Nicolas Menet

Aleksandar Terzić, Francesco Carzaniga, Nicolas Menet et al.

State-space models (SSMs) face a fundamental trade-off between efficiency and expressivity that is mainly dictated by the structure of the model's transition matrix. Unstructured transition matrices enable maximal expressivity, as measured by their ability to model finite-state automaton (FSA) transitions, but come at a prohibitively high compute and memory cost. In contrast, most structured transition matrix forms are highly efficient both in runtime and memory consumption, but suffer from limited expressivity. Building on recent work on structured sparse SSMs, we propose Flash PD-SSM, a novel SSM that achieves comparable throughput to widely-used structured SSMs with significantly better expressivity guarantees. Flash PD-SSM maintains a trainable set of structured sparse matrices, a single one of which is discretely selected at each time-step, enabling FSA expressiveness at the level of unstructured matrices while maintaining the efficiency required for training models at scale. First, we validate Flash PD-SSM against a suite of alternative models on synthetic mechanistic and state-tracking tasks, finding that its theoretical expressivity is achieved in practice. Second, on multivariate time-series tasks involving sequences of length over 17,000, we find that Flash PD-SSM defines a new state-of-the-art (SoTA) accuracy among competing SSM methods. Finally, we demonstrate that Flash PD-SSM is an effective drop-in replacement for hybrid LLMs, yielding improvements both in natural language state-tracking and in common language modeling scenarios. The model exhibits increased throughput and decreased memory consumption compared to SSMs widely used in frontier language models.

Nicolas Menet, Michael Hersche, Geethan Karunaratne et al.

With the advent of deep learning, progressively larger neural networks have been designed to solve complex tasks. We take advantage of these capacity-rich models to lower the cost of inference by exploiting computation in superposition. To reduce the computational burden per input, we propose Multiple-Input-Multiple-Output Neural Networks (MIMONets) capable of handling many inputs at once. MIMONets augment various deep neural network architectures with variable binding mechanisms to represent an arbitrary number of inputs in a compositional data structure via fixed-width distributed representations. Accordingly, MIMONets adapt nonlinear neural transformations to process the data structure holistically, leading to a speedup nearly proportional to the number of superposed input items in the data structure. After processing in superposition, an unbinding mechanism recovers each transformed input of interest. MIMONets also provide a dynamic trade-off between accuracy and throughput by an instantaneous on-demand switching between a set of accuracy-throughput operating points, yet within a single set of fixed parameters. We apply the concept of MIMONets to both CNN and Transformer architectures resulting in MIMOConv and MIMOFormer, respectively. Empirical evaluations show that MIMOConv achieves about 2-4 x speedup at an accuracy delta within [+0.68, -3.18]% compared to WideResNet CNNs on CIFAR10 and CIFAR100. Similarly, MIMOFormer can handle 2-4 inputs at once while maintaining a high average accuracy within a [-1.07, -3.43]% delta on the long range arena benchmark. Finally, we provide mathematical bounds on the interference between superposition channels in MIMOFormer. Our code is available at https://github.com/IBM/multiple-input-multiple-output-nets.

Michael Hersche, Nicolas Menet, Ronan Tanios et al.

Diffusion language models (DLMs) have emerged as a promising alternative to autoregressive (AR) models, offering sub-linear generation latency and bidirectional capabilities that are particularly appealing for code generation and editing. Achieving sub-linear latency in discrete DLMs requires predicting multiple tokens in parallel. However, standard DLMs sample tokens independently from conditional marginal distributions, failing to capture the joint dependencies among concurrently generated tokens. As a result, they often lead to syntactic inconsistencies and break multi-token structures. In this work, we introduce CoDiLA (Coherent Diffusion with Local Autoregression), a method that reconciles parallel sampling with local dependency modeling. Rather than forcing the DLM to resolve fine-grained syntax, CoDiLA delegates local decoding to a small, auxiliary AR model operating on the diffusion latents. This design allows for parallel block generation while ensuring sequential validity within each block and maintaining core DLM capabilities, including bidirectional modeling across blocks. We demonstrate that using a highly compact auxiliary AR model (e.g., 0.6B parameters) effectively eliminates coherence artifacts, establishing a new Pareto frontier for accuracy and speed in code generation benchmarks.

Nicolas Menet, Michael Hersche, Andreas Krause et al.

Coding agents are increasingly utilized in test-driven software development, yet the theoretical mechanisms behind their environment-interaction strategies remain underexplored. We provide a probabilistic framework for two dominant paradigms: code selection after generation using the execution environment, and code generation conditioned on environment feedback. First, we formalize several well-established selection heuristics as environment-aware estimators of code correctness. We theoretically prove that estimators based on fuzzy functional similarity add an inductive bias and strictly dominate estimators based on functional equivalence in terms of signal-to-noise ratio. Second, we frame backprompting as an in-context approximation of Thompson sampling. We derive a novel regret bound for reward functions with unobservable components, theoretically explaining why the effectiveness of backprompting is limited by the ambiguity of the informal task description (an irreducible regret). Using three state-of-the-art open weight models, we corroborate these findings across BigCodeBenchHard, LeetCodeDataset, and QiskitHumanEvalSim. Our formalization also suggests how to improve task descriptions effectively, leading to a new benchmark, QiskitHumanEvalSimX.

