(399.19, 694.74) (400.95, 694.74) (400.95, 704.12) (399.19, 704.12)        /F1  	<|special_separator|>
(399.19, 700.52) (432.53, 700.52) (432.53, 717.55) (399.19, 717.55)        /F1 CRTR	<|special_separator|>
(399.19, 695.10) (400.95, 695.10) (400.95, 704.48) (399.19, 704.48)        /F1  	<|special_separator|>
(399.19, 688.06) (400.95, 688.06) (400.95, 697.45) (399.19, 697.45)        /F1  	<|special_separator|>
(165.96, 700.35) (190.79, 700.35) (190.79, 717.37) (165.96, 717.37)        /F1 CRL	<|special_separator|>
(203.04, 605.09) (228.56, 605.09) (228.56, 613.62) (203.04, 613.62)        /F2 Context 1	<|special_separator|>
(137.85, 678.10) (163.37, 678.10) (163.37, 686.63) (137.85, 686.63)        /F2 Context 2	<|special_separator|>
(127.67, 670.83) (129.21, 670.83) (129.21, 679.36) (127.67, 679.36)        /F2  	<|special_separator|>
(504.85, 636.51) (504.85, 650.23) (496.32, 650.23) (496.32, 636.51)        /F2 Time	<|special_separator|>
(119.87, 614.74) (145.39, 614.74) (145.39, 623.27) (119.87, 623.27)        /F2 Context 3	<|special_separator|>
(120.24, 607.24) (121.78, 607.24) (121.78, 615.78) (120.24, 615.78)        /F2  	<|special_separator|>
(108.00, 553.37) (145.46, 553.37) (145.46, 561.92) (108.00, 561.92)      /F116 Figure 1:	<|special_separator|>
(149.59, 553.57) (476.94, 553.57) (476.94, 561.63) (149.59, 561.63)      /F107 CRTR makes representations reflect the temporal structure of combinatorial tasks.	<|special_separator|>
(481.14, 553.58) (504.00, 553.58) (504.00, 561.28) (481.14, 561.28)      /F116 t-SNE	<|special_separator|>
(107.78, 543.62) (504.00, 543.62) (504.00, 551.31) (107.78, 551.31)      /F116 visualization of representations learned by CRTR (right) and CRL (left) for Sokoban. Colors correspond to	<|special_separator|>
(108.00, 533.65) (504.44, 533.65) (504.44, 541.35) (108.00, 541.35)      /F116 trajectories; three frames from two trajectories are shown in the center and linked to their representations. CRL	<|special_separator|>
(108.00, 523.69) (504.16, 523.69) (504.16, 531.39) (108.00, 531.39)      /F116 embeddings cluster tightly within trajectories, failing to capture global structure and limiting their usefulness for	<|special_separator|>
(108.00, 513.73) (503.86, 513.73) (503.86, 521.43) (108.00, 521.43)      /F116 planning. In contrast, CRTR organizes representations meaningfully across trajectories and time (vertical axis).	<|special_separator|>
(108.00, 480.38) (504.00, 480.38) (504.00, 488.93) (108.00, 488.93)      /F116 contrastive representations overfit to instance-specific context, instead of reflecting environment	<|special_separator|>
(108.00, 469.47) (504.17, 469.47) (504.17, 478.02) (108.00, 478.02)      /F116 dynamics. Consequently, models fail to adequately capture the temporal structure that is vital for	<|special_separator|>
(108.00, 458.56) (504.00, 458.56) (504.00, 467.11) (108.00, 467.11)      /F116 effective decision-making. This failure mode - such as when the model overfits to wall layouts in	<|special_separator|>
(108.00, 447.65) (504.00, 447.65) (504.00, 456.21) (108.00, 456.21)      /F116 Sokoban (Section 4.1) - manifests as a collapse of trajectory representations into small, disconnected	<|special_separator|>
(108.00, 436.74) (265.17, 436.74) (265.17, 445.30) (108.00, 445.30)      /F116 clusters, as illustrated in Figure 1 (left).	<|special_separator|>
(107.69, 420.36) (505.25, 420.36) (505.25, 428.91) (107.69, 428.91)      /F116 To solve this, we introduce Contrastive Representations for Temporal Reasoning (CRTR), a simple,	<|special_separator|>
