ICLR 2024

We present the Fourier Sliced-Wasserstein (FSW) embedding - a novel method to embed multisets and measures over R^d into Euclidean space. Our proposed embedding approximately preserves the sliced Wasserstein distance on distributions, thereby yielding geometrically meaningful representations that better capture the structure of the input. Moreover, it is injective on measures and bi-Lipschitz on multisets - a significant advantage over prevalent methods based on sum- or max-pooling, which are provably not bi-Lipschitz, and, in many cases, not even injective. The required output dimension for these guarantees is near-optimal: roughly 2Nd, where N is the maximal input multiset size. Furthermore, we prove that it is impossible to embed distributions over R^d into Euclidean space in a bi-Lipschitz manner. Thus, the metric properties of our embedding are, in a sense, the best possible. Through numerical experiments, we demonstrate that our method yields superior multiset representations that improve performance in practical learning tasks. Specifically, we show that (a) a simple combination of the FSW embedding with an MLP achieves state-of-the-art performance in learning the (non-sliced) Wasserstein distance; and (b) replacing max-pooling with the FSW embedding makes PointNet significantly more robust to parameter reduction, with only minor performance degradation even after a 40-fold reduction.

Recent work has demonstrated that semantics specified by pretraining data influence how representations of different concepts are organized in a large language model (LLM). However, given the open-ended nature of LLMs, e.g., their ability to in-context learn, we can ask whether models alter these pretraining semantics to adopt alternative, context-specified ones. Specifically, if we provide in-context exemplars wherein a concept plays a different role than what the pretraining data suggests, do models reorganize their representations in accordance with these novel semantics? To answer this question, we take inspiration from the theory of conceptual role semantics and define a toy"graph tracing"task wherein the nodes of the graph are referenced via concepts seen during training (e.g., apple, bird, etc.) and the connectivity of the graph is defined via some predefined structure (e.g., a square grid). Given exemplars that indicate traces of random walks on the graph, we analyze intermediate representations of the model and find that as the amount of context is scaled, there is a sudden re-organization from pretrained semantic representations to in-context representations aligned with the graph structure. Further, we find that when reference concepts have correlations in their semantics (e.g., Monday, Tuesday, etc.), the context-specified graph structure is still present in the representations, but is unable to dominate the pretrained structure. To explain these results, we analogize our task to energy minimization for a predefined graph topology, providing evidence towards an implicit optimization process to infer context-specified semantics. Overall, our findings indicate scaling context-size can flexibly re-organize model representations, possibly unlocking novel capabilities.

We introduce Chunk-Distilled Language Modeling (CD-LM), an approach to text generation that addresses two challenges in current large language models (LLMs): the inefficiency of token-level generation, and the difficulty of adapting to new data and knowledge. Our method combines deep network-based LLMs with a straightforward retrieval module, which allows the generation of multi-token text chunks at a single decoding step. Our retrieval framework enables flexible construction of model- or domain-specific datastores, either leveraging the internal knowledge of existing models, or incorporating expert insights from human-annotated corpora. This adaptability allows for enhanced control over the language model's distribution without necessitating additional training. We present the CD-LM formulation along with performance metrics demonstrating its ability to improve language model performance and efficiency across a diverse set of downstream tasks. Code and data will be made publicly available.

Structured State Space Models (SSMs) have emerged as alternatives to transformers. While SSMs are often regarded as effective in capturing long-sequence dependencies, we rigorously demonstrate that they are inherently limited by strong recency bias. Our empirical studies also reveal that this bias impairs the models' ability to recall distant information and introduces robustness issues. Our scaling experiments then discovered that deeper structures in SSMs can facilitate the learning of long contexts. However, subsequent theoretical analysis reveals that as SSMs increase in depth, they exhibit another inevitable tendency toward over-smoothing, e.g., token representations becoming increasingly indistinguishable. This fundamental dilemma between recency and over-smoothing hinders the scalability of existing SSMs. Inspired by our theoretical findings, we propose to polarize two channels of the state transition matrices in SSMs, setting them to zero and one, respectively, simultaneously addressing recency bias and over-smoothing. Experiments demonstrate that our polarization technique consistently enhances the associative recall accuracy of long-range tokens and unlocks SSMs to benefit further from deeper architectures. All source codes are released at https://github.com/VITA-Group/SSM-Bottleneck.