Nicolas Menet, Andreas Krause, Abbas Rahimi

Balancing exploration and exploitation is a core challenge in sequential decision-making and black-box optimization. We introduce POETS ($\textbf{Po}$licy $\textbf{E}$nsembles for $\textbf{T}$hompson $\textbf{S}$ampling), a novel framework that bridges uncertainty quantification and policy optimization. Our approach is grounded in the insight that policies trained with Kullback-Leibler (KL) regularization implicitly encode an underlying reward function. Building on this, POETS bypasses the complex, nested process of training an uncertainty-aware reward model and separately fitting a policy to this model. Instead, we directly train a policy ensemble to capture epistemic uncertainty by matching implicitly encoded reward functions to online, bootstrapped data. To overcome the prohibitive compute and memory constraints of ensembling Large Language Models (LLMs), POETS utilizes an efficient architecture: the ensemble shares a pre-trained backbone while maintaining diversity through independent Low-Rank Adaptation (LoRA) branches. Theoretically, we prove that POETS implicitly conducts KL-regularized Thompson sampling and thus inherits strong cumulative regret bounds of ${\mathcal O}(\sqrt{T γ_T})$. Empirically, we demonstrate that POETS achieves state-of-the-art sample efficiency across diverse scientific discovery domains, including protein search and quantum circuit design. Furthermore, it improves the optimization trajectories of reinforcement learning, proving particularly robust in off-policy settings with experience replay or in small dataset regimes.

Aleksandar Terzić, Nicolas Menet, Michael Hersche et al.

Modern state-space models (SSMs) often utilize transition matrices which enable efficient computation but pose restrictions on the model's expressivity, as measured in terms of the ability to emulate finite-state automata (FSA). While unstructured transition matrices are optimal in terms of expressivity, they come at a prohibitively high compute and memory cost even for moderate state sizes. We propose a structured sparse parametrization of transition matrices in SSMs that enables FSA state tracking with optimal state size and depth, while keeping the computational cost of the recurrence comparable to that of diagonal SSMs. Our method, PD-SSM, parametrizes the transition matrix as the product of a column one-hot matrix ($P$) and a complex-valued diagonal matrix ($D$). Consequently, the computational cost of parallel scans scales linearly with the state size. Theoretically, the model is BIBO-stable and can emulate any $N$-state FSA with one layer of dimension $N$ and a linear readout of size $N \times N$, significantly improving on all current structured SSM guarantees. Experimentally, the model significantly outperforms a wide collection of modern SSM variants on various FSA state tracking tasks. On multiclass time-series classification, the performance is comparable to that of neural controlled differential equations, a paradigm explicitly built for time-series analysis. Finally, we integrate PD-SSM into a hybrid Transformer-SSM architecture and demonstrate that the model can effectively track the states of a complex FSA in which transitions are encoded as a set of variable-length English sentences. The code is available at https://github.com/IBM/expressive-sparse-state-space-model

Nicolas Menet, Jonas Hübotter, Parnian Kassraie et al.

We consider the problem of computing the probability of maximality (PoM) of a Gaussian random vector, i.e., the probability for each dimension to be maximal. This is a key challenge in applications ranging from Bayesian optimization to reinforcement learning, where the PoM not only helps with finding an optimal action, but yields a fine-grained analysis of the action domain, crucial in tasks such as drug discovery. Existing techniques are costly, scaling polynomially in computation and memory with the vector size. We introduce LITE, the first approach for estimating Gaussian PoM with almost-linear time and memory complexity. LITE achieves SOTA accuracy on a number of tasks, while being in practice several orders of magnitude faster than the baselines. This also translates to a better performance on downstream tasks such as entropy estimation and optimal control of bandits. Theoretically, we cast LITE as entropy-regularized UCB and connect it to prior PoM estimators.

Nicolas Menet, Aleksandar Terzić, Michael Hersche et al.

Bayesian optimization in large unstructured discrete spaces is often hindered by the computational cost of maximizing acquisition functions due to the absence of gradients. We propose a scalable alternative based on Thompson sampling that eliminates the need for acquisition function maximization by directly parameterizing the probability that a candidate yields the maximum reward. Our approach, Thompson Sampling via Fine-Tuning (ToSFiT) leverages the prior knowledge embedded in prompt-conditioned large language models, and incrementally adapts them toward the posterior. Theoretically, we derive a novel regret bound for a variational formulation of Thompson Sampling that matches the strong guarantees of its standard counterpart. Our analysis reveals the critical role of careful adaptation to the posterior probability of maximality--a principle that underpins our ToSFiT algorithm. Empirically, we validate our method on three diverse tasks: FAQ response refinement, thermally stable protein search, and quantum circuit design. We demonstrate that online fine-tuning significantly improves sample efficiency, with negligible impact on computational efficiency.