(108.00, 409.45) (504.00, 409.45) (504.00, 418.00) (108.00, 418.00)      /F116 theoretically grounded CL method that uses in-trajectory negatives. By design, CRTR forces the	<|special_separator|>
(108.00, 398.54) (373.42, 398.54) (373.42, 407.09) (108.00, 407.09)      /F116 model to distinguish between temporally distant states within the	<|special_separator|>
(376.11, 398.68) (396.99, 398.68) (396.99, 407.27) (376.11, 407.27)      /F134 same	<|special_separator|>
(399.68, 398.54) (504.00, 398.54) (504.00, 407.09) (399.68, 407.09)      /F116 episode. This mechanism	<|special_separator|>
(108.00, 387.63) (505.65, 387.63) (505.65, 396.18) (108.00, 396.18)      /F116 prevents it from exploiting irrelevant context - such as visual or layout cues - and instead encour-	<|special_separator|>
(108.00, 376.72) (504.00, 376.72) (504.00, 385.27) (108.00, 385.27)      /F116 ages learning temporally meaningful embeddings that reflect the problem's relevant dynamics. This	<|special_separator|>
(108.00, 365.81) (504.00, 365.81) (504.00, 374.36) (108.00, 374.36)      /F116 echoes recent findings in neuroscience, where hippocampal representations of overlapping routes	<|special_separator|>
(108.00, 354.90) (504.35, 354.90) (504.35, 363.45) (108.00, 363.45)      /F116 diverge during learning despite visual similarity [10]. Our approach similarly prioritizes temporally	<|special_separator|>
(108.00, 343.99) (306.08, 343.99) (306.08, 352.54) (108.00, 352.54)      /F116 meaningful structure over reliance on visual cues.	<|special_separator|>
(107.53, 327.60) (505.25, 327.60) (505.25, 336.16) (107.53, 336.16)      /F116 We evaluate CRTR across challenging combinatorial domains: Sokoban, Rubik's Cube, N-Puzzle,	<|special_separator|>
(108.00, 316.69) (231.29, 316.69) (231.29, 325.25) (108.00, 325.25)      /F116 Lights Out, and Digit Jumper.	<|special_separator|>
(235.87, 316.69) (504.00, 316.69) (504.00, 325.25) (235.87, 325.25)      /F116 Due to their large, discrete state spaces, sparse rewards, and high	<|special_separator|>
(108.00, 305.79) (504.00, 305.79) (504.00, 314.34) (108.00, 314.34)      /F116 instance variability, they serve as challenging testbeds for evaluating whether learned representations	<|special_separator|>
(108.00, 294.88) (358.50, 294.88) (358.50, 303.43) (108.00, 303.43)      /F116 can support efficient, long-horizon combinatorial reasoning.	<|special_separator|>
(365.51, 294.88) (504.34, 294.88) (504.34, 303.43) (365.51, 303.43)      /F116 In each case, CRTR significantly	<|special_separator|>
(108.00, 283.97) (504.00, 283.97) (504.00, 292.52) (108.00, 292.52)      /F116 improves planning efficiency over standard contrastive learning, and approaches or surpasses the	<|special_separator|>
(108.00, 273.06) (283.13, 273.06) (283.13, 281.61) (108.00, 281.61)      /F116 performance of strong supervised baselines.	<|special_separator|>
(108.00, 256.67) (273.86, 256.67) (273.86, 265.22) (108.00, 265.22)      /F116 Our main contributions are the following:	<|special_separator|>
(115.47, 236.16) (122.94, 236.16) (122.94, 244.72) (115.47, 244.72)      /F116 1.	<|special_separator|>
(127.92, 236.16) (505.65, 236.16) (505.65, 244.72) (127.92, 244.72)      /F116 Weidentify and analyze a critical failure mode in standard contrastive learning, showing its inabil-	<|special_separator|>
(127.92, 225.25) (505.75, 225.25) (505.75, 233.81) (127.92, 233.81)      /F116 ity to capture relevant temporal or causal structure in problems with a complex temporal structure.	<|special_separator|>
(115.47, 210.10) (229.28, 210.10) (229.28, 218.65) (115.47, 218.65)      /F116 2. We propose Contrastive	<|special_separator|>