Large language models (LLMs) have transformed natural language processing, with frameworks like Chatbot Arena providing pioneering platforms for evaluating these models. By facilitating millions of pairwise comparisons based on human judgments, Chatbot Arena has become a cornerstone in LLM evaluation, offering rich datasets for ranking models in open-ended conversational tasks. Building upon this foundation, we propose a statistical framework that incorporates key advancements to address specific challenges in pairwise comparison analysis. First, we introduce a factored tie model that enhances the ability to handle ties -- an integral aspect of human-judged comparisons -- significantly improving the model's fit to observed data. Second, we extend the framework to model covariance between competitors, enabling deeper insights into performance relationships and facilitating intuitive groupings into performance tiers. Third, we resolve optimization challenges arising from parameter non-uniqueness by introducing novel constraints, ensuring stable and interpretable parameter estimation. Through rigorous evaluation and extensive experimentation, our framework demonstrates substantial improvements over existing methods in modeling pairwise comparison data. To support reproducibility and practical adoption, we release leaderbot, an open-source Python package implementing our models and analyses.

The availability of multiple training algorithms and architectures for generative models requires a selection mechanism to form a single model over a group of well-trained generation models. The selection task is commonly addressed by identifying the model that maximizes an evaluation score based on the diversity and quality of the generated data. However, such a best-model identification approach overlooks the possibility that a mixture of available models can outperform each individual model. In this work, we numerically show that a mixture of generative models on benchmark image datasets can indeed achieve a better evaluation score (based on FID and KID scores), compared to the individual models. This observation motivates the development of efficient algorithms for selecting the optimal mixture of the models. To address this, we formulate a quadratic optimization problem to find an optimal mixture model achieving the maximum of kernel-based evaluation scores including kernel inception distance (KID) and Rényi kernel entropy (RKE). To identify the optimal mixture of the models using the fewest possible sample queries, we view the selection task as a multi-armed bandit (MAB) problem and propose the Mixture Upper Confidence Bound (Mixture-UCB) algorithm that provably converges to the optimal mixture of the involved models. More broadly, the proposed Mixture-UCB can be extended to optimize every convex quadratic function of the mixture weights in a general MAB setting. We prove a regret bound for the Mixture-UCB algorithm and perform several numerical experiments to show the success of Mixture-UCB in finding the optimal mixture of text and image generative models. The project code is available at https://github.com/Rezaei-Parham/Mixture-UCB.

Autoregressive (AR) models have achieved state-of-the-art performance in text and image generation but suffer from slow generation due to the token-by-token process. We ask an ambitious question: can a pre-trained AR model be adapted to generate outputs in just one or two steps? If successful, this would significantly advance the development and deployment of AR models. We notice that existing works that try to speed up AR generation by generating multiple tokens at once fundamentally cannot capture the output distribution due to the conditional dependencies between tokens, limiting their effectiveness for few-step generation. To address this, we propose Distilled Decoding (DD), which uses flow matching to create a deterministic mapping from Gaussian distribution to the output distribution of the pre-trained AR model. We then train a network to distill this mapping, enabling few-step generation. DD doesn't need the training data of the original AR model, making it more practical. We evaluate DD on state-of-the-art image AR models and present promising results on ImageNet-256. For VAR, which requires 10-step generation, DD enables one-step generation (6.3$\times$ speed-up), with an acceptable increase in FID from 4.19 to 9.96. For LlamaGen, DD reduces generation from 256 steps to 1, achieving an 217.8$\times$ speed-up with a comparable FID increase from 4.11 to 11.35. In both cases, baseline methods completely fail with FID>100. DD also excels on text-to-image generation, reducing the generation from 256 steps to 2 for LlamaGen with minimal FID increase from 25.70 to 28.95. As the first work to demonstrate the possibility of one-step generation for image AR models, DD challenges the prevailing notion that AR models are inherently slow, and opens up new opportunities for efficient AR generation. The project website is at https://imagination-research.github.io/distilled-decoding.

