rate of convergence, but also the qualitative properties of the learned solutions. Restated, the optimizer can and will encode inductive biases and change the effective expressivity of a given class of models. Furthermore, we believe the optimizer can be an effective way of encoding desiderata in the learning process. We contend that the community should aim at understanding the biases of already existing methods, as well as aim to build new optimizers with the explicit intent of inducing certain properties of the solution, rather than solely judging them based on their convergence rates. We hope our arguments will inspire research to improve our understanding of how the learning process can impact the type of solution we converge to, and lead to a greater recognition of optimizers design as a critical lever that complements the roles of architecture and data in shaping model outcomes.

Meta-learning how to Share Credit among Macro-Actions

One proposed mechanism to improve exploration in reinforcement learning is through the use of macro-actions. Paradoxically though, in many scenarios the naive addition of macro-actions does not lead to better exploration, but rather the opposite. It has been argued that this was caused by adding non-useful macros and multiple works have focused on mechanisms to discover effectively environment-specific useful macros. In this work, we take a slightly different perspective. We argue that the difficulty stems from the trade-offs between reducing the average number of decisions per episode versus increasing the size of the action space. Namely, one typically treats each potential macro-action as independent and atomic, hence strictly increasing the search space and making typical exploration strategies inefficient. To address this problem we propose a novel regularization term that exploits the relationship between actions and macro-actions to improve the credit assignment mechanism by reducing the effective dimension of the action space and, therefore, improving exploration. The term relies on a similarity matrix that is meta-learned jointly with learning the desired policy. We empirically validate our strategy looking at macro-actions in Atari games, and the StreetFighter II environment. Our results show significant improvements over the Rainbow-DQN baseline in all environments. Additionally, we show that the macro-action similarity is transferable to related environments. We believe this work is a small but important step towards understanding how the similarity-imposed geometry on the action space can be exploited to improve credit assignment and exploration, therefore making learning more effective.

MesaNet: Sequence Modeling by Locally Optimal Test-Time Training

Sequence modeling is currently dominated by causal transformer architectures that use softmax self-attention. Although widely adopted, transformers require scaling memory and compute linearly during inference. A recent stream of work linearized the softmax operation, resulting in powerful recurrent neural network (RNN) models with constant memory and compute costs such as DeltaNet, Mamba or xLSTM. These models can be unified by noting that their recurrent layer dynamics can all be derived from an in-context regression objective, approximately optimized through an online learning rule. Here, we join this line of work and introduce a numerically stable, chunkwise parallelizable version of the recently proposed Mesa layer (von Oswald et al., 2024), and study it in language modeling at the billion-parameter scale. This layer again stems from an in-context loss, but which is now minimized to optimality at every time point using a fast conjugate gradient solver. Through an extensive suite of experiments, we show that optimal test-time training enables reaching lower language modeling perplexity and higher downstream benchmark performance than previous RNNs, especially on tasks requiring long context understanding. This performance gain comes at the cost of additional flops spent during inference time. Our results are therefore intriguingly related to recent trends of increasing test-time compute to improve performance -- here by spending compute to solve sequential optimization problems within the neural network itself.