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Large Language Models (LLMs) have shown remarkable capabilities in natural language processing, mathematical problem solving, and tasks related to program synthesis. However, their effectiveness in long-term planning and higher-order reasoning has been noted to be limited and fragile. This paper explores an approach for enhancing LLM performance in solving a classical robotic planning task by integrating solver-generated feedback. We explore four different strategies for providing feedback, including visual feedback, we utilize fine-tuning, and we evaluate the performance of three different LLMs across a 10 standard and 100 more randomly generated planning problems. Our results suggest that the solver-generated feedback improves the LLM's ability to solve the moderately difficult problems, but the harder problems still remain out of reach. The study provides detailed analysis of the effects of the different hinting strategies and the different planning tendencies of the evaluated LLMs.

Direct Preference Optimization (DPO) has emerged as a more computationally efficient alternative to Reinforcement Learning from Human Feedback (RLHF) with Proximal Policy Optimization (PPO), eliminating the need for reward models and online sampling. Despite these benefits, DPO and its variants remain sensitive to hyper-parameters and prone to instability, particularly on mathematical datasets. We argue that these issues arise from the unidirectional likelihood-derivative negative feedback inherent in the log-likelihood loss function. To address this, we propose a novel LLM alignment loss that establishes a stable Bidirectional Negative Feedback (BNF) during optimization. Our proposed BNF loss eliminates the need for pairwise contrastive losses and does not require any extra tunable hyper-parameters or pairwise preference data, streamlining the alignment pipeline to be as simple as supervised fine-tuning. We conduct extensive experiments across two challenging QA benchmarks and four reasoning benchmarks. The experimental results show that BNF achieves comparable performance to the best methods on QA benchmarks, while its performance decrease on the four reasoning benchmarks is significantly lower compared to the best methods, thus striking a better balance between value alignment and reasoning ability. In addition, we further validate the performance of BNF on non-pairwise datasets, and conduct in-depth analysis of log-likelihood and logit shifts across different preference optimization methods.

The Hamiltonian Monte Carlo (HMC) algorithm is often lauded for its ability to effectively sample from high-dimensional distributions. In this paper we challenge the presumed domination of HMC for the Bayesian analysis of GLMs. By utilizing the structure of the compute graph rather than the graphical model, we reduce the time per sweep of a full-scan Gibbs sampler from $O(d^2)$ to $O(d)$, where $d$ is the number of GLM parameters. Our simple changes to the implementation of the Gibbs sampler allow us to perform Bayesian inference on high-dimensional GLMs that are practically infeasible with traditional Gibbs sampler implementations. We empirically demonstrate a substantial increase in effective sample size per time when comparing our Gibbs algorithms to state-of-the-art HMC algorithms. While Gibbs is superior in terms of dimension scaling, neither Gibbs nor HMC dominate the other: we provide numerical and theoretical evidence that HMC retains an edge in certain circumstances thanks to its advantageous condition number scaling. Interestingly, for GLMs of fixed data size, we observe that increasing dimensionality can stabilize or even decrease condition number, shedding light on the empirical advantage of our efficient Gibbs sampler.

Retrieval-Augmented Generation (RAG) has gained significant popularity in modern Large Language Models (LLMs) due to its effectiveness in introducing new knowledge and reducing hallucinations. However, the deep understanding of RAG remains limited, how does RAG help the reasoning process and can RAG help improve the reasoning capability remains question. While external documents are typically considered as a method to incorporate domain-specific information, they also contain intermediate reasoning results related to the query, this suggests that documents could enhance the reasoning capability of LLMs, which has not been previously explored. In this paper, we investigate this issue in depth and find that while RAG can assist with reasoning, the help is limited. If we conceptualize the reasoning process as a tree with fixed depth, then RAG struggles to assist LLMs in performing deeper reasoning. Additionally, the information in the documents requires preprocessing to filter out noise. We demonstrate that this preprocessing is difficult to achieve simply fine-tuning of the LLM, it often necessitates numerous additional transformer layers to solve the problem. To simplify the problem, we propose DPrompt tuning, which effectively resolves the issue within just limited transformer layers, leading to improved performance.