Discovering a unique causal structure is difficult due to both inherent identifiability issues, and the consequences of finite data. As such, uncertainty over causal structures, such as those obtained from a Bayesian posterior, are often necessary for downstream tasks. Finding an accurate approximation to this posterior is challenging, due to the large number of possible causal graphs, as well as the difficulty in the subproblem of finding posteriors over the functional relationships of the causal edges. Recent works have used meta-learning to view the problem of estimating the maximum a-posteriori causal graph as supervised learning. Yet, these methods are limited when estimating the full posterior as they fail to encode key properties of the posterior, such as correlation between edges and permutation equivariance with respect to nodes. Further, these methods also cannot reliably sample from the posterior over causal structures. To address these limitations, we propose a Bayesian meta learning model that allows for sampling causal structures from the posterior and encodes these key properties. We compare our meta-Bayesian causal discovery against existing Bayesian causal discovery methods, demonstrating the advantages of directly learning a posterior over causal structure.

Sparsely activated Mixture-of-Experts (MoE) models are widely adopted to scale up model capacity without increasing the computation budget. However, vanilla TopK routers are trained in a discontinuous, non-differentiable way, limiting their performance and scalability. To address this issue, we propose ReMoE, a fully differentiable MoE architecture that offers a simple yet effective drop-in replacement for the conventional TopK+Softmax routing, utilizing ReLU as the router instead. We further propose methods to regulate the router's sparsity while balancing the load among experts. ReMoE's continuous nature enables efficient dynamic allocation of computation across tokens and layers, while also exhibiting domain specialization. Our experiments demonstrate that ReMoE consistently outperforms vanilla TopK-routed MoE across various model sizes, expert counts, and levels of granularity. Furthermore, ReMoE exhibits superior scalability with respect to the number of experts, surpassing traditional MoE architectures. The implementation based on Megatron-LM is available at https://github.com/thu-ml/ReMoE.

Neural networks can be drastically shrunk in size by removing redundant parameters. While crucial for the deployment on resource-constraint hardware, oftentimes, compression comes with a severe drop in accuracy and lack of adversarial robustness. Despite recent advances, counteracting both aspects has only succeeded for moderate compression rates so far. We propose a novel method, HARP, that copes with aggressive pruning significantly better than prior work. For this, we consider the network holistically. We learn a global compression strategy that optimizes how many parameters (compression rate) and which parameters (scoring connections) to prune specific to each layer individually. Our method fine-tunes an existing model with dynamic regularization, that follows a step-wise incremental function balancing the different objectives. It starts by favoring robustness before shifting focus on reaching the target compression rate and only then handles the objectives equally. The learned compression strategies allow us to maintain the pre-trained model natural accuracy and its adversarial robustness for a reduction by 99% of the network original size. Moreover, we observe a crucial influence of non-uniform compression across layers.