(234.22, 210.10) (299.13, 210.10) (299.13, 218.65) (234.22, 218.65)      /F116 Representations	<|special_separator|>
(304.07, 210.10) (315.92, 210.10) (315.92, 218.65) (304.07, 218.65)      /F116 for	<|special_separator|>
(320.86, 210.10) (359.68, 210.10) (359.68, 218.65) (320.86, 218.65)      /F116 Temporal	<|special_separator|>
(364.61, 210.10) (407.52, 210.10) (407.52, 218.65) (364.61, 218.65)      /F116 Reasoning	<|special_separator|>
(412.46, 210.10) (484.38, 210.10) (484.38, 218.65) (412.46, 218.65)      /F116 (CRTR), a novel	<|special_separator|>
(489.32, 210.10) (503.99, 210.10) (503.99, 218.65) (489.32, 218.65)      /F116 and	<|special_separator|>
(127.92, 199.19) (178.72, 199.19) (178.72, 207.74) (127.92, 207.74)      /F116 theoretically	<|special_separator|>
(183.88, 199.19) (222.26, 199.19) (222.26, 207.74) (183.88, 207.74)      /F116 grounded	<|special_separator|>
(227.41, 199.19) (271.60, 199.19) (271.60, 207.74) (227.41, 207.74)      /F116 contrastive	<|special_separator|>
(276.76, 199.19) (310.06, 199.19) (310.06, 207.74) (276.76, 207.74)      /F116 learning	<|special_separator|>
(315.21, 199.19) (354.73, 199.19) (354.73, 207.74) (315.21, 207.74)      /F116 algorithm	<|special_separator|>
(359.88, 199.19) (375.12, 199.19) (375.12, 207.74) (359.88, 207.74)      /F116 that	<|special_separator|>
(380.27, 199.19) (409.63, 199.19) (409.63, 207.74) (380.27, 207.74)      /F116 utilizes	<|special_separator|>
(414.78, 199.19) (465.01, 199.19) (465.01, 207.74) (414.78, 207.74)      /F116 in-trajectory	<|special_separator|>
(470.17, 199.19) (503.99, 199.19) (503.99, 207.74) (470.17, 207.74)      /F116 negative	<|special_separator|>
(127.92, 188.28) (443.49, 188.28) (443.49, 196.83) (127.92, 196.83)      /F116 sampling to learn high-quality representations for complex temporal reasoning.	<|special_separator|>
(115.47, 173.12) (122.94, 173.12) (122.94, 181.67) (115.47, 181.67)      /F116 3.	<|special_separator|>
(127.46, 173.12) (504.00, 173.12) (504.00, 181.67) (127.46, 181.67)      /F116 We demonstrate that CRTR outperforms existing methods on 4 out of 5 combinatorial reasoning	<|special_separator|>
(127.92, 162.21) (504.00, 162.21) (504.00, 170.76) (127.92, 170.76)      /F116 tasks, and that its representations, even without explicit search, enable solving the Rubik's Cube	<|special_separator|>
(127.92, 151.30) (505.60, 151.30) (505.60, 159.85) (127.92, 159.85)      /F116 from arbitrary initial states using fewer search steps than BestFS-albeit with longer solutions.	<|special_separator|>
(108.00, 122.58) (113.98, 122.58) (113.98, 133.32) (108.00, 133.32)      /F107 2	<|special_separator|>
(125.93, 122.58) (197.09, 122.58) (197.09, 133.32) (125.93, 133.32)      /F107 Related Work	<|special_separator|>
(107.53, 098.95) (478.85, 098.95) (478.85, 107.50) (107.53, 107.50)      /F116 We build upon recent advances in self-supervised RL and contrastive representation learning.	<|special_separator|>
(108.00, 080.83) (200.09, 080.83) (200.09, 089.78) (108.00, 089.78)      /F107 Contrastive learning.	<|special_separator|>
(210.04, 080.84) (504.00, 080.84) (504.00, 089.39) (210.04, 089.39)      /F116 Contrastive learning is widely used for discovering rich representations	<|special_separator|>
(108.00, 069.93) (449.99, 069.93) (449.99, 078.49) (108.00, 078.49)      /F116 from unlabeled data [12, 11, 32, 53] to improve learning downstream tasks [63].	<|special_separator|>
(457.55, 069.93) (504.00, 069.93) (504.00, 078.49) (457.55, 078.49)      /F116 Contrastive	<|special_separator|>
(303.51, 040.05) (308.49, 040.05) (308.49, 048.60) (303.51, 048.60)      /F116 2