Text watermarking for Large Language Models (LLMs) has made significant progress in detecting LLM outputs and preventing misuse. Current watermarking techniques offer high detectability, minimal impact on text quality, and robustness to text editing. However, current researches lack investigation into the imperceptibility of watermarking techniques in LLM services. This is crucial as LLM providers may not want to disclose the presence of watermarks in real-world scenarios, as it could reduce user willingness to use the service and make watermarks more vulnerable to attacks. This work is the first to investigate the imperceptibility of watermarked LLMs. We design an identification algorithm called Water-Probe that detects watermarks through well-designed prompts to the LLM. Our key motivation is that current watermarked LLMs expose consistent biases under the same watermark key, resulting in similar differences across prompts under different watermark keys. Experiments show that almost all mainstream watermarking algorithms are easily identified with our well-designed prompts, while Water-Probe demonstrates a minimal false positive rate for non-watermarked LLMs. Finally, we propose that the key to enhancing the imperceptibility of watermarked LLMs is to increase the randomness of watermark key selection. Based on this, we introduce the Water-Bag strategy, which significantly improves watermark imperceptibility by merging multiple watermark keys.

Deep Neural Collapse (DNC) refers to the surprisingly rigid structure of the data representations in the final layers of Deep Neural Networks (DNNs). Though the phenomenon has been measured in a variety of settings, its emergence is typically explained via data-agnostic approaches, such as the unconstrained features model. In this work, we introduce a data-dependent setting where DNC forms due to feature learning through the average gradient outer product (AGOP). The AGOP is defined with respect to a learned predictor and is equal to the uncentered covariance matrix of its input-output gradients averaged over the training dataset. The Deep Recursive Feature Machine (Deep RFM) is a method that constructs a neural network by iteratively mapping the data with the AGOP and applying an untrained random feature map. We demonstrate empirically that DNC occurs in Deep RFM across standard settings as a consequence of the projection with the AGOP matrix computed at each layer. Further, we theoretically explain DNC in Deep RFM in an asymptotic setting and as a result of kernel learning. We then provide evidence that this mechanism holds for neural networks more generally. In particular, we show that the right singular vectors and values of the weights can be responsible for the majority of within-class variability collapse for DNNs trained in the feature learning regime. As observed in recent work, this singular structure is highly correlated with that of the AGOP.

The LSTM network was proposed to overcome the difficulty in learning long-term dependence, and has made significant advancements in applications. With its success and drawbacks in mind, this paper raises the question - do RNN and LSTM have long memory? We answer it partially by proving that RNN and LSTM do not have long memory from a statistical perspective. A new definition for long memory networks is further introduced, and it requires the model weights to decay at a polynomial rate. To verify our theory, we convert RNN and LSTM into long memory networks by making a minimal modification, and their superiority is illustrated in modeling long-term dependence of various datasets.

We introduce a new language representation model called BERT, which stands for Bidirectional Encoder Representations from Transformers. Unlike recent language representation models, BERT is designed to pre-train deep bidirectional representations by jointly conditioning on both left and right context in all layers. As a result, the pre-trained BERT representations can be fine-tuned with just one additional output layer to create state-of-the-art models for a wide range of tasks, such as question answering and language inference, without substantial task-specific architecture modifications. BERT is conceptually simple and empirically powerful. It obtains new state-of-the-art results on eleven natural language processing tasks, including pushing the GLUE benchmark to 80.4% (7.6% absolute improvement), MultiNLI accuracy to 86.7 (5.6% absolute improvement) and the SQuAD v1.1 question answering Test F1 to 93.2 (1.5% absolute improvement), outperforming human performance by 2.0%.