Robot learning is witnessing a significant increase in the size, diversity, and complexity of pre-collected datasets, mirroring trends in domains such as natural language processing and computer vision. Many robot learning methods treat such datasets as multi-task expert data and learn a multi-task, generalist policy by training broadly across them. Notably, while these generalist policies can improve the average performance across many tasks, the performance of generalist policies on any one task is often suboptimal due to negative transfer between partitions of the data, compared to task-specific specialist policies. In this work, we argue for the paradigm of training policies during deployment given the scenarios they encounter: rather than deploying pre-trained policies to unseen problems in a zero-shot manner, we non-parametrically retrieve and train models directly on relevant data at test time. Furthermore, we show that many robotics tasks share considerable amounts of low-level behaviors and that retrieval at the "sub"-trajectory granularity enables significantly improved data utilization, generalization, and robustness in adapting policies to novel problems. In contrast, existing full-trajectory retrieval methods tend to underutilize the data and miss out on shared cross-task content. This work proposes STRAP, a technique for leveraging pre-trained vision foundation models and dynamic time warping to retrieve sub-sequences of trajectories from large training corpora in a robust fashion. STRAP outperforms both prior retrieval algorithms and multi-task learning methods in simulated and real experiments, showing the ability to scale to much larger offline datasets in the real world as well as the ability to learn robust control policies with just a handful of real-world demonstrations.

Large Language Models (LLMs) have achieved remarkable success, yet recent findings reveal that their deeper layers often contribute minimally and can be pruned without affecting overall performance. While some view this as an opportunity for model compression, we identify it as a training shortfall rooted in the widespread use of Pre-Layer Normalization (Pre-LN). We demonstrate that Pre-LN, commonly employed in models like GPT and LLaMA, leads to diminished gradient norms in its deeper layers, reducing their effectiveness. In contrast, Post-Layer Normalization (Post-LN) preserves larger gradient norms in deeper layers but suffers from vanishing gradients in earlier layers. To address this, we introduce Mix-LN, a novel normalization technique that combines the strengths of Pre-LN and Post-LN within the same model. Mix-LN applies Post-LN to the earlier layers and Pre-LN to the deeper layers, ensuring more uniform gradients across layers. This allows all parts of the network--both shallow and deep layers--to contribute effectively to training. Extensive experiments with various model sizes from 70M to 7B demonstrate that Mix-LN consistently outperforms both Pre-LN and Post-LN, promoting more balanced, healthier gradient norms throughout the network, and enhancing the overall quality of LLM pre-training. Furthermore, we demonstrate that models pre-trained with Mix-LN learn better compared to those using Pre-LN or Post-LN during supervised fine-tuning (SFT) and reinforcement learning from human feedback (RLHF), highlighting the critical importance of high-quality deep layers. By effectively addressing the inefficiencies of deep layers in current LLMs, Mix-LN unlocks their potential, enhancing model capacity without increasing model size. Our code is available at https://github.com/pixeli99/MixLN.

Realtime environments change even as agents perform action inference and learning, thus requiring high interaction frequencies to effectively minimize regret. However, recent advances in machine learning involve larger neural networks with longer inference times, raising questions about their applicability in realtime systems where reaction time is crucial. We present an analysis of lower bounds on regret in realtime reinforcement learning (RL) environments to show that minimizing long-term regret is generally impossible within the typical sequential interaction and learning paradigm, but often becomes possible when sufficient asynchronous compute is available. We propose novel algorithms for staggering asynchronous inference processes to ensure that actions are taken at consistent time intervals, and demonstrate that use of models with high action inference times is only constrained by the environment's effective stochasticity over the inference horizon, and not by action frequency. Our analysis shows that the number of inference processes needed scales linearly with increasing inference times while enabling use of models that are multiple orders of magnitude larger than existing approaches when learning from a realtime simulation of Game Boy games such as Pokémon and Tetris.

Recent studies have indicated that effectively utilizing inference-time compute is crucial for attaining better performance from large language models (LLMs). In this work, we propose a novel inference-aware fine-tuning paradigm, in which the model is fine-tuned in a manner that directly optimizes the performance of the inference-time strategy. We study this paradigm using the simple yet effective Best-of-N (BoN) inference strategy, in which a verifier selects the best out of a set of LLM-generated responses. We devise the first imitation learning and reinforcement learning~(RL) methods for BoN-aware fine-tuning, overcoming the challenging, non-differentiable argmax operator within BoN. We empirically demonstrate that our BoN-aware models implicitly learn a meta-strategy that interleaves best responses with more diverse responses that might be better suited to a test-time input -- a process reminiscent of the exploration-exploitation trade-off in RL. Our experiments demonstrate the effectiveness of BoN-aware fine-tuning in terms of improved performance and inference-time compute. In particular, we show that our methods improve the Bo32 performance of Gemma 2B on Hendrycks MATH from 26.8% to 30.8%, and pass@32 from 60.0% to 67.0%, as well as the pass@16 on HumanEval from 61.6% to 67.1%.

Diffusion Policies have become widely used in Imitation Learning, offering several appealing properties, such as generating multimodal and discontinuous behavior. As models are becoming larger to capture more complex capabilities, their computational demands increase, as shown by recent scaling laws. Therefore, continuing with the current architectures will present a computational roadblock. To address this gap, we propose Mixture-of-Denoising Experts (MoDE) as a novel policy for Imitation Learning. MoDE surpasses current state-of-the-art Transformer-based Diffusion Policies while enabling parameter-efficient scaling through sparse experts and noise-conditioned routing, reducing both active parameters by 40% and inference costs by 90% via expert caching. Our architecture combines this efficient scaling with noise-conditioned self-attention mechanism, enabling more effective denoising across different noise levels. MoDE achieves state-of-the-art performance on 134 tasks in four established imitation learning benchmarks (CALVIN and LIBERO). Notably, by pretraining MoDE on diverse robotics data, we achieve 4.01 on CALVIN ABC and 0.95 on LIBERO-90. It surpasses both CNN-based and Transformer Diffusion Policies by an average of 57% across 4 benchmarks, while using 90% fewer FLOPs and fewer active parameters compared to default Diffusion Transformer architectures. Furthermore, we conduct comprehensive ablations on MoDE's components, providing insights for designing efficient and scalable Transformer architectures for Diffusion Policies. Code and demonstrations are available at https://mbreuss.github.io/MoDE_Diffusion_Policy/.

The rise of large language models (LLMs) has created a significant disparity: industrial research labs with their computational resources, expert teams, and advanced infrastructures, can effectively fine-tune LLMs, while individual developers and small organizations face barriers due to limited resources. In this paper, we aim to bridge this gap by presenting a comprehensive study on supervised fine-tuning of LLMs using instruction-tuning datasets spanning diverse knowledge domains and skills. We focus on small-sized LLMs (3B to 7B parameters) for their cost-efficiency and accessibility. We explore various training configurations and strategies across four open-source pre-trained models. We provide detailed documentation of these configurations, revealing findings that challenge several common training practices, including hyperparameter recommendations from TULU and phased training recommended by Orca. Key insights from our work include: (i) larger batch sizes paired with lower learning rates lead to improved model performance on benchmarks such as MMLU, MTBench, and Open LLM Leaderboard; (ii) early-stage training dynamics, such as lower gradient norms and higher loss values, are strong indicators of better final model performance, enabling early termination of sub-optimal runs and significant computational savings; (iii) through a thorough exploration of hyperparameters like warmup steps and learning rate schedules, we provide guidance for practitioners and find that certain simplifications do not compromise performance; and (iv) we observed no significant difference in performance between phased and stacked training strategies, but stacked training is simpler and more sample efficient. With these findings holding robustly across datasets and models, we hope this study serves as a guide for practitioners fine-tuning small LLMs and promotes a more inclusive environment for LLM research.

Model editing methods modify specific behaviors of Large Language Models by altering a small, targeted set of network weights and require very little data and compute. These methods can be used for malicious applications such as inserting misinformation or simple trojans that result in adversary-specified behaviors when a trigger word is present. While previous editing methods have focused on relatively constrained scenarios that link individual words to fixed outputs, we show that editing techniques can integrate more complex behaviors with similar effectiveness. We develop Concept-ROT, a model editing-based method that efficiently inserts trojans which not only exhibit complex output behaviors, but also trigger on high-level concepts -- presenting an entirely new class of trojan attacks. Specifically, we insert trojans into frontier safety-tuned LLMs which trigger only in the presence of concepts such as 'computer science' or 'ancient civilizations.' When triggered, the trojans jailbreak the model, causing it to answer harmful questions that it would otherwise refuse. Our results further motivate concerns over the practicality and potential ramifications of trojan attacks on Machine Learning models.

Human perception integrates multiple modalities, such as vision, hearing, and language, into a unified understanding of the surrounding reality. While recent multimodal models have achieved significant progress by aligning pairs of modalities via contrastive learning, their solutions are unsuitable when scaling to multiple modalities. These models typically align each modality to a designated anchor without ensuring the alignment of all modalities with each other, leading to suboptimal performance in tasks requiring a joint understanding of multiple modalities. In this paper, we structurally rethink the pairwise conventional approach to multimodal learning and we present the novel Gramian Representation Alignment Measure (GRAM), which overcomes the above-mentioned limitations. GRAM learns and then aligns $n$ modalities directly in the higher-dimensional space in which modality embeddings lie by minimizing the Gramian volume of the $k$-dimensional parallelotope spanned by the modality vectors, ensuring the geometric alignment of all modalities simultaneously. GRAM can replace cosine similarity in any downstream method, holding for 2 to $n$ modalities and providing more meaningful alignment with respect to previous similarity measures. The novel GRAM-based contrastive loss function enhances the alignment of multimodal models in the higher-dimensional embedding space, leading to new state-of-the-art performance in downstream tasks such as video-audio-text retrieval and audio-video classification. The project page, the code, and the pretrained models are available at https://ispamm.github.io/GRAM/.

Recent advances in GPU-based parallel simulation have enabled practitioners to collect large amounts of data and train complex control policies using deep reinforcement learning (RL), on commodity GPUs. However, such successes for RL in robotics have been limited to tasks sufficiently simulated by fast rigid-body dynamics. Simulation techniques for soft bodies are comparatively several orders of magnitude slower, thereby limiting the use of RL due to sample complexity requirements. To address this challenge, this paper presents both a novel RL algorithm and a simulation platform to enable scaling RL on tasks involving rigid bodies and deformables. We introduce Soft Analytic Policy Optimization (SAPO), a maximum entropy first-order model-based actor-critic RL algorithm, which uses first-order analytic gradients from differentiable simulation to train a stochastic actor to maximize expected return and entropy. Alongside our approach, we develop Rewarped, a parallel differentiable multiphysics simulation platform that supports simulating various materials beyond rigid bodies. We re-implement challenging manipulation and locomotion tasks in Rewarped, and show that SAPO outperforms baselines over a range of tasks that involve interaction between rigid bodies, articulations, and deformables. Additional details at https://rewarped.github.io/.

Reinforcement learning (RL) algorithms aim to balance exploiting the current best strategy with exploring new options that could lead to higher rewards. Most common RL algorithms use undirected exploration, i.e., select random sequences of actions. Exploration can also be directed using intrinsic rewards, such as curiosity or model epistemic uncertainty. However, effectively balancing task and intrinsic rewards is challenging and often task-dependent. In this work, we introduce a framework, MaxInfoRL, for balancing intrinsic and extrinsic exploration. MaxInfoRL steers exploration towards informative transitions, by maximizing intrinsic rewards such as the information gain about the underlying task. When combined with Boltzmann exploration, this approach naturally trades off maximization of the value function with that of the entropy over states, rewards, and actions. We show that our approach achieves sublinear regret in the simplified setting of multi-armed bandits. We then apply this general formulation to a variety of off-policy model-free RL methods for continuous state-action spaces, yielding novel algorithms that achieve superior performance across hard exploration problems and complex scenarios such as visual control tasks.